Abstract

In this paper, we investigate the local oxidation of titanium thin films under the action of picosecond laser pulses. Periodical structures were recorded by the multi-beam interference scheme utilizing various numbers of laser beams, and the relationship between spatial resolution and the contrast of the structures was studied. The Raman spectra of the laser processing regions confirmed the oxidation even under the action of a single picosecond pulse. An analytical simulation of titanium film oxidation in the interference field was provided, and obtained results are correlated with the experimental data. The results of theoretical modeling show that the thermochemical effects of picosecond laser pulses allow recording periodic structures with a period of 0.65 lines per μm. The demonstrated results are important in the adaptation of technological laser systems for the manufacture of diffractive optical elements.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The engineering of optical wavefronts, such as the transformation of the Gaussian beam to the vortex one, is applied in laser industry, optical communication, as well as medicine, and it requires the improvement of methods for manufacturing of diffraction optical elements (DOE) [1] or metasurfaces [2]. This implies resolution improving, performance, and accuracy of nanosized structure fabrication. Electron-beam lithography [3] or laser-interference lithography [4,5] has become a mature technology for DOE fabrication. Nevertheless, the procedures are dramatically expensive because of many steps that contribute to additional isotropic distortions. Therefore, the technology requires much time to process millimetre-squared regions. As a result, the development of a simpler and more accessible technology for creating DOEs is in great demand.

The direct formation of a pattern on any substance is likely to simplify the manufacturing process and increase its accuracy significantly. Laser writing methods possess such abilities. The laser-based thermochemical recording is the best compromise between the complexity of lithography and laser ablation [6]. Firstly, thermochemical laser recording was developed for controllable oxidation of thin chromium films at the beginning of 70s [68]. Under the action of a focused laser beam, the temperature rises without reaching a melting point. However, irreversible chemical and physical processes, the main of which is oxidation, occur locally in the processing region forming a “latent image” on the chromium film. The “latent image” possesses distinct physical-chemical properties different from the original film, which allows developing the image in various ways. The accuracy of the thermochemical method is much higher than a direct laser ablation, due to thermochemical “sharpening” and the lack of hydrodynamic image distortions and low thermal distortions [9,10]. Formerly, chromium films were generally applied for the manufacturing of diffraction structures due to selective etching of the film and high mechanical strength [11]. Fresnel microlens array as a generator of a helical wavefront, and an elliptical zone plate were successfully fabricated by this technique [12].

Recently, much attention has been paid to metals with optically transparent oxides (Ti, Ta, Nb, etc.) [13]. This gives at least three apparent advantages: 1) the elimination of image development stage providing «true» one-step technology; 2) the ability of online control of the technology during diffraction structure fabrication; 3) the possibility of multi-level recording to control both the lateral resolution and the thickness of an oxide layer. That allows controlling not only the amplitude but also the phase of the transmitted radiation.

However, the laser recording of DOEs on films of such metals is completely understudied. Research in the field is limited. DOE was partly demonstrated using continuous laser radiation [14], and the first attempts were made to optimise the procedure [15]. At the same time, there are significant physical and chemical problems to solve. The solution to the problems can be demonstrated using Ti films as the most studied material. The application of Ti film involves the following obstacles:

  • 1) low oxidation rate (detected in the initial experiments [14]) that may prevent obtaining high resolution;
  • 2) negative feedback on the optical reflection from the absorbed radiation as well as temperature and the thickness of the oxide, which slow the process with thin Ti films, etc.
The present work has partly resolved revealed contradictions between the recording speed and spatial resolution of structures recorded on Ti film. Simultaneously, we were inspired by the results of our previous work on multi-beam interference recording on chromium films [16] and applied the same setup for the current investigation. Thus, the following tasks were set:
  • 1) to show experimental oxidation of Ti film by both a single and number of picosecond pulses in the high-resolution optical scheme providing multi-beam interference. In the case of success, the problem of relatively low oxidation rate of Ti could be overcome, and the spatial resolution of the method could be optimized in terms of the required number of pulses;
  • 2) to model the picosecond laser oxidation to optimise the ratio of spatial resolution and image contrast.

2. Experimental procedure

In this experiment, we used Ti films (thickness of 60 nm) deposited on a glass substrate by thermal sputtering in vacuum. A laser interference setup was utilized for Ti film patterning by a multi-beam interference field. Picosecond laser (Ekspla PL2143) was used as a laser source. The shape of the beam was Gaussian with the wavelength λ = 532 nm, pulse duration τ = 300 ps, maximum pulse energy Ep = 1.3 mJ and repetition rate ν = 1 kHz. The picosecond laser source has been chosen in order to have high quality interference pattering with controlled thermal diffusion. The experimental scheme consisted of a beam splitter – diffractive optical element (deflection angle is 5 deg.). A confocal imaging system was applied to realize the interference field [17]. Divided beams were overlapping beneath the second lens providing an interference pattern in their intersection area – the same as the processing region (Fig. 1(a)). The setup was discussed in detail elsewhere [16]. The film modification was observed by varying the pulse energy (0.01 < Ep < 0.5 mJ), and changing the number of laser pulses (from 1 to 10,000) delivered to the processing region (Fig. 1 (b)).

 

Fig. 1. Schematical view of the laser setup for two-beam interference registration on Ti film (a). Macro photo of the irradiated sample in regimes of ablation and oxidation of Ti film (b). Scale bar is 300 µm.

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Fabricated structures were initially investigated via the optical microscopy (Carl Zeiss, Imager. A1 m) in a transmission/reflection mode. A white light profilometer (ZeScope Optical Surface Profiler) was used for oxide structures investigation. A micro-Raman spectrometer “inVia” (Renishaw, UK) equipped with a Leica microscope and a CCD detector cooled to -70 °C was used for the acquisition of Raman spectra of the samples in backscattering geometry and with a spectral resolution of ∼ 2 cm-1. The Raman modes were excited by the radiation of 488 nm from an argon-ion laser. The laser power was selected at a level that avoids any destructive impact on the sample. A standard scheme to focus the laser beam with a 50X and NA = 0.75 microscope objective allowed to collect scattered light from a spot of ∼2 µm diameter.

3. Results and discussion

After irradiation of Ti film, colored regions were observed (Fig. 1(b)) and investigated via the optical microscopy (Fig. 2(a)). At low laser pulse energy (0.1 < Ep < 0.2 mJ) after a single-pulse action, only a smooth region of the interference pattern can be seen. With an increase in the number of pulses (up to 10,000), we registered an increase in the contrast of the formed periodic structures. In the transmission mode, it is clear that such structures are optically transparent (Fig. 2(b)).

 

Fig. 2. The optical microscope images (made in reflection (a) and transmission (b) mode) of periodical structures after the picosecond laser multi-beam interference irradiation (pulse energy in the range 0.1 < Ep < 0.2 mJ). Low-contrast structures registered on Ti surface by a single-pulse action (a). Multi-pulse action (10,000 pulses per region) allowed to register transparent structures (b). The scale bar is 2 µm.

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The optical white light profilometer investigation confirmed the absence of titanium film ablation in the oxidation regime even by the multi-pulse laser action. It is seen that only the imprint of the interference pattern remained on the surface after the action of 1 pulse with the pulse energy of 0.1 mJ (Fig. 3(a)). However, the presence of a legible interference pattern confirms the existence of the partially transparent oxide film although its thickness does not exceed several nanometers (at the level of the measurement error). The geometrical dimensions (the thickness and the width) of the formed relief are indicated on a two-dimensional profile that is present at the bottom of each figure. A prominent relief, presumably titanium oxide with a height of 10 nm and a width of ∼ 650 nm, was formed on the film surface after 10,000 pulses at the same pulse energy (Fig. 3(b)). The initial level of Ti film is pointed in a two-dimensional profile. Investigating the same region by transmission optical microscopy has shown optically transparent structures (Fig. 2(b)).

 

Fig. 3. Optical profilometry investigation with the corresponding fragment of a two-dimensional profile (in accordance with “profile”) of the periodical structures registered on titanium film by two-beams interference field in the oxidation regime: single-pulse (a) and 10,000 pulses (Ep = 0.1 mJ) (b) action.

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An essential part of this study was the confirmation of the presence of titanium oxides in the field of interference pattern writing. Composition of the material was investigated by registration of Raman spectra (Fig. 4) of laser irradiated regions in the ablation (Fig. 4(a)) and oxidation (Fig. 4(b)) regimes. In the oxidation regime (10,000 pulses with Ep = 0.1 mJ), the spectra were recorded from the spot including the treated part of the sample, presumably related to titanium oxides, and the untreated Ti film. Processing conditions imply a more intense treatment of the sample by 10,000 pulses with Ep = 0.22 mJ, causing ablation of the substance. Note, a most intensive Raman line at 1100 cm-1 as well as intensive lines at region at ∼500-600 cm-1 belong to the glass substrate (Raman spectrum of the substrate is not shown). These lines were observed only for regions under high energy (0.22 mJ) treatment (Fig. 4(a)). This indicates that points on the ablation process resulted in removing the Ti films from the glass substrate. On the spectra, a region within ∼ 250–800 cm-1 with overlapping Raman bands characteristic for different titanium oxides is clearly visible. Thus, the composition of the analyte can include a sufficiently large number of various material phases. The positions and assignment of the Raman peaks were complicated, for the amorphous phases of titanium oxides are characterized by wide spectral lines and positions close to but not the same as the crystal ones. Deconvolution of such spectra cannot be performed unambiguously. Nevertheless, we can make several most probable assignments. The band at ∼135-140 cm-1 observed in both spectra is close to that of titanium oxide [18] and indicates presence of TiO2 in the studied area. However, it was minor to the overall signal and not dominant, which indicates a small presence of this phase in the regions under study. Comparing the spectra of the ablation (Fig. 4(a)) and oxidation (Fig. 4(b)) regions, it is clearly seen that in the last case the greatest Raman intensity is in the region of ∼ 220-300 cm-1, which is close to the frequency region characteristic for Ti2O3 oxides [19]. For example, Tristarite compounds have a Raman band at ∼ 240 cm-1 and we associated an increase of the signal in this region of the spectrum with the appearance of this phase and its further dominance in the process of sample oxidation.

 

Fig. 4. The Raman spectra of the laser irradiation regions in the ablation (a) and oxidation (b) regimes, formed by 10,000 pulses with Ep = 0.22 mJ and Ep = 0.1 mJ, respectively.

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4. Analytical modeling

The formation of transparent oxide structures with the required contrast on titanium film usually needs the action of µs or even ms pulses or multipulse action of ns pulses at low repetition rate in order to avoid heat accumulation in the film and possible deterioration of the structure contrast and resolution. The possibility of using ps pulses for deep oxidation of metal films is explained by the prolonged (µs) time of cooling of the film after the action of each pulse during the heat transfer to the substrate [20]. The film oxidation continues after each pulse during the cooling time. Picosecond pulses are preferable for recording high-resolved interference patterns due to low thermal diffusion during the pulse. Finally, the evaluation of the optimal amount of laser pulses, which is required for contrast recording and high resolution, is to be performed.

A peculiarity of laser-induced oxidation is in the absorbance of the titanium film changing from pulse to pulse with the growth of the oxide layer. To evaluate the results of the film oxidation in a multi-pulse regime, we modeleda heating-cooling cycle for each laser pulse, estimated an increase in oxide layer thickness, and respective absorbance was set as initial conditions for each consecutive pulse.

Evaluation of the temperature and oxide layer thickness for each pulse was performed using the sinusoidal approximation of the spatial distribution of laser intensity:

$$q(x )= {q_0}\left[ {1 + \cos \left( {\frac{{2\pi x}}{d}} \right)} \right]\,,$$
where q0 is the average intensity of laser radiation, d is the period of the spatial interference pattern, x is the transverse coordinate.

Further mathematical estimations consisted of solving the standard heat equation for a film on a glass substrate heated by the source with the intensity distribution (1). The heat conduction to the substrate was considered to be the same as for a uniformly heated film and proportional to the local temperature value. This technique was applied by us earlier for the description of the thermal model of a laser oxidation the chromium film [16].

Thus, the heating of the film over the initial temperature level during each laser pulse:

$${T_{heat}} = \frac{{q(x )A(x )\cdot t}}{{\rho ch}}\left( {\frac{1}{{1 + \beta \sqrt t }}} \right)\,$$
and cooling after the pulse: Tcool = Theat(t)­-­Theat(t-τ), where
$$\beta = \frac{{\sqrt \pi }}{2} \cdot \frac{{{\rho _\varPi }{c_\varPi }\sqrt {{a_\varPi }} }}{{\rho ch}}\,$$
is an amendment for the heat conductivity to the substrate; A(x) is the absorbance of the film before the pulse; ρ, c, ρΠ, cΠ are the density and heat capacity of the film and the substrate respectively; aΠ is the thermal diffusivity of the substrate, h is the initial thickness of metal film, τ is the laser pulse duration.

Evaluation of the thickness of the oxide layer was performed based on Wagner’s oxidation law [21]:

$$\frac{{\,dH}}{{dt}} = \frac{B}{H}\exp \left( { - \frac{{{T_a}}}{T}} \right)\,,$$
where B and Ta – are the oxidation rate constants for titanium.

To determine the oxide layer thickness resulting from the impact of each individual pulse, the method of “equivalent exposure time” was used [7]. This approach states that the results of non-stationary heating and oxidation are identical to the results of stationary heating at the maximum value of temperature Tmax during the equivalent time:

$${t_e} \approx \frac{{T_{\max }^2}}{{{T_a}}}\left\{ {\frac{1}{{{{ {T^{\prime}} |}_{{t_0} - 0}}}} + \frac{1}{{{{ {|{T^{\prime}} |} |}_{{t_0} + 0}}}}} \right\}\,\,,$$
where ${ {T^{\prime}} |_{{t_0} - 0}}$ and ${ {T^{\prime}} |_{{t_0} + 0}}$ are the first derivatives of the temperature at the moment of reaching Tmax, which in our case this time is the end of the pulse t0 =τ.

Next, the thickness of the oxide film due to the action of a single pulse equals:

$$H = {[{2B\exp ({ - {{{T_a}} \mathord{\left/ {\vphantom {{{T_a}} {{T_M}}}} \right.} {{T_M}}}} )} ]^{{1 \mathord{\left/ {\vphantom {1 2}} \right.} 2}}}{t_e}\,.$$
Absorbance of the film changes after each subsequent pulse on the value related to the thicknesses and optical properties of the oxide and metal layers compiling the specimen. This corrected value of absorbance of the film was then used to calculate the results of the impact of next pulse.

Estimations were performed for comparison the possibilities of metal film oxidation by a few numbers (1, 10, 100) of high-energy laser pulses of and by a high number of low-energy pulses. The highest pulse energy (Emax) was limited to avoid damaging the sample by melting of the film. Figure 5 shows distribution of the oxide layer thicknesses as a result of irradiation with various numbers of pulses (from 1 to 10,000). Estimations show that the result of the action of 10 pulses with the energy of Emax is equivalent to the result of action of 100 pulses with the energy of 0.9·Emax. Modelling shows that action of 10,000 pulses with the energy of 0.8·Emax would be enough to form a 10 nm thick oxide layer, and this conclusion correlates perfectly with experimental results.

 

Fig. 5. Spatial distribution of the oxide layer thickness on titanium film after exposure with 1, 10, 100, and 10,000 laser pulses of various energies.

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The dependence of FWHM (and thus, steepness) (Fig. 6(a)) and contrast (Fig. 6(b)) of the pattern on the number of pulses N was analyzed analytically. Modelling showed that even though the contract grows gradually with each next pulse, the value of FWHM has optimal minimum around N = 8,000. Increasing number of pulses leads to widening the FWHM due to absorption of radiation and heating at the edges of the recorded lines. A further rise of resolution might be achieved with recording using an interference pattern with smaller period; for instance, it might be increased proportionally up to 1.3 lines per µm using laser pulses with λ = 266 nm.

 

Fig. 6. Influence of the number of pulses (Emax = 8 mJ) on geometrical (a) and optical (b) properties of structures.

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5. Conclusions

  • 1. The possibility of recording periodical structures with resolution up to 0.65 lines per µm on thin titanium films was shown experimentally by applying single and multiple picosecond laser pulses;
  • 2. Optical microscopy and micro Raman spectroscopy confirmed the presence of titanium oxides and the absence of ablation in the laser-irradiated area;
  • 3. An increase in the contrast of recorded periodic structures was shown experimentally by increasing the number of pulses up to 10,000;
  • 4. Analytical modeling confirmed the possibility of using a few (about 10) high-energy pulses as well as a significantly larger number (about 10,000) of low-energy pulses for recording periodic oxide structures;
  • 5. Modeling also showed that although recording contrast increases with the number of pulses, the minimum FWHM (about 0.17 µm in the current conditions) could be achieve by applying 8,000 sequential laser pulses.

Funding

Russian Science Foundation (RSF) (18-13-00200, 17-19-01721).

Acknowledgements

This research was supported by the grant RSF-17-19-01721. The Raman spectroscopy research was supported by the grant RSF-18-13-00200.

References

1. G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016). [CrossRef]  

2. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [CrossRef]  

3. R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016). [CrossRef]  

4. E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015). [CrossRef]  

5. E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016). [CrossRef]  

6. S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981). [CrossRef]  

7. V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

8. S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980). [CrossRef]  

9. V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008). [CrossRef]  

10. V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012). [CrossRef]  

11. V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011). [CrossRef]  

12. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999). [CrossRef]  

13. E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019). [CrossRef]  

14. E. Shakhno, D. Sinev, and A. Kulazhkin, “Features of laser oxidation of thin films of titanium,” J. Opt. Technol. 81(5), 298–302 (2014). [CrossRef]  

15. V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016). [CrossRef]  

16. M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017). [CrossRef]  

17. E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010). [CrossRef]  

18. W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998). [CrossRef]  

19. R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984). [CrossRef]  

20. V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014). [CrossRef]  

21. J. Stringer, “The oxidation of titanium in oxygen at high temperatures,” Acta Metall. 8(11), 758–766 (1960). [CrossRef]  

References

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  1. G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
    [Crossref]
  2. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
    [Crossref]
  3. R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
    [Crossref]
  4. E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015).
    [Crossref]
  5. E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
    [Crossref]
  6. S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
    [Crossref]
  7. V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).
  8. S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
    [Crossref]
  9. V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
    [Crossref]
  10. V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
    [Crossref]
  11. V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
    [Crossref]
  12. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999).
    [Crossref]
  13. E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
    [Crossref]
  14. E. Shakhno, D. Sinev, and A. Kulazhkin, “Features of laser oxidation of thin films of titanium,” J. Opt. Technol. 81(5), 298–302 (2014).
    [Crossref]
  15. V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
    [Crossref]
  16. M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
    [Crossref]
  17. E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
    [Crossref]
  18. W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
    [Crossref]
  19. R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984).
    [Crossref]
  20. V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
    [Crossref]
  21. J. Stringer, “The oxidation of titanium in oxygen at high temperatures,” Acta Metall. 8(11), 758–766 (1960).
    [Crossref]

2019 (1)

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

2017 (2)

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

2016 (4)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref]

V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
[Crossref]

2015 (1)

2014 (2)

E. Shakhno, D. Sinev, and A. Kulazhkin, “Features of laser oxidation of thin films of titanium,” J. Opt. Technol. 81(5), 298–302 (2014).
[Crossref]

V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
[Crossref]

2012 (1)

V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
[Crossref]

2011 (1)

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

2010 (1)

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

2008 (1)

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

1999 (1)

1998 (1)

W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
[Crossref]

1984 (1)

R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984).
[Crossref]

1981 (1)

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

1980 (1)

S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
[Crossref]

1973 (1)

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

1960 (1)

J. Stringer, “The oxidation of titanium in oxygen at high temperatures,” Acta Metall. 8(11), 758–766 (1960).
[Crossref]

Ambrosio, A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

Capasso, F.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Chen, W. T.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Cherkashin, V. V.

Churin, E. G.

Devlin, R. C.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Garliauskas, M.

E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
[Crossref]

E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015).
[Crossref]

Gedvilas, M.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015).
[Crossref]

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

Girdauskas, V.

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

Hua, Y.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Indrišiunas, S.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

Ivanov, A.

V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
[Crossref]

Jarchuk, M.

V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
[Crossref]

Kharissov, A. A.

Khorasaninejad, M.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Kiryanov, A. V.

Kiryanov, V. P.

Kokarev, S. A.

Korol’kov, V. P.

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

Korolkov, V.

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

Korolkov, V. P.

Koronkevich, V. P.

Kotov, G.

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

Kotov, G. A.

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

Kulazhkin, A.

Li, H.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Libenson, M. N.

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

Lu, Z.

W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
[Crossref]

Ma, W.

W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
[Crossref]

Massari, M.

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref]

Matyzhonok, V.

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

Merlin, R.

R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984).
[Crossref]

Metev, S.

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
[Crossref]

Molotokaite, E.

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

Mueller, J. B.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

Nikitin, M. N.

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

Niu, J.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Oh, J.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Perry, T.

R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984).
[Crossref]

Poleshchuk, A.

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

Poleshchuk, A. G.

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999).
[Crossref]

Raciukaitis, G.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
[Crossref]

E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015).
[Crossref]

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

Romanato, F.

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref]

Rubin, N. A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

Ruffato, G.

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref]

Sametov, A. R.

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

Savtchenko, S.

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
[Crossref]

Shakhno, E.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

E. Shakhno, D. Sinev, and A. Kulazhkin, “Features of laser oxidation of thin films of titanium,” J. Opt. Technol. 81(5), 298–302 (2014).
[Crossref]

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

Shakhno, E. A.

V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
[Crossref]

V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
[Crossref]

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

Shandibina, G.

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

Shi, L.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Sinev, D.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

E. Shakhno, D. Sinev, and A. Kulazhkin, “Features of laser oxidation of thin films of titanium,” J. Opt. Technol. 81(5), 298–302 (2014).
[Crossref]

Sinev, D. A.

V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
[Crossref]

Stamenov, K.

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
[Crossref]

Stankevicius, E.

E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
[Crossref]

E. Stankevičius, M. Garliauskas, M. Gedvilas, and G. Račiukaitis, “Bessel-like beam array formation by periodical arrangement of the polymeric round-tip microstructures,” Opt. Express 23(22), 28557–28566 (2015).
[Crossref]

Stringer, J.

J. Stringer, “The oxidation of titanium in oxygen at high temperatures,” Acta Metall. 8(11), 758–766 (1960).
[Crossref]

Veiko, V.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
[Crossref]

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

Veiko, V. P.

V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
[Crossref]

V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
[Crossref]

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

Verhoglyad, A. G.

Voisiat, B.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

Wang, E.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Xie, C.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Yakovlev, E. B.

V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
[Crossref]

Yarchuk, M. V.

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

Ye, T.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Zakoldaev, R.

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

Zhang, M.

W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
[Crossref]

Zhu, X.

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Acta Metall. (1)

J. Stringer, “The oxidation of titanium in oxygen at high temperatures,” Acta Metall. 8(11), 758–766 (1960).
[Crossref]

Adv. Opt. Mater. (1)

E. Wang, L. Shi, J. Niu, Y. Hua, H. Li, X. Zhu, C. Xie, and T. Ye, “Multichannel Spatially Nonhomogeneous Focused Vector Vortex Beams for Quantum Experiments,” Adv. Opt. Mater. 7(8), 1801415 (2019).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

W. Ma, Z. Lu, and M. Zhang, “Investigation of structural transformations in nanophase titanium dioxide by Raman spectroscopy,” Appl. Phys. A 66(6), 621–627 (1998).
[Crossref]

Appl. Phys. Lett. (1)

R. Merlin and T. Perry, “Growth of amorphous Ti2O3 layers by laser-induced oxidation,” Appl. Phys. Lett. 45(8), 852–853 (1984).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Metev, S. Savtchenko, K. Stamenov, V. Veiko, G. Kotov, and G. Shandibina, “Thermochemical action of laser radiation on thin metal films,” IEEE J. Quantum Electron. 17(10), 2004–2007 (1981).
[Crossref]

J. Laser Micro/Nanoeng. (3)

E. Stankevicius, M. Garliauskas, and G. Raciukaitis, “Bessel-like beam array generation using round-tip microstructures and their use in the material treatment,” J. Laser Micro/Nanoeng. 11(3), 352–356 (2016).
[Crossref]

E. Molotokaite, M. Gedvilas, G. Raciukaitis, and V. Girdauskas, “Picosecond laser beam interference ablation of thin metal films on glass substrate,” J. Laser Micro/Nanoeng. 5(1), 74–79 (2010).
[Crossref]

V. Veiko, E. Shakhno, A. Poleshchuk, V. Korolkov, and V. Matyzhonok, “Local laser oxidation of thin metal films: ultra-resolution in theory and in practice,” J. Laser Micro/Nanoeng. 3(3), 201–205 (2008).
[Crossref]

J. Opt. Technol. (1)

J. Phys. D: Appl. Phys. (1)

S. Metev, S. Savtchenko, and K. Stamenov, “Pattern generation by laser-induced oxidation of thin metal films (microcircuit fabrication),” J. Phys. D: Appl. Phys. 13(4), L75–L76 (1980).
[Crossref]

Laser Phys. (1)

V. Veiko, M. Jarchuk, and A. Ivanov, “Diffusionless oxidation and structure modification of thin Cr films by the action of ultrashort laser pulses,” Laser Phys. 22(8), 1310–1316 (2012).
[Crossref]

Opt. Express (1)

Opt. Quantum Electron. (1)

V. P. Veiko, E. A. Shakhno, and D. A. Sinev, “Laser thermochemical writing: pursuing the resolution,” Opt. Quantum Electron. 48(6), 322 (2016).
[Crossref]

Proc. Natl. Acad. Sci. (1)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113(38), 10473–10478 (2016).
[Crossref]

Quantum Electron. (2)

V. P. Veiko, V. P. Korol’kov, A. G. Poleshchuk, A. R. Sametov, E. A. Shakhno, and M. V. Yarchuk, “Study of the spatial resolution of laser thermochemical technology for recording diffraction microstructures,” Quantum Electron. 41(7), 631–636 (2011).
[Crossref]

V. P. Veiko, E. A. Shakhno, and E. B. Yakovlev, “Effective time of thermal effect of ultrashort laser pulses on dielectrics,” Quantum Electron. 44(4), 322–324 (2014).
[Crossref]

Sci. Rep. (1)

G. Ruffato, M. Massari, and F. Romanato, “Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization,” Sci. Rep. 6(1), 24760 (2016).
[Crossref]

Science (1)

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref]

Sov. Phys. Doklady (1)

V. P. Veiko, G. A. Kotov, M. N. Libenson, and M. N. Nikitin, “Thermochemical action of laser radiation,” Sov. Phys. Doklady 18, 83–85 (1973).

Thin Solid Films (1)

M. Gedvilas, B. Voisiat, S. Indrišiūnas, G. Račiukaitis, V. Veiko, R. Zakoldaev, D. Sinev, and E. Shakhno, “Thermo-chemical microstructuring of thin metal films using multi-beam interference by short (nano-& picosecond) laser pulses,” Thin Solid Films 634, 134–140 (2017).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Schematical view of the laser setup for two-beam interference registration on Ti film (a). Macro photo of the irradiated sample in regimes of ablation and oxidation of Ti film (b). Scale bar is 300 µm.
Fig. 2.
Fig. 2. The optical microscope images (made in reflection (a) and transmission (b) mode) of periodical structures after the picosecond laser multi-beam interference irradiation (pulse energy in the range 0.1 < Ep < 0.2 mJ). Low-contrast structures registered on Ti surface by a single-pulse action (a). Multi-pulse action (10,000 pulses per region) allowed to register transparent structures (b). The scale bar is 2 µm.
Fig. 3.
Fig. 3. Optical profilometry investigation with the corresponding fragment of a two-dimensional profile (in accordance with “profile”) of the periodical structures registered on titanium film by two-beams interference field in the oxidation regime: single-pulse (a) and 10,000 pulses (Ep = 0.1 mJ) (b) action.
Fig. 4.
Fig. 4. The Raman spectra of the laser irradiation regions in the ablation (a) and oxidation (b) regimes, formed by 10,000 pulses with Ep = 0.22 mJ and Ep = 0.1 mJ, respectively.
Fig. 5.
Fig. 5. Spatial distribution of the oxide layer thickness on titanium film after exposure with 1, 10, 100, and 10,000 laser pulses of various energies.
Fig. 6.
Fig. 6. Influence of the number of pulses (Emax = 8 mJ) on geometrical (a) and optical (b) properties of structures.

Equations (6)

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q ( x ) = q 0 [ 1 + cos ( 2 π x d ) ] ,
T h e a t = q ( x ) A ( x ) t ρ c h ( 1 1 + β t )
β = π 2 ρ Π c Π a Π ρ c h
d H d t = B H exp ( T a T ) ,
t e T max 2 T a { 1 T | t 0 0 + 1 | T | | t 0 + 0 } ,
H = [ 2 B exp ( T a / T a T M T M ) ] 1 / 1 2 2 t e .

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