1 Introduction

The development of powerful lasers has allowed the investigation of atoms and molecules in intense laser beams. In recent years, the advent of laser pulses of ultrashort duration has favored studies in the femtosecond time regime. Nonlinear photoionization processes play a central role in the behavior of atoms and molecules in strong laser fields [1]. They also constitute a background to the modern physics of attosecond phenomena [2]. From a theoretical point of view, the probability of the photoionization process can be calculated at any given value of the electromagnetic field and accordingly at any point in the space region occupied by the strong laser field. On the contrary, in experiments the photoionization signal is usually averaged over the volume of a strong spatially inhomogeneous focused laser beam. This leads to the loss of spatial resolution in the observed photoionization signal. This drawback can, however, be overcome by combining the observation of the photoionization process with ion projection microscopy in divergent electrostatic field.

Field emission projection microscope, invented by E. Muller, allowed an atomic resolution and is a rather effective tool to study the surfaces of the refractory metals [3, 4]. The main elements of such a device are a very sharp metal tip, with a curvature radius r tip  ~ 10 nm, and a position-sensitive detector with accelerating divergent electric field between the tip and detector. The formation of an image of a tip is based on the radial expansion of the produced charged particles, electrons or ions, from the tip to the detector, i.e. on the projection principle, which at sufficiently small value r tip provides rather high spatial magnification at the level of M ~ 104–106.

The use of laser radiation in the projection microscope, pioneered by V. Letokhov [5], allows one to avoid strong electrostatic fields near the emitting surface, which may be rather valuable in the observation of complex organic molecules, placed at the tip, as well as in obtaining spectral information about the studied object [6, 7]. In such observations the characteristic diameter d laser of the laser focal spot is typically chosen to be by several orders of magnitude larger than the radius of the tip, d laser  » r tip .

In this paper, we show that the projection microscope can be used to observe the nonlinear photoionization processes with subfocal micrometer-scale spatial resolution, visualize the profile of the intense sharply-focused laser beam and extract its characteristic width. To develop such a technique we use a blunt needle with a curvature radius satisfying the condition, r tip  » d laser .

2 Experimental setup

We describe two types of experiments on the projection microscopy using the blunt needle. In one experiment we observe the electron signal produced as a result of photoemission from the tip (needle) and determine a magnification of our microscope, while in the other we detect the ion signal produced by the photoionization of the image molecules in the residual gas located between the tip and the detector.

Our vacuum chamber equipped with projection microscope was pumped by a Varian turbomolecular pump to a pressure of ~10−7 Torr. In the central part of the apparatus shown in Fig. 1 a silver-plate tip with a curvature radius r tip  = 0.5 mm was fixed on a manipulator. A position-sensitive detector of diameter of 24 mm located at a distance of L = 150 mm from the tip consisted of a pair of the microchannel plates and a phosphor screen. The signal from the detector was processed and transmitted to a computer. The face of the detector was held at the ground potential.

Fig. 1
figure 1

Schematic of the experimental setup

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The femtosecond laser pulses were produced by the Spectra-Physics laser system running at a repetition rate f = 1 kHz. Linearly polarized light with polarization vector coinciding with the Oy axis as shown in Fig. 1 and a wavelength λ = 800 nm, pulse duration 40 fs and energy up to 0.4 mJ/pulse, was focused in the vacuum chamber by an optical lens with a focal length 230 mm. The propagation direction of the laser beam was orthogonal to the Oy axis. The measurements made by the Newport profilometer with strongly attenuated laser beam have shown that the intensity profile in the focal spot was close to a Gaussian distribution \( I = I_{0} \exp \left( { - 2\frac{{r^{2} }}{{w_{0}^{2} }}} \right) \)with a radius w 0 ≈ 36 μm. On irradiation of the residual gas molecules by the laser radiation with the intensity of the order of 1014 W/cm2 we observed by time-of-flight mass spectrometry (TOF MS) that the ions were mainly represented by H2O+. In TOF MS we used the same needle and secondary electron multiplier as a detector.

The magnification of the projection microscope was evaluated according to the model of a capacitor close to the spherical geometry by the relationship

$$ M = \frac{L}{{\theta r_{tip} }} $$
(1)

where the compression ratio θ is due to the deviation of the real geometry from the spherical geometry. Usually the ratio θ falls in the region between 1.5 and 2 [8]. To determine the value of θ we observed the photoemission image of the same tip but covered by a nickel grid with a mesh size of 60 × 60 microns. The grid has been attached to the tip using a ‘wrapping’ procedure without any glue. Due to the different values of the work function for silver and nickel the multiphoton emission process involved n = 3 IR 800-nm photons for Ag and 4 IR photons for Ni, respectively. This made it possible to visualize the nickel grid as the ‘dark’ image. The measurement gave the value of θ = 2 and accordingly the value of magnification M = 150 for our geometry. In the next part these will be validated by observing the focused laser beam profile in the photoelectron mode.

3 Experimental results

Focusing the laser beam on the tip we were capable to detect the multiphoton photoelectron emission process with subfocal resolution. Changing the position of the lens with respect to the apparatus we found the region of the intersection of the focal spot and the apex of the needle. It was checked that the size of the image of the photoelectron signal at the position-sensitive detector was minimal, if the lens was moved along the Oz axis (Fig. 1) and maximal, if it was moved along the Oy axis. The image obtained at the potential U = −8 kV and laser pulse peak intensity I (1)0  ≈ 1010 W/cm2 is shown in Fig. 2a. Its cross section along the Ox axis, orthogonal to the laser beam propagation direction, is shown in Fig. 2b by a solid line. For comparison, the dashed line shows an approximation of the photoelectron signal shape by a Gaussian profile. Under the conditions of the experiment, on irradiation of polycrystalline silver tip characterized by the work function W Ag  = 4.3 eV [4] by 800 nm radiation with intensity of I (1)0 the Keldysh parameter [9] was evaluated to be γ (1) ≈ 60. This value suggested that the photoelectrons were produced by the multiphoton emission. Measurements of the photoelectron signal as a function of the intensity presented in Fig. 2c have shown that the multiphoton process involved n = 3 IR photons.

Fig. 2
figure 2

a The photoelectron image observed by the position-sensitive detector at negative potential U = −8 kV. The image was recorded over 30,000 laser shots. b Experimental (solid line) and approximated by the Gaussian distribution with the Gaussian radius w obs ≈ 3.8 mm (dashed line) cross section contour of the photoemission signal along the Ox axis. c Measured photocurrent dependence vs intensity, verifying a three-photon process. d Voltage dependence of the Gaussian radius w obs (dots). The approximation of the experimental data by the function \( \propto (P_{1} + \frac{{P_{2} }}{\sqrt U }) \), where P 1 ≈ 2.9 mm and P 2 ≈ 2.8 mm × kV1/2, is presented by a solid line

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The evaluation of the photoelectron signal can be done by neglecting saturation and assuming that the signal caused by the ultrashort laser pulses is proportional to the ionization rate. Under such assumptions the profile of the photoelectron signal caused by the multiphoton absorption of the Gaussian laser beam at zero initial kinetic energy of the photoelectrons K 0 = 0 and in the absence of a strong Coulomb repulsionFootnote 1 can be described by a Gaussian distribution with a half-width \( w_{n} = \frac{{w_{0} }}{\sqrt n } \). At non-zero kinetic energy of photoelectrons K 0 ≠ 0 the contour of the signal at the detector will be further broadened due to the electrons flying off the surface perpendicular to the acceleration direction. Accordingly, neglecting the influence of a magnetic field on the electron trajectories, which is justified for large values of U, one can evaluate the width of the photoelectron distribution as

$$ w_{\rm obs} \cong M\frac{{w_{0}^{(1)} }}{\sqrt n } + L\sqrt {\frac{{K_{0} }}{eU}} $$
(2)

where e is the electron charge. Approximating the experimental dependence shown in Fig. 2(d) by function (2) we obtain w (1)0  ≈ 34 ± 4 μm and K 0 ≈ 0.35 ± 0.1 eV, which agree well with the value of the width w 0 measured by the profilometer and the value of K 0 = 3ħω-W Ag , respectively. Thus all our estimations including the value of the magnification are correct.

In the next part of the experiment the laser radiation with the peak intensity I (2)0  ≅ 3×1014 W/cm2 was focused at a distance l ≈ 0.1 mm from the apex of the tip. Note, that although the intensity at the apex is rather low, ca. 107÷108 W/cm2, a background signal due to the multiphoton ionization of water at the surface can be generated and can contribute to the measurements. The tip was held at positive accelerating potential. In this case, the detector recorded the H2O+ ion bunches with the magnification M’ ≈ 125 as shown in Fig. 3a. Its cross section along the Ox axis is shown in Fig. 3b by a solid line. For comparison, the dashed line shows an approximation of the photoion signal shape by a Gaussian profile. The value of M’ was calculated from Eq. (1) after making replacement r tip  → r tip  + l. Note, that an advantage of a blunt tip was a weak dependence of the magnification of the microscope on the distance l.

Fig. 3
figure 3

a The photo-ion image on the position-sensitive detector at positive potential U = 2 kV. The image was recorded over 60,000 laser shots. b Experimental (solid line) and approximated by the Gaussian distribution with w obs ≈ 3.8 mm (dashed line) cross section contour of the photo-ion signal along the Ox axis. c Intensity dependence of the Gaussian radius w obs (dots). The inaccuracy of w obs is probably connected to the noise signal generated by the multiphoton ionization of water at the apex. The approximation of the experimental data by the function (5) with w (2)0  ≈ 35 μm and the power p, determined in a similar fashion as in the expression (4), is given by a solid line

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The ionizing potential of the H2O molecule is approximately equal to I p  ≈ 12.6 eV [10]. Therefore, under the conditions of the experiment the Keldysh parameter was close to 1, which suggested that the tunneling ionization dominated [11]. Accordingly, the ionization rate could be approximately evaluated as [9, 12]

$$ W_{i} \propto \frac{{\exp \left( { - \frac{2}{{3\sqrt {I^{*} } }}} \right)}}{{\root{4} \of {{I^{*} }}}} $$
(3)

where I* is the value of the laser light intensity in atomic units (1 at. un. ≈3.5 × 1016 W/cm2). To simplify the subsequent analysis we replace expression (3) by the power function [13]

$$ W_{i} \propto (I^{*} )^{p} $$
(4)

with the power p being \( p \cong - \frac{2}{{3\sqrt {I^{*} } \ln (I^{*} )}} - \frac{1}{4} \). Next, neglecting the initial kinetic energy of the ions which at the room temperature is about δK T  ≈ 0.03 eV and neglecting very small probability of appearance of H2O2+ as well as weak Coulomb repulsionFootnote 2 we obtain for the width of the signal

$$ w_{\rm obs} \cong M^{'} \times \frac{{w_{0}^{(2)} }}{\sqrt p } $$
(5)

Under an assumption of the Gaussian distributionFootnote 3 at I (2)0  ≈ 3×1014 W/cm2 (0.009 at. un.) this gives an evaluation w (2)0  ≈ 35 ± 5 μm which is also in a good agreement with the value measured with strongly attenuated laser beam. Intensity dependence of the Gaussian radius w obs is shown in Fig. 3c. The obtained data can be satisfactory approximated by the function (5). Note, that here we exploited the Gaussian approximation. In general, a deconvolution algorithm such as the Abel inversion used in velocity map imaging [14] should be performed.

In this proof of principle experiment we used molecules of water. In general, under the visualization of the contour of the highly intense laser radiation it is expedient to use Xe or another inert gas as an imaging gas. A pulsed gas jet can be applied for the photoion signal enhancement.

4 Discussion

The spatial resolution in our technique is limited by a nonzero initial transverse velocity component of photoions relative to the static electric field direction. Indeed, an ion possessing a nonzero energy δK is detected by a position-sensitive detector with a spatial uncertainty of

$$ \phi_{\rm obs} \cong L\sqrt {\frac{\delta K}{eU}} , $$
(6)

where L is the length of the ion path and eU—its kinetic energy. The error of determination of the initial ion position is approximately equal to Δ ≈ ϕ obs/M. Using the formula (1), this expression can be represented in the next form:

$$ \Updelta \cong \theta r_{tip} \sqrt {\frac{\delta K}{eU}} $$
(7)

For θ = 2, r tip  = 0.5 mm, eU = 10 keV and the characteristic initial kinetic energy at the room temperature δK ≈ 0.03 eV (here we neglect the Coulomb repulsion between the ionsFootnote 4) we obtain for the above scheme Δ ≈ 3.4 × 10−3 r tip  ≈ 1.6 μm. Note, that the value of δK can be decreased in a pulsed gas jet.

The spatial resolution can be improved using a sharp tip. From (8) we can expect that Δ ≈ 100 nm can be reached using a tip with a curvature radius of r tip  ≈ 30 μm. In the scheme with the base of L = 150 mm the magnification will be equal to M ≈ 2,500.

In order to distinguish the image, corresponding to the ultimate spatial value, the detector’s pixel size p S should be less than ϕ obs, given by the expression (7). For L = 150 mm, δK ≈ 0.03 eV and eU = 10 keV we obtain ϕ obs ≈ 240 μm, which corresponds to approximately 4 pixels in our case (for our scheme p S  ≈ 60 μm). It means that the present spatial resolution Δ ≈ 1.6 μm looks quite realistic.

Thus the operation range of the proposed technique for laser beam diagnostics depends on the sharpness, a curvature radius of a tip. It potentially falls in the region between ~3 × 10−3 r tip and ~r tip with a dynamic range of about few hundreds.

The useful intensity range of the method depends in the main on the spectral characteristics of the beam and a target. For the multiphoton processes it falls in the range between ~109 W/cm2, when the photoemission of the electrons from a metal tip is observed, and ~1015 W/cm2, when helium atoms [13] are used as an imaging gas. The one-photon ionization of the atoms can be carried out with a low-intensity XUV beam [2].

5 Conclusion

In this paper we have experimentally demonstrated the approach for observing nonlinear photoionization processes with sub-focal spatial micro-resolution. Using this technique we measured the profile of intense ultrashort laser pulses. It is worth noting that the method potentially allows study of the photoionization caused by a single laser pulse in a way that significantly reduces requirements on the stability of high-intense laser radiation.

Note a number of advantages. First, the developed method is not limited by the spectral sensitivity of a CCD-matrix and therefore suitable for a wide spectral range limited only by spectral transmission of a vacuum window. Second, it allows us to visualize the profile of an intense laser beam without significant attenuation. The technique can accordingly be used for direct measurement of the cross section of a sharply focused laser beam with diameter of about 1 μm, which is substantially less than the pixel size of the existing CCD-matrices. So it can be also useful for measurements in the experiments with tightly-focused intense laser beams. According to our opinion the spatial resolution can be improved to the sub-micrometer scale using a tip with a curvature radius r tip  ~ 0.1 mm. (Note, that special care should be given to the measurement of the compression ratio θ in this case.) In such geometry the technique can be applied for short wavelength beam profiling.