R-on-1 laser induced breakdown thresholds are reported for a wide range of lithium niobate crystals at laser parameters relevant for state-of-the-art optical parametric amplifiers pumped with high repetition rate ultrafast Yb-laser sources. The samples included uncoated and anti-reflection coated, blank and periodically poled MgO-doped congruent crystals and were measured at repetition rates between 10 and 1000 kHz, pulse durations of 330 fs and 1 ps, and temperatures between 20 and 170 °C.
© 2016 Optical Society of America
Recent progress in high-average-power, picosecond (ps) Yb laser amplifier technology has enabled the power scaling of near-infrared (NIR) and mid-infrared (MIR) optical parametric amplifiers (OPAs) pumped near 1 µm beyond what is possible with Ti:sapphire laser amplifier systems as pump sources at ~800 nm [1–4]. Lithium niobate (LiNbO3, LN) is an attractive nonlinear material for such OPAs due to its high nonlinear optical coefficients, broad transparency from 350 to 5200 nm, mature growth technology, and availability in periodically poled form for quasi-phase matching (i.e. PPLN). However, LN is known to exhibit photochromic damage (i.e. light induced absorption) due to e.g. long-lived excitations such as polarons [5, 6] and photorefractive damage (PRD) (i.e. light induced refractive index change)  limiting its use in high power applications. Doping LN with MgO alleviates various types of photochromic and bulk-photovoltaic photorefractive effects and increases the optical damage threshold. When taking certain precautions, even pyroelectrically induced PRD, which is triggered by local heat deposition from the strong pump beam coupled to parasitic visible light generation, can be minimized in such crystals . With PRD mitigated, the catastrophic optical breakdown threshold is the next limiting factor in developing ultrashort-pulse NIR-MIR OPAs. However, the ultrafast laser-induced damage threshold (LIDT) of LN at wavelengths near 1 µm has been rarely investigated . Here we present the results of a systematic study of a wide range of LN samples using 1.03-µm, ultrafast Yb laser systems with various pulse durations and repetition rates. The reported LIDT data provide crucial design parameters for the development of future high average power, NIR-MIR OPAs and in particular chirped-pulse OPAs (CPOPAs).
2. Experimental set-up and samples
In most experiments, a commercial ultrafast Yb-fiber laser amplifier system (Satsuma HP2, Amplitude Systemes) was employed for the damage tests. The repetition rate was varied from 10 to 1000 kHz. The pulse duration was set to either 330 fs or 1 ps. In a second set of experiments, a commercial, 1-ps Yb:YAG laser amplifier system (Amphos 400, Amphos GmbH) was utilized. Both laser systems operated at 1.03 μm.
Due to the limited number of the LN samples and surface area available, we used the R-on-1 method for measuring the laser induced damage threshold, see e.g . In R-on-1 tests, the laser pulse energy incident on the sample is gradually increased until damage is observed. In our experiments, the pulse energy was increased in a step-wise fashion with a 5-s exposure time for each step.
A fraction of the laser beam was split off and monitored by a reference photodiode (PD1) calibrated to the actual laser pulse energy or average power incident on the sample (cf. Figure 1). The increased scattering of laser light at damaged sites is routinely exploited in damage detection. We monitored light scattering at two distinct wavelengths. A photodiode (PD2) detected the scattering of a 633-nm HeNe laser beam, which was propagating collinearly with the 1.03-μm Yb-laser beam. PD2 was placed behind a short-pass filter (SPF) with a cut-off wavelength of 1.00 μm and a laser line interference filter (IF). Another photodiode (PD3) monitored the scattered light above 1 μm. The PD2 signal stays constant, while the PD3 signal increases linearly during ramping-up the incident 1.03-μm power until material modifications, stimulated polariton scattering (SPS), or damage occur. Due to the possibility of backward SPS with ps pulse durations , we used a Faraday isolator to prevent damage to the laser amplifier (Fig. 1). Since SPS can modify the scattered light intensity in the vicinity of 1.03 μm, we considered the illuminated sample site damaged when the scattering signal on PD2 (i.e. at 633 nm) increased above a certain predefined threshold, which was followed by the automatic closure of a shutter to block the damage inducing laser beam. However, in the present measurements, the so determined LIDT closely followed the drastic increase of the PD3 signal, which could be equally used for its determination. All photodiode signals were digitized and stored by a high resolution oscilloscope. A representative measurement with all diode signals is depicted in Fig. 2. The sample was translated after each damage test using a manual 3D stage and the surface was cleaned using a bulb blower air duster.
The sample was located in an oven with its front surface in or near the focal plane of an f = 300 mm singlet lens. The laser beam profile at the position of the sample was determined in an equivalent plane using a wedge on a flip-mount to redirect the beam towards a 16-bit CCD camera. The camera was positioned at the proper distance from the lens using a motorized translation stage. The estimated laser spot size (FWHM) at the laser beam waist at the front surface of the sample was ~62 μm. Various sets of experiment were also performed behind the beam waist with a laser spot size up to 200 μm. The distance between neighboring test spots was > 3 times the laser spot size. The integrated pulse compressor of the Satsuma Yb-laser system was adjusted to deliver pulse durations at FWHM of ~330 fs and ~1 ps, determined with a second-harmonic (SH) frequency resolved optical gating (FROG) apparatus. The pulse duration of the Amphos laser system was constant at ~1 ps. The threshold fluence associated with each damage event was calculated based on the actual laser beam profile measured by the CCD camera following the method described in .
In order to assess the effect of surface quality, coating, and poling, various types of 5 mol% MgO-doped congruent LN samples were studied. The blank crystal samples were manufactured by Yamaju Ceramics Co., Ltd. using the Czochralski process. The uncoated and single-layer AR-coated blank LN samples had the same dimensions of x × y × z = 2 × 3 × 3 mm3, where x corresponds to the sample length along the beam propagation direction, y is the sample width and z is the thickness along the crystallographic c or optical axis. The y × z surface specifications for all these crystals were S/D (scratch/dig) = 20/10, based on the MIL-O-13830 standard. The multilayer AR-coated blank LN samples had dimensions of 2 × 3 × 3 mm3 and 2 × 3 × 1 mm3, and the y × z surface specifications were S/D = 20/20 and S/D = 20/10, respectively.
The dimensions of the uncoated PPLN crystals with poling periods of Λ = 6.25 and 6.849 µm, were 2 × 2 × 0.5 mm3 and 2 × 2.5 × 0.75 mm3, respectively. These poling periods correspond to SH generation with a fundamental wavelength of 1.03 µm (Yb:YAG) and 1.064 µm (Nd:YAG), respectively. All periodically poled crystals had the same y × z surface specifications of S/D = 20/10.
For all measurements presented, the polarization of the incident laser beam was along the optical or z axis of the crystal.
3. Results and discussion
3.1 Beam profile distortions
For all types of samples studied, during ramping up the laser power, one could notice first an expansion of the transmitted beam profile due to self-focusing (SF) before reaching the damage threshold. Further increase in incident power led to stronger beam distortions and nonlinear light scattering behavior starting from an incident pulse energy of ~5 μJ, which was still well below the catastrophic damage threshold (cf. Figure 2 red and orange curves).
These additional changes of the beam profile occurring for average on-axis intensities exceeding 13 kW/cm2 can be attributed to the photo-refractive effect, first described for LN in . The changes persist over minutes and are still visible in the transmitted HeNe beam profile after e.g. 50 s. However, the effect is not permanent and disappears after ~45 min as shown in Fig. 3. Stronger distortions of the transmitted beam were visible for higher repetition rates when the incident average power was higher. In order to emphasize the effect of photo-refraction, a repetition rate of 1000 kHz was chosen for the measurement in Fig. 3. Similar fringe patterns were observed in [13, 14].
3.2 Influence of self-focusing on the LIDT
In all cases, optical damage occurred to the rear surface of the test samples (uncoated or AR-coated) and thus SF as a spatial manifestation of the electronic Kerr effect had to be taken into account in the analysis. In order to assess the influence of SF on the measured damage threshold, we performed damage tests at different positions of an uncoated LN sample along the focused 1.03 µm beam at a repetition rate of 100 kHz and a pulse duration of 1 ps. The total range of distance was approximately equal to the confocal range, where the change in the radius of curvature of the wave front (i.e. the expected change in the SF effect) is maximal. Figure 4 shows beam profile measurements leading to M2 values of 1.15 in the horizontal and vertical planes. The gray rectangles indicate the sample position for the different measurements with the corresponding beam profiles shown in the boxes above. The incident beam parameters for x = 0 (i.e. at the sample front side) are the beam radius at 1/e2 of the peak intensity, w(0), and the radius of the wave front curvature, R(0), which can be reconstructed from the M2 measurement. The spot size at FWHM ( = w(0) √(2ln(2)) for a Gaussian beam) amounts to 102 µm (A), 72 µm (B), 62 µm (C), 71 µm (D) and 89 µm (E) calculated from geometric mean of the horizontal and vertical beam radii wh(0) and wv(0) shown in the figure.
The blue curve and symbols in Fig. 5(a) show the incident peak on-axis LIDT fluence values for the different sample positions: 236 mJ/cm2 (A), 166 mJ/cm2 (B), 183 mJ/cm2 (C), 323 mJ/cm2 (D) and 391 mJ/cm2 (E). The associated incident pulse energy values are given in Fig. 5(b).
In order to evaluate the effect of SF on the measured LIDT fluence values, we considered the case shown in Fig. 5(a). We took Fresnel losses at the uncoated front surface into account, simulated the modification of the beam size upon propagation across the sample based on Eq. (1) , and added field enhancement due to interference effects at the uncoated rear side . Taking the experimentally determined incident beam sizes and wave front curvatures, and assuming a Kerr coefficient γ, one can calculate the incident pulse energy that will lead to a peak on-axis fluence at the backside of the sample equal to the intrinsic LIDT fluence (Fintrinsic) of the material. Here, γ is defined from the intensity dependent refractive index n = n0 + γI, where n0 is the linear part of the refractive index and I denotes the laser intensity. We note that Fintrinsic, in contrast to the actual measured incident damage threshold fluence, is a property of the material and does not depend on reflection losses or field enhancement effects. In our model, we did not consider thermal effects, i.e. variations of the LIDT with the laser spot size due to the slightly different thermal gradients were neglected in agreement with Section 3.3 below. We also neglected dispersive temporal broadening, which is justified for our sample length and pulse duration, and used the value for the peak internal power given for Gaussian temporal pulse shape by P0 = 2(E/τ)√(ln(2)/π), where E denotes the single pulse energy inside the sample and τ is the pulse duration (FWHM intensity).Eqs. (1)-(2), λ is the vacuum wavelength and the critical power for weak SF in Eq. (2) is defined as Pcr = λ2/(8πn0γ), which corresponds to self-trapping of a Gaussian beam in the paraxial approximation . The elliptical shape of the beam is taken into account by considering independent beam parameters in the vertical and horizontal planes and elliptic beam cross sections (πwhwv), when calculating the peak on-axis fluence and intensity.
For a fixed value of x = 2 mm, which is the sample thickness along the propagation direction, the extracted fit values are Fintrinsic = 760 mJ/cm2 and γ = 11 × 10−20 m2/W. The associated incident single pulse energy values are plotted in Fig. 5(b) (red curve). In order to gain insight into the accuracy of the fit and possible ambiguities, we also calculated the normalized root-mean-square error (RMSE) as a function of Fintrinsic and γ (cf. Figure 6). The results show that the potential values of Fintrinsic and γ lie in a relatively well-defined region in the parameter search space.
It shall be emphasized here that for typical beam and crystal parameters applicable to high-repetition rate, high average power, few-cycle OPA systems based on Yb-laser pump sources (i.e., beam size, pulse duration, and sample thickness), we obtained only extrinsic damage thresholds from our tests because of SF. Nevertheless, we were able to derive also a unique intrinsic LIDT in terms of peak on-axis fluence for a pulse duration of 1 ps. The measurable quantity is of course the incident threshold fluence Finc, which, in the absence of SF, would be (n0 + 1)4 / (16n03) times the Fintrinsic determined above . With n0 = 2.149 one obtains Finc ~470 mJ/cm2. This LIDT value can be regarded as a characteristic material parameter that will correspond to damage to the rear surface of uncoated samples when SF can be ignored, a situation that will occur in experiments using thinner samples or longer (e.g. 5-10 ps) pulse durations.
Our analysis of the experimental data for a pulse duration of 1 ps provided also a value for the Kerr coefficient of LN for e-polarization, γ = 11 × 10−20 m2/W. The Kerr coefficient for this polarization appears to be roughly four times lower than for o-polarization . The values derived in [18, 19] for e-polarization using the z-scan method with 55-ps pulses at 1.064 µm and 2 Hz vary between γ = 4.9 and 16.5 × 10−20 m2/W. With the same method, using 30-ps single pulses at 1.064 µm, the γ value derived in  for the e-polarization is 9.3 × 10−20 m2/W.
3.3 LIDT dependence on repetition rate and pulse duration
In order to explore the effect of a varying thermal load on the crystals due to residual absorption of the pump beam and/or its second harmonic and the effect of possible cumulative material modifications (e.g. formation of color centers, polarons during photochromic damage), we conducted the experiments at various repetition rates between 10 and 1000 kHz. For this study, blank 5 mol% MgO-doped LN samples were placed in the focal plane with a laser beam diameter FWHM = 62 µm at the front side (cf. Figure 4). The crystals were kept at room temperature.
Figure 7 shows the measured incident LIDT peak on-axis fluence (a) and intensity (b) as a function of repetition rate for two pulse durations. The related values and standard deviations are listed in Table 1. The corresponding internal damage threshold values at the rear side Frear, including Fresnel losses at the front surface and field enhancement at the backside but ignoring SF, can be obtained by multiplying the values in Table 1 by 1.615. For a pulse duration of 1 ps, the LIDT fluence and intensity drop by only 10-20% when the repetition rate is increased from 10 to 1000 kHz suggesting that the influence of thermal effects and cumulative material modifications are minor in this parameter range. In contrast, there is a dramatic drop in LIDT with 330-fs pulses as the repetition rate increases from 20 to 100 kHz. Simultaneously, white light continuum (WLC) generation could also be seen by the naked eye in this range of repetition frequencies. Above 100 kHz, however, the drop in LIDT versus repetition rate was less pronounced and no WLC was detected. The SF lengths calculated in the steady state limit  for peak powers corresponding to the LIDT values in Table 1 at τ = 330 fs are ≤ 2 mm for γ ≥ 6 × 10−20 m2/W. The large drop in LIDT from 20 to 100 kHz at τ = 330 fs is tentatively attributed to a transition to a damage regime at higher repetition rates, where thermal and/or accumulation effects limit the damage threshold. This suppresses WLC generation as well as spectral and the associated temporal broadening. At 1 ps, the longer pulse duration may facilitate stronger accumulation effects, as suggested by the lower LIDT intensities compared to those at 330 fs, which limit the damage threshold even at lower repetition rates.
Figure 8 shows typical damage sites at the rear side of the sample for different repetition rates and a pulse duration of 1 ps. The pictures were taken with a reflected light microscope at a magnification of × 100. The damage sites increase in size with increasing repetition rate in agreement with the increasing average power and the long closing time of the shutter (i.e. 17 ms). The average LIDT power incident on the sample was 0.08, 0.4, 0.8, 3.5, and 7.5 W at a repetition rate of 10, 50, 100, 500, and 1000 kHz, respectively. For the damage sites obtained at 10 and 50 kHz we could also observe a ripple structure using a transmitted light microscope (Fig. 9). The damage morphology suggests the influence of thermal effects, which may have been due to the slow shutter response time.
In the case of 330-fs pulses, the visibility of the damage sites was much lower than at 1 ps even at a magnification of × 100. The damage morphology for repetition rates between 20 and 500 kHz is similar, while it is markedly different at 1000 kHz (cf. Figure 10). At 20, 50, and 100 kHz, multiple damaged spots scattered over a few 100 μm2 area were detected.
Using either reflected or transmitted light microscopy, we did not observe bulk damage in any of the inspected samples.
3.4 Influence of AR-coating on the LIDT
The LIDTs of single and multi-layer AR-coated samples were measured at a repetition rate of 100 kHz and a pulse duration of 1 ps. Two measurement campaigns were conducted. In the first campaign, the Amphos laser amplifier system was used. The samples were placed several mm behind the focal plane with a spot size of FWHM = 200 µm at their front side. The results are shown in Fig. 11 (cf. red symbols). The same samples were then also tested using the Satsuma laser amplifier system under the same conditions as shown for the focal plane of Fig. 4 (cf. Figure 11, blue symbols). The LIDTs of uncoated samples are also shown for comparison. The LIDT values are summarized in Table 2. For AR-coated samples, Fresnel losses and field enhancement at the backside could be neglected because the surface reflection coefficients were less than 0.5%. Nevertheless, also for these samples damage occurred always on the rear side. For uncoated samples, both the incident and the internal values, ignoring SF, are provided in Table 2.
There is an almost negligible difference between uncoated and AR-coated samples with respect to the incident LIDTs. In contrast, the calculated internal LIDTs of uncoated samples are significantly higher than those of the AR-coated samples. This means that the applied AR-coatings do not improve the surface quality (reduce the defect concentration) but still help to maintain almost the same practical LIDT in terms of incident fluence (intensity) by suppressing the field enhancement effect.
Typical damage sites at the rear side of uncoated and coated samples damaged at the focus are depicted in Fig. 12. The pictures suggest that the AR-coated samples were damaged beneath the coatings [cf. Figure 12(b) and (c)] and the coating was only ablated when the shutter was not closed within its nominal closing time [cf. Figure 12(d)].
3.5 Influence of crystal temperature on the LIDT
For this study, the Amphos amplifier system (i.e. 100 kHz, 1 ps) was used. Blank, uncoated 5 mol% MgO-doped LN samples were placed behind the focal plane with a laser beam diameter FWHM = 200 µm at the front side. The LIDT was measured at three crystal temperatures: 20, 60, and 170 °C. The results are summarized in Fig. 13 and Table 3. For the internal values, Fresnel losses at the front surface and field enhancement at the backside were included based on the temperature dependent refractive index from  and SF effects were ignored. The LIDT is independent of crystal temperature within error bars in the 20-170 °C range.
Nonlinear light scattering due to the photorefractive effect decreased with increasing temperature in agreement with observations in the existing literature . This is demonstrated in Fig. 14, where the scattered power above 1 µm (i.e. PD3 signal) is plotted for different crystal temperatures. It is worth noting that although beam distortions due to the photorefractive effect decreased with increasing temperature, they were still present at a sample temperature of 170 °C. Furthermore, the parasitic SH signal seen by the naked eye was weaker at higher temperature than at lower temperature.
3.6 Influence of periodic poling on the LIDT
For this study, again the Amphos amplifier system (i.e. 100 kHz, 1 ps) was used. Uncoated 5% MgO-doped PPLN samples were placed behind the focal plane with a laser spot size at FWHM = 90 µm at the front surface. The samples were studied at room temperature, which kept the conversion efficiency to the second harmonic low.
The results shown in Fig. 15 show that the LIDT of blank and periodically poled crystals is the same within error bars suggesting that (i) the generated green light was sufficiently weak and (ii) periodic poling did not have a detrimental effect on the LIDT. The Finc values in Fig. 15 are 234 ± 13 mJ/cm2, 225 ± 7 mJ/cm2 and 211 ± 10 mJ/cm2 for blank sample, 6.25-µm period and 6.849-µm period samples, respectively.
A systematic R-on-1 laser induced damage threshold (LIDT) study was presented for a wide range of LiNbO3 crystals at typical laser and crystal parameters employed in high repetition rate optical parametric amplifier systems based on ultrafast Yb-laser pump sources. The samples included 2-mm thick (i.e. along the propagation direction), uncoated and anti-reflection (AR) coated, blank and periodically poled MgO-doped congruent crystals.
The fact that catastrophic laser damage was observed exclusively at the rear side of the crystals in both the uncoated and the AR-coated case was attributed to self-focusing due to the electronic Kerr-effect. This was confirmed by LIDT measurements at various locations along the confocal range of the focused laser beam. The modeling of the data provided the intrinsic damage threshold at 1 ps and the nonlinear index of refraction of LiNbO3, which fell in the accepted range. Based on the intrinsic LIDT, we estimated the incident LIDT fluence in the absence of self-focusing (i.e. crystal thickness << 2 mm and/or pulse durations of 5-10 ps) for uncoated crystals: ~470 mJ/cm2.
Photorefractive effects manifested themselves as a source of nonlinear light scattering complicating the detection of catastrophic LIDT and as distortions in the transmitted laser beam profile at threshold intensities a few 10% below that of catastrophic damage. The photorefractive effects observed below the catastrophic damage threshold were not permanent and their influence increased with repetition rate and decreased with crystal temperature, but was always present in the parameter range of this study. However, the LIDT of uncoated blank samples was independent of crystal temperature within error bars in the 20-170 °C range.
At a pulse duration of 1 ps, the incident LIDT fluence and intensity were approximately independent of the repetition rate between 10 and 1000 kHz suggesting that the influence of thermal and defect accumulation effects is minor in this parameter range. The measured values ranged from ~180 mJ/cm2 at 10 kHz to ~160 mJ/cm2 at 1000 kHz. In contrast, at a pulse duration of 330 fs, we observed a large drop in LIDT from ~800 to ~180 mJ/cm2 when the repetition rate increased from 20 to 100 kHz, while the LIDT stayed approximately constant at 100-120 mJ/cm2 between 500 and 1000 kHz. The strong variation of LIDT in the 20-100-kHz range was accompanied by white light continuum generation and was tentatively attributed to a combination of (i) reduced heating/accumulation effects at lower repetition rates and (ii) the resulting spectral and temporal broadening as well as WLC generation at the higher allowed pre-damage intensities.
There was an almost negligible difference between uncoated and AR-coated samples with respect to incident LIDTs. However, the calculated internal LIDTs in uncoated samples were significantly higher than in AR-coated samples. Thus, the applied AR-coatings did not improve the surface quality but still helped maintain the same LIDT in terms of incident fluence and intensity by suppressing the field enhancement effect at the rear side of the sample. The LIDT of blank and periodically poled crystals was the same within error bars suggesting that it was not influenced by the different levels of 515-nm light.
Leibniz-Gemeinschaft grant no. SAW-2012-MBI-2; European Union’s Horizon 2020 research and innovation programme under grant agreement no. 654148 Laserlab-Europe.
We thank Dr. Alexandre Mermillod-Blondin for providing the Satsuma laser.
References and links
1. M. Baudisch, H. Pires, H. Ishizuki, T. Taira, M. Hemmer, and J. Biegert, “Sub-4-optical-cycle, 340 MW peak power, high stability mid-IR source at 160 kHz,” J. Opt. 17(9), 094002 (2015). [CrossRef]
2. Y. Shamir, J. Rothhardt, S. Hädrich, S. Demmler, M. Tschernajew, J. Limpert, and A. Tünnermann, “High-average-power 2 μm few-cycle optical parametric chirped pulse amplifier at 100 kHz repetition rate,” Opt. Lett. 40(23), 5546–5549 (2015). [CrossRef] [PubMed]
4. M. Puppin, Y. Deng, O. Prochnow, J. Ahrens, T. Binhammer, U. Morgner, M. Krenz, M. Wolf, and R. Ernstorfer, “500 kHz OPCPA delivering tunable sub-20 fs pulses with 15 W average power based on an all-ytterbium laser,” Opt. Express 23(2), 1491–1497 (2015). [CrossRef] [PubMed]
5. S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105(8), 083102 (2009). [CrossRef]
6. S. Kato, S. Kurimura, H. H. Lim, and N. Mio, “Induced heating by nonlinear absorption in LiNbO3-type crystals under continuous-wave laser radiation,” Opt. Mater. 40, 10–13 (2015). [CrossRef]
7. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966). [CrossRef]
8. J. R. Schwesyg, M. Falk, C. R. Phillips, D. H. Jundt, K. Buse, and M. M. Fejer, “Pyroelectrically induced photorefractive damage in magnesium-doped lithium niobate crystals,” J. Opt. Soc. Am. B 28(8), 1973–1987 (2011). [CrossRef]
9. I. Pipinyte, R. Grigonis, K. Stankeviciute, S. Kicas, R. Drazdys, R. C. Echardt, and V. Sirutkaitis, “Laser-induced-damage thresholds of periodically poled lithium niobate for 1030 nm femtosecond laser pulses at 100 kHz and 75 MHz,” Proc. SPIE 8786, 87861N (2013). [CrossRef]
11. H. Jang, A. Zukauskas, C. Canalias, and V. Pasiskevicius, “Highly efficient backward stimulated polariton scattering in periodically poled KTiOPO4,” CLEO 2015, paper STh4H.1.
12. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” Appl. Phys. (Berl.) 40(8), 3389–3396 (1969). [CrossRef]
13. R. Rupp, J. Marotz, K. Ringhofer, S. Treichel, S. Feng, and E. Kratzig, “Four-wave interaction phenomena contributing to holographic scattering in LiNbO3 and LiTaO3,” IEEE J. Quantum Electron. 23(12), 2136–2141 (1987). [CrossRef]
16. M. D. Crisp, N. L. Boling, and G. Dubé, “Importance of Fresnel reflections in laser surface damage of transparent dielectrics,” Appl. Phys. Lett. 21(8), 364–366 (1972). [CrossRef]
17. J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4(1), 35–110 (1975). [CrossRef]
18. I. A. Kulagin, R. A. Ganeev, R. I. Tugushev, A. I. Ryasnyansky, and T. Usmanov, “Analysis of third-order nonlinear susceptibilities of quadratic nonlinear optical crystals,” J. Opt. Soc. Am. B 23(1), 75–80 (2006). [CrossRef]
19. R. A. Ganeev, I. A. Kulagin, A. I. Ryasnyanskii, R. I. Tugushev, and T. Usmanov, “The nonlinear refractive indices and nonlinear third-order susceptibilities of quadratic crystals,” Opt. Spectrosc. 94(4), 561–568 (2003). [CrossRef]
20. R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32(8), 1324–1333 (1996). [CrossRef]
21. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008). [CrossRef]
22. J. Rams, A. Alcazar-de-Velasco, M. Carrascosa, J. M. Cabrera, and F. Agullo-Lopez, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178(1), 211–216 (2000). [CrossRef]