非线性光子晶体中的非线性衍射高阶次谐波
|
摘要
提出一种在非线性光子晶体中实现非线性衍射高阶次谐波的方案。基于观察到的多个锥形四次谐波,理论分析了实现五次谐波和六次谐波的可行性。当仅有一种激光光束入射到非线性光子晶体中时,可观察到红、绿和蓝锥形光的同时输出,这可为环形三基色、连续环形谐波以及环形白色光源的实现提供参考。其中,蓝色锥形光波可能源于有倒易矢量参与的级联五次非线性衍射谐波过程。同一基频波长下非线性切伦科夫五次谐波的辐射锥角均大于低阶次谐波的辐射角,且不同基频波长下的非线性切伦科夫五次谐波存在最小的辐射锥角。当入射基频波长为3319.5 nm时,五次谐波中e光的形成过程为非线性布拉格衍射,这可为六次非线性衍射谐波的产生提供有利条件。
A scheme for realizing high-order nonlinear diffraction harmonics in a nonlinear photonic crystal is described. Based on the multiple conical fourth-order harmonics observed, the feasibility of realizing the fifth-order and sixth-order harmonics via nonlinear diffraction is theoretically analyzed. The simultaneous generation of red, green, and blue conical harmonics is observed under only one input laser beam, which is beneficial to the realization of three primary colors, continuous harmonics and even ring white light sources. The blue conical output harmonics may be attributed to the cascaded nonlinear diffraction process of fifth-order harmonic involving the reciprocal vectors. Under the same fundamental wavelength, the conical angle of the fifth-order nonlinear ?erenkov harmonic is always larger than those of the other lower-order harmonics. Moreover, there always exists a minimum conical angle for the fifth-order nonlinear ?erenkov harmonics under different input wavelengths. When the input fundamental wavelength is 3319.5 nm, the generation process for the fifth-order harmonic e light is corresponding to nonlinear Bragg diffraction, which is helpful for the effective generation of a sixth-order nonlinear diffraction harmonic.
A scheme for realizing high-order nonlinear diffraction harmonics in a nonlinear photonic crystal is described. Based on the multiple conical fourth-order harmonics observed, the feasibility of realizing the fifth-order and sixth-order harmonics via nonlinear diffraction is theoretically analyzed. The simultaneous generation of red, green, and blue conical harmonics is observed under only one input laser beam, which is beneficial to the realization of three primary colors, continuous harmonics and even ring white light sources. The blue conical output harmonics may be attributed to the cascaded nonlinear diffraction process of fifth-order harmonic involving the reciprocal vectors. Under the same fundamental wavelength, the conical angle of the fifth-order nonlinear ?erenkov harmonic is always larger than those of the other lower-order harmonics. Moreover, there always exists a minimum conical angle for the fifth-order nonlinear ?erenkov harmonics under different input wavelengths. When the input fundamental wavelength is 3319.5 nm, the generation process for the fifth-order harmonic e light is corresponding to nonlinear Bragg diffraction, which is helpful for the effective generation of a sixth-order nonlinear diffraction harmonic.
引文
[1] Armstrong J A, Bloembergen N, Ducuing J, et al. Interactions between light waves in a nonlinear dielectric[J]. Physical Review, 1962, 127(6): 1918-1939.
[2] Fejer M M, Magel G A, Jundt D H, et al. Quasi-phase-matched second harmonic generation: tuning and tolerances[J]. IEEE Journal of Quantum Electronics, 1992, 28(11): 2631-2654.
[3] Yamamoto K, Mizuuchi K, Kitaoka Y, et al. Highly efficient quasi-phase-matched second-harmonic generation by frequency doubling of a high-frequency superimposed laser diode[J]. Optics Letters, 1995, 20(3): 273-275.
[4] Zhu S N, Zhu Y Y, Yang Z J, et al. Second-harmonic generation of blue light in bulk periodically poled LiTaO3[J]. Applied Physics Letters, 1995, 67(3): 320-322.
[5] Yoo S J B, Bhat R, Caneau C, et al. Quasi-phase-matched second-harmonic generation in AlGaAs waveguides with periodic domain inversion achieved by wafer-bonding[J]. Applied Physics Letters, 1995, 66(25): 3410-3412.
[6] Paul A, Bartels R A, Tobey R, et al. Quasi-phase-matched generation of coherent extreme-ultraviolet light[J]. Nature, 2003, 421(6918): 51-54.
[7] Gu B Y, Dong B Z, Zhang Y, et al. Enhanced harmonic generation in aperiodic optical superlattices[J]. Applied Physics Letters, 1999, 75(15): 2175-2177.
[8] Uesu Y, Yokota H, Kawado S, et al. Three-dimensional observations of periodically poled domains in a LiTaO3 quasiphase matching crystal by second harmonic generation tomography[J]. Applied Physics Letters, 2007, 91(18): 182904.
[9] Ni P G, Ma B Q, Wang X H, et al. Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching[J]. Applied Physics Letters, 2003, 82(24): 4230-4232.
[10] Ma B Q, Wang T, Sheng Y, et al. Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice[J]. Applied Physics Letters, 2005, 87(25): 251103.
[11] Chen B Q, Ren M L, Liu R J, et al. Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals[J]. Light: Science & Applications, 2014, 3(7): e189.
[12] Park H, Camper A, Kafka K, et al. High-order harmonic generations in intense MIR fields by cascade three-wave mixing in a fractal-poled LiNbO3 photonic crystal[J]. Optics Letters, 2017, 42(19): 4020-4023.
[13] Zhang Y, Qi Z, Wang W, et al. Quasi-phase-matched ?erenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide[J]. Applied Physics Letters, 2006, 89(17): 171113.
[14] Saltiel S M, Neshev D N, Fischer R, et al. Generation of second-harmonic conical waves via nonlinear Bragg diffraction[J]. Physical Review Letters, 2008, 100(10): 103902.
[15] Saltiel S M, Neshev D N, Fischer R, et al. Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures[J]. Japanese Journal of Applied Physics, 2008, 47(8): 6777-6783.
[16] Saltiel S M, Neshev D N, Krolikowski W, et al. Multiorder nonlinear diffraction in frequency doubling processes[J]. Optics Letters, 2009, 34(6): 848-850.
[17] Saltiel S M, Sheng Y, Voloch-Bloch N, et al. ?erenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures[J]. IEEE Journal of Quantum Electronics, 2009, 45(11): 1465-1472.
[18] Saltiel S M, Neshev D N, Krolikowski W, et al. Nonlinear diffraction from a virtual beam[J]. Physical Review Letters, 2010, 104(8): 083902.
[19] Sheng Y, Saltiel S M, Krolikowski W, et al. ?erenkov-type second-harmonic generation with fundamental beams of different polarizations[J]. Optics Letters, 2010, 35(9): 1317-1319.
[20] Wang W J, Sheng Y, Kong Y F, et al. Multiple ?erenkov second-harmonic waves in a two-dimensional nonlinear photonic structure[J]. Optics Letters, 2010, 35(22): 3790-3792.
[21] Shapira A, Arie A. Phase-matched nonlinear diffraction[J]. Optics Letters, 2011, 36(10): 1933-1935.
[22] Sheng Y, Wang W J, Shiloh R, et al. ?erenkov third-harmonic generation in χ(2) nonlinear photonic crystal[J]. Applied Physics Letters, 2011, 98(24): 241114.
[23] Sheng Y, Roppo V, Kong Q, et al. Tailoring ?erenkov second-harmonic generation in bulk nonlinear photonic crystal[J]. Optics Letters, 2011, 36(13): 2593-2595.
[24] Sheng Y, Wang W J, Shiloh R, et al. Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal[J]. Optics Letters, 2011, 36(16): 3266-3268.
[25] Kalinowski K, Kong Q, Roppo V, et al. Wavelength and position tuning of ?erenkov second-harmonic generation in optical superlattice[J]. Applied Physics Letters, 2011, 99(18): 181128.
[26] Wang W J, Sheng Y, Roppo V, et al. Enhancement of nonlinear Raman-Nath diffraction in two-dimensional optical superlattice[J]. Optics Express, 2013, 21(16): 18671-18679.
[27] Roppo V, Kalinowski K, Sheng Y, et al. Unified approach to ?erenkov second harmonic generation[J]. Optics Express, 2013, 21(22): 25715-25726.
[28] Karpinski P, Chen X, Shvedov V, et al. Nonlinear diffraction in orientation-patterned semiconductors[J]. Optics Express, 2015, 23(11): 14903-14912.
[29] Zhang Y, Gao Z D, Qi Z, et al. Nonlinear ?erenkov radiation in nonlinear photonic crystal waveguides[J]. Physical Review Letters, 2008, 100(16): 163904.
[30] Chen C D, Lu J, Liu Y H, et al. ?erenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide[J]. Optics Letters, 2011, 36(7): 1227-1229.
[31] Huang H, Huang C P, Zhang C, et al. Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear ?erenkov radiation[J]. Applied Physics Letters, 2012, 100(2): 022905.
[32] Li H X, Mu S Y, Xu P, et al. Multicolor ?erenkov conical beams generation by cascaded-χ(2) processes in radially poled nonlinear photonic crystals[J]. Applied Physics Letters, 2012, 100(10): 101101.
[33] Ren H J, Deng X W, Zheng Y L, et al. Nonlinear ?erenkov radiation in an anomalous dispersive medium[J]. Physical Review Letters, 2012, 108(22): 223901.
[34] An N, Zheng Y L, Ren H J, et al. Conical second harmonic generation in one-dimension nonlinear photonic crystal[J]. Applied Physics Letters, 2013, 102(20): 201112.
[35] Ren H J, Deng X W, Zheng Y L, et al. Enhanced nonlinear ?erenkov radiation on the crystal boundary[J]. Optics Letters, 2013, 38(11): 1993-1995.
[36] Ma B Q, Kafka K, Chowdhury A E. Fourth-harmonic generation via nonlinear diffraction in a 2D LiNbO3 nonlinear photonic crystal from mid-IR ultrashort pulses[J]. Chinese Optics Letters, 2017, 15(5): 051901.
[37] Ma B Q, Tian S H, Wang Y. Quasi-phase matching and ?erenkov radiation harmonics in nonlinear photonic crystals with fractal superlattices[J]. Chinese Journal of Lasers, 2016, 43(2): 0202007. 马博琴, 田少华, 王也. 分形超晶格非线性光子晶体中的准相位匹配和切伦科夫辐射谐频[J]. 中国激光, 2016, 43(2): 0202007.
[2] Fejer M M, Magel G A, Jundt D H, et al. Quasi-phase-matched second harmonic generation: tuning and tolerances[J]. IEEE Journal of Quantum Electronics, 1992, 28(11): 2631-2654.
[3] Yamamoto K, Mizuuchi K, Kitaoka Y, et al. Highly efficient quasi-phase-matched second-harmonic generation by frequency doubling of a high-frequency superimposed laser diode[J]. Optics Letters, 1995, 20(3): 273-275.
[4] Zhu S N, Zhu Y Y, Yang Z J, et al. Second-harmonic generation of blue light in bulk periodically poled LiTaO3[J]. Applied Physics Letters, 1995, 67(3): 320-322.
[5] Yoo S J B, Bhat R, Caneau C, et al. Quasi-phase-matched second-harmonic generation in AlGaAs waveguides with periodic domain inversion achieved by wafer-bonding[J]. Applied Physics Letters, 1995, 66(25): 3410-3412.
[6] Paul A, Bartels R A, Tobey R, et al. Quasi-phase-matched generation of coherent extreme-ultraviolet light[J]. Nature, 2003, 421(6918): 51-54.
[7] Gu B Y, Dong B Z, Zhang Y, et al. Enhanced harmonic generation in aperiodic optical superlattices[J]. Applied Physics Letters, 1999, 75(15): 2175-2177.
[8] Uesu Y, Yokota H, Kawado S, et al. Three-dimensional observations of periodically poled domains in a LiTaO3 quasiphase matching crystal by second harmonic generation tomography[J]. Applied Physics Letters, 2007, 91(18): 182904.
[9] Ni P G, Ma B Q, Wang X H, et al. Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching[J]. Applied Physics Letters, 2003, 82(24): 4230-4232.
[10] Ma B Q, Wang T, Sheng Y, et al. Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice[J]. Applied Physics Letters, 2005, 87(25): 251103.
[11] Chen B Q, Ren M L, Liu R J, et al. Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals[J]. Light: Science & Applications, 2014, 3(7): e189.
[12] Park H, Camper A, Kafka K, et al. High-order harmonic generations in intense MIR fields by cascade three-wave mixing in a fractal-poled LiNbO3 photonic crystal[J]. Optics Letters, 2017, 42(19): 4020-4023.
[13] Zhang Y, Qi Z, Wang W, et al. Quasi-phase-matched ?erenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide[J]. Applied Physics Letters, 2006, 89(17): 171113.
[14] Saltiel S M, Neshev D N, Fischer R, et al. Generation of second-harmonic conical waves via nonlinear Bragg diffraction[J]. Physical Review Letters, 2008, 100(10): 103902.
[15] Saltiel S M, Neshev D N, Fischer R, et al. Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures[J]. Japanese Journal of Applied Physics, 2008, 47(8): 6777-6783.
[16] Saltiel S M, Neshev D N, Krolikowski W, et al. Multiorder nonlinear diffraction in frequency doubling processes[J]. Optics Letters, 2009, 34(6): 848-850.
[17] Saltiel S M, Sheng Y, Voloch-Bloch N, et al. ?erenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures[J]. IEEE Journal of Quantum Electronics, 2009, 45(11): 1465-1472.
[18] Saltiel S M, Neshev D N, Krolikowski W, et al. Nonlinear diffraction from a virtual beam[J]. Physical Review Letters, 2010, 104(8): 083902.
[19] Sheng Y, Saltiel S M, Krolikowski W, et al. ?erenkov-type second-harmonic generation with fundamental beams of different polarizations[J]. Optics Letters, 2010, 35(9): 1317-1319.
[20] Wang W J, Sheng Y, Kong Y F, et al. Multiple ?erenkov second-harmonic waves in a two-dimensional nonlinear photonic structure[J]. Optics Letters, 2010, 35(22): 3790-3792.
[21] Shapira A, Arie A. Phase-matched nonlinear diffraction[J]. Optics Letters, 2011, 36(10): 1933-1935.
[22] Sheng Y, Wang W J, Shiloh R, et al. ?erenkov third-harmonic generation in χ(2) nonlinear photonic crystal[J]. Applied Physics Letters, 2011, 98(24): 241114.
[23] Sheng Y, Roppo V, Kong Q, et al. Tailoring ?erenkov second-harmonic generation in bulk nonlinear photonic crystal[J]. Optics Letters, 2011, 36(13): 2593-2595.
[24] Sheng Y, Wang W J, Shiloh R, et al. Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal[J]. Optics Letters, 2011, 36(16): 3266-3268.
[25] Kalinowski K, Kong Q, Roppo V, et al. Wavelength and position tuning of ?erenkov second-harmonic generation in optical superlattice[J]. Applied Physics Letters, 2011, 99(18): 181128.
[26] Wang W J, Sheng Y, Roppo V, et al. Enhancement of nonlinear Raman-Nath diffraction in two-dimensional optical superlattice[J]. Optics Express, 2013, 21(16): 18671-18679.
[27] Roppo V, Kalinowski K, Sheng Y, et al. Unified approach to ?erenkov second harmonic generation[J]. Optics Express, 2013, 21(22): 25715-25726.
[28] Karpinski P, Chen X, Shvedov V, et al. Nonlinear diffraction in orientation-patterned semiconductors[J]. Optics Express, 2015, 23(11): 14903-14912.
[29] Zhang Y, Gao Z D, Qi Z, et al. Nonlinear ?erenkov radiation in nonlinear photonic crystal waveguides[J]. Physical Review Letters, 2008, 100(16): 163904.
[30] Chen C D, Lu J, Liu Y H, et al. ?erenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide[J]. Optics Letters, 2011, 36(7): 1227-1229.
[31] Huang H, Huang C P, Zhang C, et al. Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear ?erenkov radiation[J]. Applied Physics Letters, 2012, 100(2): 022905.
[32] Li H X, Mu S Y, Xu P, et al. Multicolor ?erenkov conical beams generation by cascaded-χ(2) processes in radially poled nonlinear photonic crystals[J]. Applied Physics Letters, 2012, 100(10): 101101.
[33] Ren H J, Deng X W, Zheng Y L, et al. Nonlinear ?erenkov radiation in an anomalous dispersive medium[J]. Physical Review Letters, 2012, 108(22): 223901.
[34] An N, Zheng Y L, Ren H J, et al. Conical second harmonic generation in one-dimension nonlinear photonic crystal[J]. Applied Physics Letters, 2013, 102(20): 201112.
[35] Ren H J, Deng X W, Zheng Y L, et al. Enhanced nonlinear ?erenkov radiation on the crystal boundary[J]. Optics Letters, 2013, 38(11): 1993-1995.
[36] Ma B Q, Kafka K, Chowdhury A E. Fourth-harmonic generation via nonlinear diffraction in a 2D LiNbO3 nonlinear photonic crystal from mid-IR ultrashort pulses[J]. Chinese Optics Letters, 2017, 15(5): 051901.
[37] Ma B Q, Tian S H, Wang Y. Quasi-phase matching and ?erenkov radiation harmonics in nonlinear photonic crystals with fractal superlattices[J]. Chinese Journal of Lasers, 2016, 43(2): 0202007. 马博琴, 田少华, 王也. 分形超晶格非线性光子晶体中的准相位匹配和切伦科夫辐射谐频[J]. 中国激光, 2016, 43(2): 0202007.