Nonlinear Cherenkov radiation at the interface of two different nonlinear media

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1 Nonlinear Cherenkov radiation at the interface of two different nonlinear media Xiaohui Zhao, 1, Yuanlin Zheng, 1, Huaijin Ren, 3 Ning An, 4 Xuewei Deng, 5,6 and Xianfeng Chen 1,, 1 State Ke Laborator of Advanced Optical Communication Sstems and Networks, Department of Phsics and Astronom, Shanghai Jiao Tong Universit, 8 Dongchuan Road, Shanghai 4, China Ke Laborator for Laser plasmas (Ministr of Education), Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong Universit, 8 Dongchuan Road, Shanghai 4, China 3 Institute of Applied Electronics, China Academ of Engineering Phsics, Mianang, Sichuan 619, China 4 Shanghai Institute of Laser Plasma, China Academ of Engineering Phsics, Shanghai, 18 China 5 Laser Fusion Research Center, China Academ of Engineering Phsics, Mianang, Sichuan 619, China 6 wdeng@caep.ac.cn fchen@sjtu.edu.cn Abstract: We discuss the nonlinear response due to the spatial modulation of the second-order susceptibilit at the interface between two nonlinear media, and eperimentall demonstrate that the nonlinear Cherenkov radiation is enhanced b the interface of two nonlinear crstals with a large disparit in χ (). In our eperiment, the intensit of the nonlinear Cherenkov radiation generated at the nonlinear interface was approimatel 4 to 1 times that at the crstal boundar. This result suggests potential applications to efficient frequenc conversion. 16 Optical Societ of America OCIS codes: (19.19) Nonlinear optics; (19.435) Nonlinear optics at surfaces; (19.6) Harmonic generation and miing. References and links 1. A. Zembrod, H. Puell, and J. Giordmaine, Surface radiation from non-linear optical polarisation, Opt. Quantum Electron. 1, 64 (1969).. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, Nonlinear Cherenkov radiation in an anomalous dispersive medium, Phs. Rev. Lett. 18, 391 (1). 3. Y. Zhang, Z. Gao, Z. Qi, S. Zhu, and N. Ming, Nonlinear Čerenkov radiation in nonlinear photonic crstal waveguides, Phs. Rev. Lett. 1, (8). 4. C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, Cerenkov third-harmonic generation via cascaded χ () processes in a periodic-poled LiTaO 3 waveguide, Opt. Lett. 36, 17 (11). 5. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Čerenkov third-harmonic generation in nonlinear photonic crstal, Appl. Phs. Lett. 98, (11). 6. N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, Cherenkov high-order harmonic generation b multistep cascading in χ () nonlinear photonic crstal, Appl. Phs. Lett. 1, 113 (1). 7. N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequenc generation in one nonlinear medium, Photonics Res. 3, 16 (15). 8. C. Chen, X. Hu, Y. Xu, P. Xu, G. Zhao, and S. Zhu, Čerenkov difference frequenc generation in a twodimensional nonlinear photonic crstal, Appl. Phs. Lett. 11, (1). 9. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium, Appl. Phs. Lett. 13, 111 (13). 1. W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopanov, Efficient, tunable, and coherent TH source based on GaSe crstal, Opt. Lett. 7, 1454 (). 11. A. Aleksandrovsk, A. Vunishev, A. Zaitsev, A. Ikonnikov, and G. Pospelov, Ultrashort pulses characteriation b nonlinear diffraction from virtual beam, Appl. Phs. Lett. 98, 6114 (11). 1. Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Konov, Three-dimensional ferroelectric domain visualiation b Čerenkov-tpe second harmonic generation, Opt. Epress 18, (1). 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 185

2 13. X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crstal, Opt. Lett. 39, 5885 (14). 14. S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Konov, and Y. S. Kivshar, Cerenkov-tpe second-harmonic generation in two-dimensional nonlinear photonic structures, IEEE J. Quantum Electron. 45, 1465 (9). 15. M. Aoub, P. Roedig, J. Imbrock, and C. Den, Cascaded Čerenkov third-harmonic generation in random quadratic media, Appl. Phs. Lett. 99, 4119 (11). 16. P. Tien, R. Ulrich, and R. Martin, optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide, Appl. Phs. Lett. 17, 447 (197). 17. M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsk, Cerenkov configuration second harmonic generation in proton-echanged lithium niobate guides, IEEE. J. Quantum Electron. 6, 1384 (199). 18. Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, Role of a localied modulation of χ () in Čerenkov second-harmonic generation in nonlinear bulk medium, Opt. Lett. 37, 3864 (1). 19. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, Enhanced nonlinear Cherenkov radiation on the crstal boundar, Opt. Lett. 38, 1993 (13).. R. W. Bod, Nonlinear Optics (Academic, 3). 1. Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, Theoretical stud of Čerenkov-tpe second-harmonic generation in periodicall poled ferroelectric crstals, J Opt. Soc. Am. B 9, 31 (1).. A. Sugiama, H. Fukuama, T. Sasuga, T. Arisawa, and H. Takuma, Direct bonding of Ti: sapphire laser crstals, Appl. Opt. 37, 1 (1998). 1. Introduction Nonlinear Cherenkov radiation (NCR) [1], an etension of the Cherenkov radiation well known in particle phsics to nonlinear optics, has attracted considerable interest in recent ears. In NCR, when the phase velocit of the fundamental wave (FW) eceeds that of the second harmonic (SH) wave, the SH radiates at an angle θ = arccos(ν /ν 1 ), where ν 1 and ν denote the phase velocities of the FW and SH, respectivel. This angle is determined b the dispersion relation of the nonlinear crstal and generall requires the crstal to be normall dispersive. Previous studies demonstrated that, under anomalous-like dispersion conditions, NCR can also be generated b modulating the phase velocit of the polariation wave []. NCR has been thoroughl researched in different nonlinear processes, such as second [3] and cascaded high-order harmonic generation [4 6], sum-frequenc generation [7], and difference-frequenc generation [8]. Such studies suggest potential applications to efficient frequenc conversion [9], terahert wave generation [1], ultrashort pulse-sharping [11], non-destructive domain-wall detection and imaging [1, 13], and so on. Generall, efficient NCR occurs in nonlinear crstals with a random domain structure and in artificial periodic domain reversed structures [14, 15], as well as waveguide structures [16, 17]. The domain wall, which is the interface between antiparallel domains, modulates the secondorder nonlinear coefficient χ () from 1 to -1. As NCR is a longitudinal auto-phase-matched process, domain structures can provide reciprocal vectors to compensate the phase mismatching in the transverse direction. Recent theoretical [18] and eperimental [19] studies showed that NCR can be enhanced at crstal boundaries b a sharp spatial modulation of χ () from 1 to. However, for some nonlinear media, especiall UV-transparent crstals, the intensit of NCR generated at the boundar is not ver high since the nonlinear coefficient is comparativel small. The scenario where NCR is generated at an interface between two different quadratic crstals, where χ () modulates from C 1 to C (constants), has not been full discussed. Theoreticall, if the vacuum on the one side of the boundar is substituted b a nonlinear crstal with a much higher χ () than the other, NCR is epected to be enhanced at the interface, as a result of the sharp χ () modulation. In this letter, we fabricated a structure where two crstals with different nonlinear coefficients are tightl abutted upon each other, We then demonstrated, both theoreticall and eperimentall, that NCR in a bulk medium can be enhanced b the presence of another medium. As the 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 186

3 radiation angle is determined b the dispersion relationship of the medium, the added crstal does not change the NCR properties. We observed a four- to tenfold enhancement of NCR under normal dispersion conditions. In an anomalous dispersion environment, enhanced NCR was also recorded.. The coupled wave equation and simulation (a) Medium 1 NCR C χ () 1 FW o C χ () Medium I.3. (b) Radiation Angle ( ) I.3..1 (c) 1 1 Radiation Angle ( ) I (d) 1 1 Radiation Angle ( ) Fig. 1. NCR Simulation at an interface. (a) Structure of a nonlinear medium. The = plane is the interface between media 1 and, which have different second nonlinear coefficients C 1 χ () and C χ (), respectivel. The FW is incident along the ais. (b), (c) and (d) are the simulation results under the conditions C 1 = 1, C = 1; C 1 = 1, C = ; C 1 = 1, C = 1, respectivel. To anale the second harmonic (SH) generated at the nonlinear interface, we consider two semi-infinite media with different second-order nonlinear coefficients C 1 χ () and C χ (),asin Fig. 1(a). For simplicit, the refractive inde is assumed to be homogenous. The FW incident along the ais is a Gaussian beam with width a. Considering the slowl varing envelope approimation, the coupled wave equation of SH is [, 1]: ( + i k )A (,)= i k n g()χ () (A 1 e /a ) e iδk, (1) where n is the refractive inde of the SH, A 1 and A denote the comple amplitudes of the FW and SH, respectivel. The phase mis-matching is Δk = k k 1, where k 1 and k are the wave vectors of the FW and SH, and g() is the spatial modulation function of χ () along the ais: { C 1 g()= () C <. The FW amplitude is assumed to be constant. Using the Fourier transform, we can solve the coupled wave equation, and the intensit of SH I (,k )= A (,k ) can then be epressed as: [ k I (,k )= χ ()] I 1 sinc [ (Δk k /k ) ] n π (C 1 +C ) 8 ae a k π 8 + i(c 1 C ) ad( ak ) (3), where k = k sinθ is the transverse wave vector of the SH, θ is the radiation angle, and D ( ak ) denotes the Dawson function. Equation (3), indicates that, when C 1 C =, the SH intensit I gathers in the direction defined b k =, since e a k /8 decreases sharpl with increasing k. When C 1 C, the radiation angle of the SH is determined b the term containing sinc [(Δk k /k )/]. 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 187

4 The solution of Δk k /k = isk = k (k 1), assuming k k. From the geometrical relationship, we can deduce the radiation angle satisfing k cosθ = k 1, which is eactl the longitudinal phase-matching condition of NCR. Nonlinearit enhancement can be attributed mainl to the term of C 1 C, whose absolute value is directl proportional to the SH intensit, according to Eq. (3). The SH intensit depends on the sharp change of χ (), i.e., if the absolute value of C 1 C increases, the NCR intensit is enhanced. The simulation results for different parameters are depicted in Figs. 1(b) 1(d). The FW wavelength is 8 nm. Both the FW and NCR are o-polaried. The interaction length is μm. Since we are concerned about the spatial modulation of χ () at the medium interface, other properties of media 1 and are supposed to be the same in the simulation. For simplicit and without loss of generalit, the dispersion of a β BaB O 4 crstal () is assumed for the media on both sides of the interface, unless otherwise stated. The simplest situation is to consider a whole bulk medium where C 1 = C. The result is a general phase-mismatched SH generation, with an etremel weak SH output that is collinear with the FW at ero angle, as shown in Fig. 1(b). In Fig. 1(c), the modulation function of χ () changes from 1 to. It describes NCR at the boundar of a nonlinear crstal. The radiation angle of the efficient SH is ±11.8,asisthe calculated Cherenkov angle in. Figure 1(d) shows the simulation result in agreement with our analsis where C 1 = 1, C = 1. The NCR intensit is a hundred times that in Fig. 1(c). Notabl, the NCR radiation angle is the same as that in Fig. 1(c) since it depends solel on the dispersion relationship between the SH and FW. 3. Eperiment results and discussion In the eperiment, two different nonlinear crstals tightl abutted upon each other under high pressure were used to achieve a sharp modulation of χ (). For Sample 1, as shown in Fig. (a), we chose a -cut crstal of sie 5 mm() 1 mm() 1 mm() and a -cut 5 mol% MgO : LiNbO 3 (LN) crstal of sie 1 mm() 1 mm() 5 mm(). The nonlinear coefficient of LN is much greater than that of. And the orientation of the nonlinearit effects the polariation direction of nonlinear polariation wave and further determines the polariation direction of NCR. If the FW is o-polaried, the effective second-order nonlinear coefficient is d 11 in, and d 33 in LN, and the absolute value of C 1 C is about 14 []. For Sample [Fig. (b)], the orientation of the LN crstal was changed to -cut and its sie was 5 mm() 1 mm() 1 mm(). If the nonlinear process is oo-e, the effective second-order nonlinear coefficients in and LN are both d 31, and the absolute value of C 1 C is about 48. (a) LN k k o 1o d 33 (b) k e k 1o LN k np θ α k 1o k np k 1o d 31 Fig.. Schematic eperimental samples viewed from the top. (a) Sample 1: -cut and -cut LN. (b) Sample : -cut and -cut LN. The phase-matching geometries in both scenarios are shown in Fig.. Since the two crstals are just pressed together, there is an air gap with a thickness of about several micron. The FW is incident from to LN with an incident angle of α with respect to the interface. Reflection 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 188

5 and refraction of the FW occur as a result of the refractive-inde inhomogeneit. However this does not qualitativel affect NCR generation at the nonlinear interface emitting into the side. The nonlinear polariation wave, stimulated b the obliquel incident FW, propagates along the interface. Its wave vector is k np = k 1 sinα. When eceeding the threshold (k np k ), Cherenkov radiation is emitted at an angle θ = arccos(k np /k ). This remains unchanged, regardless of the presence of LN on the other side. Figure 3(a) shows a schematic of our eperiment. The FW was provided b a regenerative amplifier delivering 5 -fs pulses at a 1 -kh repetition rate with a wavelength centering at 8 nm and an average power of 4. mw. The FW was loosel focused b a 1 -mm focal-length lens to a beam waist of 5 μm. The beam was obliquel incident onto crstal and reflected at the -LN interface. The output light was then projected onto a screen. (a) Lens FW α NCR LN Rotating (d) α=66.4 (b) 35 Screen 3 Internal NCR angle ( ) 5 15 Simulation Sample Internal FW incident angle ( ) (e) (c) 3 I 1 Sample 1 Enhancement factor Internal FW incident angle ( ) 5 Enhancement factor (f) α=63.8 (g) (h) α=6. (i) Fig. 3. (a) Schematic eperimental setup. (b) Internal NCR angle θ under normal dispersion versus FW incident angle α. Theoretical prediction (solid curve) and eperimental results (smbols) are in good agreement. (c) Measured intensit and enhancement factor of SH generated at the -LN interface and boundar of crstal. (d), (f) and (h) are the recorded patterns with varing FW incident angle at the -LN interface. (e), (g) and (i) are the recorded patterns of the FW incident on the crstal boundar with the same angle as in (d), (f) and (h), respectivel. Sample 1 was first illuminated b the o-polaried FW. B turning the incident angle α, o- polaried second harmonic wave could be observed at different radiation angles. This is NCR in a normal dispersion environment, displaed as an oo-o nonlinear process in. We measured the internal NCR angle θ as a function of the FW incident angle α. The theoretical prediction and eperimental results are in good agreement, as shown in Fig. 3(b). Both at the boundar of the single crstal and at the interface of Sample 1, the relationship between θ and α depends solel on the dispersion. The recorded patterns with different FW incident angles 66.4,63.8, and 6. are presented in Figs. 3(d), 3(f), and 3(h), respectivel. For comparison, the NCR generated at the boundar of the single crstal was also observed [see Figs. 3(e), 3(g), and 3(i)]. Obviousl, at the same FW reflection angle, the intensit of NCR generated at the interface of Sample 1 was much higher than that generated at the boundar. This observation verifies the preceding simulation result that NCR is enhanced at an interface where the modulation of χ () is sufficientl large. The enhancement factor ranges from approimatel 4 [Fig. 3(d)] to 1 [Fig. 3(h)] 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 189

6 and varies with the FW reflection angle [Fig. 3(c)]. The qualit of the interface, and the partial reflection of the FW from it, degrade the conversion efficienc as the two crstals are simpl pressed together to form the interface and an air gap between them is unavoidable. Using diffusion bonding [] or other direct bonding techniques, the interface of the two nonlinear materials ma be much smoothed and the NCR intensit can be further enhanced. Sample was used to repeat the eperiment. Compared with Sample 1, the o-polaried NCR was not enhanced because of the absence of d 11 in LN. However, an e-polaried SH can be observed if the incident angle α is smaller than 7 [Figs. 4(b)-4(e)]. This oo-e process occurs under anomalous-like dispersion conditions, considering the refractive inde of. When the SH wave vector k e k 1o sinα, the NCR condition is satisfied. The eperiment results and theoretical prediction are also in good agreement [Fig. 4(a)]. This phenomenon was not observed in Sample 1 or in single, because d 31 is much smaller than d 11 in and the d 13 of LN is ero. In an anomalous-like dispersion environment, the SH intensit ma be further enhanced b using other crstals with a high nonlinear coefficient. (a) Iinternal NCR angle ( ) 4 3 Simulation Sample 1 forbidden region Internal FW incident angle ( ) (b) α=8. α=69. (c) (d) α=67.7 (e) α=66. Fig. 4. (a) The internal NCR angle θ under anomalous dispersion versus the incident angle of FW α. (b)-(e) are the recorded patterns varing with the incident angle of FW. The advantage of this method is that another material can be used to enhance the nonlinear process in the crstal of interest, without changing its properties. For eample, in an LN crstal, light with wavelength below 38 nm is absorbed, but can be used to enhance ultraviolet SH generation in. Our scheme ma provide a new wa for practical applications to ultraviolet laser sources and efficient nonlinear processes. 4. Conclusion In summar, we demonstrated both theoreticall and eperimentall, that NCR generation can be enhanced at the nonlinear interface of two different nonlinear materials. The sharper the change in nonlinear coefficient, the higher the NCR intensit. Under normal dispersion conditions, the NCR generated at a -LN interface is enhanced b a factor in the range of 4 to 1, compared with that at the boundar of a single crstal. Under anomalous dispersion conditions, an oo-e tpe of NCR was observed as a result of the enhancement at the nonlinear interface. The added nonlinear material does not change the properties of the Cherenkov radiation, such as the emission angle. Acknowledgments This work was supported in part b the National Basic Research Program 973 of China under Grant No.11CB8811, the National Natural Science Foundation of China under Grant Nos , 61359, and , the Foundation for Development of Science and Technolog of Shanghai under Grant No. 13JC1483, the Innovative Foundation of Laser Fusion Research Center, and in part b the Presidential Foundation of the China Academ of Engineering Phsics (Grant No.1513). 16 OSA 13 Jun 16 Vol. 4, No. 1 DOI:1.1364/OE OPTICS EXPRESS 183