Asymmetric nonlinear-mode-conversion in an optical waveguide with<i>PT</i> symmetry

doi:10.1007/s11467-022-1177-y

Front. Phys.

2022, Vol. 17

Issue (5) : 52504 https://doi.org/10.1007/s11467-022-1177-y

RESEARCH ARTICLE

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Changdong Chen^1,²(

), Youwen Liu^1,², Lina Zhao³, Xiaopeng Hu⁴, Yangyang Fu^1,²(

)

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

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Abstract

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.

Keywords nonlinear mode conversion meta-grating PT symmetry optical waveguide

Corresponding Author(s): Changdong Chen,Yangyang Fu

Issue Date: 30 June 2022

Cite this article:

Changdong Chen,Youwen Liu,Lina Zhao, et al. Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry[J]. Front. Phys. , 2022, 17(5): 52504.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1177-y
https://academic.hep.com.cn/fop/EN/Y2022/V17/I5/52504

Fig.1 (a) The schematic configuration of asymmetric NMC. Active and passive modulations taking a period of

Λ

, with

Δ ? (y) = c o s (q y) + i s i n (q y)

, are applied on the LN waveguide layer with a thickness of d= 1.01 μm, giving rise to a one-way wave-vector

q

along y direction. (b) The mode dispersions in LN waveguide for FW (from 0.8 μm to 1.6 μm) and the corresponding SH. There is only one intersection at about 1.064 μm that is a probable FW wavelength to realize phase-matched frequency-doubling process. (c) Forward and backward phase-matching conditions induced by PT symmetry for

T M 2 2 ω

mode in the dispersion diagram of SH. (d) The sketch map of entire process of the asymmetric NMC only for forward-propagation, can two FW photons (0^th order mode) be transformed into one SH photon (0^th order mode) via the coupling between the interactions resulting from nonlinearity and PT symmetry.

Fig.2 The dependences of nonlinear mode conversion on propagation distance without PT-symmetry modulation. (a)

T M 0 ω

mode of FW. (b)

T M 0 2 ω

mode of SH. (c)

T M 2 2 ω

mode of SH.

Fig.3 Asymmetric mode conversion with nonlinearity and PT-symmetry modulation together. The mode intensities, respectively for

T M 0 ω

mode of FW,

T M 0 2 ω

mode of SH and

T M 2 2 ω

mode of SH, vary with the change of propagation distance under the situations of forward-propagation (a?c) and backward-propagation (d?f).

Fig.4 The excited

T M 0 2 ω

mode intensity changes with the variation of the modulation depth of PT-symmetry. The insets illustrate the mode intensities that can be eventually generated with distinct modulation depth

Δ ξ = 0,

Δ ξ = 0.25

and

Δ ξ = 0.45

Fig.5 Asymmetric NMC in a purely passive system respectively for the forward (a, b) and backward (c, d) propagations.

1	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
4	A. Miri M. , Alu A. . Exceptional points in optics and photonics. Science, 2019, 363( 6422): eaar7709 https://doi.org/10.1126/science.aar7709
5	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

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