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Highly efficient volume phase gratings have been fabricated in low-iron soda lime glass using femtosecond (fs) laser pulses with 1030 nm wavelength and 270 fs pulse duration. Optical simulations based on rigorous coupled-wave analysis theory were performed to determine optimal grating parameters and designs for the application of the gratings for light management in solar modules, suggesting a very effective blazed-like design. Several of such blazed phase gratings have been fabricated and analyzed by measuring their diffraction efficiencies into first and higher orders. Up to 77% of the incoming light in the wavelength region relevant for silicon-based photovoltaics were diffracted by these gratings. Typical induced refractive index changes between 0.002 and 0.006 were derived by comparing the experimental efficiencies with the simulation results.
© 2015 Optical Society of America
1. Introduction
Light management approaches are crucial to further increase the efficiency of photovoltaic devices [1–3]. One topic that is currently under investigation within the research community is the optimization of light management in solar modules, i.e. to redirect light that is incident on optically non-active module components, such as front side contacts, to the area of the solar cell absorber material [4]. Currently, the photovoltaic market is dominated by crystalline silicon solar cells with front side metallization. The front contacting scheme usually consists of three bus bars (width of about 1 - 2 mm) and grid fingers (width of about 50 - 100 µm) that together cover 5-10% of the active cell area causing shadowing of the absorber material. Furthermore, light impinging onto the spaces between adjacent cells of the module is usually lost for the solar-to-electrical power generation, too. A promising approach to redirect this light to the absorber material is to apply appropriate diffractive microstructures to the part of the solar modules above the cells, i.e. the encapsulation foil or the cover glass [5] like shown schematically in Fig. 1. Recently, volume optics within the EVA polymer encapsulation fabricated by fs laser pulses have been demonstrated [6].
Fig. 1 Sketch of optical microstructures and the light management in a solar module around the front side metallization.
However, when considering long-term stability or vertical distance to the absorber material, it appears advantageous to create diffractive microstructures by fs laser irradiation in the cover glass rather than in the encapsulation polymer.
A lot of work has been done on volume modification of transparent dielectrics using focused ultrashort laser pulses. Various interesting applications such as optical memory [7,8], microwelding [9–11], waveguide formation [12] and selective etching [13,14] have been investigated. Furthermore, modifications in fused silica arranged as volume bragg gratings with low grating periods and high period stability were investigated for use as reflection elements [15–17]. From this work, it is well-known that laser-induced nonlinear processes on the molecular scale in glass have the potential to create pure refractive index changes of long-term stability. With properly chosen laser parameters, focused fs pulses can generate an electron plasma in the focal volume, inducing a permanent structural change on the molecular level. In fused silica, for instance, the large molecular ring structures composed of several SiO2 molecules can break and recombine into smaller rings, thereby increasing both density and refractive index locally [18]. Filamentations, occurring as a result of the dynamic balance between self-focusing through Kerr-effect and defocusing through the created electron plasma [19], can be utilized to generate structural modifications with lengths far beyond the Rayleigh length of the laser beam.
In this study, we follow this approach by fabricating high-efficient phase gratings with fs laser pulses inside soda lime glass with the goal to reduce optical losses in solar modules by redirecting the incoming light onto the active area of standard silicon solar cells. Optical simulations based on rigorous coupled-wave analysis (RCWA) theory were performed to determine efficient phase grating designs and parameters. Optimized diffraction gratings were then inscribed with a fs laser into the glass and characterized. The induced refractive index changes were determined by comparing the diffraction efficiencies of the fabricated phase grating with the simulation results.
2. Experimental
The phase gratings have been fabricated using a Yb:KGW laser system (PHAROS, LightConversion) emitting 270 fs laser pulses with a wavelength of 1030 nm. The laser features a maximum repetition rate of 350 kHz; for this study, the repetition rate was set to 20 kHz. The Gaussian fs laser pulses were focused in the volume of 3.2 mm thick low iron soda lime glass (used as front glass in solar modules and provided by f | solar GmbH) using either an aspherical lens (AL) with numerical aperture (NA) of 0.4 or 0.5, or a 63x microscope objective (MO) with a NA of 0.65 was used. The focussing optic is mounted above a motorised xy-table (maximum speed: 100 mm/s, step resolution: 0.5 µm) with vacuum chuck which positioned and fixed the glass substrate samples. Laser pulse energy was varied using an adjustable λ/2 plate combined with a thin film polariser, hence the polarisation of the incoming laser light hitting the sample was linear. The focus position could be varied to arbitrary depths in the glass volume. The induced micromodifications in the glass were characterized using an optical microscope in phase contrast mode (Olympus BX61).
The length of the refractive index changes, with a typical diameter of 2 – 3 µm, was varied within a range from 25 to 150 µm in a depth of 650 µm into the glass by changing the laser pulse energy, see Fig. 2(a). The influence of spherical aberration on the modification length was taken into account. The modification thresholds for persistent refractive index changes were found to be at around 1 µJ for a single fs laser pulse, depending only slightly on the used focusing optics. The lengths of the modification increased with higher pulse energies until reaching a saturation level between 100 and 150 µm at 6 – 11 µJ. In Fig. 2(b) an optical micrograph cross section of single modifications is shown.
Fig. 2 (a) Pulse energy dependence of induced modification length for three different focusing optics (b) Phase contrast microscope image of a cross section of induced refractive index changes.
In the results presented in this work, the laser repetition rate was set to 20 kHz. A dedicated computer program was used for the irradiation which controls the translation stage and the electronic laser shutter in a way that the shutter is opened while the stage with the mounted sample is moved. By partially overlapping subsequent single fs laser pulses in one dimension with a stage speed of 20 mm/s resulting in a pulse-to-pulse distance of 1 µm, we were able to induce refractive index changes that form a one dimensional phase grating, see sketch in Fig. 3(a). Writing a large number of such parallel, equally spaced lines into the glass volume, phase gratings could be fabricated. The diffraction efficiencies of the phase gratings were measured using a CCD camera by comparing the light intensity I0 after passing through unstructured glass and the intensity of the 0th diffraction order I0th after passing through the phase grating. The intensity difference (I0 − I0th) is apparently equal to the sum of intensities diffracted into higher orders of diffraction when only a negligible difference in reflection between treated and untreated glass is existent. In this study the change in reflection between unirradiated regions and areas containing phase gratings was measured to be < 1%, validating the above assumption of low reflection. In this work, we will usually discuss the diffraction efficiency defined as
Fig. 3 (a) Sketch of a simple phase grating (b) ηD for a phase grating with a = 6 µm, b = 3 µm, λ = 785nm.
Laser diodes with wavelengths of 405, 514, 635 and 785 nm have been used in connection with isotropic optical fibers to characterize the diffraction efficiencies of the fabricated gratings in the wavelength region interesting for photovoltaic use. The illumination was checked for equal intensity in p- and s- polarization with respect to the grating orientation in all cases to ensure comparability with the numerical simulations (see below).
3. Results and discussion
3.1 Simulation results
In our study we performed optical simulations based on rigorous coupled-wave analysis (RCWA), also called Fourier Model Method (FMM), using a freely available software package [20] to determine efficient phase grating parameters. The package solves Maxwell’s equations in layered periodic structures and the results contain the spectra for the different diffraction orders. Our first approach for the simulations were rather ‘simple’ 1D phase gratings, which can be characterized by the following parameters: induced refractive index Δn, modification length l, grating period a, modification width b, see Fig. 3(a). The refractive index of the unmodified soda lime glass was determined to 1.52 by transmission and reflection measurements,; the incidence angle was kept constant at 0° in the simulations while the wavelength of the incoming plane wave has been varied. Every calculation has been conducted for s- and p-polarized incoming light, then summed up and normalized. As a typical and instructive example, a phase grating with parameters a = 6 µm, b = 3 µm, and λ = 785 nm has been chosen. The diffraction efficieny ηD (see Eq. (1)) was calculated in dependence of modification length (l = 0 .. 300 µm), and refractive index change (Δn = 0.001 .. 0.01). The results are given as a contour plot in Fig. 3(b), where the colour coding for ηD is given as legend at the right side of the figure.
The simulation results for this ‘simple’ phase grating reveal that an overall diffraction efficiency into higher orders of about 55% can be achieved when suitable parameters for length l (about 50, 150 and 250 µm) and refractive index change Δn = 0.01 are used. Furthermore, a periodic behaviour can be observed for ηD when the length of the modifications increases. This can be understood qualitatively as to be due to the phase delay the traversing light is acquiring on its way through the modified regions; when the light diffracted in the bottom part of the structure length is delayed by λ/2 relative to that diffracted in the top part, destructive interference will suppress diffraction into higher orders. This effect has a strong impact on the design of efficient gratings, since modification lengths around the efficiency maxima have to be created. Also, we note that our structure appears to be in the thin grating regime (Raman-Nath regime) [21] which, however, is not to be expected considering its geometrical extensions and similar gratings acting as thick gratings [16].
In an attempt to maximize the diffraction efficiency ηD, we performed various simulations with other geometry parameters. It turned out that larger dimensions (a > 6µm, b > 3µm) only decreased the peak efficiency, while smaller dimensions could in principle provide higher efficiency in some cases. As our setup, however, cannot produce finer lines (bmin ≈2µm) with sufficiently high Δn, such gratings could not be fabricated in this study. Respecting these experimental constrains, the grating design discussed above is the relative optimum achievable by way of ‘simple’ gratings in this work.
3.2 Comparison with fabricated phase gratings
The diffraction efficiency calculated above is comparable to a recently reported value of about 50% for a phase grating under illumination at 405 nm wavelength [22]. To compare in detail the simulation results presented in section 3.1 with experimental values, we produced phase gratings corresponding to the calculations, i.e. having a grating period of a = 6 µm and grating line width of b = 3 µm. A modification length of 150 µm was achieved by focusing fs laser pulses with an energy of 6 µJ through MO_0.65 into the glass substrate. Laser diodes with emission wavelengths of 405, 514, 635 and 785 nm have been used to irradiate the gratings and characterize their diffraction efficiencies. For comparison, simulations for the same wavelengths have been performed. In Figs. 4(a)–4(d) the experimental and simulation results of the diffraction efficiency ηD for the investigated wavelengths are plotted as a function of modification length. By correlating the experimental values with the corresponding calculation results (phase grating parameters a = 6 µm, b = 3 µm) at a modification length of 150 µm and the respective wavelength, we were able to determine a wavelength dependent refractive index change in a range of Δn = 0.0049 – 0.0061.
Fig. 4 Experimental and simulation results of ηD for a phase grating with a = 6 µm, b = 3 µm and l = 150 µm at wavelength (a) 405 nm (b) 514nm (c) 635 nm and (d) 785 nm.
The corresponding calculations are represented as red dashed lines in Fig. 4. Furthermore, the simulation results for an average value of the determined refractive index increases for the four investigated wavelengths are displayed (black lines) while experimentally measured values of the diffraction efficiency are presented as red dots. Analyzing the fabricated phase grating, we were able to experimentally obtain a maximum value of ηD of 54% at 405 nm illumination, decreasing with increasing wavelength and reaching 19% at 785 nm. This means that up to 54% of the incoming light is being diffracted into higher diffraction orders. When considering the determined refractive index changes we received by correlating the experimental with the corresponding simulation results, the range of the induced refractive index can be specified to Δn = (5.5 ± 0.6) ⋅10−3. This range is in considerable agreement with the refractive index increase of 0.01 reported for single ultrashort laser pulse processing of fused silica [23]. With regards to the intended application of the presented gratings in solar modules, we prioritized writing speed over precision in our experiments. Nevertheless we found good diffraction efficiencies even for somewhat imprecise gratings when evaluating our results. Reasonable writing speed is an important factor to improve the light management of already completely built solar modules by way of a laser post-treatment.
The decrease in efficiency with increasing wavelength can also be observed in the calculated results while the periodic behavior of ηD with the modification length l is maintained for different wavelengths. Looking for an optimization of the total diffraction efficiency, a further increase of the induced refractive index changes as well as an extension of the modification length to about 170 µm would be beneficial for all four wavelengths investigated. In our experiments, however, neither an increase of laser pulse energy nor a change of the focusing optics enabled us to extend the modification length beyond 150 µm, see Fig. 2. Also, an increase of the refractive index change to more than 0.006 could not be achieved.
Overall, the results of the optical simulations are in good agreement with the experiment results of the fabricated phase grating. Therefore, it appears reasonable to estimate the value of the refractive index change induced in soda lime glass by fs laser pulses. More generally, this method provides a sufficient precise and reliable tool to determine the laser-induced refractive index changes in transparent materials, which are otherwise often difficult to measure experimentally due to their small values. Another approach addressing this problem reported by Berlich et al. [24] is to use an iterative Fourier transform technique to spatially resolve an accurate estimate of the refractive index profile with high spatial resolution.
3.3 Optimized blazed design
Having optimized the parameters of a ‘simple’ phase grating through numerical simulations, the next step is to look for a more effective grating design. Our basic idea was to fabricate blazed gratings with an approximately triangular cross section, in order to favour diffraction into larger angles and to suppress the 0th order. This is apparently beneficial for the intended application, e.g. guiding incoming light around the front side metallization of solar cells. We have conducted various calculations for such blazed phase gratings for the whole interesting wavelength range and then evaluated their total diffraction efficiency by extracting a spectrally averaged ηPV
Simulations for a two-, three- and four-step blaze design were performed revealing an increasing efficiency with larger number of steps. However, we chose to work with the three-step blazed phase grating in order to facilitate fabrication. The design is shown schematically in Fig. 5(a).
Fig. 5 (a) Sketch of a three-step blazed phase grating (b) ηPV for a three-step blazed phase grating with a = 8 µm, b = 2 µm, λ = 300 – 1100 nm.
The calculated total diffraction efficiency ηPV (see Eq. (2)) for a pertinent grating with a = 8µm, b = 2µm and l = 150µm (the two shorter grating blocks have lengths of 100 and 50 µm) is shown in Fig. 5(b). The obtained values of ηPV reveal that about 70% averaged diffraction efficiency can be reached when using a modification length in the range of 100 – 150 µm and a Δn of 0.006 as was achieved for the simple grating. Furthermore, the high-efficiency region turns out to be rather broad indicating a robust design structure with respect to slight variations of the modification length.
Due to this attractive properties, a three-step blazed grating with the above-mentioned parameters has been realized by writing grating lines with different laser pulse energies just next to each other leading to different modification lengths and achieving the desired blaze design. It has been produced with pulse energies of 8.0, 3.0 and 1.5 µJ leading to the requested modification lengths of 150, 100 and 50 µm inside the glass volume. Experimentally measured and calculated diffraction efficiencies ηD for the four investigated wavelengths are presented in Figs. 6(a)–6(d) as a function of the modification length. Correlation of the experimental (red dots) and simulated results at the respective wavelengths determine a wavelength dependent refractive index change of Δn = 0.0017 – 0.0029. The calculations involving the actual refractive index change are represented as red dashed lines while the simulation results for the mean refractive index increase are displayed as black lines in Fig. 6.
Fig. 6 Experimental and simulation results of ηD for a three-step blazed phase grating with a = 8 µm, b = 2 µm and l = 150 µm at wavelengths (a) 405 nm (b) 514nm (c) 635 nm and (d) 785 nm.
Experimentally, up to 77% of the incoming light could be diffracted into higher diffraction orders, i.e. in the case of λ = 405, 514nm. A decrease in efficiency with increasing wavelength can be observed both in calculated and experimental results. But even for longer wavelengths, up to 43% of the incoming light is diffracted into higher orders. Slight deviations between experimental und calculated results are observed at wavelengths of 405 and 785 nm. These variations may, at least partially, be due to deviations of the actual shape of the laser-generated structures from the geometrically idealized blaze grating design used in the simulations. In addition, there appears to be a wavelength dependence of the induced refractive index, indicating a smaller Δn at the shortest wavelength used (405 nm). By comparing the experimental and calculated results for the three-step blazed grating, the (average) induced refractive index change was determined to be Δn = (2.3 ± 0.6) ⋅10−3.
Compared to the ‘simple‘ grating, the determined value of Δn for the blazed grating is smaller by roughly a factor of 2. One possible reason for this difference is the variation of pulse energy to generate the different refractive index filament lengths of 150, 100 and 50 µm, which may cause different Δn in the three adjacent blocks; the simulation can then apparently provide only an effective average value. Another aspect is the close proximity of the three blocks which might cause different modification conditions when writing the second and third block. And finally, since the absorption of the incoming laser pulses and therefore the modification of the material is a strongly nonlinear effect, already small variations of laser input parameters such as focal width might have a significant impact on Δn.
For the addressed application of light management in photovoltaics, optimal functionality requires that already the diffraction angle of the first order is large enough to redirect all incoming light normally incident on a contact finger to a position aside from it. If we consider a typical, 70 µm wide contact finger and a vertical distance of 2 mm from grating to finger (i.e., grating created about 1 mm below glass surface), the minimum angle required for the first diffraction order would be 2.0°. For a diffraction grating with 8 µm grating period, as shown in this work, even the shortest wavelength (405 nm) features already a diffraction angle of 2.9° for the 1st order. Larger wavelengths and higher diffraction orders lead to higher angles, so that the three step blazed grating design as described above appears to be well suited for our intended application of improving the light management in solar modules.
Assuming an area shadowed by contacts of typically 5% and a typicall cell conversion efficiency of 20%, the potential for improvement can be estimated to about 1% increase of absolute solar power conversion efficiency. To achieve this, it would be desirable to generate higher Δn which, according to our simulations, could cause diffraction efficiencies above 90%. Principally, such an increase of Δn appears possible: Eaton et al. measured the induced refractive index in their fabricated waveguides to 0.02 when using high-repetition laser pulses (500 kHz) [25], and just recently, Hashimoto et al. demonstrated that they were able to create high refractive index changes of up to 0.03 with low repetition rate laser sources (1 kHz) [26]. They assume that the movement of generated voids in the glass network distributes to a strong densification and therefore to a high induced refractive index. It will be an aspect of future work to utilize these effects for the fabrication of light management microstructrues in glass.
4. Conclusion and outlook
In conclusion, we have demonstrated that we can create efficient phase gratings in the volume of soda lime glass using femtosecond laser pulses. Up to 54% of the incoming light with a wavelength of 405 nm at normal incidence can be diffracted into higher diffraction orders when a ‘simple’ phase grating design with optimized grating parameters is used. Optical simulations based on rigorous coupled-wave analysis theory were performed to determine the most efficient phase grating parameters. By comparing the experimental efficiencies with the simulation results, we found the induced refractive index change to be (5.5 ± 0.6) ⋅10−3.
As a next step, we conducted various calculations for a blazed grating design as a promising layout for high-efficient phase gratings. Evaluating the simulation results, we fabricated a three-step blazed transmission grating which showed diffraction efficiencies of up to 70% for incoming white light, addressing the spectral region relevant for photovoltaics. By comparing the experimental and simulated results, the induced average refractive index increase was determined to (2.3 ± 0.6) ⋅10−3 for the blazed phase grating design. Hence, our optical simulations deliver a reliable tool to determine the induced change in refractive index which is otherwise difficult to measure experimentally because of its low magnitude and small spatial extent. An attractive application for the gratings presented here is their use in solar modules as elements to guide light around shadowed areas. The respective potential for an increase of solar cell efficiency can be estimated to 1% absolute (5% relative) when the whole module is processed for precisely adjusted light management microstructures.
Currently, the quantitative effect on photo current of high-efficient phase gratings integrated into the front glass of miniature solar modules is under investigation, accompanied by an evaluation of the functionality under varying incidence angles. These results will be reported in a forthcoming publication.
Acknowledgments
The authors would like to thank the German Federal Ministry for Education and Research (“Bundesministerium für Bildung und Forschung”) for the financial support within the joint research graduate school ‘StrukturSolar’ of Anhalt University of Applied Sciences and Martin-Luther-University Halle-Wittenberg (Förderkennzeichen: 03SF0417A) and the Centre for Innovation Competence SiLi-nano® (Förderkennzeichen: 03Z2HN12). The help from f | solar GmbH in providing the solar glasses is gratefully acknowledged.
References and links
1. T. Yamada, H. Nakamura, T. Sugiura, K. Sakuta, and K. Kurokawa, “Reflection loss analysis by optical modeling of PV module,” Sol. Energy Mater. Sol. Cells 67(1), 405–413 (2001). [CrossRef]
2. J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, “Combined effect of light harvesting strings, anti-reflective coating, thin glass, and high ultraviolet transmission encapsulant to reduce optical lsses in solar modules,” Prog. Photovolt. Res. Appl. 22(7), 830–837 (2014). [CrossRef]
3. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004). [CrossRef]
4. G. Seifert, I. Schwedler, J. Schneider, and R. B. Wehrspohn, “Light management in solar modules,” in Photon Management in Solar Cells, eds. R.B. Wehrspohn, U. Rau, A. Gombert (Wiley-VCH 2015), pp. 323–347.
5. J. Jaus, M. Duell, J. Eckert, F. Adurodija, B. Li, R. A. Mickiewicz, and D. M. Doble, “Approaches to improving energy yield from PV modules,” Proc. SPIE 7773, 77730S (2010). [CrossRef]
6. L. Kuna, G. C. Eder, C. Leiner, and G. Peharz, “Reducing shadowing losses with femtosecond-laserwritten deflective optical elements in the bulk of EVA encapsulation,” Prog. Photovolt. Res. Appl. 23(9), 1120–1130 (2015). [CrossRef]
7. E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T.-H. Her, J. P. Callan, and E. Mazur, “Three-dimensional optical storage inside transparent materials,” Opt. Lett. 21(24), 2023–2025 (1996). [CrossRef] [PubMed]
8. W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, and K. Itoh, “Optical seizing and merging of voids in silica glass with infrared femtosecond laser pulses,” Opt. Lett. 25(22), 1669–1671 (2000). [CrossRef] [PubMed]
9. S. Richter, S. Döring, A. Tünnermann, and S. Nolte, “Bonding of glass with femtosecond laser pulses at high repetition rates,” Appl. Phy. A 103(2), 257–261 (2011). [CrossRef]
10. I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoeng. 2(1), 57–63 (2007). [CrossRef]
11. T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44(5), L687–L689 (2005). [CrossRef]
12. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996). [CrossRef] [PubMed]
13. C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process. 84(1–2), 47–61 (2006). [CrossRef]
14. D. Wortmann, J. Gottmann, N. Brandt, and H. Horn-Solle, “Micro- and nanostructures inside sapphire by fs-laser irradiation and selective etching,” Opt. Express 16(3), 1517–1522 (2008). [CrossRef] [PubMed]
15. C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 102(1), 35–38 (2011). [CrossRef]
16. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006). [CrossRef]
17. T. Clausnitzer, T. Kämpfe, F. Brückner, R. Heinze, E. B. Kley, A. Tünnermann, O. Parriaux, and A. V. Tishchenko, “Highly dispersive dielectric transmission gratings with 100% diffraction efficiency,“ Proc. SPIE 6883, 68830U (2008).
18. J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003). [CrossRef]
19. W. Watanabe, T. Tamaki, Y. Ozeki, and K. Itoh, Progress in Ultrafast Intense Laser Science VI (Springer Berlin Heidelberg, 2010), Ch. 9.
20. V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012). [CrossRef]
21. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980). [CrossRef]
22. M. Muchow, T. Büchner, and G. Seifert, “Femtosecond laser-induced optical microstructures inside glass volume for light management in solar modules,” in Proc. of 29th EU PVSEC (2014), pp. 214–217.
23. D. M. Krol, “Femtosecond laser modification of glass,” J. Non-Cryst. Solids 354(2), 416–424 (2008). [CrossRef]
24. R. Berlich, J. Choi, C. Mazuir, W. V. Schoenfeld, S. Nolte, and M. Richardson, “Spatially resolved measurement of femtosecond laser induced refractive index changes in transparent materials,” Opt. Lett. 37(14), 3003–3005 (2012). [CrossRef] [PubMed]
25. S. M. Eaton, M. L. Ng, R. Osellame, and P. R. Herman, “High refractive index contrast in fused silica waveguides by tightly focused, high-repetition rate femtosecond laser,” J. Non-Cryst. Solids 357(11), 2387–2391 (2011). [CrossRef]
26. F. Hashimoto, T. Yoshino, Y. Ozeki, and K. Itoh, “Large increase in refractive index inside silica glass after the movement of voids caused by femtosecond laser pulses,” Jpn. J. Appl. Phys. 53(4), 042601 (2014). [CrossRef]
