1. College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China 2. Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT, Nanjing 211106, China 3. Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China 4. National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, and School of Physics, Nanjing University, Nanjing 210093, China
Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.
M. Bender C. , Boettcher S. . Real spectra in Non-Hermitian Hamiltonians Having PT symmetry. Phys. Rev. Lett., 1998, 80( 24): 5243 https://doi.org/10.1103/PhysRevLett.80.5243
2
Y. Sun G. , C. Tang J. , P. Kou S. . Biorthogonal quantum criticality in non-Hermitian many-body systems. Front. Phys., 2022, 17( 3): 33502 https://doi.org/10.1007/s11467-021-1126-1
3
El-Ganainy R. , G. Makris K. , Khajavikhan M. , H. Musslimani Z. , Rotter S. , N. Christodoulides D. . Non-Hermitian physics and PT symmetry. Nat. Phys., 2018, 14( 1): 11 https://doi.org/10.1038/nphys4323
Guo A. , J. Salamo G. , Duchesne D. , Morandotti R. , Volatier-Ravat M. , Aimez V. , A. Siviloglou G. , N. Christodoulides D. . Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 2009, 103( 9): 093902 https://doi.org/10.1103/PhysRevLett.103.093902
6
Fu Y. , Xu Y. , Chen H. . Zero index metamaterials with PT symmetry in a waveguide system. Opt. Express, 2016, 24( 2): 1648 https://doi.org/10.1364/OE.24.001648
7
Laha A. , Dey S. , K. Gandhi H. , Biswas A. , Ghosh S. . Exceptional point and toward mode-selective optical isolation. ACS Photonics, 2020, 7( 4): 967 https://doi.org/10.1021/acsphotonics.9b01646
8
Hodaei H. , A. Miri M. , Heinrich M. , N. Christodoulides D. , Khajavikhan M. . Parity−time-symmetric microring lasers. Science, 2014, 346( 6212): 975 https://doi.org/10.1126/science.1258480
9
Peng B. , K. Ozdemir S. , Liertzer M. , J. Chen W. , Kramer J. , Yilmaz H. , Wiersig J. , Rotter S. , Yang L. . Chiral modes and directional lasing at exceptional points. Proc. Natl. Acad. Sci. USA, 2016, 113( 25): 6845 https://doi.org/10.1073/pnas.1603318113
10
Zhang N. , Y. Gu Z. , Y. Wang K. , Li M. , Ge L. , M. Xiao S. , H. Song Q. . Quasiparity−time symmetric microdisk laser. Laser Photonics Rev., 2017, 11( 5): 1700052 https://doi.org/10.1002/lpor.201700052
11
Chang L. , S. Jiang X. , Y. Hua S. , Yang C. , M. Wen J. , Jiang L. , Y. Li G. , Z. Wang G. , Xiao M. . Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators. Nat. Photonics, 2014, 8( 7): 524 https://doi.org/10.1038/nphoton.2014.133
12
Peng B. , K. Ozdemir S. , C. Lei F. , Monifi F. , Gianfreda M. , L. Long G. , H. Fan S. , Nori F. , M. Bender C. , Yang L. . Parity–time-symmetric whispering-gallery microcavities. Nat. Phys., 2014, 10( 5): 394 https://doi.org/10.1038/nphys2927
13
D. Chen C. , N. Zhao L. . The effect of thermal-induced noise on doubly-coupled-ring optical gyroscope sensor around exceptional point. Opt. Commun., 2020, 474 : 126108 https://doi.org/10.1016/j.optcom.2020.126108
14
D. Chen C. , J. Xie Y. , W. Huang S. . Nanophotonic optical gyroscope with sensitivity enhancement around “mirrored” exceptional points. Opt. Commun., 2021, 483 : 126674 https://doi.org/10.1016/j.optcom.2020.126674
15
Chen M. , F. Li Z. , Tong X. , D. Wang X. , H. Yang F. . Manipulating the critical gain level of spectral singularity in active hybridized metamaterials. Opt. Express, 2020, 28( 12): 17966 https://doi.org/10.1364/OE.393429
16
Liang Y. , Gaimard Q. , Klimov V. , Uskov A. , Benisty H. , Ramdane A. , Lupu A. . Coupling of nanoantennas in loss-gain environment for application in active tunable metasurfaces. Phys. Rev. B, 2021, 103( 4): 045419 https://doi.org/10.1103/PhysRevB.103.045419
17
Cao Y. , Fu Y. , Zhou Q. , Xu Y. , Gao L. , Chen H. . Giant Goos−Hänchen shift induced by bounded states in opticalPT-symmetric bilayer structures. Opt. Express, 2019, 27( 6): 7857 https://doi.org/10.1364/OE.27.007857
18
Fu Y. , Fei Y. , Dong D. , Liu Y. . Photonic spin Hall effect in PT symmetric metamaterials. Front. Phys., 2019, 14( 6): 62601 https://doi.org/10.1007/s11467-019-0938-8
19
Feng L. , El-Ganainy R. , Ge L. . Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics, 2017, 11( 12): 752 https://doi.org/10.1038/s41566-017-0031-1
20
Greenberg M. , Orenstein M. . Irreversible coupling by use of dissipative optics. Opt. Lett., 2004, 29( 5): 451 https://doi.org/10.1364/OL.29.000451
21
Feng L. , Ayache M. , Q. Huang J. , L. Xu Y. , H. Lu M. , F. Chen Y. , Fainman Y. , Scherer A. . Nonreciprocal light propagation in a silicon photonic circuit. Science, 2011, 333( 6043): 729 https://doi.org/10.1126/science.1206038
22
N. Ghosh S. , D. Chong Y. . Exceptional points and asymmetric mode conversion in quasi-guided dual-mode optical waveguides. Sci. Rep., 2016, 6( 1): 19837 https://doi.org/10.1038/srep19837
23
Chatzidimitriou D. , Pitilakis A. , Yioultsis T. , E. Kriezis E. . Breaking reciprocity in a non-Hermitian photonic coupler with saturable absorption. Phys. Rev. A, 2021, 103( 5): 053503 https://doi.org/10.1103/PhysRevA.103.053503
24
Pitilakis A. , Chatzidimitriou D. , V. Yioultsis T. , E. Kriezis E. . Asymmetric Si-slot coupler with nonreciprocal response based on graphene saturable absorption. IEEE J. Quantum Electron., 2021, 57( 3): 8400210 https://doi.org/10.1109/JQE.2021.3071247
25
Lin Z. , Ramezani H. , Eichelkraut T. , Kottos T. , Cao H. , N. Christodoulides D. . Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett., 2011, 106( 21): 213901 https://doi.org/10.1103/PhysRevLett.106.213901
26
Feng L. , L. Xu Y. , S. Fegadolli W. , H. Lu M. , E. B. Oliveira J. , R. Almeida V. , F. Chen Y. , Scherer A. . Experimental demonstration of a unidirectional reflectionless parity−time metamaterial at optical frequencies. Nat. Mater., 2013, 12( 2): 108 https://doi.org/10.1038/nmat3495
27
F. Jia Y. , X. Yan Y. , V. Kesava S. , D. Gomez E. , C. Giebink N. . Passive parity−time symmetry in organic thin film waveguides. ACS Photonics, 2015, 2( 2): 319 https://doi.org/10.1021/ph500459j
28
Y. Zhu X. , L. Xu Y. , Zou Y. , C. Sun X. , He C. , H. Lu M. , P. Liu X. , F. Chen Y. . Asymmetric diffraction based on a passive parity−time grating. Appl. Phys. Lett., 2016, 109( 11): 111101 https://doi.org/10.1063/1.4962639
29
Zhao H. , S. Fegadolli W. , K. Yu J. , F. Zhang Z. , Ge L. , Scherer A. , Feng L. . Metawaveguide for asymmetric interferometric light−light switching. Phys. Rev. Lett., 2016, 117( 19): 193901 https://doi.org/10.1103/PhysRevLett.117.193901
30
Wang W. , Q. Wang L. , D. Xue R. , L. Chen H. , P. Guo R. , M. Liu Y. , Chen J. . Unidirectional excitation of radiative-loss-free surface plasmon polaritons in PT-symmetric systems. Phys. Rev. Lett., 2017, 119( 7): 077401 https://doi.org/10.1103/PhysRevLett.119.077401
31
Y. Fu Y. , D. Xu Y. , Y. Chen H. . Negative refraction based on purely imaginary metamaterials. Front. Phys., 2018, 13( 4): 134206 https://doi.org/10.1007/s11467-018-0781-3
32
Chang L. , F. Li Y. , Volet N. , Wang L. , Peters J. , E. Bowers J. . Thin film wavelength converters for photonic integrated circuits. Optica, 2016, 3( 5): 531 https://doi.org/10.1364/OPTICA.3.000531
33
Jankowski M. , Langrock C. , Desiatov B. , Marandi A. , Wang C. , Zhang M. , R. Phillips C. , Loncar M. , M. Fejer M. . Ultrabroadband nonlinear optics in nanophotonic periodically poled lithium niobate waveguides. Optica, 2020, 7( 1): 40 https://doi.org/10.1364/OPTICA.7.000040
34
H. Sun D. , W. Zhang Y. , Z. Wang D. , Song W. , Y. Liu X. , B. Pang J. , Q. Geng D. , H. Sang Y. , Liu H. . Microstructure and domain engineering of lithium niobate crystal films for integrated photonic applications. Light Sci. Appl., 2020, 9( 1): 197 https://doi.org/10.1038/s41377-020-00434-0
35
Luo R. , He Y. , X. Liang H. , X. Li M. , Lin Q. . Highly tunable efficient second-harmonic generation in a lithium niobate nanophotonic waveguide. Optica, 2018, 5( 8): 1006 https://doi.org/10.1364/OPTICA.5.001006
36
Wang C. , Y. Li Z. , H. Kim M. , Xiong X. , F. Ren X. , C. Guo G. , F. Yu N. , Loncar M. . Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides. Nat. Commun., 2017, 8( 1): 2098 https://doi.org/10.1038/s41467-017-02189-6
37
Rose A. , Huang D. , R. Smith D. . Controlling the second harmonic in a phase-matched negative-index metamaterial. Phys. Rev. Lett., 2011, 107( 6): 063902 https://doi.org/10.1103/PhysRevLett.107.063902
38
Rose A. , R. Smith D. . Overcoming phase mismatch in nonlinear metamaterials. Opt. Mater. Express, 2011, 1( 7): 1232 https://doi.org/10.1364/OME.1.001232
39
Suchowski H. , O’Brien K. , J. Wong Z. , Salandrino A. , Yin X. , Zhang X. . Phase mismatch–free nonlinear propagation in optical zero-index materials. Science, 2013, 342( 6163): 1223 https://doi.org/10.1126/science.1244303
