Open Access
Add to BibSonomy
Abstract
We experimentally investigate the spectral broadening in fused silica in the multiphoton absorption regime. Under standard conditions of laser irradiation, linear polarization of laser pulses is more advantageous for supercontinuum generation. However, with high non-linear absorption, we observe more efficient spectral broadening for circular polarizations for both Gaussian and doughnut-shaped beams. The multiphoton absorption in fused silica is studied by measuring the total transmission of laser pulses and by the intensity dependence of the self-trapped exciton luminescence observation. The strong polarization dependence of multiphoton transitions fundamentally affects the broadening of the spectrum in solids.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Supercontinuum generation is a nonlinear optical process in which laser light is converted to light with a large spectral bandwidth [1]. Broadening of the spectrum of laser pulses occurs in a nonlinear environment due to self-phase modulation (mainly for femtosecond pulses) [2–4], Raman scattering or four-wave mixing (picosecond pulses and longer) [5]. The study of the supercontinuum generation has been ongoing since the 1960s, however, the development of this research topic continues constantly thanks to new technological possibilities and high demand for new applications [6].
The generation of the supercontinuum can be seen as the creation of a new laser light source with unique properties suitable, for example, for optical communication [7], spectroscopy [8,9], shortening laser pulses [10], ultrafast amplifiers [11], fluorescence microscopy [12], etc. Depending on the spectrum properties required for any application we choose a suitable non-linear environment. These are mostly broadband semiconductors with a high nonlinear refractive index (sapphire, diamond, YAG) [13,14], dielectrics (fused silica) or their variants in the form of optical fibers, waveguides, and photonic crystals with possible doping [15–17].
Another important factor influencing spectral broadening is the polarization state of the incoming laser light. It is generally assumed that linear polarization of the incoming laser causes greater spectral broadening than elliptical or circular polarization [18–20]. In many cases, however, complex mechanisms, such as filamentation, enter these processes, and it turns out that an enhancement of supercontinuum generation can occur for various polarization states. These anomalies were observed mainly in gases [21–23], in this work we focused on experimental observation of spectral broadening in the most common material to produce optical fibers – fused silica – and we show that in the regime of strong multiphoton absorption we can observe more effective spectral broadening for circular polarizations.
2. Materials and methods
Our experiment uses a Ti:sapphire laser system Astrella (Coherent) providing ${\tau _{\textrm{FWHM}}} = 40\; \textrm{fs}$ laser pulses at ${f_{\textrm{rep}}} = 1\; \textrm{kHz}$ repetition rate at central wavelength of ${\lambda _0} = 800\; \textrm{nm}$. The laser beam is first guided through an attenuator - a half-wave plate and a polarizer. A quarter-wave plate is used to control the polarization state from linear to circular. Doughnut-shaped laser pulses (radial polarization or optical vortex) are formed using S-waveplate. The laser beam was then focused by a lens with a focal length of $f = 10\; \textrm{cm}$ onto the sample corresponding to numerical aperture of $NA = 0.035$.
A fused silica plate with a thickness of $t = 1\; \textrm{mm}$ is used for the spectral broadening experiments. The focus of the laser beam is located in the middle of the sample, approximately $500\; \mathrm{\mu m}$ below its surface. The transmitted light is collected by a doublet lens, attenuated by neutral filters and focused again by a doublet lens on the slit of the monochromator with a CCD camera. In a similar way, the light coming from the luminescence is collected, here not in the main beam, but at an angle of about $30$ degrees (the main passing beam is, on the contrary, dumped). Exposure time of the CCD camera was set to $100\; \textrm{ms}$ and the spectra were obtained by accumulation ($10 - 100$) of the measured signal. The measurement of the transmitted energy of individual pulses was carried out using an energy meter located immediately behind the sample (averaged over thousands of laser pulses).
3. Results and discussion
In this experimental work, we focused on the observation of the spectral broadening of ultrashort laser pulses of $40\; \textrm{fs}$. In addition, we studied the spectral broadening for different polarization states (linear and circular polarizations) and two different pulse shapes – Gaussian beam and doughnut-shaped laser beam. Supercontinuum generation is strongly dependent on the polarization of the incoming light, as well as on the local intensity of the laser radiation. Several non-linear phenomena (e.g. self-focusing and self-phase modulation, filamentation, multiphoton absorption) occur simultaneously with the broadening of the spectrum, so the overall interaction of ultrashort high-energy pulses with fused silica is complex.
In Fig. 1, we can see the spectra in log-scale of laser pulses after passing through $t = 1\; \textrm{mm}$ of fused silica for Gaussian and doughnut spatial profiles, including the original laser spectrum. We always compare the two different extreme polarization states, in the case of a Gaussian beam (Fig. 1(a)) it is linear and circular polarization, and in the case of a doughnut-shaped beam (Fig. 1(b)) we have radial polarization (linear at every point) and optical vortex (circular polarization with angular momentum). For smaller energies of laser pulses, linear (radial) polarization dominates the broadening of the spectrum, but when the energy increases, the situation is reversed (in the case of doughnut-shaped laser pulses for approximately ${E_\textrm{p}} = 40\; \mathrm{\mu J}$) and we observe a wider spectrum for circular polarization (optical vortex). The biggest difference is found in the spectral region $680 - 750\; \textrm{nm}$. In the case of doughnut-shaped beam starting from energies ${E_\textrm{p}} = 60\; \mathrm{\mu J}$ the spectral intensity is greater for circular polarization than the linear one at every point above the $- 8\; \textrm{dB}$ level. This is probably due to the higher multiphoton absorption of linearly polarized light. The high multiphoton absorption in the case of the linear polarization limits the level of intensity that can be reached in fused silica before excitation of electrons to the conduction band. Self-phase modulation and self-steepening are thus more limited as compared to the case of circular polarization which could result in a narrower spectrum. However, this is not a simple attenuation of the intensity, since a similarly broad spectrum as in the case of circular polarization (optical vortex) cannot be achieved with linear polarization for any pulse energy of incident laser beam. Another explanation may be the large difference in filament formation for the two polarization states. Kerr nonlinearities are apparently suppressed in the case of circular polarization [24,25], which causes smaller self-focusing. It is thus possible that the formed filament is longer for circular polarization and has less tendency to break up and eventually create multiple filaments [26]. On the other hand, for multiple filamentation in the case linear polarization, each filament is subject to the intensity clamping effect and the dispersion landscape of the material. Therefore, with increasing input intensity, we no longer achieve a greater broadening of the spectrum [3]. On the contrary, multiple filaments unfavorably affect the spatial and temporal profile of the pulses and spectral intensity tends to lose the smoothness [3].
Fig. 1. Measured spectral broadening of ultrashort laser pulses in fused silica for a) Gaussian beam and b) doughnut-shaped beam in log-scale. Gray hatching shows $- 8\; \textrm{dB}$ level and the bandwidths are provided in the figures. The dashed green line is the original laser spectrum. The spectra are corrected to the spectral sensitivity of the spectrograph, including polarization.
We note that the bandwidth values are affected by the choice of the threshold for its definition. Several thresholds were tested. The one at -8 dB seems to us to represent the best the broadening we observe while focusing on intensity levels that are substantial in comparison with that of the transmitted initial main pulse.
As already mentioned, for energies in pulses smaller than ${E_\textrm{p}} = 40\; \mathrm{\mu J}$, we still observe more efficient spectral broadening for linear polarizations, which is in agreement with the available literature [18]. However, in our experiment we operate in the intensity regions where we can no longer neglect the strongly nonlinear multiphoton absorption. We therefore performed a measurement of the total transmitted energy of the pulses. It appears that the increase in the efficiency of the spectral broadening for circular polarizations occurs for the transmission of less than $50{\%}$ of the original pulse energy (see Fig. 2). The maximum pulse energy for which we performed this measurement was ${E_\textrm{p}} = 80\; \mathrm{\mu J}$ with a transmission of only about $30{\%}$ (for both polarizations). At higher energies, gradual pronounced damage of the material (visible in a differential interference contrast microscope) already occurred. From the measurements it is seen that the transmission ratio of both polarization states tends to $1$ with increasing pulse energies. This can be explained by the increase of the effect of quantum tunneling with higher powers [27,28], which is independent of the polarization.
Fig. 2. Total measured transmitted energy of doughnut-shaped laser pulses for radial polarization (black circles) and optical vortex (red squares).
In the next part of this work, we focused on the manifestation of multiphoton absorption, which also strongly depends on the polarization of the incoming laser pulses and thus affects the spectral broadening. The bandgap of fused silica is approximately ${E_\textrm{g}} \approx 9\; \textrm{eV}$ [29,30], so 6-photon absorption is required (at $800\; \textrm{nm}$ wavelength) to excite electrons into the conduction band. Free excitons are then created from the hot electrons, from which self-trapped excitons (STEs) are formed [31]. Part of STEs radiatively recombines after a characteristic time and the luminescence in the visible part of the spectrum occurs [32]. The yield of the observable luminescence is proportional to the number of excited carriers by multiphoton absorption. We measured STE luminescence as a function of laser pulse intensity for both pulse shapes and polarization states. In Fig. 3 we can find an example of luminescence spectra for doughnut-shaped laser pulses, where we can see both a non-linear behavior of the luminescence yield with respect to the energy of the pulses, and also significantly smaller luminescence yield for circular polarization (optical vortex).
Fig. 3. Luminescence spectra of self-trapped excitons (STEs) in fused silica exited by doughnut-shaped laser pulses via multiphoton absorption.
The resulting dependence of the luminescence intensity (obtained by integrating the luminescence spectral intensity from Fig. 3) on the pulse energy can be found in Fig. 4 for both Gaussian and doughnut-shaped pulses, and for both polarization states. There is a strongly non-linear growth of the total luminescence intensity in the multiphoton absorption regime, where its slope in the log-log scale is fitted by a linear function for estimating the order of multiphoton transitions. The slope of the curve decreases with increasing pulse energy, which is caused by channel closing and the beginning of quantum tunneling [27,28,33]. At pulse energies above ${E_\textrm{p}} = 80\; \mathrm{\mu J}$ (for a Gaussian profile), irreversible modification and gradual degradation of the material already occurs. In Fig. 4(a) for Gaussian pulses, we also find the ratio of the luminescence yield for linear and circular polarization for Gaussian pulses (right axis, blue crosses). The ratio, that has initially values around $4$ in the multiphoton regime, gradually decreases to a value of $1$, where quantum tunneling mainly figures and the effect of polarization during multiphoton transitions is lost.
Fig. 4. Intensity of STE luminescence as a function of pulse energy in log-log scale for a) Gaussian and b) doughnut-shaped laser pulses. Linear (radial) polarization is represented by black circles, circular polarization (optical vortex by red squares). Blue crosses are the ratio between them (right axis). The multiphoton regime section (green) is fitted with line, the slope represents the order of multiphoton absorption process ($5 - 6$ for Gaussian beam, $6 - 7$ for doughnut-shaped laser beam).
4. Conclusion
In summary, we have reported the polarization dependence of spectral broadening in fused silica. We have shown that in the regime of relatively small pulse energies, below a few tens of microjoules, the linear polarization is still dominant in spectral broadening. When the pulse energy increases above $40\; \mathrm{\mu J}$, and we can no longer neglect the highly nonlinear multiphoton absorption, a more efficient supercontinuum generation for circular polarizations occurs. One of the main reasons for the higher efficiency of circular polarization (optical vortex) is certainly the lower transition rate of multiphoton transitions and more efficient filamentation process. On the STE luminescence yield, we showed how the multiphoton absorption differs for different polarization states and pulse energies, and simultaneously we also performed total absorption measurements.
Funding
European Regional Development Fund and the state budget of the Czech Republic (CZ.02.1.01/0.0/0.0/15_003/0000445).
Acknowledgment
The authors would like to thank T. J.-Y. Derrien and O. Novák for fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
Data availability
All data underlying the results are presented in this paper.
References
1. R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970). [CrossRef]
2. R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8(1), 1–3 (1983). [CrossRef]
3. A. Dubietis, G. Tamošauskas, R. Šuminas, V. Jukna, and A. Couairon, “Ultrafast supercontinuum generation in bulk condensed media,” Lith. J. Phys. 57(3), 3 (2017). [CrossRef]
4. A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999). [CrossRef]
5. M. Nakazawa and M. Tokuda, “Continuum spectrum generation in a multimode fiber using two pump beams at 1.3 µm wavelength region,” Jpn. J. Appl. Phys. 22(4A), L239 (1983). [CrossRef]
6. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
7. T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32(10), 906–907 (1996). [CrossRef]
8. C. Lin and R. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976). [CrossRef]
9. C. Calabrese, A. M. Stingel, L. Shen, and P. B. Petersen, “Ultrafast continuum mid-infrared spectroscopy: probing the entire vibrational spectrum in a single laser shot with femtosecond time resolution,” Opt. Lett. 37(12), 2265–2267 (2012). [CrossRef]
10. B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22(3), 687–693 (2005). [CrossRef]
11. R. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron 15(6), 432–444 (1979). [CrossRef]
12. C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Önfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tunable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D: Appl. Phys. 37(23), 3296–3303 (2004). [CrossRef]
13. R. Grigutis, G. Tamošauskas, V. Jukna, A. Risos, and A. Dubietis, “Supercontinuum generation and optical damage of sapphire and YAG at high repetition rates,” Opt. Lett. 45(16), 4507–4510 (2020). [CrossRef]
14. M. Zukerstein, M. Kozák, F. Trojánek, and P. Malý, “Simple technique for the compression of nanojoule pulses from few-cycle laser oscillator to 1.7-cycle duration via nonlinear spectral broadening in diamond,” Opt. Lett. 43(15), 3654–3657 (2018). [CrossRef]
15. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air–silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19(4), 765–771 (2002). [CrossRef]
16. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St.J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12(13), 2864–2869 (2004). [CrossRef]
17. A. N. Ghosh, M. Klimczak, R. Buczynski, J. M. Dudley, and T. Sylvestre, “Supercontinuum generation in heavy-metal oxide glass based suspended-core photonic crystal fibers,” J. Opt. Soc. Am. B 35(9), 2311–2316 (2018). [CrossRef]
18. J. Botineau and R. H. Stolen, “Effect of polarization on spectral broadening in optical fibers,” J. Opt. Soc. Am. 72(12), 1592–1596 (1982). [CrossRef]
19. A. S. Sandhu, S. Banerjee, and D. Goswami, “Suppression of supercontinuum generation with circularly polarized light,” Opt. Commun. 181(1-3), 101–107 (2000). [CrossRef]
20. A. Srivastava and D. Goswami, “Control of supercontinuum generation with polarization of incident laser pulses,” Appl. Phys. B: Lasers Opt. 77(2-3), 325–328 (2003). [CrossRef]
21. S. Rostami, M. Chini, K. Lim, J. P. Palastro, M. Durand, J.-C. Diels, L. Arissian, M. Baudelet, and M. Richardson, “Dramatic enhancement of supercontinuum generation in elliptically-polarized laser filaments,” Sci. Rep. 6(1), 20363 (2016). [CrossRef]
22. H. Yang, J. Zhang, Q. Zhang, Z. Hao, Y. Li, Z. Zheng, Z. Wang, Q. Dong, X. Lu, Z. Wei, Z. Sheng, J. Yu, and W. Yu, “Polarization-dependent supercontinuum generation from light filaments in air,” Opt. Lett. 30(5), 534–536 (2005). [CrossRef]
23. N. Chen, T.-J. Wang, Z. Zhu, H. Guo, Y. Liu, F. Yin, H. Sun, Y. Leng, and R. Li, “Laser ellipticity-dependent supercontinuum generation by femtosecond laser filamentation in air,” Opt. Lett. 45(16), 4444–4447 (2020). [CrossRef]
24. G. Fibich and B. Ilan, “Self-focusing of circularly polarized beams,” Phys. Rev. E 67(3), 036622 (2003). [CrossRef]
25. S. N. Vlasov, V. I. Kryzhanovskfi, and V. E. Yashin, “Use of circularly polarized optical beams to suppress self-focusing instability in a nonlinear cubic medium with repeaters,” Sov. J. Quantum Electron. 12(1), 7–10 (1982). [CrossRef]
26. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
27. T. Otobe, Y. Shinohara, S. A. Sato, and K. Yabana, “Theory for Electron Excitation in Dielectrics under an Intense Linear and Circularly Polarized Laser Fields,” J. Phys. Soc. Jpn. 88(2), 024706 (2019). [CrossRef]
28. M. Kozák, T. Otobe, M. Zukerstein, F. Trojánek, and P. Malý, “Anisotropy and polarization dependence of multiphoton charge carrier generation rate in diamond,” Phys. Rev. B 99(10), 104305 (2019). [CrossRef]
29. E. Güler, G. Uğur, Ş. Uğur, and M. Güler, “A theoretical study for the band gap energies of the most common silica polymorphs,” Chin. J. Chem. Phys. 65, 472–480 (2020). [CrossRef]
30. K. Sugioka, S. Wada, H. Tashiro, and K. Toyoda, “Multiwavelength excitation by vacuum-ultraviolet beams coupled with fourth harmonics of a Q-switched Nd:YAG laser for high-quality ablation of fused quartz,” Appl. Phys. Lett. 67(19), 2789–2791 (1995). [CrossRef]
31. D. Grojo, M. Gertsvolf, S. Lei, T. Barillot, D. M. Rayner, and P. B. Corkum, “Exciton-seeded multiphoton ionization in bulk SiO2,” Phys. Rev. B 81(21), 212301 (2010). [CrossRef]
32. A. N. Trukhin, K. Smits, J. Jansons, and A. Kuzmin, “Luminescence of polymorphous SiO2,” Radiat. Meas. 90, 6–13 (2016). [CrossRef]
33. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, A. El-Khamhawy, and D. von der Linde, “Multiphoton ionization in dielectrics: comparison of circular and linear polarization,” Phys. Rev. Lett. 97(23), 237403 (2006). [CrossRef]
