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The spatial distribution of the optical parametric fluorescence generated in a negative uniaxial nonlinear crystal is asymmetric with respect to the pump when the pump beam has a slight divergence angle. The formation mechanism of this phenomenon and the influence of parameters were analyzed and discussed from a theoretical standpoint. Moreover, two potential applications of this phenomenon were experimentally demonstrated, showing the temporal contrast improvement of ultra-intense lasers and the intensity enhancement of special light sources induced by the optical parametric generation.
© 2017 Optical Society of America
1. Introduction
Optical parametric frequency down-conversion in a quadratic nonlinear crystal is widely used for the generation and amplification of broadband and/or intense radiations [1–3]. Efficient three-wave interactions, such as optical parametric generation (OPG) and optical parametric amplification (OPA)/optical parametric chirped-pulse amplification (OPCPA), require phase-matching. Taking a negative uniaxial crystal and type I phase-matching, for example, the pump (i.e., extraordinary ray) is polarized in the plane containing the optic axis and its wave vector, while the signal and idler (i.e., ordinary rays) both have a polarization perpendicular to that of the pump [4]. For the ordinary ray, the refractive index is constant for any arbitrary propagation direction, and the phase-matching directions are therefore symmetric in space with respect to the pump [5]. This allows many choices for types of arrangements of OPG and OPA/OPCPA. However, in an actual system the pump beam is not a perfect collimated beam (i.e., a plane wave) without any divergence or convergence. Beam divergence should be considered for a Gaussian beam and if the nonlinear crystal is positioned away from the beam waist. Moreover, to enhance the nonlinear effect, the pump beam is usually focused by a lens or telescope to increase the intensity, in which case the divergence or convergence cannot be neglected. In a divergent pump beam with a finite diameter, the propagation directions of different rays are slightly different. For a single pump ray inside the beam, the phase-matching directions are still symmetric with respect to the ray. However, for the entire divergent pump beam, the phase-matching directions are asymmetric with respect to the beam. Generally, the optical parametric fluorescence generated in a negative uniaxial crystal is considered to possess a cone shape in three-dimensional (3D) space or a ring shape in 2D space that are symmetric with respect to the pump beam, and this phenomenon has been demonstrated in various experiments [5–7]. However, once the above condition is taken into account, the spatial distribution of the fluorescence would become asymmetric. Actually, this phenomenon has already been reported and analyzed in previous publications [7–9], however, to the best of our knowledge, the detail influences of main parameters of waves (pump, signal and idler), crystals and phase-matching conditions have not yet been introduced. Moreover, its potential applications also have not been experimentally demonstrated.
According to our research, in some cases the spatial asymmetry of the optical parametric fluorescence is not a disadvantage, and could be used to improve some capabilities of an optical parametric device. For example, the asymmetry can be used to reduce the amplified optical parametric fluorescence (AOPF) in an ultra-intense laser system containing OPA/OPCPA amplifiers [10, 11], and accordingly the temporal contrast of the output would be effectively improved [12, 13]. This capability is quite attractive considering the recent rapid development of petawatt-class ultra-high ultrashort lasers with peak intensities of >1020 W/cm2 and a required temporal contrast of >108 [14–21]. In addition, this phenomenon could be used to increase the intensity of special light sources generated by OPG, such as ultra-broadband or mid-infrared light [22–24], and this capability is also very useful for the intensity enhancement of required light sources. In the following sections, the spatial asymmetry of the optical parametric fluorescence induced by a divergent pump beam in OPG was studied. The formation mechanism was then analyzed by the phase-matching method, and the detailed asymmetry of the fluorescence and the influence of different parameters were simulated theoretically under various conditions. Finally, two proposed potential applications were experimentally demonstrated based on the laser conditions present in our laboratory.
2. Theoretical analysis
The geometries and the phase-matching diagrams (i.e., certain sets of signals and idlers) of OPG for plane and spherical wave pumps are shown in Fig. 1. An x-y-z coordinate system is set up, where the pump beam propagates along the z-axis and the optic axis of the crystal is in the x-z plane. The phase-matching angle θ and the deviation angle δ are used to indicate the spatial attitude of the crystal and the divergence of the pump, respectively, which are measured from the optic axis to the z-axis and from the z-axis to a certain pump ray, respectively. The orientation angle α is measured from the z-axis and is used to analyze the spatial distribution of the fluorescence, where its positive and negative directions are illustrated by the arrows. The generated photons with shorter and longer wavelengths are defined as the fluorescence signal (FS) and fluorescence idler (FI), respectively.
Fig. 1 Schematic of OPG with a (a) perfect collimated (plane wave) and (b) divergent (spherical wave) pump beam. α is the orientation angle in space measured from the z-axis, θ is the phase-matching angle measured from the optic axis to the z-axis, and δ is the deviation angle measured from the z-axis to a certain ray of the pump. FS: fluorescence signal, FI: fluorescence idler, P: pump beam, C: optic axis.
When the pump is a perfect collimated beam (i.e., plane wave), the FS and FI for different pump rays shift along the x-axis in space, but the parallelism is not changed and the fluorescence remains symmetric about the pump beam. When the pump beam possesses a divergence angle, however, the situation is different. For a pump ray with a positive deviation angle δ, the included angle between the FS and FI decreases and both the FS and FI rotate around the y-axis with a positive δ value. For a pump ray with a negative δ, the included angle increases, and the rotation of the FS and FI is negative. In this condition, the previous symmetry is destroyed, and the spatial divergence of the fluorescence in the positive orientation is smaller than that in the negative orientation. Accordingly, the intensity of the fluorescence in the positive orientation is stronger than that in the negative orientation.
For a pump ray with a 2D deviation angle (δx, δy) and a FS ray propagating in the (αx, αy) direction, the phase mismatch among the three waves is given by
where the angular frequencies ωs, ωi and ωp of FS, FI and the pump satisfy ωs + ωi = ωp. When the small-angle approximation is introduced, the Eq. (1) can be rewritten asAnd this approximation is reasonable in this paper due to small divergence angles of the pump beam and small orientation angles of the fluorescence. In the type I phase-matching, the refractive indices ns and ni of FS and FI (i.e., ordinary rays) can be calculated directly using the Sellmeier Equation, and np of the pump (i.e., extraordinary ray) satisfies [4]where ne is the principal value of the extraordinary refractive index. In an undepleted pump approximation without any input signal, the mean number of fluorescence photons at the output of the nonlinear crystal is given by [5]andwhere L is the crystal length, deff is the effective nonlinear coefficient, and Ip is the pump intensity.Using Eqs. (2) and (4), the evolution of the phase-matching curve and the fluorescence intensity for various orientations αx in the x-z plane are simulated based on a 517 nm-wavelength pump light and a type I Beta Barium Borate (BBO) crystal. When θ is 23.3° [Fig. 2(a)], which is larger than the collinear phase-matching angle of 23.26°, the phase-matching curves are symmetric about the z-axis (αx = 0) in the case of δ = 0. However, for a δx of 0.5 mrad, the phase-matching curves separate and move toward the negative direction of αx. The inverse is true for a δx of 0.5 mrad, where the phase-matching curves move closer to each other and toward the positive direction of αx. In this case, the phase-matching curves for a divergent pump merge and separate in the positive and negative direction of αx, respectively. Figure 2(b) shows the intensity of the fluorescence generated by a flat-top pump beam with a 1 mrad divergence angle (full angle), where the fluorescence intensity in the positive direction of αx is obviously higher than that in the negative direction. For the second case, θ is reduced to 23.1° [Fig. 2(c)], which is smaller than the collinear phase-matching angle. When the deviation angle δx is reduced from 0 to −0.5 mrad, the phase-matching curves move close to each other in the spectrum region and toward the negative direction of αx in space. Conversely, when δx is increased to 0.5 mrad, the phase-matching curves separate in the spectrum region and move toward the positive direction of αx. As a result, the phase-matching curves in the positive direction of αx merge spatially, however those in the negative direction of αx separate in space. Similar to the previous case, the fluorescence intensity in the positive direction of αx is higher than that in the negative direction, as shown in Fig. 2(d). For convenience, therefore, in the following discussion we will define the positive direction of αx at which the fluorescence intensity is the highest as the fluorescence enhancement direction (FED), the negative direction of αx at which it is the weakest as the fluorescence weakening direction (FWD), and the ratio of the fluorescence intensities in FED and FWD as the fluorescence intensity contrast.
Fig. 2 Characteristics of optical parametric fluorescence in a type I BBO crystal pumped by a 517 nm-wavelength light. The phase-matching angle θ is (a, b) 23.3° and (c, d) 23.1°. (a, c) Phase-matching curves in the x-z plane for −0.5, 0 and 0.5 mrad deviation angles (δx) . (b, d) Fluorescence intensity distributions in the x-z plane for the pump beam with a 1 mrad divergence angle.
The spatial distributions of the fluorescence for 2D orientations αx (orientation in the x-z plane) and αy (orientation in the y-z plane) are simulated based on Eq. (4) and analyzed under different conditions. For the case when θ is larger than the collinear phase-matching angle, the initial simulation is based on the following parameters: the divergence angle of the pump beam is 1 mrad, no fluorescence bandwidth limitation, the pump intensity is 1 GW/cm2, the BBO crystal length is 12 mm, and the phase-matching angle θ is 23.3°. As shown in Fig. 3, the fluorescence has a conical distribution in space, and the αx and αy direction distribution is asymmetric and symmetric with respect to the z-axis, respectively. The fluorescence intensity contrast shown in Fig. 3(a) is around 1.13. To analyze the influence of each parameter on the fluorescence intensity contrast separately, the initial parameters are changed individually while all other parameters are held to the same values used in the initial simulation. First, the divergence angle of the pump beam is increased to 2 mrad [Fig. 3(b)]; second, a 10 nm fluorescence bandwidth limitation centered at 1034 nm is introduced [Fig. 3(c)]; third, the pump intensity is increased to 10 GW/cm2 [Fig. 3(d)]; fourth, the crystal length is reduced to 2 mm [Fig. 3(e)]; and finally, the phase-matching angle θ is increased to 23.34° [Fig. 3(f)]. The fluorescence intensity contrast is seen to increase in Figs. 3(b), 3(c) and 3(f) and decrease in Figs. 3(d) and 3(e). Figure 4 shows several 2D intensity distributions of the fluorescence in the αx direction for various pump divergence angles, fluorescence bandwidth limitations, pump intensities, crystal lengths and phase-matching angles. It can be seen that the fluorescence intensity contrast increases with increasing pump divergence angle, crystal length and phase-matching angle, and decreases with increasing fluorescence bandwidth and pump intensity. Figure 4 also shows that the pump intensity only influences the fluorescence intensity contrast without changing the conical angle of the fluorescence. However, the conical angle may be increased while the pump divergence angle, the fluorescence bandwidth and the phase-matching angle are increased or the crystal length is reduced. The intensity peaks appear in around the degenerate phase-matching directions, and which is stronger in the FED rather than in the FWD. Nevertheless, when the total energies on the positive and the negative directions are integrated individually, the amounts are almost the same.
Fig. 3 3D fluorescence intensity distributions in the case of θ larger than the collinear phase-matching angle. (a) The pump divergence angle is 1 mrad, the pump intensity is 1 GW/cm2, the crystal length is 12 mm, and the phase-matching angle θ is 23.3°. Holding all other variables constant with those in (a), the intensity distributions in the case when (b) the pump divergence angle is increased to 2 mrad, (c) the fluorescence bandwidth is limited to 10 nm around 1034 nm, (d) the pump intensity is increased to 10 GW/cm2, (e) the crystal length is reduced to 2 mm, and (f) the phase-matching angle θ is increased to 23.34°.
Fig. 4 In the case of θ larger than the collinear phase-matching angle, 2D fluorescence intensity distributions in the x-z plane for various (a) pump divergence angles, (b) fluorescence bandwidth limitations (centered at 1034 nm), (c) pump intensities, (d) crystal lengths and (e) phase-matching angles θ.
For the case of θ smaller than the collinear phase-matching angle, as shown in Fig. 2(d), it is quite different from the previous case that the fluorescence has a continuous spatial distribution along the αx direction. When the simulation parameters are set at a 1 mrad pump divergence angle, a 1 GW/cm2 pump intensity, a 12 mm crystal length and a 23.1° phase-matching angle, Fig. 5(a) shows the simulation results for three kinds of fluorescence bandwidths: no limitation, <950 nm and >1150 nm. And the result illustrates that the spatial asymmetry of the fluorescence distribution is too small to be neglected, however, which also shows that the distribution is strongly depended on the concentrated fluorescence bandwidth. Next, the case of a 20 nm fluorescence bandwidth limitation centered at 1250 nm is discussed, and the 2D intensity distributions of the fluorescence in the αx direction are simulated while each parameter is changed individually. The result shown in Figs. 5(b)-5(f) is similar to the previous case shown in Figs. 4(a)-4(e), and it is seen that the fluorescence intensity contrast is proportional to the pump divergence angle, the crystal length and the phase-matching angle and is inversely proportional to the fluorescence bandwidth and the pump intensity. Besides, unlike Fig. 4(b), the conical angle of the fluorescence in Fig. 5(c) is reduced instead of increased while the fluorescence bandwidth increases.
Fig. 5 In the case of θ smaller than the collinear phase-matching angle, (a) 2D fluorescence intensity distributions in the x-z plane with and without fluorescence bandwidth limitations. Distributions with a limited fluorescence bandwidth centered at 1250 nm for various (a) pump divergence angles, (b) fluorescence bandwidths, (c) pump intensities, (d) crystal lengths and (e) phase-matching angles θ.
As discussed above, the spatial asymmetry of the optical parametric fluorescence is caused by the divergence angle of the pump beam and is also influenced by four other parameters: the fluorescence bandwidth, the pump intensity, the crystal length and the phase-matching angle. In actuality, this phenomenon exists in most experiments, and is very hard to avoid.
3. Applications and demonstrations
To verify the first potential application of the temporal contrast improvement for ultra-intense lasers, and according to our laser conditions, a simple demonstration experiment was designed. As shown in Fig. 6(a), a 100 μJ and 500 fs pulse centered at 1034 nm from a Yb:CaF2 chirped-pulse amplification laser was divided into two pulses. A ~100 μJ pulse was injected into a 20 mm-long type I Lithium Triborate (LBO) crystal for a second-harmonic generation (SHG), which was used as the pump for a two-stage type I non-collinear OPA (NOPA). The other ~10 nJ pulse was used as the signal. At the first and second OPAs, 12 and 15 mm-long BBO crystals were used, respectively, where the non-collinear angles inside the crystals were around 0.3°. A detector comprising an iris, a lens, a prism and a charge coupled device (CCD) camera was positioned in the signal direction for the detection of the weak AOPF. To capture the AOPF only in the signal direction and filter stray lights, the output of the two-stage OPA was filtered by the iris in space, focused by the lens to the CCD camera, and the residual green pump light was separated in space by the prism. As shown in Fig. 6(b), four kinds of arrangements of the two-stage OPA were used for comparison. In these arrangements, the signals for the first and the second OPAs propagated, respectively, along the directions of FWD & FWD (i), FWD & FED (ii), FED & FWD (iii), and FED & FED (iv). At the very beginning, a shutter was used to stop the signal of the two-stage OPA, and the far-field patterns of the generated AOPF for arrangements i–iv were captured, as shown in Fig. 6(c). The weakest AOPF was achieved in the “FWD & FWD” (i) arrangement as shown in Fig. 6(b)(i), and the strongest AOPF appeared in the “FED & FED” (iv) arrangement as shown in Fig. 6(b)(iv). After that, the shutter was opened and the amplified signals for the four kinds of arrangements were measured in the same environment. The results were 4.34 (i), 4.17 (ii), 3.77 (iii), and 3.41 (iv) μJ. Among these conditions, for the “FWD & FWD” arrangement [Fig. 6(b)(i)], the generated AOPF was the weakest and the amplified signal was the strongest and, therefore, the temporal contrast should be the best. On the contrary, for the “FED & FED” arrangement [Fig. 6(b)(iv)], the strongest AOPF and the weakest amplified signal were observed at the same time and, therefore, the temporal contrast should be the worst. Comparing the results in Figs. 6(b)(ii) and 6(b)(iii), we find that the AOPF is mainly dependent upon the second stage of OPA for three main reasons. First, in our experiment, the distance between the two stages of OPA was around 0.5 m. Compared with the second OPA, the first OPA was closer to the waist of the pump beam, causing the divergence angle of the pump at the first OPA to be slightly smaller than that at the second OPA. This meant that the spatial asymmetry of the generated AOPF at the first OPA was minor. Second, the second OPA was closer to the detector than the first OPA, and therefore more AOPF generated at the second OPA could be collected by the detector. Third, a longer BBO crystal was used in the second OPA, and therefore more AOPF would be generated. Consequently, as shown in Fig. 6(c), when the FED was used in the second OPA, the detected AOPF increased significantly. For the signal amplification difference in the four kinds of arrangements, we believe the main reason was the spatial walk-off of the pump beam [25]. As shown in Fig. 6(b), when the signal was propagated along the FWD, the spatial separation between the signal and pump beams was reduced by the spatial walk-off of the pump beam (i.e., extraordinary ray), and the amplification was relatively higher. Otherwise, when the signal was propagated along the FED, the amplification was lower. Moreover, in 2011 P. J. M. Johnson et al. presented and demonstrated a method for broadband NOPA by using an anamorphic focusing (divergent) pump, which is ideally suited for narrowband pump sources [26]. The formation mechanism of this effect could also be explained based on Fig. 2(a), when the perfect collimated pump is replaced by a 1 mrad divergent pump, the phase-matching curve (red curve) would be changed into a phase-matching region (enclosed by the blue and black curves). And accordingly the gain bandwidth could be extended significantly. Besides, we could also find that the enclosed area of the phase-matching region in the FWD (negative side of αx) is larger than that in the FED (positive side of αx), which means the gain bandwidth in the FWD is even broader.
Fig. 6 (a) Two-stage OPA setup schematic for AOPF comparison. (b) The signal direction within the two-stage OPA (first OPA & second OPA) was, respectively, along the (i) FWD & FWD, (ii) FWD & FED, (iii) FED & FWD, and (iv) FED & FED. (c) Detected far-field patterns of AOPF in the four kinds of arrangements. FED: fluorescence enhancement direction, FWD: fluorescence weakening direction, P: pump beam, S: signal beam, C: optic axis, AOPF: amplified optical parametric fluorescence, OPA: optical parametric amplification.
According to the above demonstration and analysis, for a non-collinear OPA/OPCPA with a negative uniaxial nonlinear crystal, it is suggested that the signal be propagated in the FWD. In this arrangement, the amplification can be improved owing to the compensation of the spatial walk-off of the pump and, importantly, the AOPF can be reduced owing to the spatial asymmetry of the optical parametric fluorescence. Moreover, an even broader gain bandwidth could be obtained, as well.
Generally, OPG is used to generate light sources with special properties that cannot be directly produced in oscillators or by other methods, and so our second potential application was to increase the intensity of such lights. As shown in Fig. 2(d), the visible and the infrared optical parametric fluorescence generated in OPG have a similar asymmetric distribution in space. Therefore, the spatial asymmetry of the visible fluorescence was demonstrated here instead owing to the lack of an infrared CCD camera. As shown in Fig. 7(a), a ~40 μJ and 500 fs pump pulse centered at 517 nm was generated by SHG in a 20 mm-long type I LBO crystal, which was then slightly focused onto a 15 mm-long type I BBO crystal for OPG. The angle θ at the BBO was around 23.0°, while the convergence angle was around 2 mrad (full angle) and could be precisely changed by adjusting a commercial telescope. A commercial near-infrared detector card (SIGMAKOKI, SIRC-1) was used to display the generated visible fluorescence, the transmission pump and the residual fundamental within the pump, which has no response to the generated infrared fluorescence. As shown in Fig. 7(b), in the first demonstration experiment, the BBO was positioned with its optic axis pointing to the first quadrant of the x-z plane, the spatial walk-off of the pump light was in the negative direction of the x-axis, and the fluorescence ring was much stronger on the positive side of the x-axis (the FED, which points to the first quadrant of the x-z plane). In the second demonstration experiment, to rule out the potential influence of the spatial non-uniformity of the pump beam, the BBO crystal was rotated by 180° about the z-axis so that its optic axis as well as the FED pointed to the second quadrant of the x-z plane. Thus, both the spatial walk-off direction of the pump and the spatial asymmetry of the optical parametric fluorescence were rotated by 180° around the z-axis, and the strongest fluorescence was located at the negative side of the x-axis (i.e., along the FED). Consequently, as introduced previously, for an OPG within a negative uniaxial nonlinear crystal, the FED is in the acute angle region formed by the pump direction and the crystal’s optic axis. This is the arrangement suggested for the generation of intense lights with special properties, such as ultra-broadband and mid-infrared.
Fig. 7 (a) Experimental setup for demonstration. (b) Schematics of and photographs showing the observed walk-off directions of the pump and asymmetrical fluorescence rings in the first (upper) and second (lower) experiments. The divergence angle of the pump beam is around 2 mrad, and the absolute value of θ is around 23.0°. C: optic axis, ω: angular frequency of fundamental at LBO.
4. Conclusions
In conclusion, the spatial asymmetry of the optical parametric fluorescence generated by OPG within a negative uniaxial nonlinear crystal was introduced and analyzed. The formation mechanism of this asymmetry is the asymmetric phase-matching in space caused by the divergence angle of the pump beam. The fluorescence intensity contrast, defined as the ratio between the strongest and the weakest intensities in space, is influenced by five parameters: the pump divergence angle, the fluorescence bandwidth, the pump intensity, the crystal length and the phase-matching angle. The fluorescence intensity contrast is proportional to the pump divergence angle, the crystal length and the phase-matching angle, and it is inversely proportional to the fluorescence bandwidth and the pump intensity. In actual experiments, this phenomenon could be used for two potential applications: to improve the temporal contrast for ultra-intense lasers such as petawatt-class lasers, and to enhance the intensity of a special light source generated by OPG such as ultra-broadband or mid-infrared. In addition, the spatial asymmetry of the phase-matching around a divergent pump beam would cause some space-dependent intensity and phase distortions, which could be used to explain some experimental results observed in an optical parametric process.
Funding
A portion of this work was supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) (JP25247096).
Acknowledgements
Z. L. acknowledges helpful discussions with Dr. Xiaoyang Guo and Dr. Zhan Jin.
References and links
1. H.-J. Krause and W. Daum, “Efficient parametric generation of high-power coherent picosecond pulses in lithium borate tunable from 0.405 to 2.4 μm,” Appl. Phys. Lett. 60(18), 2180–2182 (1992). [CrossRef]
2. N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Sub-two-cycle, carrier-envelope phase-stable, intense optical pulses at 1.6 μm from a BiB3O6 optical parametric chirped-pulse amplifier,” Opt. Lett. 37(20), 4182–4184 (2012). [CrossRef] [PubMed]
3. L. Yu, X. Liang, L. Xu, W. Li, C. Peng, Z. Hu, C. Wang, X. Lu, Y. Chu, Z. Gan, X. Liu, Y. Liu, X. Wang, H. Lu, D. Yin, Y. Leng, R. Li, and Z. Xu, “Optimization for high-energy and high-efficiency broadband optical parametric chirped-pulse amplification in LBO near 800 nm,” Opt. Lett. 40(14), 3412–3415 (2015). [CrossRef] [PubMed]
4. R. W. Boyd, Nonlinear Optics, 3rd ed. (Elsevier (Singapore) Pte Ltd., 2010).
5. F. Devaux and E. Lantz, “Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal,” Eur. Phys. J. D 8(1), 117–124 (2000). [CrossRef]
6. F. K. Hsu and C. W. Lai, “Absolute instrument spectral response measurements using angle-resolved parametric fluorescence,” Opt. Express 21(15), 18538–18552 (2013). [CrossRef] [PubMed]
7. G. Tamosauskas, J. Galinis, A. Dubietis, and A. Piskarskas, “Observation of spontaneous parametric down-conversion excited by high brightness blue LED,” Opt. Express 18(5), 4310–4315 (2010). [CrossRef] [PubMed]
8. R. Ramírez-Alarcón, H. Cruz-Ramírez, and A. B. U’Ren, “Effects of crystal length on the angular spectrum of spontaneous parametric downconversion photon pairs,” Laser Phys. 23(5), 055204 (2013). [CrossRef]
9. T. Stanislauskas, I. Balčiūnas, V. Tamuliene, R. Budriūnas, and A. Varanavičius, “Analysis of Parametric fluorescence amplified in a noncollinear optical parametric amplifier pumped by the second harmonic of a femtosecond Yb:KGW laser,” Lith. J. Phys. 56(1), 1–8 (2016). [CrossRef]
10. F. Tavella, A. Marcinkevičius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8(10), 219 (2006). [CrossRef]
11. C. Homann and E. Riedle, “Direct measurement of the effective input noise power of an optical parametric amplifier,” Laser Photonics Rev. 7(4), 580–588 (2013). [CrossRef]
12. K. Kondo, H. Maeda, Y. Hama, S. Morita, A. Zoubir, R. Kodama, K. A. Tanaka, Y. Kitagawa, and Y. Izawa, “Control of amplified optical parametric fluorescence for hybrid chirped-pulse amplification,” J. Opt. Soc. Am. B 23(2), 231–235 (2006). [CrossRef]
13. J. Moses, S.-W. Huang, K.-H. Hong, O. D. Mücke, E. L. Falcão-Filho, A. Benedick, F. Ö. Ilday, A. Dergachev, J. A. Bolger, B. J. Eggleton, and F. X. Kärtner, “Highly stable ultrabroadband mid-IR optical parametric chirped-pulse amplifier optimized for superfluorescence suppression,” Opt. Lett. 34(11), 1639–1641 (2009). [CrossRef] [PubMed]
14. J. Wang, J. Ma, Y. Wang, P. Yuan, G. Xie, and L. Qian, “Noise filtering in parametric amplification by dressing the seed beam with spatial chirp,” Opt. Lett. 39(8), 2439–2442 (2014). [CrossRef] [PubMed]
15. H. Kiriyama, T. Shimomura, H. Sasao, Y. Nakai, M. Tanoue, S. Kondo, S. Kanazawa, A. S. Pirozhkov, M. Mori, Y. Fukuda, M. Nishiuchi, M. Kando, S. V. Bulanov, K. Nagashima, M. Yamagiwa, K. Kondo, A. Sugiyama, P. R. Bolton, T. Tajima, and N. Miyanaga, “Temporal contrast enhancement of petawatt-class laser pulses,” Opt. Lett. 37(16), 3363–3365 (2012). [CrossRef] [PubMed]
16. S. G. Liang, H. J. Liu, N. Huang, Q. B. Sun, Y. S. Wang, and W. Zhao, “Temporal contrast enhancement of picosecond pulses based on phase-conjugate wave generation,” Opt. Lett. 37(2), 241–243 (2012). [CrossRef] [PubMed]
17. Y. Huang, C. Zhang, Y. Xu, D. Li, Y. Leng, R. Li, and Z. Xu, “Ultrashort pulse temporal contrast enhancement based on noncollinear optical-parametric amplification,” Opt. Lett. 36(6), 781–783 (2011). [CrossRef] [PubMed]
18. P. Yuan, G. Xie, D. Zhang, H. Zhong, and L. Qian, “High-contrast near-IR short pulses generated by a mid-IR optical parametric chirped-pulse amplifier with frequency doubling,” Opt. Lett. 35(11), 1878–1880 (2010). [CrossRef] [PubMed]
19. R. C. Shah, R. P. Johnson, T. Shimada, K. A. Flippo, J. C. Fernandez, and B. M. Hegelich, “High-temporal contrast using low-gain optical parametric amplification,” Opt. Lett. 34(15), 2273–2275 (2009). [CrossRef] [PubMed]
20. A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J. P. Rousseau, J. P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, “10-10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation,” Opt. Lett. 30(8), 920–922 (2005). [CrossRef] [PubMed]
21. N. Stuart, T. Robinson, D. Hillier, N. Hopps, B. Parry, I. Musgrave, G. Nersisyan, A. Sharba, M. Zepf, and R. A. Smith, “Comparative study on the temporal contrast of femtosecond mode-locked laser oscillators,” Opt. Lett. 41(14), 3221–3224 (2016). [CrossRef] [PubMed]
22. H. H. Lim, O. Prakash, B. J. Kim, K. Pandiyan, M. Cha, and B. K. Rhee, “Ultra-broadband optical parametric generation and simultaneous RGB generation in periodically poled lithium niobate,” Opt. Express 15(26), 18294–18299 (2007). [CrossRef] [PubMed]
23. M. Levenius, V. Pasiskevicius, F. Laurell, and K. Gallo, “Ultra-broadband optical parametric generation in periodically poled stoichiometric LiTaO3.,” Opt. Express 19(5), 4121–4128 (2011). [CrossRef] [PubMed]
24. P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31(1), 71–73 (2006). [CrossRef] [PubMed]
25. D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, and M. S. Bowers, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14(2), 460–474 (1997). [CrossRef]
26. P. J. M. Johnson, V. I. Prokhorenko, R. J. D. Miller, and E. Philip, “Enhanced bandwidth noncollinear optical parametric amplification with a narrowband anamorphic pump,” Opt. Lett. 36(11), 2170–2172 (2011). [CrossRef] [PubMed]
