Photosensitivity in Glasses

Abstract

A photosensitive glass containing a small amount of a photosensitive metal such as Au, Ag, or Cu, and a sensitizer of $\mathrm{CeO_{2}}$, is expressed a function of the redox reaction induced by the irradiation of ultraviolet () light. In particular, a photosensitive glass is an indispensable material in the photolithography technique, which is valuable in the microprocessing of glass substrates. Here we aim to discuss the photosensitivity of glass from the perspectives of photochemical, photophysical, and photothermal mechanisms. In particular, from three different points of view (photothermal, photochemical, and photophysical interactions), various intriguing phenomena induced by ultrashort pulse lasers are addressed. Furthermore, a new type of photosensitivity exhibiting nonreciprocal characteristics is also discussed.

The well-cited story of the origin of glass is an episode in the Natural History by Pliny of ancient Rome. He wrote a romance-packed story. His unintentional discovery story is as follows [11.1]:

There is a story that once a ship belonging to some traders in natural soda put in here and that they scattered along the shore to prepare a meal. Since, however, no stones suitable for supporting their cauldrons were forthcoming, they rested them on lumps of soda from their cargo. When these became heated and completely mingled with the sand on the beach a strange translucent liquid flowed forth in streams; and this, it is said, was the origin of glass.

Even now, thousands of years later, glass is used in our life. Glass, including stained glass, gives us a beautiful impression of light, but also acts as a functional material with refractory properties, thermal shock resistance, water resistance, and excellent chemical stability. Besides, it is well known that various phenomena associated with a change in optical properties of materials can be caused by external energy. Table 11.1 shows typical physical phenomena that cause changes in optical properties. The changes in refractive index and birefringence basically lead to the control of the polarization characteristics. If these changes are large, the reflection characteristics are also changed. In addition, the light scattering phenomenon can occur according to the shape of the material, while the changes in the absorption coefficient are directly reflected in the absorption characteristics of the materials.

Table 11.1 Typical physical phenomena that cause changes in optical properties

Even now many studies are performed using such interesting phenomena induced by external fields. In particular, photosensitive glass is one of the key materials used to achieve the printing and reproducing processes. Such a technique is suggestive of a photographic plate consisting of a glass plate covered by the light-sensitive emulsion of silver salts. In 1937, R. H. Dalton at Corning Glass Works found that certain copper-containing glasses, when exposed to ultraviolet light, would develop a more intense red color on subsequent heat treatment than that produced in unexposed glass. A few years later, in 1941, S. D. Stookey deduced that the effect produced by ultraviolet exposure and heat treatment was very sensitive to the oxidation state of the copper in the glass and also showed that the process was actually a combination of photochemical and thermal reduction of cuprous ions to colloidal copper [11.2]. He also found that gold and silver are better photosensitive agents than copper and that cerium acts as a sensitizer material [11.3]. W. H. Armistead also proposed silver-containing photosensitive glasses [11.4]. Such photosensitive glass typically includes chemical components that cause the coloring and the opaque crystallization by using UV light or x-ray irradiation and the successive thermal treatment. Typical mechanisms of photosensitivity are interpreted as follows: when the photons such as in UV light or x-rays are irradiated, a portion of the electrons excited from the sensitizer (e. g., $\mathrm{Ce^{3+}}$ ions) is trapped by the photosensitive metal ions, and then the metal ions are reduced to metal atoms (e. g., Au, Ag, and Cu)

$$ \mathrm{Ce^{3+}}+h\nu\rightarrow\mathrm{Ce^{4+}}$$

(11.1)

$$ \mathrm{M^{+}}+\mathrm{e^{-}}\rightarrow\mathrm{M^{0}}\text{ (M: Au, Ag, and Cu)}$$

(11.2)

Further thermal treatment promotes aggregation of metal atoms to colloids

$$n\mathrm{M^{0}}\rightarrow\mathrm{M_{\mathit{n}}^{0}}$$

(11.3)

For example, in the case of the partial crystallization of glass composed of a $\mathrm{Li_{2}O}$-$\mathrm{SiO_{2}}$ system, since such colloids act as the crystal nuclei [11.5], the photoirradiated regions are colored. Since an etching rate of $\mathrm{Li_{2}O}$-$\mathrm{SiO_{2}}$ crystals in hydrofluoric () acid is significantly higher than that of glass matrices, selective etching is possible in the regions where $\mathrm{Li_{2}O}$-$\mathrm{SiO_{2}}$ crystals are grown. Such glass is commonly called photosensitive machinable glass. Of course, such photoreduction based on irreversible photoinduced homogeneous nucleation is included in the interactions between light and glass, which have been widely studied in photochromic glass [11.6], polychromatic glass [11.7], and photocatalytic glass [11.8]. In recent years, the studies of photosensitive glass, such as the writing of a Bragg grating into an optical fiber [11.10, 11.11, 11.12, 11.13, 11.14, 11.9] and the persistent spectral hole burning in glass [11.15, 11.16, 11.17, 11.18, 11.19] have been pursued both in respect to understanding the mechanisms and applying them to new devices. These reactions are basically realized by the various photoinduced structural changes as a result of the optical absorption of the glass. Therefore, since the excited photoreaction is more active in the vicinity of the glass surface, it is more difficult to induce directly inside a material. The excitation is generally performed by using a laser source in the ultraviolet or visible region owing to its high temporal and spatial coherence [11.20, 11.21, 11.22, 11.23]. It is difficult to react the glass with a laser beam with a wavelength that is not in the photon absorption region of the glass. On the other hand, by using a subpicosecond pulse width laser beam, even if its wavelength is not resonant with a glass, it becomes possible to cause various interactions based on the nonlinear optical phenomena [11.24]. Recent progress in producing intense ultrashort laser pulses [11.25, 11.26] not only pushes the photosensitive glass technologies towards the next stage, but it also opens the door to precise and efficient direct-writing inside glass. The light-matter interactions using ultrashort pulses provide many advantages including resistless and maskless pattering, high flexibility, and high speed machining, compared to other sources of UV light or longer pulse lasers [11.27]. In particular, recent ultrashort pulse laser sources with an average power in excess of ${\mathrm{10}}\,{\mathrm{W}}$ [11.28] have become commercially available and widely used in the field of material processing. From the viewpoint of photosensitive glass technologies, this chapter is focused on various interactions between the material and the ultrashort laser pulses.

1 Photothermal Interaction in Glass

1.1 Suppression of Thermal Effects

In general, when considering light-matter interactions, the material firstly absorbs a photon. In the case of transparent materials such as glass, the excitation of electrons from the valence band to the conduction band is initiated through nonlinear processes such as multiphoton or tunnel ionization [11.29, 11.30]. The electrons can then further absorb the photon via the inverse bremsstrahlung process leading to electron heating or avalanche ionization. Although this situation can also be achieved by nanosecond lasers, in this case the initial electrons are mainly generated by the contribution of defects and impurities [11.27]. The fluctuation associated with the optical breakdown threshold can be reduced by employing ultrashort lasers, which results in high reproducibility and controllability [11.31, 11.32]. Since pulse width is shorter than the electron–phonon coupling time (in the order of ps), the laser energy can be injected into the material before the thermal diffusion occurs [11.29, 11.32]. Since it is easy to achieve the power density over $\mathrm{TW/cm^{2}}$ by a condensing lens, the above-mentioned nonlinear optical effects can be space-selectively induced in the vicinity of the focus point [11.29, 11.33].

Fig. 11.1

Timescales of various electron and lattice processes in laser-excited solids. Figure was rearranged on the basis of [11.34]

Based on the timescales of various electron and lattice processes in laser-excited solids (Fig. 11.1) [11.34], it is clear that the transition into the thermal process occurs on the order of picoseconds. This is the border between thermal and nonthermal processing. Thermal diffusion length $(L_{\text{th}})$ is defined by the pulse width and the thermal diffusion coefficient of the material as follows

$$L_{\text{th}}=\sqrt{2\kappa\tau_{\mathrm{p}}}\;,$$

(11.4)

where $\kappa$ ($=\alpha_{\mathrm{t}}\rho c_{\mathrm{p}}$) is the thermal conductivity obtained by the thermal diffusivity $\alpha_{\mathrm{t}}$, the specific heat $c_{\mathrm{p}}$, and the density $\rho$, and $\tau_{\mathrm{p}}$ is the pulse width. Assuming the electron–phonon coupling time is ${\mathrm{1}}\,{\mathrm{ps}}$, the $L_{\text{th}}$ is considered to be about ${\mathrm{10}}\,{\mathrm{nm}}$ at the boundary between thermal and nonthermal processing. Since the pulse width is shorter than a typical thermal relaxation time, more precise calculation using a two-temperature model should be required. Thus, the photoinduced reaction by the single femtosecond pulse or the low pulse repetition rate is considered to proceed in the nonthermal process. Since the thermal accumulation can occur according to multiple-pulse irradiation, it is also possible to control the thermal effect [11.35].

1.2 Material Modification

The propagation of intense ultrashort laser pulses in transparent materials causes not only linear effects including diffraction, dispersion, and aberration, but also nonlinear effects such as self-focusing, filamentation, and plasma defocusing [11.36]. The strength of such effects depends on the experimental conditions and the laser parameters. The synergetic contribution of these nonlinear effects and the suppression of thermal effects produces unique subdiffraction-limited processing at an arbitrary location in the material. The intensity distribution in the focal spot of the ultrashort laser pulse will ideally have a Gaussian spatial profile. Thus, the modified region can be limited to only the central area of the focal spot by adjusting the laser intensity to match the threshold intensity (Fig. 11.2a). By adjusting the laser intensity corresponding to the threshold intensity for a reaction (Fig. 11.2b), in principle, the diffraction limit does not put any constraint on the fabrication resolution. Assuming that thermal diffusion in ultrashort laser processing is negligible, the combination of the high numerical aperture () objective and the multiphoton absorption effect enables subwavelength fabrication resolutions beyond the diffraction limit of light [11.37].

Fig. 11.2

(a) Schematic illustration of subdiffraction-limited processing based on multiphoton absorption. (b) Beam profile (dotted line) and spatial distributions of laser energy absorbed by materials via two- (solid line) and three-photon (line) absorption. The solid horizontal line indicates the reaction threshold. After [11.27]

However, in practice, the deterioration of the intensity distribution at the focus point also occurs. Since many articles relating to such nonlinear effects including self-focusing have been published [11.38], here we focus on the spherical aberration owing to refractive index mismatch. Indeed, spherical aberrations influence the propagation of ultrashort pulses inside a material, leading to the elongation of the modified region in the direction of the laser propagation [11.39]. To interpret experiments with the presence of refractive index mismatch, the electric field distributions near the focus of an objective with NA inside a material (refractive index: $n_{2}$) can be expressed as [11.40]

$$\begin{aligned}\displaystyle E(r,z)&\displaystyle=\int_{0}^{\phi}\sqrt{\cos\varphi_{1}}\sin\varphi_{1}(\tau_{\mathrm{s}}+\tau_{\mathrm{p}}\cos\varphi_{2})\\ \displaystyle&\displaystyle\quad\times J_{0}(k_{0}rn_{1}\sin\varphi_{1})\\ \displaystyle&\displaystyle\quad\times\exp(\mathrm{i}\Phi+\mathrm{i}k_{0}zn_{2}\cos\varphi_{2})\mathrm{d}\varphi_{1}\;,\end{aligned}$$

(11.5)

where $\phi=\sin^{-1}({\text{NA}})$ is the half-angle of the light convergence cone, $k_{0}=2\uppi/\lambda$ is the wave number in a vacuum, $r=\sqrt{x^{2}+y^{2}}$ is the radial coordinate, and $\varphi_{1}$ and $\varphi_{1}$ are the angles of the incident and refracted ray respectively, which are related to each other through Snell’s law,

$$\varphi_{2}=\sin^{-1}\left(\frac{n_{1}}{n_{2}}\sin\varphi_{1}\right).$$

(11.6)

The coefficients $t_{\mathrm{s}}$ and $t_{\mathrm{p}}$ are the Fresnel transmission coefficients for $\mathrm{s}$ and $\mathrm{p}$ polarizations

$$ t_{\mathrm{s}}=\frac{2\sin\varphi_{2}\cos\varphi_{1}}{\sin(\varphi_{1}+\varphi_{2})}\;,$$

(11.7)

$$ t_{\mathrm{p}}=\frac{2\sin\varphi_{2}\cos\varphi_{1}}{\sin(\varphi_{1}+\varphi_{2})\sin(\varphi_{1}-\varphi_{2})}\;. $$

(11.8)

$J_{0}$ is the zero-order Bessel function. The function is the spherical aberration function caused by the mismatching of the refractive indices [11.42]

$$\Phi=-k_{0}d(n_{1}\cos\varphi_{1}-n_{2}\cos\varphi_{2})\;,$$

(11.9)

where $d$ represents the distance between sample surface and geometrical focus. This term linearly increases with the distance of $d$, leading to the increase of the laser-induced damage threshold, owing to the spreading of the laser energy along the laser propagation direction [11.40].

1.3 Thermal Accumulation

Figure 11.3a-da shows the shape changes in the photoinduced structures depending on the pulse repetition rate $(R_{\text{rate}})$ [11.41]. For lower $R_{\text{rate}}$ than the thermal diffusion timescale (e. g., ${\mathrm{1}}\,{\mathrm{kHz}}$), it is considered that heat accumulation does not occur in the photoexcited region. Therefore, even though the temperature elevation is more than several thousand degrees higher at the focus, the localized structural changes such as a defect formation are observed only in a laser focal region [11.43, 11.44]. Such a phenomenon is due to the thermal energy diffusion out of the photoexcited region during the interpulse time (Fig. 11.3a-db). On the other hand, when heat accumulation occurs by irradiation at ${\mathrm{250}}\,{\mathrm{kHz}}$, the modification volume is much larger compared to that for ${\mathrm{1}}\,{\mathrm{kHz}}$ (Fig. 11.3a-dc). When the multiple pulses are focused at a high $R_{\text{rate}}$, the following pulse excites the photoexcited region before heat diffuses out, resulting in a larger heat-affected zone (Fig. 11.3a-dd). S. M. Eaton et al have also observed cumulative heating during direct waveguide writing in glass using a high $R_{\text{rate}}$ femtosecond laser [11.45, 11.46]. Typically, two boundaries are concentric-circularly observed around the photoexcited region (Fig. 11.3a-dc). The formation of the outermost boundary can be explained by a viscoelastic model [11.35]. On the other hand, during the laser irradiation, convection of material was observed in the region inside the inner boundary. As a result, interesting phenomena ranging from the precipitation of crystals [11.48], the material composition change [11.49, 11.50], to the phase separation [11.47], occur in this region.

Fig. 11.3a-d

Optical microscope images of photoinduced structures by femtosecond laser irradiation at (a) ${\mathrm{1}}\,{\mathrm{kHz}}$ and (b) ${\mathrm{250}}\,{\mathrm{kHz}}$. Time profiles of the simulated temperature at the focus for (c) ${\mathrm{1}}\,{\mathrm{kHz}}$ and (d) ${\mathrm{250}}\,{\mathrm{kHz}}$. The pulse energy was ${\mathrm{2.0}}\,{\mathrm{J}}$ in both cases. Reprinted from [11.41] with the permission of AIP Publishing

1.4 Element Migration

Element migration and phase separation inside the inner boundary can be space-selectively induced by femtosecond laser pulses with high $R_{\text{rate}}$ [11.47]. Since the interpulse time at ${\mathrm{200}}\,{\mathrm{kHz}}$ $(\tau_{\text{int}}={\mathrm{5}}\,{\mathrm{\upmu{}s}})$ is much shorter than the thermal diffusion obtained by (11.4), the photoinduced structure in a glass sample is affected by the thermal accumulation. Figure 11.4a,b shows backscattering electron images (s) and electron probe x-ray microanalysis () spectra maps on the glass surface polished to the depth of focal spot location. Typical calcium aluminosilicate (CSA) glass was used in the experiments [11.47]. The glass composition is shown in Table 11.2. We have evaluated the difference in element migration induced by femtosecond laser pulses with the different $R_{\text{rate}}$. The laser fluence was ${\mathrm{4.27\times 10^{3}}}\,{\mathrm{J/cm^{2}}}$ at ${\mathrm{1}}\,{\mathrm{kHz}}$ and ${\mathrm{8.12\times 10^{1}}}\,{\mathrm{J/cm^{2}}}$ at ${\mathrm{200}}\,{\mathrm{kHz}}$. Laser writing with a speed of ${\mathrm{50}}\,{\mathrm{\upmu{}m/s}}$ was performed in the parallel direction to the optical axis from bottom to top surface.

Fig. 11.4a,b

BEIs and element maps on a CSA glass surface polished to the depth of focal spot location of the femtosecond laser pulses. The laser parameters are (a) ${\mathrm{4.27\times 10^{3}}}\,{\mathrm{J/cm^{2}}}$ at ${\mathrm{1}}\,{\mathrm{kHz}}$ and (b) ${\mathrm{8.12\times 10^{1}}}\,{\mathrm{J/cm^{2}}}$ at ${\mathrm{200}}\,{\mathrm{kHz}}$. Reprinted with permission from [11.47]

Table 11.2 Composition of calcium aluminosilicate glass ($\mathrm{mol\%}$)

In the case of $R_{\text{rate}}={\mathrm{200}}\,{\mathrm{kHz}}$, the heat was diffused only $\approx{\mathrm{2}}\,{\mathrm{\upmu{}m}}$ during the $\tau_{\text{int}}$ of ${\mathrm{5}}\,{\mathrm{\upmu{}s}}$. Meanwhile, in the case of ${\mathrm{1}}\,{\mathrm{kHz}}$ $(\tau_{\text{int}}={\mathrm{1}}\,{\mathrm{ms}})$, the heat already diffused away from the focal spot to $\approx{\mathrm{30}}\,{\mathrm{\upmu{}m}}$ before the arrival of the next pulse [11.47]. It is known that modifying ions such as $\mathrm{Ca^{2+}}$ and $\mathrm{Na^{+}}$ in a glass matrix can migrate according to a temperature gradient. Indeed, for the ${\mathrm{200}}\,{\mathrm{kHz}}$ case, Ca concentration was decreased (increased) in the center (surrounding) area of the photoexcited region, while Si was concentrated in the center part due to its characteristic strong network former properties (Fig. 11.4a,bb). On the other hand, no apparent element migration was observed in the case of ${\mathrm{1}}\,{\mathrm{kHz}}$ (Fig. 11.4a,ba). We have confirmed that the temperature at the focus exceeds ${\mathrm{1000}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ just after the laser irradiation and a temperature gradient over several tens of $\mathrm{{}^{\circ}\mathrm{C}/m}$ was formed throughout the inner boundary corresponding to the element migration region. Therefore, this element migration phenomenon might largely be due to thermomigration (Soret effect) [11.51]. The iteration of the thermal expansion and the pressure wave originating from pulse-to-pulse temperature elevation may also be related to this phenomenon [11.52].

1.5 Phase Separation

Space-selective phase separation can be successfully induced inside a sodium silicate ($\mathrm{Na_{2}O}$-$\mathrm{SiO_{2}}$) glass by changing the local composition from a miscible domain to an immiscible one via femtosecond-pulsed laser irradiation with high $R_{\text{rate}}$ [11.53]. Previously, the phase separation of the $\mathrm{Na_{2}O}$-$\mathrm{SiO_{2}}$ glass system has been investigated [11.54, 11.55]. For example, in the case of ${\mathrm{12}}\,{\mathrm{mol\%}}$ $\mathrm{Na_{2}O}$ concentration, three behaviors were noted depending on the heat-treatment temperatures: spinodal dome for temperatures below ${\mathrm{700}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$, immiscibility dome for treatments between 700 and ${\mathrm{775}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$, and miscibility region above ${\mathrm{800}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$, in agreement with the phase diagram of the $\mathrm{Na_{2}O}$-$\mathrm{SiO_{2}}$ system reported by Haller et al [11.56] and shown in Fig. 11.5.

Fig. 11.5

Metastable immiscibility diagram for the $\mathrm{Na_{2}O}$-$\mathrm{SiO_{2}}$ system from data of [11.56]. The dashed line indicates the heat-treated temperature at ${\mathrm{575}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$

To test the phase separation of the $\mathrm{Na_{2}O}$-$\mathrm{SiO_{2}}$ glass system, glass samples with $\mathrm{Na_{2}O}$ concentrations from $\mathrm{21}$ to ${\mathrm{30}}\,{\mathrm{mol\%}}$ were prepared. Femtosecond laser pulses operating at ${\mathrm{250}}\,{\mathrm{kHz}}$ ($\tau_{\mathrm{p}}$: ${\mathrm{80}}\,{\mathrm{fs}}$, $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\text{int}}$: ${\mathrm{4}}\,{\mathrm{\upmu{}s}}$) were irradiated inside a glass sample via objective lens (${\mathrm{20}}\times$, NA$\mathrm{0.45}$). The pulse energy was tuned to be ${\mathrm{3}}\,{\mathrm{\upmu{}J}}$ by the neutral density filter. After the laser irradiation, the glass samples were heat treated at ${\mathrm{575}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$. At this temperature, the initial compositions lie outside the immiscible region. The distribution of the $\mathrm{Na_{2}O}$ concentration in the photoexcited region was estimated by the peak shift of the Raman band (Fig. 11.6). The $\mathrm{Na_{2}O}$ concentration at the center part increased approximately ${\mathrm{10}}\,{\mathrm{mol\%}}$ compared to the initial concentration, while the concentration at the region approximately ${\mathrm{30}}\,{\mathrm{\upmu{}m}}$ away from the center slightly increased. This composition change means that $\mathrm{Na_{2}O}$ migrated toward the outside and $\mathrm{SiO_{2}}$ migrated toward the center during laser irradiation. Consequently, since the glass composition was changed space-selectively from the immiscible region to the miscible, the laser-induced element migration leads to local phase separation.

Fig. 11.6

Profiles of $\mathrm{Na_{2}O}$ concentration as a function of the distance from the center of focus area. It should be noted that in the case of the ${\mathrm{21}}\,{\mathrm{mol\%}}$ sample, the $\mathrm{Na_{2}O}$ concentration was separated into two at around the center. After [11.53]

Figure 11.7a-e shows scanning electron microscope () images of the photoexcited region in the ${\mathrm{26}}\,{\mathrm{mol\%}}$ $\mathrm{Na_{2}O}$ glass sample. After laser irradiation, the glass sample was treated with heat at ${\mathrm{575}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$, and then polished to the depth of focal location. The observation surface was also etched with HF solution. A granular surface was observed after ${\mathrm{3}}\,{\mathrm{h}}$ of heat treatment, suggesting that the relative volume fraction of the $\mathrm{Na_{2}O}$-rich phase was sufficient for the phase separation (Fig. 11.7a-ec). For heat treatment than longer ${\mathrm{12}}\,{\mathrm{h}}$, a cocontinuous structure was observed (Fig. 11.7a-ed,e). In particular, pore size between the phase separated structures increased with increasing heat treatment time. It is known that the pore size and specific surface area are proportional to the heat-treatment time [11.57]. These results suggest that the pore size and specific surface area are tunable.

Fig. 11.7a-e

SEIs on the surface of the ${\mathrm{26}}\,{\mathrm{mol\%}}$ $\mathrm{Na_{2}O}$ sample polished to the depth of focal spot location and etched with HF solution. (a) Low magnification SEI, and (b) high magnification SEI at around the center of (a). High magnification SEIs for heat-treatment times of (c) ${\mathrm{3}}\,{\mathrm{h}}$, (d) ${\mathrm{12}}\,{\mathrm{h}}$, and (e) ${\mathrm{48}}\,{\mathrm{h}}$. The numbers 1 and 2 correspond to the locations in (b). The magnifications in (c–e) are the same. With permission of Springer from [11.53]

1.6 Partial Crystallization

According to the effect of the thermal accumulation, the precipitation of functional crystals inside glass can be realized. In experiments, typical zinc-tellurite () and niobium-tellurite () glasses have been used [11.58]. Each glass composition is shown in Table 11.3.

Table 11.3 Compositions of tellurite glasses ($\mathrm{mol\%}$)

The BEIs and the EPMA element maps of the photoexcited region in ZT and NT glass samples are shown in Fig. 11.8a,b. The observation was performed after polishing to the depth of the focus location. It is known that the thermal diffusivity of tellurite glass is typically $\approx{\mathrm{5\times 10^{-7}}}\,{\mathrm{m^{2}/s}}$. Therefore, temperature at the photoexcited region is increased by the irradiation of laser pulses with the $\tau_{\text{int}}$ of ${\mathrm{5}}\,{\mathrm{\upmu{}s}}$. In the case of the ZT glass sample, Zn concentration at the center part decreased, while Te concentration increased, corresponding to the brighter contrast in BEIs (Fig. 11.8a,ba). The cracks surrounding the modified region could be due to sample polishing. Meanwhile, no apparent migration of oxygen was observed. Although Nukui et al reported crystallization of $\alpha$-$\mathrm{TeO_{2}}$ and $\mathrm{Zn_{2}Te_{3}O_{8}}$ in zinc-tellurite glass at high temperatures $(\approx{\mathrm{900}}\,{\mathrm{{}^{\circ}\mathrm{C}}})$ [11.59], such crystallization has not been observed in our experiments. We assumed that higher temperature and/or longer laser irradiation time were required to precipitate crystals, despite the $\mathrm{TeO_{2}}$ rich region formed in the center of the focal volume. On the other hand, in the case of the NT glass sample, phase separation into two compounds of Te- or Nb-rich phases were observed. In particular, the shape of the Nb-rich region was a needle-like structure (Fig. 11.8a,bb). It should be noted that the crystalline solid solution of $\mathrm{Nb_{2}Te_{4}O_{13}}$ ($\mathrm{Nb_{2}O_{5}}+\mathrm{4TeO_{2}}$) is precipitated for the NT glass with higher $\mathrm{Nb_{2}O_{5}}$ concentration [11.60].

Fig. 11.8a,b

BEIs on (a) ZT glass and (b) NT glass surfaces polished to the depth of focal spot location after ${\mathrm{200}}\,{\mathrm{kHz}}$ repetition rate femtosecond laser pulses irradiation. Reprinted with permission from [11.47]

1.7 Ferroelectric Single-Crystal Waveguide

We have also demonstrated local crystallization in glass induced by femtosecond laser irradiation. The three-dimensional () waveguides composed of single crystals of $\mathrm{LaBGeO_{5}}$ can be space-selectively written in glass [11.61]. The spherical aberration due to varying the focal spot location inside the material can be dynamically compensated for by switching a hologram displayed on the spatial light modulator () [11.62]. Figure 11.9a-d shows electron backscatter diffraction () results for the laser-crystallized track of a ferroelectric $\mathrm{LaBGeO_{5}}$ single crystal. Although faint scratches, surface debris, and transverse cracks due to the polishing were observed, these crystal orientation maps clearly indicate the single hexagonal crystal orientation (Fig. 11.9a-da–c). To confirm the absence of low-angle grain boundaries, we have also observed the angular misorientations with respect to the average orientation (Fig. 11.9a-dd). This result suggests that the crystal orientation is uniform to within $1^{\circ}$.

Fig. 11.9a-d

EBSD results for a $\mathrm{LaBGeO_{5}}$ single-crystal track written by femtosecond laser pulses. The laser parameters are as follows: writing speed: ${\mathrm{42}}\,{\mathrm{\upmu{}m/s}}$, pulse energy $(E_{\mathrm{p}})$: ${\mathrm{1.2}}\,{\mathrm{\upmu{}J}}$, pulse repetition rate $(R_{\text{rate}})$: ${\mathrm{250}}\,{\mathrm{kHz}}$. Spherical aberration correction was performed by SLM. (a) Crystal orientation IPF maps, (b) color coding corresponding to the crystal orientation parallel to each reference axis, (c) illustration of the lattice orientation for a hexagonal crystal, and (d) the angular deviations from the average orientation. From [11.61]

2 Photochemical Interaction in Glass

2.1 Photo-Oxidation of Transition Metal Ions

The space-selective and permanent valence state manipulation of transition and heavy metal ions inside a silicate glass can be successfully induced by focusing femtosecond laser pulses [11.64]. In experiments, Mn and Fe ion codoped silicate glass was used. The glass composition was $\mathrm{70SiO_{2}}$-$\mathrm{20Na_{2}O}$-$\mathrm{10CaO}$-$\mathrm{0.1MnO}$-$\mathrm{0.05Fe_{2}O_{3}}$ ($\mathrm{mol\%}$). A ${\mathrm{4}}\,{\mathrm{\upmu{}m}}$ focal spot was formed inside the Mn and Fe ion codoped glass sample by the irradiation of femtosecond laser pulses via ${\mathrm{10}}\times$, NA $\mathrm{0.30}$ objective. The laser parameters were as follows: wavelength, $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$; pulse width, $\tau_{\mathrm{p}}$: ${\mathrm{120}}\,{\mathrm{fs}}$; pulse repetition rate, $R_{\text{rate}}$: ${\mathrm{1}}\,{\mathrm{kHz}}$; pulse energy, $E_{\mathrm{p}}$: ${\mathrm{0.4}}\,{\mathrm{mJ}}$; number of pulses, $N_{\text{pulse}}$: 16 pulses. The laser-irradiated area with a diameter of about ${\mathrm{30}}\,{\mathrm{\upmu{}m}}$ was colored purple. Although the initial glass did not show apparent absorption in the wavelength from $\mathrm{400}$ to ${\mathrm{1000}}\,{\mathrm{nm}}$, the increase of the absorption in the wavelength from $\mathrm{300}$ to ${\mathrm{1000}}\,{\mathrm{nm}}$ was observed at the laser-processed area (Fig. 11.10). The broad peak at ${\mathrm{520}}\,{\mathrm{nm}}$ is assigned to the absorption of $\mathrm{Mn^{3+}}$ ions [11.65]. Furthermore, the peak at ${\mathrm{320}}\,{\mathrm{nm}}$ is also assigned to the absorption of hole-trapped centers as observed in the x-ray-irradiated silicate glass [11.66]. It should be noted that $\mathrm{Mn^{2+}}$ ions in the initial glass were oxidized to $\mathrm{Mn^{3+}}$ by the femtosecond-laser-excited nonlinear optical process. The mechanism of the observed phenomenon have been proposed [11.29]: free electrons are excited via the multiphoton absorption and the following avalanche ionization. $\mathrm{Mn^{2+}}$ ions capture a hole resulting in the formation of $\mathrm{Mn^{3+}}$ ions, since $\mathrm{Fe^{3+}}$ ions, which are also active sites in glass matrix, may act as electron trapping centers. Other mechanisms should also be taken into consideration. It is well known that the filamentation of ultrashort laser pulses is accompanied by the generation of a white-light supercontinuum [11.67]. Since such a white light includes a shorter wavelength component, it is also possible to oxidize $\mathrm{Mn^{2+}}$ ions into $\mathrm{Mn^{3+}}$.

Fig. 11.10

Absorption spectral change of the $\mathrm{Mn^{2+}}$ and $\mathrm{Fe^{3+}}$ codoped silicate glass by femtosecond laser irradiation (blue: before, red: after). The inset shows the difference in absorption spectrum. A purple butterfly image colored by the laser writing is also shown. After [11.63]. Copyright 2005 The Japan Society of Applied Physics

2.2 Photoreduction of Rare-Earth Ions

The reduction reaction of rare-earth ions in fluoride glass can also be photoinduced by irradiation by the femtosecond laser [11.68]. The $\mathrm{Eu^{3+}}$-doped fluorozirconate glass of $\mathrm{53ZrF_{4}}$-$\mathrm{20NaF}$-$\mathrm{20BaF_{2}}$-$\mathrm{3.9LaF_{3}}$-$\mathrm{3AlF_{3}}$-$\mathrm{0.1EuF_{3}}$ ($\mathrm{mol\%}$) was used in these experiments. As the reference glass sample, the $\mathrm{Eu^{2+}}$-doped fluoroaluminate glass of $\mathrm{35AlF_{3}}$-$\mathrm{20CaF_{3}}$-$\mathrm{14.9YF_{4}}$-$\mathrm{10MgF_{2}}$-$\mathrm{10SrF_{3}}$-$\mathrm{10BaF_{2}}$-$\mathrm{0.1EuF_{2}}$ was also prepared in a reducing atmosphere. A ${\mathrm{10}}\,{\mathrm{\upmu{}m}}$ focal spot was formed inside the $\mathrm{Eu^{3+}}$-doped fluorozirconate glass sample by the irradiation of femtosecond laser pulses via ${\mathrm{10}}\times$, NA $\mathrm{0.30}$ objective. The laser parameters were as follows: $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{120}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{200}}\,{\mathrm{kHz}}$, $E_{\mathrm{p}}$: ${\mathrm{1.0}}\,{\mathrm{J}}$, $N_{\text{pulse}}$: $\mathrm{2\times 10^{5}}$ pulses. The photoluminescence () spectra of the $\mathrm{Eu^{3+}}$-doped fluorozirconate glass sample before and after femtosecond laser irradiation are shown in Fig. 11.11a. All PL peaks observed in the initial glass sample can be assigned to the ${}^{5}\mathrm{D}_{0}\rightarrow{}^{7}\mathrm{F}_{j}$ ($j=0$, 1, 2) transition of $\mathrm{Eu^{3+}}$. Since Eu ions are present in the trivalent state in the initial glass sample, no apparent emission of $\mathrm{Eu^{2+}}$ was detected. After the laser irradiation, the PL peaks at $\mathrm{360}$ and ${\mathrm{400}}\,{\mathrm{nm}}$, which are assigned to the ${}^{6}\mathrm{P}_{7/2}\rightarrow^{8}\mathrm{S}_{7/2}$ and $4\mathrm{f}^{6}5\mathrm{d}^{1}\rightarrow 4\mathrm{f}^{7}$ transitions of $\mathrm{Eu^{2+}}$, respectively, were observed. To reveal the valence number of Eu in glass, the electron spin resonance () spectra of the $\mathrm{Eu^{3+}}$-doped fluorozirconate glass sample before and after laser irradiation were measured (Fig. 11.11b). The ESR spectrum of the $\mathrm{Eu^{2+}}$-doped fluoroaluminate glass sample was also shown as reference. Although the initial $\mathrm{Eu^{3+}}$-doped fluorozirconate glass did not show apparent signals, the distinct signals similar to those of the $\mathrm{Eu^{2+}}$-doped fluoroaluminate glass were detected after laser irradiation. Two signals at about ${\mathrm{330}}\,{\mathrm{mT}}$ (splitting coefficient $g\approx{\mathrm{2.0}}$) can be assigned to hole-trapped V-type centers and to electrons trapped by $\mathrm{Zr^{4+}}$ ions [11.70]. These results suggest that some of the $\mathrm{Eu^{3+}}$ ions were reduced to $\mathrm{Eu^{2+}}$ by femtosecond laser irradiation.

Fig. 11.11

(a) Photoluminescence (PL) spectral change of $\mathrm{Eu^{3+}}$-doped fluorozirconate glass by femtosecond laser irradiation (blue: before, red: after). Inset shows the picture that emerged in the $\mathrm{Eu^{3+}}$-doped fluorozirconate glass by laser writing under UV illumination of ${\mathrm{365}}\,{\mathrm{nm}}$. (b) ESR spectra of $\mathrm{Eu^{3+}}$-doped fluorozirconate glass before (blue) and after (red) femtosecond laser irradiation. A reference ESR spectrum for $\mathrm{Eu^{2+}}$-doped fluoroaluminate glass fabricated in a reducing atmosphere is also shown (green). After [11.63]. Copyright 2005 The Japan Society of Applied Physics

2.3 Precipitation of Metal Nanoparticles

The photosensitivity of $\mathrm{Ag^{+}}$-doped phosphate glass is practically used in the individual monitoring of ionizing radiation as well as in monitoring of environmental natural radiation. This phenomenon is based on radiophotoluminescence (). The mechanisms of RPL have been proposed as follows. When the phosphate glass containing $\mathrm{Ag^{+}}$ ions is exposed to ionizing radiation, the excited electrons are captured into $\mathrm{Ag^{+}}$ and the valence changes to $\mathrm{Ag^{0}}$. The holes are also captured by $\mathrm{PO_{4}}$ tetrahedra, and then $\mathrm{Ag^{2+}}$ ions are produced by the interaction between holes and $\mathrm{Ag^{+}}$ ions. Such $\mathrm{Ag^{0}}$ and $\mathrm{Ag^{2+}}$ ions act as fluorescent centers in the phosphate glass [11.71, 11.72]. The advantages of such glass dosimeters are: (1) RPL intensity is proportional to the amount of irradiation, and (2) the fluorescence center can be eased by annealing at a high temperature of ${\mathrm{400}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ [11.73, 11.74]. However, details of the mechanisms of the RPL excitation and emission in this glass have not been fully understood. In this section, we discuss the mechanisms of RPL in $\mathrm{Ag^{+}}$-doped phosphate glass based on the observed phenomena [11.69, 11.75]. In these experiments, the commercially available $\mathrm{Ag^{+}}$ doped phosphate glass was used. The photoreduction was performed by the x-rays emitted from an x-ray tube operated at ${\mathrm{30}}\,{\mathrm{kV}}$ and ${\mathrm{20}}\,{\mathrm{mA}}$, or from femtosecond laser pulses operating at ${\mathrm{800}}\,{\mathrm{nm}}$ ($\tau_{\mathrm{p}}$: ${\mathrm{120}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{250}}\,{\mathrm{kHz}}$, $E_{\mathrm{p}}$: ${\mathrm{3}}\,{\mathrm{\upmu{}J}}$) [11.63]. In the case of x-ray irradiation, the orange (yellow + blue) color RPL emission was observed and increased with increasing x-ray absorption dose (Fig. 11.12a,b). This result agreed with that of previous reports [11.76, 11.77]. Typical RPL emission and its excitation spectra for x-ray-irradiated $\mathrm{Ag^{+}}$-doped phosphate glass could be fitted to two distinct peaks (Fig. 11.13). The RPL emission and excitation peaks were respectively deconvolved by two peaks of $\mathrm{460}$ and ${\mathrm{560}}\,{\mathrm{nm}}$, and $\mathrm{315}$ and ${\mathrm{373}}\,{\mathrm{nm}}$. The time decay of the RPL emission intensity of two peaks of ${\mathrm{560}}\,{\mathrm{nm}}$ (yellow) and ${\mathrm{460}}\,{\mathrm{nm}}$ (blue) just after x-ray irradiation is also shown in Fig. 11.14. Yokota, Imagawa and Perry have reported that since many $h$$\mathrm{PO_{4}}$ are also photoinduced in the glass matrix, the $\mathrm{Ag^{2+}}$ ions are produced by the following reaction [11.76, 11.78]

$$\mathrm{Ag^{+}}+h\mathrm{PO_{4}}\rightarrow\mathrm{Ag^{2+}}\;.$$

(11.10)

These results suggest that the yellow RPL emission at ${\mathrm{560}}\,{\mathrm{nm}}$ is attributed to $\mathrm{Ag^{2+}}$ ion generation.

Fig. 11.12a,b

Radiophotoluminescence emission images of $\mathrm{Ag^{+}}$-doped phosphate glass as a function of x-ray absorbed dose: (a) under visible light, (b) under UV light. Reprinted from [11.69], with permission from Elsevier

Fig. 11.13

Typical radiophotoluminescence (RPL) emission and excitation spectra of $\mathrm{Ag^{+}}$-doped phosphate glass after x-ray irradiation. Gaussian peak fitting for RPL emission and excitation spectra are also shown as dashed lines. After [11.69]

Fig. 11.14

Profiles of RPL emission intensity at ${\mathrm{560}}\,{\mathrm{nm}}$ (brown circles) and ${\mathrm{460}}\,{\mathrm{nm}}$ (gray circles) as a function of elapsed time. After [11.69]

Unlike in the x-ray, in the case of femtosecond laser irradiation ${\mathrm{20}}\,{\mathrm{\upmu{}m}}$ spots with fluorescence peaking at ${\mathrm{460}}\,{\mathrm{nm}}$ were observed (Figs. 11.15a,b and 11.16). Such a blue RPL emission peak at ${\mathrm{460}}\,{\mathrm{nm}}$ originates from $\mathrm{Ag^{0}}$ generation in the $\mathrm{Ag^{+}}$-doped phosphate glass. Indeed, the formation of Ag nanoparticles due to the aggregation of Ag atoms in $\mathrm{Ag^{+}}$-doped silicate glass by femtosecond laser irradiation and following an annealing process was reported [11.58]. The reason why RPL emission from $\mathrm{Ag^{0}}$ is dominant for femtosecond laser excitation is considered to be as follows. It is known that the phosphorous-related radiation-induced defects are typically classified into two structures, of phosphorous-oxygen hole centers (s) and phosphorous-oxygen electron centers (s) [11.79]. POHCs are hole-trapping defects characterized by an unpaired electron shared by two nonbridging oxygen atoms. POECs consist of unpaired electrons localized on the central P atom in $\mathrm{PO_{4}}$ tetrahedra. In the case of x-ray, with much shorter wavelength than that for laser light, two such types of defects are induced. On the other hand, electron plasma via multiphoton absorption can be excited by femtosecond laser irradiation. We assumed that the formation of POECs would be suppressed because of the competition between the reduction of $\mathrm{Ag^{+}}$ ions into $\mathrm{Ag^{0}}$ and the generation of POECs.

Fig. 11.15a,b

Optical microscope images of the photoinduced structures in the $\mathrm{Ag^{+}}$-doped phosphate glass by femtosecond laser irradiation. Images were taken under visible light (a) and UV light (b). Reprinted from [11.69] with permission from Elsevier

Fig. 11.16

PL spectral change of the $\mathrm{Ag^{+}}$-doped phosphate glass by femtosecond laser irradiation (broken line: before, solid line: after). After [11.75]

3 Photophysical Interaction in Glass

3.1 Classification of Photoinduced Structures in Silica Glass

It is not only photothermal and photochemical modifications inside glass, which are presented in the previous section, that can be induced by ultrashort pulse laser irradiation. In addition, a permanent structural densification of the glass structure can be induced by the irradiation of the intense femtosecond laser pulses, because high-order nonlinear absorption allows energy deposition predominantly within the focal volume [11.80]. Although the process during femtosecond laser interaction with a material is now well investigated, the actual structural changes in various materials are not fully understood [11.81]. According to irradiated femtosecond laser intensity, the photoinduced structures in silica glass can be classified into three different types of modification or damage: a smooth positive refractive-index change due to densification (type-I); optical anisotropy of form birefringence due to self-assembled nanostructure (type-II); and voids and cracks due to Coulomb explosion (type-III) [11.82, 11.83]. Since the photoexcited region at relatively low laser intensity is homogeneously densified by fast cooling following shockwave generation [11.84, 11.85], the refractive index is increased (Fig. 11.17a-c).

Fig. 11.17a-c

Refractive index profiles of the photoinduced structure by femtosecond laser irradiation in (a,b) $\mathrm{3GeO_{2}}$-$\mathrm{97SiO_{2}}$ glass and (c) pure $\mathrm{SiO_{2}}$ glass. The laser parameters were as follows: $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{120}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{200}}\,{\mathrm{kHz}}$, $E_{\mathrm{p}}$: ${\mathrm{2.35}}\,{\mathrm{\upmu{}J}}$, writing speed: ${\mathrm{100}}\,{\mathrm{\upmu{}m/s}}$, number of scans: (a,c) one time, (b) $\mathrm{10}$ times. The refractive indices at near both ends of the profiles correspond to those for the original glass samples. After [11.80]

The type-I modification in refractive index without cracks can be applied to various optical devices such as waveguides and couplers [11.86, 11.87]. Based on investigations regarding the structural change in silica glass by femtosecond laser irradiation, the densification of the photoexcited region within the focal volume is suggested to be caused by shockwave generation [11.88]. Type-III modification including voids and cracks (Fig. 11.18) has expected applications to data storage and photonic crystals [11.89, 11.90]. Such destructive modifications of type-III, induced by the higher laser intensity, are derived from an electron-ion plasma through avalanche ionization via inverse bremsstrahlung [11.91, 11.92].

Fig. 11.18

Void array produced by microexplosions inside fused silica. The laser parameters were as follows: $\lambda$: ${\mathrm{780}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{100}}\,{\mathrm{fs}}$, $E_{\mathrm{p}}$: ${\mathrm{0.5}}\,{\mathrm{\upmu{}J}}$. Reprinted from [11.85] with permission of AIP Publishing

Permanent birefringence induced by femtosecond laser pulses in fused silica was first observed by Sudrie et al [11.93, 11.94]. Such optical anisotropy is exhibited by the type-II modification. Kazansky et al have also observed polarization-dependent anisotropic light scattering during femtosecond laser irradiation in Ge-doped silica glass [11.95]. Finally, we have also reported the direct observation of an intermediate type-II structure composed of periodically varying oxygen defect concentration by using electron microscopy [11.96, 11.97]. These periodic nanostructures with a pitch as small as ${\mathrm{200}}\,{\mathrm{nm}}$ were ruled in the direction parallel to the laser polarization direction (Fig. 11.19a-d). Furthermore, since the concentration of the oxygen defects were periodically changed according to such nanostructures, low refractive index regions i. e., negative birefringence, also periodically appeared in the nanoscale [11.98]. Until now, many types of optical devices ranging from retardation plates [11.98], microreflectors [11.99], to microfluidic channels [11.100] based on such birefringent nanostructures have been demonstrated. The mechanism for self-assembly of the polarization-dependent periodic nanostructure is, however, still not fully understood [11.101].

Fig. 11.19a-d

Secondary electron images (s) and backscattering electron images (BEIs) of $\mathrm{SiO_{2}}$ glass (a,b) and $\mathrm{GeO_{2}}$ glass (c,d) polished close to the depth of focal spot. $k_{\text{ph}}$ and $E$ are the laser propagation direction and the polarization direction, respectively

3.2 Structural Densification (Type-I)

In this section, time-resolved observation of pressure wave generation and propagation are described. This shockwave, resulting from a rapid relaxation of thermoelastic stress, is a possible origin for the photoinduced refractive index change [11.102, 11.103, 11.104]. It is known that a pure silica ($\mathrm{SiO_{2}}$) glass exhibits an anomalous behavior in fictive temperature $(T_{\mathrm{f}})$ [11.105]. $T_{\mathrm{f}}$ is one of the characteristic properties of the glass structure, providing the temperature for reaching a quasithermal equilibrium state. Although the density of usual glass is decreased at higher $T_{\mathrm{f}}$, that of $\mathrm{SiO_{2}}$ glass is conversely increased with increasing in $T_{\mathrm{f}}$. Therefore the structure of $\mathrm{SiO_{2}}$ glass frozen by more rapid cooling becomes higher density [11.105, 11.106]. To reveal the effect of the laser-induced shockwave on the structural modification, we observed a transient lens () effect by using a pump–probe method. A detailed experimental system for TrL observation (Fig. 11.20) has been reported elsewhere [11.103].

Fig. 11.20

Schematic of experimental system for the TrL method. After [11.88]

Typical TrL signals obtained by tuning the pump pulse energies are shown in Fig. 11.21a. The negative signal at ${\mathrm{0}}\,{\mathrm{ps}}$ delay time is interpreted in terms of an optical Kerr effect and plasma formation [11.107, 11.108]. In the case of higher pump pulse energy, the TrL signals clearly oscillated with the passage of delay time. Such oscillation of TrL signals indicates a shockwave generation and propagation [11.103]. Furthermore, the amplitude of the TrL oscillation was increased with increasing pump pulse energy, and we confirmed that the shockwave can be generated by pump pulse energy more than ${\mathrm{90}}\,{\mathrm{nJ}}$ (Fig. 11.21b).

Fig. 11.21

(a) TrL signals observed with various pump pulse energies. The baselines for the TrL signals are shown by dashed lines. (b) Plot of the oscillation amplitude as a function of the pump pulse energy. The oscillation amplitude was defined by the difference in TrL signal intensity between the first positive peak and the second negative peak (arrow in inset). After [11.88]

Interestingly, when the pump pulse energy was lower than the threshold of shockwave generation, the TrL signal after the initial response temporarily kept a constant negative value (Fig. 11.22a). This phenomenon is considered to be caused by a refractive index lens effect. In particular, such a positive refractive index change induced by femtosecond laser pulses with a pulse energy lower than the threshold of shockwave generation can also be observed by changing the distance ($d$) between focal positions of the pump and probe (Fig. 11.22b). The positive (negative) TrL signal in the case of the positive (negative) $d$ clearly indicates that the photoexcited region acts as a convex lens. Such positive refractive index change reached a maximum at the pump pulse energy of about ${\mathrm{85}}\,{\mathrm{nJ}}$ and disappeared below ${\mathrm{65}}\,{\mathrm{nJ}}$. We speculate that this threshold $(\approx{\mathrm{65}}\,{\mathrm{nJ}})$ of the transient positive refractive index change is the threshold of the type-I modification in $\mathrm{SiO_{2}}$ glass.

Fig. 11.22

(a) TrL signals observed below the pump pulse energy threshold of shockwave generation. (b) The temporarily constant intensity $(I_{\text{const}})$ in (a) as a function of the pump pulse energy. After [11.88]

We have also associated the TrL signals with the structural changes revealed by the Raman measurements (Fig. 11.23a). The measured Raman intensities were subtracted from a luminescence background due to the nonbridging oxygen hole center () at ${\mathrm{650}}\,{\mathrm{nm}}$ [11.109], and corrected for temperature and frequency dependence of the first order (Stokes) Raman scattering [11.110]. Typical Raman peaks at about $\mathrm{450}$, $\mathrm{490}$, $\mathrm{600}$ and ${\mathrm{800}}\,{\mathrm{cm^{-1}}}$ have been identified [11.111, 11.112]. The ${\mathrm{800}}\,{\mathrm{cm^{-1}}}$ peak has been attributed to the bending vibration of the $\mathrm{Si{-}{}O}$ bonds. In addition, the sharp Raman peaks at ${\mathrm{490}}\,{\mathrm{cm^{-1}}}$ (D1) and $\approx{\mathrm{600}}\,{\mathrm{cm^{-1}}}$ (D2) have been respectively attributed to the oxygen breathing modes in four- and three-membered rings of $\mathrm{SiO_{4}}$ tetrahedra. The D2 peak intensity increased with increasing laser pulse energy, which suggests structural densification (Fig. 11.23b). The threshold shown in D2 peak intensity $(\approx{\mathrm{90}}\,{\mathrm{nJ}})$ was similar to the threshold of shockwave generation (Fig. 11.21b). From the comparison, we suggested that the structural densification according to the formation of the smaller ring structure could be caused by shockwave generation.

Fig. 11.23

(a) Raman spectra of the modified region induced by various pump pulse energies. (b) Variation of D2 peak intensity as a function of the pump pulse energy. The intensities were normalized by that of the initial glass. After [11.88]

We proposed the mechanism of type-I modification in $\mathrm{SiO_{2}}$ glass based on the elastic deformation [11.102, 11.113]. The absorbed laser energy via nonlinear optical process is transferred into the lattice system in glass, resulting in temperature elevation. Since this temperature elevation occurs much faster than the elastic deformation [11.108], the thermoelastic stress is concentrated at the photoexcited region. Such stress is relaxed through shockwave generation, followed by structural densification. Although it is not clear whether the generation of the shockwave is triggered by the thermal expansion and/or electron plasma formation, another group has also argues for a cold defect-driven mechanism of densification resulting from defect relaxation [11.114]. The photoinduced shock (i. e., pressure) can also be estimated from the TrL signal fitted by the phase distribution (Fig. 11.24). From the maximum of the phase shift $(\Updelta\phi={\mathrm{0.4}}\,{\mathrm{rad}})$ (Fig. 11.24b), the refractive index change was estimated. The phase shift $\Updelta\phi$ is expressed by the formula using the refractive index change $\Updelta n$

$$\Updelta\phi=2\uppi\frac{\Updelta nl}{\lambda_{\text{probe}}}\;,$$

(11.11)

where $l$ is the length of the photoexcited region along the laser propagation direction. Assuming the $l$ is ${\mathrm{30}}\,{\mathrm{\upmu{}m}}$ at ${\mathrm{300}}\,{\mathrm{nJ}}$, the refractive index change was estimated to be $\mathrm{8.5\times 10^{-4}}$. The refractive index change is also expressed by the density change based on the Lorenz–Lorentz relation [11.115]

$$\Updelta n=\frac{n_{0}^{4}-1}{4n_{0}}\left(\frac{\Updelta\rho}{\rho_{0}}\right),$$

(11.12)

where $\rho_{0}$ and $n_{0}$ are the density and the refractive index of an initial $\mathrm{SiO_{2}}$ glass respectively. Finally. the following formula is obtained

$$\frac{\Updelta\rho}{\rho_{0}}=\Updelta\phi\frac{\lambda_{\text{probe}}}{2\uppi l}\frac{4n_{0}}{n_{0}^{4}-1}\;.$$

(11.13)

Using the refractive index of a $\mathrm{SiO_{2}}$ glass at $\lambda_{\text{probe}}={\mathrm{400}}\,{\mathrm{nm}}$ $(n_{0}={\mathrm{1.47}})$, the density change for $\Updelta\phi={\mathrm{0.4}}\,{\mathrm{rad}}$ was estimated to be about ${\mathrm{0.14}}\%$. Furthermore, the stress associated with the density change is also given by [11.116]

$$\Updelta P=K\frac{\Updelta\rho}{\rho_{0}}\;,$$

(11.14)

where $K$ is the bulk modulus of a $\mathrm{SiO_{2}}$ glass ($={\mathrm{37}}\,{\mathrm{GPa}}$ at ${\mathrm{293}}\,{\mathrm{K}}$). The maximum stress induced by the shockwave was estimated to be about ${\mathrm{50}}\,{\mathrm{MPa}}$ at ${\mathrm{300}}\,{\mathrm{nJ}}$. From the thermoelastic simulation, the initial stress induced by the shockwave of ${\mathrm{50}}\,{\mathrm{MPa}}$ in the photoexcited region must be ${\mathrm{520}}\,{\mathrm{MPa}}$, corresponding to the stress generated by the thermal expansion of ${\mathrm{1.4}}\%$. Meanwhile, it has been reported that the pressure at the photoexcited region estimated from Raman spectra reaches higher than several GPa [11.112]. This difference suggests that temperature elevation is also related to the structural densification.

Fig. 11.24

(a) TrL signal observed at the pump pulse energy of ${\mathrm{300}}\,{\mathrm{nJ}}$ (brown circles). The calculated curve (solid line) from the time-dependent phase distribution of the probe pulse is also shown. (b) The phase distributions of probe pulses at $\mathrm{450}$, $\mathrm{900}$, and ${\mathrm{1500}}\,{\mathrm{ps}}$. The phase distributions include the contributions from a laser-induced shockwave and the refractive index change in the central region. After [11.88]

3.3 Self-Organization of Structural Defects (Type-II)

In addition to the homogeneous densification (type-I modification), the proposed mechanisms of the polarization-dependent self-assembled periodic nanostructure (type-II modification) are discussed in this section. In these experiments, femtosecond laser pulses operating at ${\mathrm{250}}\,{\mathrm{kHz}}$ ($\tau_{\mathrm{p}}$: ${\mathrm{80}}\,{\mathrm{fs}}$, $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\text{int}}$: ${\mathrm{4}}\,{\mathrm{\upmu{}s}}$) were focused via an objective lens (${\mathrm{100}}\times$, NA $\mathrm{0.80}$). The depth of focal spot was located approximately ${\mathrm{100}}\,{\mathrm{\upmu{}m}}$ below the sample surface and then a beam waist diameter was evaluated to be about ${\mathrm{1}}\,{\mathrm{\upmu{}m}}$. After laser irradiation, the glass sample was polished to the depth of focal location, then inspected by SEM (Fig. 11.19a-d). It is well known that the surface morphology and the density are reflected in the SEIs and the BEIs respectively. Although slight striation generated during the polishing process was visible on the SEIs of $\mathrm{GeO_{2}}$ glass, we assumed that no apparent morphological changes such as cracks exist in the focal position for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass. On the other hand, the BEIs clearly indicate that the stripe-like dark regions were periodically aligned perpendicular to the laser polarization direction. Previously, we have confirmed that such dark contrast in BEIs was caused by the periodic modulation of the oxygen defect concentration (Fig. 11.25a,b).

Fig. 11.25a,b

Auger spectra maps and corresponding line profiles of (a) O and (b) Si on the same $\mathrm{SiO_{2}}$ glass surface polished close to the depth of focal spot. Reprinted with permission from [11.96]. Copyright 2003 by the American Physical Society

In the case of $\mathrm{SiO_{2}}$ glass, the fact that the Auger signal of oxygen in the dark contrast regions was low compared to other regions evidently indicates that the oxygen-deficient regions ($\mathrm{SiO_{2-\mathit{x}}}$; $x\approx{\mathrm{0.4}}$) were periodically distributed. The diameters of the photoinduced structures for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass were about $\mathrm{2.0}$ and ${\mathrm{1.0}}\,{\mathrm{\upmu{}m}}$ respectively (Fig. 11.19a-d). We assumed that the difference in the size of the photoinduced regions, in which the polarization-dependent periodic nanostructures are formed, is derived from the self-focusing effect. Since the nonlinear self-focusing effect is initiated by the Kerr effect, the intensity-dependent refractive index is defined as [11.36]

$$n=n_{0}+n_{2}I\;,$$

(11.15)

where $n_{0}$ is the initial refractive index and $I$ is the laser intensity. The nonlinear refractive index ($n_{2}$) in esu units is also given by [11.117]

$$n_{2}=\frac{12\uppi^{2}}{n_{2}^{2}c}\chi^{(3)}\;,$$

(11.16)

where $c$ is the speed of light and $\chi^{(3)}$ is the third-order nonlinear susceptibility. The beam waist diameter $(w_{0})$ is inversely proportional to the refractive index $(n_{0})$ and the nonlinear index change $(\Updelta n)$ under the self-focusing effect [11.118]

$$w_{0}\propto\frac{1.22\lambda_{0}}{\sqrt{8n_{0}\Updelta n}}\;,$$

(11.17)

where $\lambda_{0}$ is the laser wavelength. The laser pulse energy $(E_{\mathrm{p}})$, $w_{0}$, $n_{0}$, and $\chi^{(3)}$ for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass are listed in Table 11.4. The single bond strengths $(B_{\mathrm{{M{-}{}O}}})$ for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass are also shown [11.119].

Table 11.4 Typical femtosecond laser-irradiated condition, the minimum beam diameter $w_{0}$, the refractive index $n_{0}$, nonlinear susceptibility $\chi^{(3)}$, and single bond strength $B_{\text{M--O}}$ from the literature for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass

At the present, mechanistic explanations of the polarization-dependent periodic nanostructure formation in glass have been proposed [11.122, 11.123, 11.124, 11.125, 11.96]. The first model was proposed by an extension of the surface ripple formation theory and interpreted in terms of the interference between the incident light field and the bulk electron plasma longitudinal wave [11.96]. The initial model of photon–plasmon interference is proposed as follows. Since the incident photon energy $(\lambda={\mathrm{800}}\,{\mathrm{nm}}={\mathrm{1.55}}\,{\mathrm{eV}})$ is smaller than the energy gap of the material $(E_{\mathrm{g}}=9.1$ and ${\mathrm{5.4}}\,{\mathrm{eV}}$ for $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass respectively [11.121]), the ionization of the material at the focus of the intense femtosecond laser pulses takes place via multiphoton absorption. As a result, the multiphoton ionization under the sufficiently high light intensity (i. e., $\approx{\mathrm{10^{14}}}\,{\mathrm{W/cm^{2}}}$) becomes dominant, followed by the formation of electron plasma [11.126]. The excited electrons oscillate in the electric field of the laser pulses, and then this oscillation is damped through electron–ion collisions [11.127]. The oscillatory energy of the excited electrons is converted into thermal energy by collisions with ions (inverse bremsstrahlung heating), and the temperature of the plasma also increases. The laser pulses can interact with the plasma only at frequencies $\omega_{\text{ph}}> \omega_{\mathrm{p}}$, where $\omega_{\text{ph}}$ and $\omega_{\mathrm{p}}$ are the light and plasma frequency respectively

$$\omega_{\mathrm{p}}=\sqrt{\frac{e^{2}N_{\mathrm{e}}}{\epsilon_{0}m_{\mathrm{e}}}}\;,$$

(11.18)

where $e$ is the electron charge, $N_{\mathrm{e}}$ is the electron density, and $\epsilon_{0}$ is the permittivity of free space. The critical density $N_{\text{crit}}$ $(\omega_{\mathrm{p}}\approx\omega_{\mathrm{p}})$ is

$$N_{\text{crit}}=\frac{\omega_{\text{ph}}^{2}\epsilon_{0}m_{\mathrm{e}}}{e^{2}}=\frac{4\uppi^{2}\epsilon_{0}m_{\mathrm{e}}c^{2}}{e^{2}}\frac{1}{\lambda_{0}^{2}}\;,$$

(11.19)

which gives $N_{\text{crit}}={\mathrm{1.7\times 10^{21}}}\,{\mathrm{cm^{-3}}}$ for $\lambda_{0}={\mathrm{800}}\,{\mathrm{nm}}$. According to the theoretical calculation by the nonlinear optical Schrödinger equation with additional plasma generation terms, to reach the critical density, the absorption rate of laser energy about $\mathrm{10}$ times larger should be required [11.128]. The pump–probe experiments have also revealed that the permanent structural modification was observed at least at the electron density of $\approx{\mathrm{10^{19}}}\,{\mathrm{cm^{-3}}}$ [11.129]. Furthermore, the 3-D finite-difference time-domain () simulation results based on the Drude model have indicated that a plasma density of ${\mathrm{5\times 10^{20}}}\,{\mathrm{cm^{-3}}}$ is most reproducible for the experimental observations [11.130]. Besides, the numerical simulations using the nonlinear Schrödinger equation show that an optical breakdown happens before the geometrical focus, leading to the formation of voids (type-III modification) under electron density of more than ${\mathrm{10^{20}}}\,{\mathrm{cm^{-3}}}$ [11.131]. Moreover, two-plasmon decay and stimulated Raman scattering instabilities can be observed in an underdense plasma at electron density $(N_{\mathrm{e}}\approx N_{\text{crit}}/4)$ [11.132]. Based on a mechanism analogous to the parametric decay of stimulated Raman scattering [11.133], assuming electrons with an electron temperature $(T_{\mathrm{e}})$ of ${\mathrm{10}}\,{\mathrm{eV}}$ are excited by the laser pulses with the intensity of ${\mathrm{3\times 10^{14}}}\,{\mathrm{W/cm^{2}}}$, the threshold intensity for two-plasmon instability was estimated to be approximately ${\mathrm{2.5\times 10^{14}}}\,{\mathrm{W/cm^{2}}}$. The intensity threshold $(I_{\text{th}})$ for two-plasmon decay instability is given by [11.134]

$$I_{\text{th}}=\frac{{\mathrm{2.5\times 10^{16}}}T_{\mathrm{e}}}{\lambda L}\;.$$

(11.20)

Finally, the period $(\Lambda)$ of the polarization-dependent nanostructure is obtained by following analytical expression

$$\Lambda=\dfrac{\lambda_{0}}{2c\sqrt{\frac{1}{3v_{\mathrm{e}}^{2}\left(1-2\frac{\omega_{\mathrm{p}}}{\omega_{\text{ph}}}\right)-\frac{N_{\mathrm{e}}^{2}}{2c^{2}}\left(1-\frac{\omega_{\mathrm{p}}}{\omega_{\text{ph}}}\right)}}},$$

(11.21)

where $v_{\mathrm{e}}$ $(=2\kappa_{\mathrm{B}}T_{\mathrm{e}}/m_{\mathrm{e}})$ is the thermal speed of electrons and $\kappa_{\mathrm{B}}$ is the Boltzmann constant. This expression indicates that the period increases with increase of $v_{\mathrm{e}}$ and $N_{\mathrm{e}}$. We believe that the generation of the $3/2\omega_{\text{ph}}$ harmonic observed in the experiments on femtosecond direct writing in $\mathrm{SiO_{2}}$ glass is evidence for the two-plasmon decay [11.135, 11.136]. The other mechanism attempting to explain the polarization-dependent periodic nanostructure formation is the transient nanoplasmonic model [11.123, 11.124, 11.137]. This theory is the following: When the intense ultrashort light pulses are focused into transparent dielectrics, ionization hot spots can be created in the vicinity of the focus, due to localized inhomogeneous nonlinear multiphoton ionization at generated defects or color centers. Hot spots produced in a previous laser pulse can evolve into spherical nanoplasmas [11.123, 11.124] during several subsequent pulses by a feedback mechanism based on the memory effect [11.138]. Due to such a memory effect, it is easier to ionize material on the next laser pulse. It should be noted that this effect does not cause any damage such as reduction of light transmission [11.138]. The initial underdense nanoplasmas $(N_{\mathrm{e}}<N_{\text{crit}})$ grow gradually on successive pulses. The local field enhancement at the boundary of the nanoplasma promotes an asymmetric growth from the initial spherical plasma via ellipsoidal plasmas into plasma planes in the direction perpendicular to the laser polarization. The asymmetric growth of plasma accelerates as $N_{\mathrm{e}}$ approaches $N_{\text{crit}}$. The local electric fields at the equator $(E_{\text{equator}})$ and poles $(E_{\text{poles}})$ of the nanoplasma sphere for an overall electric field E will be the following

$$E_{\text{equator}}=\frac{3\epsilon_{\text{dm}}E}{\epsilon_{\text{np}}+2\epsilon_{\text{dm}}}\;,$$

(11.22)

$$E_{\text{poles}}=\frac{3\epsilon_{\text{np}}E}{\epsilon_{\text{np}}+2\epsilon_{\text{dm}}}\;,$$

(11.23)

where $\epsilon_{\text{dm}}$ and $\epsilon_{\text{np}}$ are the real parts of the permittivity for dielectric medium and nanoplasma respectively. The local field enhancement factor $D_{\mathrm{e}}$ is proportional to the ratio between the dielectric material and plasma permittivities [11.139]

$$D_{\mathrm{e}}=\frac{E_{\text{equator}}}{E_{\text{poles}}}=\frac{\epsilon_{\text{dm}}}{\epsilon_{\text{np}}}\;.$$

(11.24)

For dielectric materials, the range of the subcritical plasma permittivity is confined to ${\mathrm{0}}<\epsilon_{\text{np}}<\epsilon_{\text{dm}}$. In these conditions $(D_{\mathrm{e}}> {\mathrm{1}})$, the local field is enhanced towards the equator and suppressed at the poles. The plasma permittivity depends on the electron density

$$\epsilon_{\text{np}}=1-\frac{N_{\mathrm{e}}}{N_{\text{crit}}}\;.$$

(11.25)

As $N_{\mathrm{e}}$ increases, the plasma permittivity decreases and reaches 0 at the plasma critical density. At these conditions, (11.24) predicts that very high enhancement factors are possible. The evolution of inhomogeneously localized nanoplasmas into plasma nanoplanes is shown schematically in Fig. 11.26a-d. Multiple plasma nanoplanes in the focal volume are expected to affect the field propagation in a similar way to planar metallic waveguides, which leads to a prediction of nanostructure period equal to $\lambda/2n$.

Fig. 11.26a-d

Transient nanoplasmonic model based on the evolution of plasma nanospheres into nanoplanes. Randomly distributed plasma nanospheres (size is a few tens of nanometers) (a) grow asymmetrically in the presence of the laser field over hundreds of laser pulses ($E$ and $k$ indicate the polarization direction and laser propagation direction, respectively) (b) to become ellipsoidal (c) and finally flatten and merge to become micrometer-sized nanoplanes (d). Reprinted with permission from [11.137]

3.4 Control of Self-Assembled Nanostructures (Type-II)

Up to now, several investigations regarding control of the period of the self-assembled nanostructure in silica glass by the laser parameters have been performed [11.100, 11.140, 11.141, 11.96]. The grating periods against the laser wavelength, pulse energy, and number of pulses were linearly increased, decreased, and decreased, respectively. Recently, Lancry et al have shown that such nanoplanes with oxygen defects are characterized by glass decomposition leading to nanovoid formation [11.142]. Richter et al have also confirmed this nanoporosity using small-angle x-ray scattering [11.143]. The formation of these nanopores can be expected to enable new applications ranging from nanofluidics, chromatography and molecular sieves to five-dimensional () optical storage [11.101, 11.144, 11.145]. Oliveira et al have also reported the formation of $\mathrm{SiO_{\mathit{x}}}$ nanocrystals within nanoplanes that is in agreement with oxide decomposition [11.146]. Although a significant birefringence in titanium silicate glass [11.147] and borosilicate crown glass [11.148] induced by femtosecond laser irradiation have been reported, no apparent birefringence has been observed in the case of BK7, Pyrex, soda-lime silicate glasses or $\mathrm{16SnO_{2}}$-$\mathrm{84SiO_{2}}$ [11.149]. In this section, polarization-dependent porous periodic nanostructures embedded in $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass are demonstrated. We also discuss the origin of the birefringence induced by creation of oxygen deficiencies and the nanopores [11.150]. To confirm the details of nanograting structures induced by femtosecond laser irradiation in $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass, we observed the cleaved surface along the nanoplanes with oxygen defects using a field emission scanning electron microscope () [11.151]. It is possible to characterize the original cleaved surface without a conductive coating by applying a low accelerating voltage and very low current. Figure 11.27a-h shows SEIs on the cleaved surface of the writing regions in $\mathrm{GeO_{2}}$ glass by femtosecond laser pulses with different pulse energy for each polarization. In the case of pulse energy of ${\mathrm{0.2}}\,{\mathrm{\upmu{}J}}$, these apparently show periodic nanostructures corresponding to areas of density contrast (Fig. 11.27a-ha,b). Nanopores with diameters of approximately ${\mathrm{10}}\,{\mathrm{nm}}$ were observed within the nanoplanes when the laser polarization was parallel to the writing direction (Fig. 11.27a-hc,d). Evidently, these nanogratings consisting of mesoporous nanoplanes were self-aligned perpendicular to the laser polarization. Such periodic nanostructures consisting of mesoporous nanoplanes cause the strong refractive index contrast, leading to the form birefringence. In the case of pulse energy of ${\mathrm{2.4}}\,{\mathrm{\upmu{}J}}$, hollow structures with multiple large voids of several micrometers were created (Fig. 11.27a-hf,h). Based on the fact that the molecular $\mathrm{O_{2}}$ was detected by Raman spectroscopy [11.142, 11.152], these voids are filled with $\mathrm{O_{2}}$ generated by the decomposition of $\mathrm{GeO_{2}}$ to $\mathrm{GeO_{2-\mathit{x}}}+x/2\mathrm{O_{2}}$. This phenomenon is similar to $\mathrm{SiO_{2}}$ glass [11.96].

Fig. 11.27a-h

SEIs of the cleaved surfaces including the laser traces written by femtosecond laser pulses with the $E_{\mathrm{p}}$ of (a–d) ${\mathrm{0.2}}\,{\mathrm{\upmu{}J}}$ or (e–h) ${\mathrm{2.4}}\,{\mathrm{\upmu{}J}}$. The laser parameters were as follow: $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{70}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{250}}\,{\mathrm{kHz}}$, writing speed: ${\mathrm{250}}\,{\mathrm{\upmu{}m/s}}$, objective: ${\mathrm{0.80}}\,{\mathrm{NA}}$. The polarization direction ($E$) was perpendicular (a,b,e,f) or parallel (c,d,g,h) to the writing direction $(S)$. $k_{\mathrm{w}}$ indicates the laser propagation direction. High-magnification SEIs in the dashed area in (a,c,e,g) are also shown in (b,d,f,h), respectively. Reprinted with permission from [11.150]

We compared the mesoporous nanoplanes for $\mathrm{SiO_{2}}$ and $\mathrm{GeO_{2}}$ glass (Fig. 11.28a-d). Superficially regarded, the average size of nanopores in $\mathrm{GeO_{2}}$ glass $(<{\mathrm{10}}\,{\mathrm{nm}})$ [11.150] was slightly smaller than that in $\mathrm{SiO_{2}}$ glass $({\mathrm{10}}{\sim}{\mathrm{30}}\,{\mathrm{nm}})$ [11.142], though their packing density seems to be higher. The magnitude of birefringence can be expressed by the grating periodicity, the layer thickness, and the refractive indices of these two layers. The birefringence of the periodic nanostructure for ordinary $(n_{\mathrm{o}})$ and extraordinary $(n_{\mathrm{e}})$ waves is [11.115]

$$\begin{aligned}\displaystyle\Updelta n&\displaystyle=n_{\mathrm{e}}-n_{\mathrm{o}}\\ \displaystyle&\displaystyle=\sqrt{fn_{1}^{2}+(1-f)n_{2}^{2}}-\frac{n_{1}n_{2}}{\sqrt{fn_{2}^{2}+(1-f)n_{1}^{2}}}\;,\end{aligned}$$

(11.26)

where $f$ is the filling factor, and $n_{1}$ and $n_{2}$ are the refractive indices for the platelets constituting the periodic nanostructure.

Fig. 11.28a-d

SEIs of the cleaved surfaces including the laser traces in (a,b) $\mathrm{GeO_{2}}$ glass and (c,d) $\mathrm{SiO_{2}}$ glass written by femtosecond laser pulses with the $E_{\mathrm{p}}$ of (a,c) ${\mathrm{0.2}}\,{\mathrm{\upmu{}J}}$ or (b,d) ${\mathrm{0.4}}\,{\mathrm{\upmu{}J}}$. Insets show the high-magnification SEIs in the dashed areas, respectively. Reprinted with permission from [11.150]

As shown in Fig. 11.29, these periodic nanostructures, in which thin regions of refractive index $n_{1}$ and larger regions of index $n_{2}$ are alternately formed, are aligned in the direction parallel to the laser polarization direction. In addition, based on the Maxwell–Garnett theory, the effective refractive index $(n_{1})$ of the mesoporous nanoplanes is [11.153]

$$\begin{aligned}\displaystyle n_{1}^{2}&\displaystyle=n_{\text{defect}}^{2}\\ \displaystyle&\displaystyle\quad\times\left[1-\frac{3\phi(n_{\text{defect}}^{2}-n_{\text{pore}}^{2})}{2n_{\text{defect}}^{2}+n_{\text{pore}}^{2}+\phi(n_{\text{defect}}^{2}-n_{\text{pore}}^{2})}\right],\end{aligned}$$

(11.27)

where $\phi$ is the porosity, and $n_{\text{pore}}$ $(=1)$ and $n_{\text{defect}}$ are the refractive indices for the nanopores and for the surrounding oxygen defect regions, respectively.

Fig. 11.29

Schematic of the nanograting structure photoinduced in the focal region. $n_{\text{bg}}$: refractive index of the initial glass, $n_{1}$, $n_{2}$: local refractive indices of nanoplane, $f=t_{1}/\Lambda$: filling factor, $\Lambda$: period of the nanograting, $t_{1}$: width of the region with index $n_{1}$, $n_{\text{pore}}={\mathrm{1}}$: refractive index of the nanopore, $n_{\text{defect}}$: refractive index of the region surrounding the nanopores

We have evaluated the birefringence from the phase retardation measured by polarization microscopy $(\Gamma=L\,B)$, where $\Gamma$ is the measured phase retardation and $B$ is the birefringence. The thickness $(L)$ of the photoinduced periodic nanostructure along the laser propagation direction was determined by crossed-Nicols observation from the side of the sample. Initially, depending on the pulse energy, the $\Gamma$ for both $\mathrm{GeO_{2}}$ and $\mathrm{SiO_{2}}$ glasses was increased, then decreased at $\mathrm{0.4}$ or ${\mathrm{0.8}}\,{\mathrm{\upmu{}J}}$, respectively (Fig. 11.30). On the other hand, the birefringence for $\mathrm{GeO_{2}}$ glass was monotonically decreased, while in the case of $\mathrm{SiO_{2}}$ glass, the birefringence was increased and then gradually changed to a decrease depending on the pulse energy. For $\mathrm{SiO_{2}}$ glass, the maximum of birefringence was obtained at about ${\mathrm{0.2}}\,{\mathrm{\upmu{}J}}$. The higher birefringence for $\mathrm{GeO_{2}}$ glass achieved by the lower pulse energy compared to $\mathrm{SiO_{2}}$ glass is considered to be due to the ease of defect formation. Indeed, the birefringence of $\mathrm{0.005}$ for $\mathrm{GeO_{2}}$ glass was obtained at a pulse energy of ${\mathrm{0.12}}\,{\mathrm{\upmu{}J}}$, compared to that of $\mathrm{0.003}$ for $\mathrm{SiO_{2}}$ glass at the same pulse energy. Neglecting the effect on the refractive index change by the oxygen defects [11.154], our results are in good agreement with previous studies [11.98]. The parameters for calculation and the results are listed in Table 11.5.

Fig. 11.30

(a) Phase retardation and (b) birefringence in $\mathrm{GeO_{2}}$ and $\mathrm{SiO_{2}}$ glass induced by femtosecond laser pulses as a function of the $E_{\mathrm{p}}$. After [11.150]

Table 11.5 Parameters for calculation of local refractive index change in $\mathrm{SiO_{2}}$ glass and $\mathrm{GeO_{2}}$ glass

It is known that $\mathrm{GeO_{2}}$ glass is more thermodynamically unstable than $\mathrm{SiO_{2}}$ glass, therefore two types of oxygen defects, such as the neutral oxygen monovacancy (; Ge–Ge) and the neutral oxygen divacancy (; $\mathrm{Ge^{2+}}$), are easily generated. Furthermore, it is also known that the structural relaxation of glass at about the glass transition temperature changes dramatically depending on impurities such as OH ions. We confirmed the decrease of birefringence associated with the annihilation of photoinduced defects by isochronal annealing experiments [11.150]. Figure 11.31 shows Arrhenius plots of the photoinduced phase retardation inside $\mathrm{GeO_{2}}$ and $\mathrm{SiO_{2}}$ glass by femtosecond laser pulses with a pulse energy of $\mathrm{0.2}$ and ${\mathrm{0.4}}\,{\mathrm{\upmu{}J}}$, respectively, as a function of the annealing temperature for ${\mathrm{1}}\,{\mathrm{h}}$. The amount of phase retardation after annealing at various temperatures are plotted against inverse temperature based on the Arrhenius equation

$$\frac{\Gamma_{0}-\Gamma}{\Gamma_{0}}=A\exp\left(-\frac{E_{\mathrm{a}}}{\kappa_{\mathrm{B}}T}\right),$$

(11.28)

where $\Gamma_{0}$ and $\Gamma$ are the phase retardation of the birefringent structure before and after successive annealing at various temperatures, respectively. Symbols of $E_{\mathrm{a}}$, $A$, $T$, and $\kappa_{\mathrm{B}}$ are the activation energy for birefringence relaxation, the frequency factor, the absolute temperature, and the Boltzmann constant respectively. In the case of $\mathrm{GeO_{2}}$ glass, the birefringent structures composed of the oxygen defects and nanopores were relaxed completely by annealing temperature, which is about ${\mathrm{100}}\,{\mathrm{K}}$ higher than the glass transition point $(T_{\mathrm{g}}\approx{\mathrm{823}}\,{\mathrm{K}})$. In good agreement with previously reported results [11.155, 11.156], the best linear fit was obtained with activation energy of $\mathrm{0.2}$ or ${\mathrm{1.9}}\,{\mathrm{eV}}$ for $\mathrm{GeO_{2}}$ or $\mathrm{SiO_{2}}$, respectively. These results imply that the birefringence relaxation originates from oxygen vacancy annihilation.

Fig. 11.31

Arrhenius plots of photoinduced phase retardation in $\mathrm{GeO_{2}}$ and $\mathrm{SiO_{2}}$ glass by femtosecond laser pulses as a function of the annealing temperature for ${\mathrm{1}}\,{\mathrm{h}}$. The $E_{\mathrm{p}}$ for $\mathrm{GeO_{2}}$ and $\mathrm{SiO_{2}}$ glass was $\mathrm{0.2}$ and ${\mathrm{0.4}}\,{\mathrm{\upmu{}J}}$, respectively. After [11.150]

We have also confirmed the effect of the impurities in $\mathrm{SiO_{2}}$ glass on the annihilation of photoinduced $\Gamma$ by thermal treatment [11.157]. In these experiments, we used $\mathrm{SiO_{2}}$ glass samples doped with anions of Cl, F, and OH (Table 11.6). After birefringent structure formation by femtosecond laser irradiation inside various anion-doped $\mathrm{SiO_{2}}$ glasses, we observed annihilation of the photoinduced $\Gamma$ under annealing at various temperatures (Fig. 11.32). The temperature at the steep decrease of the $\Gamma$ was affected by the doped anion species in glass, which were approximately their $T_{\mathrm{g}}$ (Fig. 11.32a). The differences in the temperature at the relaxation of birefringent structure, including the oxygen defects and nanopores, were considered to be caused by the difference in the amount of oxygen deficiency defects brought by the doped anion species in glass. Although the size of nanopores and the porosity in the nanoplanes with oxygen defects did not change below the glass transition temperature, we assumed that nanopores in glass start to be eliminated at about the glass transition temperature, where the $\Gamma$ began to decrease steeply [11.157]. We have also confirmed that the thermal stabilities became higher in various anion-doped $\mathrm{SiO_{2}}$ glass in the order $\text{OH100}> \text{Cl6300}\simeq\text{OH1000}> \text{F9400}$ (Fig. 11.32b). From these results, we can conclude that the doped anion species and their concentrations are dominant factors in the formation of the photoinduced birefringent structure.

Table 11.6 Anion concentration in $\mathrm{SiO_{2}}$ glass samples

Fig. 11.32

(a) Phase retardation $(\Gamma)$ of birefringence exhibited by the nanogratings after annealing at various temperatures for ${\mathrm{1}}\,{\mathrm{h}}$. (b) Plots of the change ratio of the photoinduced $\Gamma$ in $\mathrm{SiO_{2}}$ glass samples including various anion dopants. Dotted lines show fitting curves with $y=1-\exp(-ax)$. Dashed line shows the half value of the initial phase retardation $(\Gamma_{0})$. After [11.150]

3.5 Evolution of Optical Anisotropy

To expand the application of polarization-dependent photosensitivity in glass, we focus on the controllability of birefringence induced by femtosecond double pulses using three different experimental configurations. First, to reveal the effect of the temporally shaped femtosecond laser pulses, the double pulses in parallel polarization direction with each other with the time delay $(\tau_{\text{delay}})$ up to ${\mathrm{5}}\,{\mathrm{ps}}$ were produced using an acousto-optic phase dispersion filter () (Fig. 11.33a-fa). The total pulse energy and the irradiated number of pulses $(N_{\text{pulse}})$ were fixed at $\mathrm{100}$ shots and ${\mathrm{0.68}}\,{\mathrm{\upmu{}J}}$, respectively. In the second experiments, the pulse energy ratios of the first pulses $(E_{\mathrm{p}}^{\text{1st}})$ to the total pulse energy $(E_{\mathrm{p}}^{\text{tot}}=E_{\mathrm{p}}^{\text{1st}}+E_{\mathrm{p}}^{\text{2nd}}={\mathrm{0.68}}\,{\mathrm{\upmu{}J}})$ were changed (Fig. 11.33a-fb). The polarization direction, $\tau_{\text{delay}}$ and the $N_{\text{pulse}}$ were set to be vertical $(E\ 90^{\circ})$, ${\mathrm{3}}\,{\mathrm{ps}}$ and $\mathrm{100}$ shots, respectively. The double pulses with various $\tau_{\text{delay}}$ and $E_{\mathrm{p}}^{\text{1st}}/E_{\mathrm{p}}^{\text{tot}}$ were produced by changing the second-order dispersion component of pulse shape. The interpulse time $(\tau_{\text{int}})$ was fixed at ${\mathrm{0.1}}\,{\mathrm{ms}}$. We also performed the experiments using double pulses with various $\tau_{\text{delay}}$ and the mutually orthogonal polarization direction on each other (Fig. 11.33a-fc). The detailed optical system has been reported elsewhere [11.101]. The $E_{\mathrm{p}}$ of orthogonally polarized double pulses and the $N_{\text{pulse}}$ were fixed at ${\mathrm{1.0}}\,{\mathrm{\upmu{}J}}$ $(={\mathrm{0.5}}\,{\mathrm{\upmu{}J}}+{\mathrm{0.5}}\,{\mathrm{\upmu{}J}})$ and $\mathrm{250000}$ shots, respectively. In the all experiments, the laser power was independent of the polarization direction. The photoinduced birefringent structures were inspected by a polarization microscope to measure the phase retardation $(\Gamma)$. From the results of the first experiments (Fig. 11.33a-fd), interestingly, the $\Gamma$ induced by the single pulses with horizontal $(E\ 0^{\circ})$ or vertical $(E\ 90^{\circ})$ polarization direction was apparently different regardless of the same pulse energy. Meanwhile, there was no big difference in the $\Gamma$ in the case of the double pulses [11.144]. Furthermore, the $\Gamma$ induced by the double pulses was larger than that for single pulses in $\tau_{\text{delay}}$ up to ${\mathrm{5}}\,{\mathrm{ps}}$. This phenomenon is interpreted in terms of the enhancement of electron excitation via the laser-plasma interaction during the lifetime of plasma excited by the first pulses [11.158]. From the results of the second experiments (Fig. 11.33a-fe), the $\Gamma$ reached a maximum at the one-to-one double pulses. In addition, the $\Gamma$ was symmetrically changed with respect to the equally divided double pulses. The enhancement effect on the generation of free electrons excited by the first pulses was remarkable for the $E_{\mathrm{p}}^{\text{1st}}/E_{\mathrm{p}}^{\text{tot}}$ ranging from $\mathrm{0.2}$ to $\mathrm{0.8}$. The origin of the symmetric variation of the $\Gamma$ to the $E_{\mathrm{p}}^{\text{1st}}/E_{\mathrm{p}}^{\text{tot}}$ is considered to be as follows. The electron-hole pairs are produced through multiphoton absorption by the first pulses. The excited electrons absorb even more laser energy leading to the increase of electron temperature and density (avalanche ionization). Such an electron plasma is relaxed first by electron–phonon coupling, then via radiative and/or nonradiative transition, and eventually an oxygen-deficient center is formed. If the second pulses arrive before the lifetime of electron plasma, the second pulses are employed to assist the avalanche ionization [11.159]. Assuming that the ionization processes for the first pulses and the second pulses are independent from each other as multiphoton ionization and avalanche ionization, respectively, in a series flows of the electron excitation by double pulses, the $\Gamma$ to the $E_{\mathrm{p}}^{\text{1st}}/E_{\mathrm{p}}^{\text{tot}}$ could change symmetrically. On the other hand, the asymmetric evolution of $\Gamma$ was also unambiguously induced by the orthogonally polarized double pulses on each other, regardless of the fact that the pulse energy and pulse duration were set at the same conditions (Fig. 11.33a-ff). In the case of single pulses, a small difference in the $\Gamma$ existed depending on the polarization direction; however, the difference for the orthogonally polarized double pulses was several times larger. Such asymmetric change of $\Gamma$ for orthogonally polarized double pulses could be interpreted as follows. Assuming that horizontal and vertical polarized pulses produce different heating, and vertical pulses produce more heating than horizontal pulses, the horizontally polarized first pulses in the next double pulses may not completely erase the birefringent structure produced by the vertically polarized second pulses in the previous double pulses. In contrast, when the pulse sequence is reversed, the vertically polarized first pulses in the next double pulses will erase the birefringent structure produced by the horizontally polarized second pulses in the previous double pulses. Finally, such asymmetric photosensitivity of glass induced by the orthogonally polarized double pulses is considered to be derived from femtosecond pulses with tilted intensity fronts exhibiting a nonreciprocal quill writing effect [11.101, 11.160].

Fig. 11.33a-f

Schematic of three different experimental configurations: (a) time-delayed double pulses with the same linear polarization direction, (b) time-delayed double pulses with various intensity ratios (polarization direction: $E$ $90^{\circ}$), and (c) time-delayed double pulses in mutually orthogonal polarization directions. AOPDF: acoustic optic phase dispersion filter, $\lambda/2$: half-wave plate, BS1, BS2: polarizing beam splitters, delay: optical delay line. (d) Plots of the phase retardation $(\Gamma)$ versus $\tau_{\text{delay}}$ induced by the linearly polarized double pulses (light brown: $E$ $0^{\circ}$, dark brown $E$ $90^{\circ}$). The $\Gamma$ values for single pulses $(E_{\mathrm{p}}={\mathrm{0.68}}\,{\mathrm{\upmu{}J}},N_{\text{pulse}}={\mathrm{100}})$ with each polarization direction are also shown. (e) Plots of the $\Gamma$ versus $E_{\mathrm{p}}^{\text{1st}}/E_{\mathrm{p}}^{\text{tot}}$ induced by the linearly polarized double pulses ($E$ $90^{\circ}$, $\tau_{\text{delay}}={\mathrm{3}}\,{\mathrm{ps}}$, $E_{\mathrm{p}}={\mathrm{0.68}}\,{\mathrm{\upmu{}J}}$). Dashed green line in (e) indicates the quadratic fitting for eye guidance. (f) Plots of the $\Gamma$ versus delay induced by the orthogonally polarized double pulses ($E_{\mathrm{p}}={\mathrm{1.0}}\,{\mathrm{\upmu{}J}}$, $N_{\text{pulse}}={\mathrm{250000}}$). The $\Gamma$ values for single pulses with each polarization direction are also shown. Beige dotted line in (f) indicates the fitting curve by Gaussian integral function

We have also inferred the formation dynamics of the periodic nanostructure based on the $\Gamma$ change induced by the double pulses with longer delays up to ${\mathrm{1700}}\,{\mathrm{ps}}$. In these experiments, the $E_{\mathrm{p}}^{\text{tot}}$ and the $N_{\text{pulse}}$ were fixed at ${\mathrm{0.5}}\,{\mathrm{\upmu{}J}}$ and $\mathrm{100}$ shots respectively. Figure 11.34 shows the variation of the $\Gamma$ as a function of the $\tau_{\text{delay}}$ for each $\tau_{\text{int}}$. As the reference, the single-pulse experiments with the same or the half $E_{\mathrm{p}}$ were also performed. The $\Gamma$ initially slightly increased and then reached the maximum at about ${\mathrm{10}}\,{\mathrm{ps}}$. Despite the same $E_{\mathrm{p}}^{\text{tot}}$, the $\Gamma$ for double pulses were up to twice as large as those for single pulses. Thereafter, the $\Gamma$ asymptotically approached the $\Gamma$ induced by the single pulses with the half-pulse energy $(E_{\mathrm{p}}={\mathrm{0.25}}\,{\mathrm{\upmu{}J}})$. The decrease of $\Gamma$ suggests that the free electrons excited by the first-arrival pulse in double pulses have been relaxed before the arrival of the delayed second pulse. Furthermore, the asymptotic behavior could be interpreted in terms of the memory effect arising from metastable color centers or permanent changes in electronic structure associated with chemical reorganization [11.123]. The $\Gamma$ also depended on the pulse repetition rate, i. e., interpulse time $(\tau_{\text{int}})$. The optimal $\tau_{\text{int}}$ to obtain the maximum $\Gamma$ was ${\mathrm{20}}\,{\mathrm{\upmu{}s}}$ corresponding to $R_{\text{rate}}$ of ${\mathrm{50}}\,{\mathrm{kHz}}$ [11.161]. As mentioned in the previous section, since the excessive thermal accumulation occurred when $\tau_{\text{int}}<{\mathrm{20}}\,{\mathrm{\upmu{}s}}$, we speculate that the structural relaxation of oxygen defects and/or nanopores temporarily formed makes the $\Gamma$ value smaller [11.101]. On the other hand, the reason for the smaller $\Gamma$ for $\tau_{\text{int}}> {\mathrm{20}}\,{\mathrm{\upmu{}s}}$ is considered to be caused by the decrease in nonlinear absorptivity depending on the thermally excited electrons.

Fig. 11.34

Variation of the $\Gamma$ as a function of the $\tau_{\text{delay}}$ for each $\tau_{\text{int}}$. Inset shows the $\Gamma$ versus $\tau_{\text{int}}$ at $\tau_{\text{delay}}={\mathrm{10}}\,{\mathrm{ps}}$. Dashed and dotted lines are the $\Gamma$ values induced by the single pulses with the same or half energy, respectively

Considering the energy levels of $\mathrm{SiO_{2}}$ glass excited by femtosecond double pulses (Fig. 11.35), the maximum $\Gamma$ value obtained at ${\mathrm{10}}\,{\mathrm{ps}}$ suggests that this timescale is similar to the nonradiative relaxation lifetime from the self-trapped excitons (s) [11.162]. Since the electrons once excited by the first-arrival pulse are trapped at STEs, it becomes easy to interact with the second-arrival pulse. Finally, the enhancement effect of the interaction between the electrons trapped at STE level and the second-arrival pulse continues during several hundred picoseconds, which corresponds to the STE decay time.

Fig. 11.35

Schematic of the dynamics model of oxygen defect generation in $\mathrm{SiO_{2}}$ glass

4 Anisotropic Photosensitivity of Glass

As mentioned in the above sections, photosensitivity, the term given to describe an object's response to light, is a material property that is relevant to many phenomena and applications ranging from photosynthesis, photography and optical data storage to ultrafast laser writing. It has been a common belief that, in the case of an isotropic medium such as glass, if you change the polarization of an isotropic laser beam, the photosensitivity and the corresponding photoinduced material modifications would not change. However, a single intense ultrashort pulse laser beam with a tilted pulse front can interact with the glass differently depending on the light polarization. Typically, optical anisotropy manifests itself as differing responses of the material to light with different polarizations [11.163]. Optical anisotropy may have a microscopic origin being attributed to material structure (e. g., crystal [11.164]). In addition, the external stress or polarized light (photoinduced birefringence) can also produce such a phenomenon [11.165]. Furthermore, optical anisotropic phenomena may originate from gradients, or macro- or subwavelength scale interfaces (form birefringence) [11.115]. Apparently, in an isotropic medium including a glass, the optical anisotropy is forbidden by symmetry, i. e., such a medium responds equally to light with different polarizations. Therefore, photosensitivity of glass, including nonlinear optical phenomena such as multiphoton absorption and optical Kerr effect, is not affected by the light polarization direction. Recently, two remarkable phenomena relating to nonreciprocal photosensitivity induced by femtosecond laser pulses have been reported. The first is a nonreciprocal response that is a material modification depending on light propagation direction in a noncentrosymmetric crystal [11.166]. The second is a quill writing effect that is a material modification depending on the laser writing direction in glass [11.160, 11.167, 11.168]. Such nonreciprocal photosensitivities are considered to relate to the mutual orientation of the light polarization azimuth and the pulse front tilt () [11.169]. The PFT is a tilt between the pulse front and a direction perpendicular to the beam, which is particularly notable for broadband pulses such as femtosecond laser pulses. Femtosecond laser pulses with different polarization directions were focused in a dot shape inside aluminosilicate glass via ${\mathrm{50}}\times$, NA $\mathrm{0.80}$ objective. The glass composition was $\mathrm{67.8SiO_{2}}$-$\mathrm{17CaO}$-$\mathrm{10.6Al_{2}O_{3}}$-$\mathrm{4.6B_{2}O_{3}}$ ($\mathrm{mol\%}$). The laser parameters were as follows: $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{70}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{250}}\,{\mathrm{kHz}}$, $E_{\mathrm{p}}$: ${\mathrm{2.4}}\,{\mathrm{\upmu{}J}}$. To reveal the effect of the PFT on the photoinduced structure in glass, the beam shape and the power were set as the same after passing through the microscope objective for all polarization directions. Although there was no apparent asymmetry in the laser intensity distribution in focal plane, unexpectedly, the intensity of the white light emission from the focal region depended clearly on the polarization direction (Fig. 11.36a). Furthermore, despite the time-integrated intensities of white light being almost the same, the temporal light intensity at ${\mathrm{615}}\,{\mathrm{nm}}$ during laser irradiation was apparently different according to the laser polarizations (Fig. 11.36b).

Fig. 11.36

(a) Emission spectra from focus in $\mathrm{SiO_{2}}$ glass during exposure of femtosecond laser pulses with mutually orthogonal polarization directions. The pump laser power at ${\mathrm{800}}\,{\mathrm{nm}}$ was reduced by a factor of $\mathrm{10^{5}}$ using a notch filter. The results of two independent measurements for each polarization show good reproducibility. (b) Temporal changes of light intensity at ${\mathrm{615}}\,{\mathrm{nm}}$ as a function of irradiation time

The photoinduced structures were also different according to the polarization directions. In particular, at a certain polarization, strong coloration regions surrounded by asymmetrically distributed bubbles were observed (Fig. 11.37a,b). Such colored regions correspond to the element migration region caused by the high fluence and heat accumulation [11.35, 11.41, 11.45]. The Raman spectra of the photoinduced structures were also different according to the polarization directions (Fig. 11.37c,d). Line profiles along the photoinduced structures clearly indicated the difference in the peak intensities at about $150{\sim}190$ and ${\mathrm{500}}\,{\mathrm{cm^{-1}}}$. These are assigned to the coupled tetrahedral $\mathrm{SiO_{4}}$ groups [11.170, 11.171] and the bending vibration modes of $\mathrm{Si(Al){-}{}O{-}{}Si(Al)}$ bridges in glass [11.172], respectively.

Fig. 11.37

(a,b) Optical microscope images of the modified regions by the femtosecond laser pulses with mutually orthogonal polarization directions. (c,d) Profiles of Raman spectra along the dotted lines in (a,b). From [11.169]

We have also observed light absorption at the coloration region, indicating that the absorbance was changed in a cosine-like dependence on the polarization azimuth angle $\alpha$ (Fig. 11.38a). The refractive index changes were also observed by using a quantitative phase imaging (Fig. 11.38b). The refractive index change $(\Updelta n)$ is estimated from

$$\Updelta n=\frac{\Updelta\varphi\lambda}{2\uppi d}\;,$$

(11.29)

where $\Updelta\varphi$ is the phase shift at wavelength $\lambda$ and $d$ is the thickness of the structure along the light propagation direction. The map of the phase shift at $\lambda={\mathrm{550}}\,{\mathrm{nm}}$ corresponding to the refractive index change is also shown in Fig. 11.38c. Assuming $d\approx{\mathrm{20}}\,{\mathrm{\upmu{}m}}$, the minimum value of about $\Updelta n\approx{\mathrm{-2\times 10^{-2}}}$ was obtained at the polarization azimuth $\alpha=90$ and $270^{\circ}$. From these results, since all the laser parameters except polarization direction were set the same, the photosensitivities of glasses induced by femtosecond laser pulses are clearly anisotropic according to the laser polarization direction.

Fig. 11.38

(a) Absorbance of the modified region for ${\mathrm{400}}\,{\mathrm{nm}}$ as a function of the polarization angle $(\alpha)$ of writing femtosecond laser pulses. Line indicates the fitting curve by $\cos 2\alpha$. (b) Photoinduced phase change in the center of a modified region as a function of $\alpha$. (c) Maps of phase change for the modified regions by femtosecond laser pulses with mutually orthogonal polarization directions. Darker contrast corresponds to more negative index change. From [11.169]

By using the GRENOUILLE device, we have characterized the spatiotemporal properties of our femtosecond laser pulses (Fig. 11.39). This indicated that our laser pulses have Gaussian intensity profiles and a small PFT of about ${\mathrm{1.8}}\,{\mathrm{fs/mm}}$. We believe that such a small PFT was derived from a slight misalignment of the prism pair or a slight beam divergence [11.173, 11.174]. Since the PFT is proportional to the beam diameter and can be significantly increased in the vicinity of the beam waist, we estimated that PFT reaches $\approx{\mathrm{180}}\,{\mathrm{fs/mm}}$ ${\mathrm{10}}\,{\mathrm{\upmu{}m}}$ before the geometrical focus in air.

Fig. 11.39

Typical measured GRENOUILLE trace. The black dashed line indicates zero delay. The shift of the trace center in delay axis indicates the PFT. From [11.169]

5 Nonreciprocal Photosensitivity of Glass

The control of the quill writing effect caused by the anisotropic trapping of the electron plasma by the PFT enables the formation of the individual photoinduced structures, i. e., type-II or type-II modifications in silica glass [11.160]. To visualize the effect of the PFT, we have observed the photoinduced structure by switching the sign of the PFT [11.167]. The four laser-written traces with alternating writing directions were induced by scanning the focus spot with pulse energy of ${\mathrm{1.4}}\,{\mathrm{\upmu{}J}}$ and writing speed of ${\mathrm{50}}\,{\mathrm{\upmu{}m/s}}$ (Fig. 11.40a,b). The laser-written traces clearly indicate the directional dependence (i. e., traces in right-to-left: type-II modification, traces in left-to-right: type-III modification) (Fig. 11.40a,ba). By adding a mirror in the experimental configuration, we reversed the direction of the PFT (Fig. 11.40a,bb). The directional dependence was clearly changed in reverse. Comparing these results, the photoinduced structures written by the opposite direction of the PFT provide evidence that the PFT is responsible for the directional dependence in the photosensitivity induced by the femtosecond laser.

Fig. 11.40a,b

Microscope images inspected without polarizers (bright images) and with crossed polarizers (dark images) of the laser traces written by femtosecond laser pulses. To switch the sign of the PFT, experimental configurations with (a) two mirrors or (b) three mirrors were employed. Red lines show the PFT. $k_{\text{ph}}$ is the laser propagation direction. Reproduced from [11.167], with the permission of AIP Publishing

Such directional dependence of structural modification provided by the direction of the PFT is also related to the previously mentioned polarization-dependent heating phenomenon. We have also observed weak dependence of the absorbed laser power, and in contrast, strong dependence of the hot plasma emission on the polarization direction. From these results, we speculated that two different types of excitation are photoinduced, despite the absorbed laser energy not changing in the polarization direction. One is an isotropic heating by electron acceleration via inverse bremsstrahlung and the other is an anisotropic strong heating provided by the mutual direction of the polarization and the PFT [11.169]. Such nonreciprocal photosensitivity of glass induced by the femtosecond laser with suitable PFT can effect the structural change in glass (Fig. 11.41a-ha,b,e,f). A series of laser traces were photoinduced in silica glass by alternately switching the writing direction. Similar to the previously mentioned experiments in Fig. 11.37, all the laser parameters except the polarization direction were set the same. The pulse energy and the writing speed were ${\mathrm{2.0}}\,{\mathrm{\upmu{}J}}$ and ${\mathrm{100}}\,{\mathrm{\upmu{}m/s}}$ respectively. The laser-written traces were observed by optical microscope under a Nomarski-DIC illumination (back-illumination) or a crossed-polarized () configuration. These images indicate that the nonreciprocal photosensitivity appearing as the difference in the structural modification is tunable by the polarization direction. Indeed, the structural densification was also effected by the nonreciprocal photosensitivity (Fig. 11.41a-hc,d,g,h). For a certain polarization direction to the laser writing direction, the intensity distribution of the characteristic Raman peak at ${\mathrm{492}}\,{\mathrm{cm^{-1}}}$ (D1), suggesting structural densification, became asymmetric. Detailed analysis of these Raman shifts towards higher frequency revealed that a large stress of about ${\mathrm{3.2}}\,{\mathrm{GPa}}$ was applied in the birefringent structures. This is in good agreement with the calculation from the phase retardation $(\Gamma=\gamma dP)$, where $\gamma$ is the photoelastic constant of silica glass $(\approx{\mathrm{3.5}}\,{\mathrm{nm/(cm{\,}MPa)}})$, $P$ is the internal stress, and $d={\mathrm{4}}\,{\mathrm{\upmu{}m}}$ is the length of the photoinduced structure. On the other hand, the structural densification was observed at the edge of the collateral damage. We attribute this new type of light-matter interaction to the spatiotemporal couplings in ultrashort light pulses. We anticipate that the nonreciprocal photosensitivity of glass induced by ultrashort laser pulses will open the door for a novel light-matter interaction.

Fig. 11.41a-h

Nonreciprocal structural changes in silica glass. The top schematics indicate the direction of laser polarization $(E)$ and propagation $(k_{\text{ph}})$. Images in Nomarski-DIC (a,e) and crossed-polarizers (b,f) of the lines written with orthogonally polarized femtosecond laser pulses. Blue arrows show the writing directions. The laser parameters were as follows: $\lambda$: ${\mathrm{800}}\,{\mathrm{nm}}$, $\tau_{\mathrm{p}}$: ${\mathrm{70}}\,{\mathrm{fs}}$, $R_{\text{rate}}$: ${\mathrm{250}}\,{\mathrm{kHz}}$, $E_{\mathrm{p}}$: ${\mathrm{2.0}}\,{\mathrm{J}}$, writing speed: ${\mathrm{100}}\,{\mathrm{\upmu{}m/s}}$, objective: ${\mathrm{0.80}}\,{\mathrm{NA}}$. (c,g) Profiles of Raman spectra along the green dotted lines in (a,e). Raman intensity profiles at ${\mathrm{492}}\,{\mathrm{cm^{-1}}}$ (D1) are also shown in (d,h)