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1 Introduction

Laser surface nanostructuring is an effective tool for large area processing. In this respect, we consider the laser interference approach and application of the colloidal/contact particle lens array technique. The latter is studied in more detail taking into account the effect of the neighboring spheres on their focusing ability. The advantages of using bi-chromatic femtosecond laser beams are discussed. Laser irradiation results in formation of either ablation craters or bumps. The features of the mechanisms of creation of such structures on nanoscales are discussed. Attention is paid primarily to laser swelling—the least studied but very promising effect, which is used first of all for the surface nanostructuring of polymers and glasses. The relaxation mechanism of laser swelling of polymers describing this phenomenon as a volume relaxation of glassy materials within the glass transition region is considered.

Laser nanostructuring within the material bulk can be achieved by a tightly focused laser beam using both the nonlinear light absorption and the strongly nonlinear material response. Some theorems concerning 3D photochemical information recording are formulated. In more detail, the 3D nanostructuring is considered in terms of nanopolymerization. The fluctuation limit for voxel size is determined and a way for the spatial resolution improvement by means of quencher diffusion is proposed.

Nanostructured materials can also be produced even by laser exposure without tight focusing if irradiation leads to the development of instability resulting in the formation of nanoclusters or nanoinhomogeneities in an initially homogeneous medium. Examples of such an instability are the photo-induced formation of metal nanoclusters within dielectric matrices and the laser-induced bubbling. We consider the synthesis and the properties, including the nonlinear optical ones, of photo-induced nanocomposites based on a polymer matrix with photo-induced gold nanoclusters. The nanocluster growth model based on the theory of first-order phase transition is presented. We review the existing experimental data on laser bubbling of polymers. Two models for laser bubbling of polymers based on the droplet explosion mechanism and the cavitation mechanism are considered.

2 Surface Nanostructuring

2.1 Colloidal Particle Lens Arrays and Interference Lithography

Nanostructuring of materials has a significant effect on their physical and chemical properties, which underlies many advanced nanotechnologies. Owing to recent advances in laser systems, laser radiation is one of the most effective tools for modifying materials. At the same time, fabrication of nanostructures using the most readily available visible and near-UV lasers encounters the problem of overcoming the diffraction limit in focusing the laser beam. To produce nanostructures by laser pulses, the laser radiation field should be highly localized, using near-field optics in particular. This can be achieved by a variety of techniques [1], including those that employ field enhancement beneath an atomic force microscope tip [2], near-field optical microscope probes, various near-field masks [3], and interference lithography [4]. A promising area of research is the so-called laser particle nanolithography [3], namely, fabrication of submicron- and nanometer-scale structures via laser radiation field localization using transparent micro- and nanoobjects placed on the surface of the material. Here, colloidal particle lens array (CPLA) proved to be an efficient near-field focusing device for laser nanoprocessing of materials [5–11] (Fig. 13.1). It should be noted that surface nanostructuring can be performed by different ways without laser radiation. For instance, e-beam technologies offer opportunities for creating nanofeatures with quite sophisticated structure [12]. Thus, in order to be competitive, laser technology should, at least in principle, provide an opportunity for creating nanostructures simultaneously on large surface areas. From this point of view, the latter two approaches, namely, interference lithography and CPLA-mediated laser structuring, are very promising.

Fig. 13.1
figure 1

a The structure on polyimide (swelling) obtained by four-beam interference technique: an AFM image (XeCl laser, 308 nm, fluence = 60 mJ/cm\(^{2})\). (See paper by Verevkin et al. [13]). b Polystyrene spheres 1 \(\upmu \)m in diameter on a polymethylmethacrylate (PMMA) substrate. c Typical AFM picture of structures on the surface of PMMA (left) and vitreous glass (right) substrates. CPLA mediated irradiation by femtosecond pulses from a TiSa laser (see paper [14] and the text below)

Full size image

Comparing these two approaches reveals their advantages and disadvantages. It is worth noting that interference lithography of vacuum UV laser beams is considered in paper [15] as a future of laser lithography enabling a spatial resolution of up to 11 nm. At the same time, while femtosecond laser pulses are employed for the material surface nanostructuring, the CPLA approach has evident preference over the interference technique from the point of view of the ability of simultaneous modification of large areas. There are several papers devoted to the femtosecond interference approach for laser nanostructuring of material surfaces [16]. Nevertheless, it is evident that this technique has some constraints from this point of view. Indeed, the longitudinal spatial length of a 50 femtosecond pulse is about d \(=15\,\upmu \)m. This significantly limits the number of features contained in the interference structures obtained by this technique. Below, we mainly focus on the CPLA mediated surface nanostructuring by means of a femtosecond laser pulse.

High focusing ability of microspheres together with high nonlinearity of the material response to irradiation by femtosecond pulses provides an opportunity for fine-structuring of the material surfaces. On the contrary, multiple re-scattering of the laser light within an array of spheres [17–20] can diminish the advantages of the considered setup. It is shown that electrodynamic interaction between the spheres can reduce the field enhancement, elongate the focus volume drastically, thus changing the aspect ratio of the laser-irradiated zone, and shift the maximum of the laser field towards the inner part of the sphere. All of these effects can have a significant impact on the material response and thereby on the nanostructuring process (see recent paper [20] for detail).

Recently, efforts to provide a more efficient modification of materials by optimization of the femtosecond pulse shape (typically via spectral phase modulation) have been reported [21–23]. The idea is that the more powerful front part of the pulse efficiently promotes seed electrons by multi-photon ionization, while the following tail could be effective in the impact ionization process. However, the second harmonic can also be a powerful tool for generation of seed electrons [24]. Below, we consider several reasons why conversion of some part of the beam energy to the second harmonic can be useful for the CPLA-mediated nanostructure formation.

For a laser intensity level of more than \(10^{12}~\mathrm{{W/cm}}^{2}\) and a short pulse duration of about 50 fs, any modification of a material that is linearly transparent at the wavelength of the irradiation is caused by ionization (or electron excitation from the valence to the conduction band). For such a short pulse length, either multiple photon or tunnel ionization mechanism dominates, depending on the value of the adiabatic (Keldysh) parameter, \(\gamma _A\) [25]. If \(\gamma _A >>1\), then the direct transition from the ground state to the conduction band can be interpreted as a multi-photon transition with rate given by \(\mathrm{{W}}_{\upomega }\,\propto I_{\upomega }^{K}\). For the typical cases described below, the value of \(\gamma _A= 1\) corresponds to the intensity \(I\approx 10^{14}\,\mathrm{{W/{cm}}^{2}}\). Since the order of transition \({K}_{2\upomega }=\mathrm{{K}}_{\upomega }/2\), the transition rate for the same laser intensities not exceeding \(I\approx 10^{14}\,\mathrm{{W/{cm}}^{2}}\) is larger at SH than at FF. Moreover, conversion of several percent of the initial pulse energy into the second harmonic can significantly increase the multi-photon ionization rate (see [24] for detail). Combined effect of FF and SH, as is shown in [24], can be more effective than that of FF and SH applied separately because the seed electrons generated by SH can be multiplied by the impact ionization process promoted by FF. Thus, when some part of the laser energy is converted into SH, one can expect a lower modification threshold.

When the laser light is focused by means of a spherical microlens, the strong field maximum is formed beneath the sphere. The smaller wavelength of SH compared to FF allows the microlens to focus the light into a smaller spot. Indeed, FDTD calculation of the field intensity distribution on glass surfaces beneath the polystyrene sphere (typical experimental conditions) shows that irradiation at SH results in about a factor of 1.9 smaller focal spot compared to FF (800 nm). As was mentioned above, the multi-photon absorption order at FF is twice that at SH. However, it can easily be shown that even with allowance for the different orders of the multi-photon absorption processes, SH is advantageous over FF for the localized material modification.

It was discussed above that when CPLAs are employed for the laser beam focusing, coupling of the spherical modes of the constituent microspheres results in multiple cross scattering of light within the array. However, this deteriorative effect may be different at the FF and SH wavelengths. For both the SH and the FF, the presence of the neighbors results in a smaller enhancement and a weaker localization of the field beneath the central sphere. Our calculations show that the effects of the neighboring spheres on both the laser field enhancement and the localization by a spherical microlens is less for SH than for FF. It is interesting to note that the focal volume elongation effect is much more pronounced for FF than for SH.

Thus, calculations show that the CPLA focusing systems provide a better field localization at SH than at FF. As was argued above, conversion of only a small fraction of the beam energy into SH can significantly lower the modification threshold. This also means that even if the major part of the energy remains in FF, the localization of the modification process would be governed by SH for near-threshold fluences. Thus, more localized structures can be obtained.

Experimentally, PS spheres about 1 \(\upmu \)m in diameter were deposited both on PMMA and glass plate substrates. In our experiments [14], we used the Titanium Sapphire laser system Spitfire-Pro (Spectra Physics Co.) in a single-shot regime. The pulse duration was 50 fs, the energy of a single pulse was 1.7 mJ, the central wavelength was 800 nm, and the beam diameter was 7 mm. A flat-convex lens with a focal length of 15 cm was used for the beam focusing. We studied the formation of periodic pit and hillock (hole and bump) nanostructures in different irradiation regimes. The samples were irradiated by single femtosecond pulses of fundamental frequency (FF), of the second harmonic (SH), or by bi-chromatic FF+SH pulses. A thin (100 \(\upmu )\) BBO crystal (oee or II type) was used for the SH generation with a maximum integral efficiency of 5 %. Crystal orientation was varied for the efficiency (phase matching) adjustment. The crystal was placed after the lens to avoid space separation of the FF and SH pulses [26]. A blue glass filter was used for the SH selection. The fluence was changed by moving the sample along the axis of the focused beam, keeping it far from the air breakdown area. In what follows, when speaking about the fluence of a bi-color pulse, we assume the fluence of the FF alone before matching the BBO orientation.

When the fluence of the laser pulse is increased above a certain threshold level (threshold intensity is about \(5\times 10^{11}\,\mathrm{{W/cm}}^{2}\) for SH+FF and \(10^{12}\,\mathrm{{W/cm}}^{2}\) for FF), the spheres are eliminated from the substrate within the irradiated area. This process is similar to the cleaning phenomenon (see [27]). When increasing the fluence up to fifteen percent from the cleaning threshold, we obtain well-defined structures. They are ablation craters on PMMA substrates and swelling bumps on glass substrates (see Fig. 13.1c, d). For glass substrates, the elimination threshold, and correspondingly the fluence of the structure formation, are almost twofold lower in the case of irradiation by an FF+SH combination compared to the sole FF. For PMMA substrates, this difference proves to be even more pronounced. In both cases, the fluence of the structure formation for the FF+SH irradiation is significantly smaller than the fluence of cleaning for irradiation by the FF alone. The addition of SH results in more localized structures both on glass and PMMA substrates, allowing one to reach an ablation-pit radius of about 100 nm. When filtering out the FF radiation and keeping the SH alone, the structures appear only if the sample is shifted closer to the focus of the beam relative to the position in which the FF+SH structuring occurs. The shift provides an SH fluence higher than that in the FF+SH beam taking into account the attenuation by the filter. This means that FF radiation in a bi-color beam significantly contributes to the modification process.

Conversion of a part of the energy of the fundamental frequency into the second harmonic beyond the focusing lens precludes spatial separation of the SH and FF signals. If the BBO crystal were located before the lens, the FF pulse would go first and the SH pulse behind. Our calculations of temporal intensity distributions of the FF and of the SH within a bi-chromatic pulse at the output of a BBO crystal taking into account the dispersion of group velocity shows that in our case both pulses (FF and SH) propagate together. It is clear, however, that for a more efficient use of the bi-chromatic pulses, the SH pulse should be the leading one.

Thus, it is shown that conversion of about 5 % of the laser pulse energy into the second harmonic provides a decrease in the modification threshold and a change in the morphology of obtained structures. The results indicate a higher sensitivity of the materials to SH and also suggest that for the near-threshold fluences, the localization of the modification process is governed by SH, resulting in production of finer structures.

2.2 Nanoablation and Nanoswelling

Laser ablation, a technique for polymer surface processing via layer-by-layer material removal by laser pulses, has been extensively studied in the past 25 years. The main trends in the development of this technique were reviewed elsewhere [28]. In particular, a model was constructed for the laser ablation of strongly absorbing polymers by nano and femtosecond laser pulses [29, 30]. Note, however, that there is no appropriate model for the ablation of weakly absorbing polymers and that specific features of the ablation of such polymers with femtosecond laser pulses have not been fully examined.

Convex surface structures can be produced through laser swelling with no material removal. Laser exposure of polymers and polymer-like materials below the ablation threshold produces a bump (hump) (see Fig. 13.1a, d and [31–35]). This effect may be due to both expansion of the irradiated material and substance redistribution over the surface through hydrodynamic effects. The former process is usually referred to as laser swelling, whereas the formation of bumps on an initially smooth surface exposed to laser radiation is often referred to as bumping. In producing nanofeatures, swelling is preferable because the response of the material to irradiation is then more local. Swelling is also of interest because it leads to the formation of regions with increased free volume. The kinetics of chemical reactions in polymer matrices is sensitive to free volume. Therefore, laser swelling can be used to produce surface nanostructures with enhanced reactivity. Given that chemical reactions in “nanoreactors” have a number of specific features, it is reasonable to anticipate that studies of laser-induced surface nanostructuring through swelling will give interesting, unexpected results. Porous convex structures can be selectively doped with luminescent dyes.

Sometimes (see, e.g., [36, 37]) swelling is due to the formation of micro- and nanocavities in the irradiated region during the stress relief. We consider this phenomenon in a special section below. At the same time, surface nanoswelling near the swelling threshold seems to obey a different mechanism.

Relaxation model for the laser swelling of polymers has been formulated in [38]. Laser heating of a polymer material to a temperature greater than the glass transition temperature converts the material to a rubber state. In this state, the Young modulus significantly decreases while the thermal-expansion coefficient significantly increases, reaching about \(10^{-3}\,\mathrm{{K}}^{-1}\).

This transition requires the rearrangement of some parts of polymer chains containing 5–20 monomer parts. This process is a cooperative one and consists of simultaneous movement of the whole group of segments. In polymers, this process is related to \(\alpha \)-relaxation. The relaxation time strongly depends on temperature.

The heating occurs during the laser pulse, while the cooling is provided by heat diffusion. Due to the finite time of relaxation, the change in volume follows the change in temperature with some delay. Typically, this delay means that sharp heating of the material during a short laser pulse will continue to increase the material volume for some time after the pulse is over. During cooling of the material after the end of the pulse, the volume at some time can reach an equilibrium value for the temperature at that time. When the cooling goes further, the volume will decrease with delay and when the cooling proceeds up to the room temperature there is a chance that the relaxation being slower and slower cannot compensate for the change in temperature because the relaxation time strongly increases with decreasing temperature. This results in the creation of a permanent hump, or the residual swelling.

If \(u_r\) is the relaxing volume change in the rubber state, then the simplest equation yielding the evolution of \(u_r\) can be written as

$$\begin{aligned} \dot{u}_r ={(u_{r0} (T)-u_r )}/{\tau (T)}. \end{aligned}$$
(13.1)

Equation (13.1) is similar to the Kelvin-Voigt equation for a viscous elastic body when the outer stress is given and the deformation relaxes to the steady state. In this case, the temperature provides a steady value of \(u_{r0} =\alpha _1 (T-T_1)\) to which the actual volume change relaxes. Here, \(\alpha _{1}\) is the thermal-expansion coefficient in the rubber state, and we use \(\mathrm{{T}}_{1}\) instead of \(\mathrm{{T}}_\mathrm{{g}}\) to allow for some uncertainty in determining of the glass transition temperature.

It can be shown that experimental data on the swelling of dye-doped PMMA exposed to nanosecond frequency-doubled Nd : YAG laser pulses [39] and swelling dynamics in undoped PMMA exposed to 248-nm KrF excimer laser radiation [40] fit well the relaxation model. When comparing to the model with the experimental data, we employed the approximation [41] for the dependence of relaxation time on temperature with \({T}_{2}=\,\)const:

$$\begin{aligned} \tau =\tau _0 \exp ({T^{*}}/{(T-T_2 })). \end{aligned}$$
(13.2)

Thus, near the ablation threshold the swelling seems to have a relaxation nature.

When considering swelling on nano and microscales [42], one cannot use the above point-like model because of the fundamental non-uniformity of the laser heating and the influence of the outer, not heated neighboring parts of the material.

The simplest generalization of the relaxation model could be a hydrodynamic model which, taking into account that the shear modulus above the glass transition point is three orders of magnitude smaller than the bulk modulus, considers swelling in terms of heating and cooling of a viscous compressible liquid with strongly temperature-dependent shear and bulk viscosities. In the limit of the homogeneous heating corresponding to the point-like model (13.1) one easily obtains Kelvin-Voigt equation (13.1) with the relaxation time \(\tau ={\left( {\xi +{4\eta }/3} \right) }/K\), where \(\xi \) and \(\eta \) are the bulk and shear viscosities, respectively, and K is the bulk modulus.

In the case where the laser heating is significantly localized as it is with the nanoswelling, the so-called “beaker” approximation [43] is used. Here, the simultaneous heating of the beaker, a cylinder domain of radius R and length L, within the material bulk contacting the material surface to a temperature above the glass transition one is considered. During the cooling it is assumed that the temperature is equal within the cylinder and the material outside the beaker is kept in glass state. Approximate consideration of this simplified model for the height of the hump \(\mathrm{{h}}<<\mathrm{{R}}\) reduces the height evolution problem to the Kelvin-Voigt equation with the temperature-dependent relaxation time

$$ \tau ={\left( {\xi +\eta \left( {4/3+{2L^{2}}/{R^{2}}} \right) } \right) }/{2K(1+\beta )} \, \mathrm{{and}} \, \beta ={\left( {8\alpha _s L} \right) }/{KR^{2}}, $$

where \(\alpha _s\) is the surface tension. The above expressions indicate important dependence of the swelling kinetics on different kinds of viscosity, dimensions of the heated region, R and L, as well as on the surface tension.

It should be noted however, that the complete hydrodynamic theory for laser swelling should have a solution (either analytical or numerical) of the full hydrodynamic equation together with the heat diffusion equation in deformed medium allowing for the temperature dependence of the surface tension and the outer stress due to the thermo acoustic response of the medium to sharp laser heating. This theory is now in progress.

A fundamental problem of the theory of laser swelling is the absence of both real experimental and analytical data on bulk viscosity and its dependence on temperature and pressure, while the temperature dependence of shear viscosity on temperature is known to follow relation (13.2) or similar relation (see, e.g., [44] for a review).

3 3D Nano-Structuring

Contrary to the surface nano patterning, lasers have no real competitors in 3D nano and micro-structuring within the material bulk. Thus, the successive recording modes such as direct laser writing (DLW) are acceptable. Below, we consider the two main ways for 3D structuring. The first is 3D bitwise information recording, and the second is formation of connected nanostructures by 3D laser nanopolymerization. In both cases, we deal with the spatial resolution problem. It should be noted that the peak of scientific activity within the field of 3D laser information recording was in the beginning and the middle of the 2000s, whereas the 3D nanopolymerization is a rapidly developing and topical technology at the moment. Nevertheless, the approaches developed for information recording are interesting and apply for nanopolymerization as well, especially since femtosecond laser polymerization is one of the possible ways of information recording although now it is used mainly for the creation of photonic structures.

3.1 3D Photochemical Information Recording

3D optical memory provides increased density of information storage compared to the conventional 2D systems where bitwise information is recorded on the surfaces of the disk. There are different approaches to recording and reading of bitwise information within the bulk of material [45–50]. In what follows, we consider bitwise information recording provided by the local absorption of an appropriate amount of photons. Thereby, the speed of photon absorption does not matter. An example is the well-known fluorescent memory [46, 47] in which the absorbed photons are used to provide the photochemical reaction with a product that is fluorescent when excited at the wavelength of reading. The widely discussed recording with photochromic molecules [48] is also of this type. Here, the photochemical isomerization is used to provide information reading through changes in the local optical properties of the materials. Since this type of recording is often associated with the photochemical reaction, we call it photochemical recording.

Usually, the 3D bitwise recording is provided by sequential (parallel) focusing of the laser beam (beams) in the position (positions) of recorded bit (bits). Namely, “unity” is recorded if a specific bit position is irradiated and “zero” is recorded otherwise. However, the problem is that when unity is recorded in a given position, spurious cross-talk writing occurs in the neighboring positions. The limitations imposed by this circumstance are discussed in this section for both single- and two- photon absorption (see [51] for detail).

We now consider how to maximize the recording density of a 3D array of voxels (bits of information) using focused laser beams. This problem was solved for a 3D photochemical bitwise laser-assisted information recording [51], but it is also important, e.g., for the laser polymerization considered below. In [51], a quantity was introduced to characterize the spurious recording level, namely, the ratio of the number of photons absorbed at a given point when unity is written into all other points to the number of photons that would be absorbed at a given point when unity is written into it. We introduce the concept of a permissible cross-talk recording level \(\eta _{p}\). The laser beams are assumed to be Gaussian. Analysis of single-photon recording indicates that an increase in the number of layers with a permissible value of \(\eta _{p}\) should be accompanied by an increase in the distance between the bits within the layers in such a way that the information density calculated per square centimeter of the disk does not increase. This means that the transition from 2D to 3D information recording with single-photon absorption does not increase the recording density per unit surface area. Therefore, 3D single-photon information recording is ineffective. At the same time, analysis of two-photon information recording indicates that for a given permissible spurious exposure, there is an optimal configuration of recording points which maximizes the volume recording density. In particular, for a numerical aperture of the objective NA \(= 1\), the refractive index of the medium \(n = 1.5\), wavelength \(\lambda = 800\) nm, and permissible spurious recording level \(\eta _{p}=0.1\), the volume recording density \(\rho _{inf}\) may reach 3 \(\times 10^{13}\) bit \(\mathrm{{cm}}^{-3}\). This means that a disk 12 cm in diameter and 0.5 mm in thickness may contain about 20 TB of information. At \(\eta _{p} = 0.1\), the separation between the layers will be 0.75 \(\upmu \mathrm{{m}}\). Thus, the disk will have 670 layers. The permissible spurious exposure level is determined by the reading procedure. At NA \(= 1\) and \(\eta _{p} = 0.7\), such a disk may contain 65 TB of information.

3.2 3D Nanopolymerization

3.2.1 Fluctuation Limit

The most versatile technique for producing 3D nanostructures is sequential processing of a polymerizable medium using a well-focused femtosecond laser beam (for more detail, see in Chap. 12). Femtosecond lasers make it possible to effectively use two-photon absorption for polymerization initiation. Since there is a nonlinear absorption and gelation threshold, the process takes place only in a small region around the beam spot. The forming blob of polymer gel, commonly referred to as a voxel, may be less than 100 nm in size [52, 53]. Translating the sample relative to the beam by a precision positioning system, one can create 3D patterns composed of individual voxels (see [54]). Even though laser polymerisation has been the subject of intense experimental studies, very little work has been directed towards theoretical modeling of the process.

In laser nanopolymerization, the threshold for the response of a substance to laser exposure is determined by a percolation-like transition associated with the formation of gel, namely, a 3D network of macromolecules. In the case of homogeneous polymerization, the percolation transition has a threshold in terms of the monomer conversion to polymer. Recent work [55] has shown, however, that the minimum size of the nanofeatures produced by laser nanopolymerization is limited by random inhomogeneities in the network of polymer molecules (Fig. 13.2). When the threshold is exceeded only slightly, the resulting voxel is of a purely fluctuation nature. The properties of such voxels were studied in [55]. It has been shown that different samples of fluctuation voxels are dissimilar. The centroid and size of voxels fluctuate from implementation to implementation, and the number of voxels may differ from unity. In other words, irradiation results are irreproducible under such conditions. To make up reproducible voxels, these should have a non-fluctuating core, as is shown in Fig. 13.2c. A generalized analytical formula for various spatial distributions of the monomer conversion to polymer is derived in [55]. This formula can be used to estimate the minimum radius of a reliably produced voxel with negligible fluctuations. To this end, the results of the existing gradient percolation theory (percolation for a given spatial distribution of the percolation parameter) were generalized to a wider range of spatial distributions compared to those considered in the literature. The formula was verified using Monte Carlo simulation.

Fig. 13.2
figure 2

Schematic illustrating the fabrication of a small voxel by laser exposure using a threshold response of the material: a, b ideal case in which any small increase in intensity (or in appropriate integral characteristics of the exposure) above the threshold produces a voxel, which can thus be made as small as desired; c, d percolation transition as a threshold process in which \(\sigma _{+}\) and \(\sigma _{-}\) fluctuation zones form at the voxel boundary; d the resulting voxel is of a purely fluctuation nature when the threshold is exceeded only slightly (\(R_\mathrm{{vox}}\) is the voxel radius)

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Analysis shows that despite the threshold-like response of the media to the laser irradiation fluctuation nature of the percolation transition precludes reducing the size of a voxel to much below the size of the laser beam limited by diffraction. Additional tools should be used to lower this limit. One of the ways is to employ a two-beam technique of direct laser writing DLW STED [56]. Another approach is addressed below.

3.2.2 Diffusion-Assisted Direct Writing

Quencher or inhibitor of polymerization is used to introduce one more threshold in the polymerization process. It is believed that this additional threshold helps improve the spatial resolution. A quencher molecule interacts with a free radical one, thereby preventing the polymerization process to proceed. Due to this reaction, the quencher molecule is consumed. Thus, the laser light should produce some amount of radicals through the initiation reaction in order to consume almost all the quenchers to start the polymerization process at the particular point. It is an old idea of the additional threshold [57]. A new idea is to employ the diffusion of the quencher [58]. While the diffusion of small radicals as well as macromolecules can be detrimental to spatial resolution [59], the diffusion of the quencher, which inhibits the polymerization, can have a positive effect.

One of the prominent positive effects of the quencher diffusion is recovery of the initial quencher spatial concentration upon irradiation. When writing two adjacent lines, the quencher in the interstice is consumed. When the lines are written at a sub-diffraction distance to each other, the quencher in the interstice is totally consumed and the polymerization is started as though it was a single feature, as is seen in Fig. 13.3b. However, when the quencher recovers to its initial concentration before writing the next neighboring line, such limitation of the spatial resolution relaxes (Fig. 13.3c).

Moreover, quencher diffusion also helps improve the spatial resolution in terms of the size of an elementary voxel. To understand this quencher diffusion effect, we consider a basic photo-polymerization model. The evolution of spatial distributions of the number densities of the quencher molecules (Q), free radicals (R), and free monomer molecules (M) can be modeled by the following set of equations:

$$\begin{aligned} \frac{{\partial R}}{{\partial t}} = S\left( {\overrightarrow{r} ,t} \right) - k_{{tQ}} QR,\;\frac{{\partial Q}}{{\partial t}} = D_{Q} \Delta Q - k_{{tQ}} QR, \end{aligned}$$
(13.3)
$$\begin{aligned} - \frac{{\partial M}}{{\partial t}} = k_{p} RM,p = \frac{{M_{0} - M}}{{M_{0} }} \end{aligned}$$
(13.4)

Free radicals are generated as a result of the absorption of laser light by a photo-initiator. For two-photon absorption, the source term is proportional to the square of the local field intensity I, pulse duration \(t_{p}\), and pulse repetition rate \({R}_{p}\): \(S\propto {I^2} (\overrightarrow{r}, t)\,{t_p}{R_p}.\) As a result of the quenching reaction, both the quencher and the radical are consumed with the reaction rate \(K_{tQ}\). The diffusion coefficient of the quencher is \(D_{Q}\) and \(\Delta \) is the Laplacian. The polymerization rate is given by (13.4) and is proportional to the monomer number density \(M\), the radical number density, and the propagation constant \(k_{p}\). The conversion p indicates the degree of polymerization (here, \(M_{0}\) is the starting number density of the monomer).

Consider the set of equations (13.3) in more detail. If the line scan is much slower than the diffusion of the quencher, one can consider long-lasting irradiation with a source that is constant in time. In order to understand the main effect, we consider the one-dimensional problem in half-space (coordinate \(x>0\)) with \(S=S_{0}\) for \(x>0\) and with the boundary condition \(Q=Q_{0}\) at \(x=0\). The stationary solution of set (13.3) with the above boundary condition satisfies the equation \(D_Q {\partial ^{2}Q}/{\partial x^{2}}=S_0\) and yields \(Q=Q_0 \left( {x/{x_c }-1} \right) ^{2}\) for \(x<x_c\), and \(Q=0\) for \(x>x_c\). Here, \(x_c =\sqrt{{2D_Q Q_0}/{S_0}}\) (see Fig. 13.4).

This means that the quencher is localized within the scale \({x}_{c}\) which depends on the laser intensity. The larger the intensity, the larger S and the smaller the scale of quencher localization \(x_{c}\). It should be noted that for \(x>x_{c}\) the stationary solution for radical concentration R is no longer valid and the process in this domain occurs as if there is no quencher at all.

Fig. 13.3
figure 3

a Formation of a single sub-diffraction sized feature is possible due to the polymerization threshold.b When the quencher diffusion is not effective, the formation of two features at a sub-diffraction distance is limited by tails of the distributions of the energy absorbed during scans (blue dotted lines). The total absorbed energy (black line) exceeds the threshold not only where the nanofeatures are expected to form, but also in the interstice. c Formation of the second feature at a sub-diffraction distance from the first one assisted by the quencher diffusion. The energy absorbed during the first scan causes both the consumption of the quencher and the formation of the polymer feature. Since the quencher is diffusion-regenerated between scans, the only effect of the irradiation that remains is the formation of the polymer feature (green line). This allows creation of the second feature at a sub-diffraction distance

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A similar consideration was employed in [60–62] to clarify the UV oxidation phenomenon for polymers such as PVC and PMMA. Here, oxygen effectively reacting with the radicals plays the role of a quencher. The above model explained the discovered kinetic features of the process by the formation of an oxidized domain just beneath the irradiated surface and a non-oxidized one within the material bulk. In the latter domain, the photo-activated processes occur as if there is no oxygen at all. It is important to note that the length of the oxidized domain depends on the light intensity.

Coming back to the polymerization, we consider the size of the irradiated domain of finite length L and allow the quencher to diffuse on both sides (see Fig. 13.4b). In this case, as is seen in Fig. 13.4b, a domain of size \(d=L-2x_c\) where the quenching is not effective, will form in the middle of the irradiated zone. The length d decreases with decreasing irradiation intensity. For a sufficiently small intensity, d could be significantly smaller than L. While L is typically comparable to the beam size, d can be made much smaller.

The irradiation time, conversely, does not affect the size of the quencher-free domain. An increase in the irradiation time (or a decrease in the scan speed in the case of direct laser writing DLW) only causes an increase in the polymerization degree (conversion) within the quencher-free domain (Fig. 13.4d). On the contrary, in the threshold model (without the quencher diffusion), the maximum polymerization degree of a nanofeature can be increased by applying a higher irradiation dose either by increasing the beam intensity or the irradiation time (Fig. 13.4c). However, the higher dose inevitably results in increased size of the polymer feature. By employing the diffusion of the quencher, one can handle both the size and the maximum conversion of the polymer feature separately. The formation of sharp spatial distributions of the conversion is important for achieving a high spatial resolution, a high mechanical stability, and resistance to fluctuations discussed above.

Fig. 13.4
figure 4

a Concentration of the quencher is localized within the scale \(x_c =\sqrt{{2D_Q Q_0 }/{S_0}}\). b In the case of the irradiated domain of finite length L, there is a quencher-free domain of size d dependent on the irradiation intensity. By decreasing the laser intensity, d can be decreased to sizes much smaller than L. c Schematic of the conversion profiles in threshold polymerization regime for different irradiation doses. d Schematic of the conversion profiles in the model of stationary quencher diffusion for different irradiation times and fixed irradiation intensity

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Use of the approach based on the quencher diffusion allowed the authors of [58] to fabricate woodpile structures with an interlayer period of 400 nm, which is comparable to what has been achieved by the two-beam DLW-STED technique currently regarded as state-of-the-art.

3.3 Nano-Stucturing Through Instabilities

Above we considered laser nano- and micro-structuring of materials that was provided by tightly focused laser beams. However, nanostructured materials can also be produced even by laser exposure without tight focusing if irradiation leads to the development of an instability [63] resulting in the formation of nanoclusters or nanoinhomogeneities in an initially homogeneous medium. The examples of such instabilities are laser- induced bubbling and photo-induced formation of metal nanoclusters within dielectric matrices. The development of such inhomogeneities typically has a significant effect on the optical properties of such materials, which may be of considerable practical interest. In this context, it is important to produce materials capable of such nanostructuring under laser irradiation.

3.3.1 Photo-Induced Nanocomposites

In this chapter, we consider the photo-induced formation of metal nanoclusters, i.e., nanocomposites. The most widespread chemical method for the preparation of nanoparticles is the reduction of metal compounds in solution in the presence of various stabilizers [64]. Another approach to the fabrication of polymer-matrix nanocomposites was developed in [65]. Here, the nanoparticles are not implanted into the polymer, but produced directly in a polymer matrix by reducing dopants. The key feature of this approach is that the polymer performs a number of functions, acting, on the one hand, as a matrix for nanoparticles and, on the other hand, as a stabilizer intended to prevent nanoparticle aggregation and ensure a uniform nanoparticle distribution throughout the polymer and temporal stability of the nanocomposite. In these studies, films 20–200 \(\upmu \)m in thickness were produced by casting and spin-coating with PMMA solutions. The atomic gold precursor in the film was \(\mathrm{{HAuCl}}_{4}\), which was added to a polymer solution. The formation of gold nanoparticles was initiated by UV irradiation of the \(\mathrm{{HAuCl}}_{4}\)-containing PMMA films.

Fig. 13.5
figure 5

Effects of the UV irradiation and heat treatment on the attenuation spectrum of a composite: a UV irradiation eliminates the peak at 320 nm due to HAuCl4. The subsequent heat treatment gives rise to a peak due to the formation of gold nanoparticles in the polymer; b effect of heat treatment at \(75{\,}^\circ \mathrm{{C}}\) on the attenuation spectrum of a 50-mm thick PMMA film (peak-attenuation wavelength \(\lambda = 540\) nm). c Bulk PMMA sample synthesized by polymerization. The left sample is a freshly prepared polymer. The right sample is UV-irradiated by a XeCl laser through a figured steel stencil over 20 min and subsequently annealed over 3 min at \(160{\,}^\circ \mathrm{{C}}\) (for details see [71]). Color parts are the domains containing Au nanoparticles

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As the UV source, we used a DRP-400 high/medium pressure mercury lamp or a XeCl excimer laser. The nucleation and growth of gold nanoparticles were followed using attenuation coefficient measurements in the UV and visible spectral regions. Figure 13.5a illustrates the effect of UV irradiation on the attenuation coefficient of the composites. The spectrum of the non-irradiated sample has a prominent peak at 320 nm, which corresponds to the peak-absorption wavelength of \(\mathrm{{HAuCl}}_{4}\). It is clear from Fig. 13.5a that UV exposure leads to \(\mathrm{{HAuCl}}_{4}\) photolysis, as is evidenced by the disappearance of the 320-nm peak. At the same time, there is no absorption in the visible range after this step (initiation of the nanoparticle formation). Next, the irradiation was ceased and the sample was placed in a thermostat maintained at a certain temperature. The formation of nanoparticles was inferred from changes in the attenuation spectrum in the plasmon resonance region of gold nanoparticles. The time variation of the attenuation spectrum was studied in a wide temperature range (20–80 \(^\circ \mathrm{{C}}\)). Typical spectra are presented in Fig. 13.5b. As is seen in Fig. 13.5b, thermostating gives rise to an attenuation peak in the plasmon resonance region of gold nanoparticles. Based on the Mie theory [66] and modern models for the size-dependent permittivity of metal particles [67, 68], one can derive the attenuation spectrum of spherical particles, neglecting particle-particle interactions. Note that the shape of the attenuation spectrum is size-dependent. Namely, as the particle radius increases, the attenuation peak grows both in magnitude and relative to the UV absorption, becomes sharper, and shifts towards the longer wavelengths. For the larger particle radii, the peak begins to broaden, and another feature corresponding to the next mode of the plasmon resonance emerges. Analysis of the evolution of the attenuation spectrum during annealing demonstrates that the shape of the spectrum varies insignificantly. The same refers to the peak position and width. Since the evolution of the spectrum is associated with the formation and growth of gold nanoparticles in the film, this behavior of the spectrum suggests that annealing increases the number density of nanoparticles, whereas the particle size distribution remains essentially unchanged. We propose the following model for the photo-induced formation of gold nanoparticles in polymer films [69]. Absorption of an UV photon by a precursor molecule initiates a sequence of chemical reactions, leading to the reduction of gold atoms and the formation of a supersaturated solid solution of gold atoms in the polymer matrix. Subsequent decomposition of the solid solution gives gold nanoparticles, which act as nuclei of a new phase, metal gold. Raising the annealing temperature markedly accelerates gold diffusion and, accordingly, the formation of nanoparticles. Therefore, the formation of gold nanoparticles in this model can be described in terms of the theory of first-order phase transitions. However, attempts to describe the kinetics of gold nanoparticle formation using Zeldovich and Lifshitz–Slezov theories [70] have been unsuccessful because these theories predict a shift of the particle size distribution to larger sizes over time, i.e., an increase in average particle size, whereas in our experiments the particle number density increased with the time, but their size distribution remained unchanged. The above experimental data can be understood if the stabilizing effect of the matrix is taken into account [69]. In a rate equation similar to the Fokker—Planck equation in the Zeldovich theory for the time variation of the particle size distribution, the stabilization effect is represented by an extra relaxation term which corresponds to the transition of a growing nanoparticle to a stabilized, inactive state with a particular transition frequency. The stabilization leads to a steady-state particle size distribution and a monotonic increase in the total number of nanoparticles with a fixed size distribution. Taking this into account allows one to adequately describe the measured spectra and particle growth data and determine model parameters, such as the parameter related to the particle lifetime in the active state and the particle flux through the critical point in particle size space.

As was pointed out above, the synthesis of metal nanoparticles in transparent dielectric matrices considerably changes both the linear and nonlinear optical properties of the material. That the nanocomposites described above result from photo-induced processes allows one to produce nanostructured regions of arbitrary shape and to control the properties and size distribution of the resulting clusters by adjusting the irradiation conditions. Such nanocomposites can be produced using UV lamps, but the use of laser radiation is critical for the fabrication of complex architectures within bulk materials for photonic applications.

The above UV-induced changes in the optical properties of studied materials permit one to prepare diffraction gratings [71]. Good efficiency of diffraction transformation was shown with visible and IR laser radiation. Diffraction gratings made of polymer materials containing gold nanoparticles demonstrated the best efficiency for an IR laser beam (wavelength 1550 nm) at a level of 1.8 %, which corresponds to a refractive-index change of \(4\times 10^{-5}\).

To examine the UV-induced nonlinear optical properties, a highly sensitive method based on a spectrally resolved two-beam coupling technique was used for detection of electronic optical nonlinearity in thin polymeric films in the infrared spectral range. The experimental setup [71, 72] has an erbium-doped fiber laser generating 100 fs pulses with high repetition rate at a wavelength of 1570 nm as the light source. Cross phase modulation during interaction of two beams with high and low intensity in the focal area leads to large relative spectrum changes at the edge of the laser spectrum band. Thus, spectral analysis allows getting information about the nonlinear optical properties of studied media. The nonlinearity activation time was measured using a time delay between the pump and probe femtosecond laser pulses; its common value for a fast electronic nonlinear response does not exceed the pulse duration (100 fs). High values of the UV-induced nonlinear refractive index (\(n_{2})\) and two-photon absorption coefficients due to UV-induced gold nanoparticles were obtained in studied materials. The nonlinear optical coefficients were found for the samples based on PMMA with gold nanoparticles making up about 5 % in mass. The nonlinear refractive index was \(-1.3\times 10^{-13}\,\mathrm{{cm}}^{2}/\mathrm{{W}}\), which is a factor of 300 larger than the nonlinearity of quartz. The two-photon absorption for these samples was \(8\times 10^{-9}\) cm/W.

Thus, we demonstrate the initially homogeneous materials that become nanostructured due to UV laser irradiation. Metal nanoparticles are formed within the irradiated domains. This results in a dramatic change in the linear and nonlinear optical properties of these materials, thus showing good prospects for their application in photonics.

One example of optical nanocomposite devices is the so-called random lasers [73–76], in which feedback is due to scattering by nanoparticles. Popov et al. [77] reported random lasing in gold nanoparticles embedded in a polymer matrix (PMMA) containing a laser dye. But those particles were inserted into the matrix. The approach described above can in principle be used to produce random lasers in UV-irradiated regions of the material. At the same time, the above photo generation of gold nanoclusters in a polymer matrix encounters several problems which limit the use of this technology in photonics. One problem is the large number of small particles formed, which make a significant contribution to the optical loss. One way to alleviate this problem is to increase the free volume in the matrix, which might cause the smallest particles to aggregate. Yakimovich et al. [78] used methyl methacrylate/ 2-ethylhexyl acrylate co-polymers as matrices. Ethylhexyl acrylate is known to increase the free volume. The results demonstrate that, all other factors being the same, the attenuation peak of the nanoparticles in such matrices is shifted towards the longer wavelengths, indicating an increase in average nanoparticle size. In general, the larger the nanoparticle, the greater the ratio of its scattering and absorption coefficients, which is also essential for a number of applications.

Another problem is that the above procedure gives films, whereas many applications, including random laser fabrication, require bulk materials rather than films. These bulk materials can be synthesized by means of polymerization. The problem here is that [79] the synthesis of bulk PMMA containing \(\mathrm{{HAuCl}}_{4}\) is very difficult, despite the good solubility of this precursor in MMA. This compound converts to a metal precipitate in the course of polymerization even if the concentration of \(\mathrm{{HAuCl}}_{4}\) is less than \(0.5\times 10^{-3}\) mol/L. Polymerization starts only when the reduction of the precursor has completely finished. This problem was overcome in our group by Agareva et al. [71, 80]. The proper choice of the precursor, initiator, and regime of polymerization yielded bulk PMMA samples containing a wide range of precursor concentrations. It was demonstrated that the UV irradiation of synthesized bulk PMMA followed by annealing allowed gold nanoparticles to form within only UV-irradiated areas of the polymer matrix. The result of the XeCl laser irradiation of a bulk polymer performed through a figured steel stencil followed by annealing at \(160\,{^\circ }\mathrm{{C}}\) for 3 min is presented in Fig. 13.5c.

3.3.2 Laser Bubbling

Another example of structuring through an instability is the bubbling phenomenon. Under the effect of laser radiation just near the ablation threshold sometimes one can observe numerous cavities within the irradiated polymer. The cavity (bubble, void) formed within the laser irradiated materials can be due to cavitation bubbles [81] created during the rarefaction wave propagation (originated from the reflection of a pressure wave from the free surface of the sample). The creation of cavitation bubbles relies on the glass transition temperature (\({T}_{g})\) of the polymer and excess of the laser heated material temperature over \({T}_{g}\), as well as on the value of the maximum tensile stress provided by the laser pulse.

A detailed approach for the KrF excimer laser polymer bubbling is published in [36]. According to [36], the threshold of laser bubbling is related to a homogeneous nucleation threshold followed from the Zeldovich formula. However, at the moment, this theory is not developed enough to compare its results with the experimental data. However, a more comprehensive analysis shows that other steps of the cavity creation, namely, the cavity growth due to tensile stress during propagation of the rarefaction wave followed by its collapse or relaxation upon passage also are very important and crucial.

In [37], the phenomenon of bubbling within the Paraloid B72 polymer samples prepared by a casting technique due to single pulse irradiation by a KrF laser for the sub-ablation fluences was clarified experimentally. A methodology relying on the observation of morphological alterations in the bulk material (Paraloid B72) by using third-harmonic generation is developed. This non-destructive procedure permits detailed and accurate imaging of the structurally laser-modified zone extent in the vicinity of the irradiated area. Visualization and quantitative determination of the contour of the laser-induced swelling/ bulk material interface are carried out and the data on the position of this interface for the laser fluence are reported.

In order to address these data theoretically, an alternative to the above cavitation bubble generation mechanisms, which can be considered for polymer films fabricated by the casting method, is suggested.

Consider a liquid droplet of radius r within the polymer matrix. This droplet can be originated from solvent residuals due to casting. Upon laser irradiation, both the matrix and the droplet are heated, and the droplet reaches its boiling temperature. If the pressure of the (liquid) droplet saturated vapor is equal to the surface tension pressure, then the cavity will expand. The evaporating droplet will provide enough gaseous molecules to support the bubble growth. If the growth proceeds up to the complete evaporation of the liquids, then the pressure will change from the saturated pressure to the pressure of an ideal gas with a fixed number of gas molecules within the bubble. Due to the subsequent cooling of the matrix, the pressure of the vapor inside the bubble decreases, and the bubble starts to collapse once the surface tension pressure overcomes the vapor pressure. Strong dependence of the viscosity on temperature can prevent the elimination of a bubble and stabilize it with some final size. According to this model, the distance from the surface at which the bubbles remain is the position of the rear border of the bubbling zone \(z_{rear}\) measured experimentally. The growth and collapse of a bubble was addressed using the Rayleigh-Plesset equation [82] for the case of small bubbles in a high-viscous liquid (in which inertial terms are neglected). In this simplified model, it was assumed that the gas temperature inside the bubble is equal to the temperature of the surrounding material. The temperature evolution was described by a simple heat diffusion equation, \({\partial T}/{\partial t=a{\partial ^{2}T}/{\partial z^{2}}}\), with the initial conditions \(T(z,0) = {T}_{room} + (\alpha \phi /c_{P} \rho )\mathrm{{e}}^{-\alpha z}\) and boundary condition \(\partial {T}/\partial {z}{\vert }_{z=0} = 0\). Here, \(\phi \) is the laser fluence and \(\alpha \) is an effective absorption coefficient. It follows from the solution of this equation that for each point \(z>0\) the temperature initially increases, then approaches the maximum value \({T}_{max}(z)\), and finally decreases. Analysis of the above model of bubble dynamics shows that for different fluences the position of the rear border of the bubbling zone \({z}_{rear}\), corresponds to a fixed value of the maximum temperature \(T_{\max } (z_{rear} ,\phi )\approx T^{*}\) with \({T}^{*}=\) const. For the considered experimental data, this constant was determined to be 394 K. It was shown that \(z_{rear} (\phi )\) determined from the above equation fits the reported experimental data with \(\alpha _{eff} =1000\,\mathrm{{cm}}^{-1}\).