Efficient high harmonic generation in nonlinear photonic moiré superlattice
Tingyin Ning, Yingying Ren, Yanyan Huo, Yangjian Cai
Efficient high harmonic generation in nonlinear photonic moiré superlattice
Photonic moiré superlattice as an emerging platform of flatbands can tightly confine the light inside the cavity and has important applications not only in linear optics but also in nonlinear optics. In this paper, we numerically investigate the third- and fifth-order harmonic generation (THG and FHG) in photonic moiré superlattices fabricated by the nonlinear material silicon. The high conversion efficiency of THG and FHG is obtained at a relatively low intensity of fundamental light, e.g., the maximum conversion efficiency of THG and FHG arrives even up to be 10−2 and 10−9 at the fundamental intensity of 30 kW/m2, respectively, in the moiré superlattice of near flat band formed by the twist angle 6.01°. The results indicate the photonic moiré superlattice of a high-quality factor and flatbands is a promising platform for efficient nonlinear processes and advanced photonic devices.
moiré superlattice / resonant mode / harmonic generation
[1] |
R.W. Boyd, Nonlinear Optics, 3rd Ed., Elsevier, Academic Press, 2008
|
[2] |
P. A. Franken , A. E. Hill , C. W. Peters , G. Weinreich . Generation of optical harmonics. Phys. Rev. Lett., 1961, 7(4): 118
CrossRef
ADS
Google scholar
|
[3] |
M. Kauranen , A. V. Zayats . Nonlinear plasmonics. Nat. Photonics, 2012, 6(11): 737
CrossRef
ADS
Google scholar
|
[4] |
Y. Kivshar . All-dielectric meta-optics and non-linear nanophotonics. Natl. Sci. Rev., 2018, 5(2): 144
CrossRef
ADS
Google scholar
|
[5] |
B. Sain , C. Meier , T. Zentgraf . Nonlinear optics in all-dielectric nanoantennas and metasurfaces: A review. Adv. Photonics, 2019, 1(2): 024002
CrossRef
ADS
Google scholar
|
[6] |
C. K. Chen , A. R. B. de Castro , Y. R. Shen . Surface-enhanced second-harmonic. Phys. Rev. Lett., 1981, 46(2): 145
CrossRef
ADS
Google scholar
|
[7] |
M. W. Klein , C. Enkrich , M. Wegener , S. Linden . Second harmonic generation from magnetic metamaterials. Science, 2006, 313(5786): 502
CrossRef
ADS
Google scholar
|
[8] |
M. Celebrano , X. Wu , M. Baselli , S. Großmann , P. Biagioni , A. Locatelli , C. De Angelis , G. Cerullo , R. Osellame , B. Hecht , L. Duò , F. Ciccacci , M. Finazzi . Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation. Nat. Nanotechnol., 2015, 10(5): 412
CrossRef
ADS
Google scholar
|
[9] |
Y. Zhang , N. K. Grady , C. Ayala-Orozco , N. J. Halas . Three-dimensional nanostructures as highly efficient generators of second harmonic light. Nano Lett., 2011, 11(12): 5519
CrossRef
ADS
Google scholar
|
[10] |
A. Karnieli , Y. Li , A. Arie . The geometric phase in nonlinear frequency conversion. Front. Phys., 2022, 17(1): 12301
CrossRef
ADS
Google scholar
|
[11] |
P. P. Markowicz , H. Tiryaki , H. Pudavar , P. N. Prasad , N. N. Lepeshkin , R. W. Boyd . Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals. Phys. Rev. Lett., 2004, 92(8): 083903
CrossRef
ADS
Google scholar
|
[12] |
S. Diziain , R. Geiss , M. Zilk , F. Schrempel , E. B. Kley , A. Tünnermann , T. Pertsch . Second harmonic generation in free-standing lithium niobite photonic crystal L3 cavity. Appl. Phys. Lett., 2013, 103(5): 051117
CrossRef
ADS
Google scholar
|
[13] |
S. Yamada , B. S. Song , S. Jeon , J. Upham , Y. Tanaka , T. Asano , S. Noda . Second-harmonic generation in a silicon-carbide-based photonic crystal nanocavity. Opt. Lett., 2014, 39(7): 1768
CrossRef
ADS
Google scholar
|
[14] |
M. Siltanen , S. Leivo , P. Voima , M. Kauranen , P. Karvinen , P. Vahimaa , M. Kuittinen . Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating. Appl. Phys. Lett., 2007, 91(11): 111109
CrossRef
ADS
Google scholar
|
[15] |
T. Ning , H. Pietarinen , O. Hyvärinen , R. Kumar , T. Kaplas , M. Kauranen , G. Genty . Efficient second-harmonic generation in silicon nitride resonant waveguide gratings. Opt. Lett., 2012, 37(20): 4269
CrossRef
ADS
Google scholar
|
[16] |
G. Quaranta , G. Basset , O. J. F. Martin , B. Gallinet . Recent advances in resonant waveguide gratings. Laser Photonics Rev., 2018, 12(9): 1800017
CrossRef
ADS
Google scholar
|
[17] |
V. S. Ilchenko , A. A. Savchenkov , A. B. Matsko , L. Maleki . Nonlinear optics and crystalline whispering gallery mode cavities. Phys. Rev. Lett., 2004, 92(4): 043903
CrossRef
ADS
Google scholar
|
[18] |
J. S. Levy , M. A. Foster , A. L. Gaeta , M. Lipson . Harmonic generation in silicon nitride ring resonators. Opt. Express, 2011, 19(12): 11415
CrossRef
ADS
Google scholar
|
[19] |
Z. F. Bi , A. W. Rodriguez , H. Hashemi , D. Duchesne , M. Loncar , K. M. Wang , S. G. Johnson . High-efficiency second-harmonic generation in doubly-resonant (2) microring resonantors. Opt. Express, 2012, 20(7): 7526
CrossRef
ADS
Google scholar
|
[20] |
G. Li , S. Zhang , T. Zentgraf . Nonlinear photonic metasurfaces. Nat. Rev. Mater., 2017, 2(5): 17010
CrossRef
ADS
Google scholar
|
[21] |
A. Krasnok , M. Tymchenko , A. Alù . Nonliear metasurfaces: A paradigm shift in nonlinear optics. Mater. Today, 2018, 21(1): 8
CrossRef
ADS
Google scholar
|
[22] |
T. Huang , X. Zhao , S. Zeng , A. Crunteanu , P. P. Shum , N. Yu . Planar nonlinear metasurface optics and their applications. Rep. Prog. Phys., 2020, 83(12): 126101
CrossRef
ADS
Google scholar
|
[23] |
S. Liu , M. B. Sinclair , S. Saravi , G. A. Keeler , Y. Yang , J. Reno , G. M. Peake , F. Setzpfandt , I. Staude , T. Pertsch , I. Brener . Resonantly enhanced second-harmonic generation using III−V semiconductor all-dielectric metasurfaces. Nano Lett., 2016, 16(9): 5426
CrossRef
ADS
Google scholar
|
[24] |
D. Rocco , M. A. Vincenti , C. De Angelis . Boosting second harmonic radiation from AlGaAs nanoantennas with epsilon-near-zero materials. Appl. Sci. (Basel), 2018, 8(11): 2212
CrossRef
ADS
Google scholar
|
[25] |
Y. Yang , W. Wang , A. Boulesbaa , I. I. Kravchenko , D. P. Briggs , A. Puretzky , D. Geohegan , J. Valentine . Nonlinear Fano-resonant dielectric metasurfaces. Nano Lett., 2015, 15(11): 7388
CrossRef
ADS
Google scholar
|
[26] |
L. Xu , M. Rahmani , K. Z. Kamali , A. Lamprianidis , L. Ghirardini , J. Sautter , R. Camacho-Morales , H. Chen , M. Parry , I. Staude , G. Zhang , D. Neshev , A. E. Miroshnichenko . Boosting third-harmonic generation by a mirror-enhanced anapole resonator. Light Sci. Appl., 2018, 7(1): 44
|
[27] |
C. W. Hsu , B. Zhen , A. D. Stone , J. D. Joannopoulos , M. Soljacic . Bound states in the continuum. Nat. Rev. Mater., 2016, 1(9): 16048
CrossRef
ADS
Google scholar
|
[28] |
L. Kang , H. Bao , D. H. Werner . Efficient second-harmonic generation in high Q-factor asymmetric lithium niobite metasurfaces. Opt. Lett., 2021, 46(3): 633
CrossRef
ADS
Google scholar
|
[29] |
Z. Han , F. Ding , Y. Cai , U. Levy . Significantly enhanced second-harmonic generations with all-dielectric antenna array working in the quasi-bound states in the continuum and excited by linearly polarized plane waves. Nanophotonics, 2021, 10(3): 1189
CrossRef
ADS
Google scholar
|
[30] |
Z. Liu , Y. Xu , Y. Lin , J. Xiang , T. Feng , Q. Cao , J. Li , S. Lan , J. Liu . High-Q quasi-bound states in the continuum for nonlinear metasurfaces. Phys. Rev. Lett., 2019, 123(25): 253901
CrossRef
ADS
Google scholar
|
[31] |
L. Carletti , S. S. Kruk , A. A. Bogdanov , C. De Angelis , Y. Kivshar . High-harmonic generation at the nanoscale boosted by bound states in the continuum. Phys. Rev. Res., 2019, 1(2): 023016
CrossRef
ADS
Google scholar
|
[32] |
S. Xiao , M. Qin , J. Duan , F. Wu , T. Liu . Polarization-controlled dynamically switchable high-harmonic generation from all-dielectric metasurfaces governed by dual bound states in the continuum. Phys. Rev. B, 2022, 105(19): 195440
CrossRef
ADS
Google scholar
|
[33] |
S. Xiao , M. Qin , J. Duan , T. Liu . Robust enhancement of high-harmonic generation from all-dielectric metasurfaces enabled by polarization-insensitive bound states in the continuum. Opt. Express, 2022, 30(18): 32590
CrossRef
ADS
Google scholar
|
[34] |
G. Zograf , K. Koshelev , A. Zalogina , V. Korolev , R. Hollinger , D. Y. Choi , M. Zuerch , C. Spielmann , B. Luther-Davies , D. Kartashov , S. V. Makarov , S. S. Kruk , Y. Kivshar . High-harmonic generation from resonant dielectric metasurfaces empowered by bound states in the continuum. ACS Photonics, 2022, 9(2): 567
CrossRef
ADS
Google scholar
|
[35] |
Y. Cao , V. Fatemi , S. Fang , K. Watanabe , T. Taniguchi , E. Kaxiras , P. Jarillo-Herrero . Unconventional superconductivity in magic-angle graphene superlattices. Nature, 2018, 556(7699): 43
CrossRef
ADS
Google scholar
|
[36] |
Y. Cao , V. Fatemi , A. Demir , S. Fang , S. L. Tomarken , J. Y. Luo , J. D. Sanchez-Yamagishi , K. Watanabe , T. Taniguchi , E. Kaxiras , R. C. Ashoori , P. Jarillo-Herrero . Correlated insulator behavior at half-filling in magic-angle graphene superlattices. Nature, 2018, 556(7699): 80
CrossRef
ADS
Google scholar
|
[37] |
W. Zhang , D. Zou , Q. Pei , W. He , H. Sun , X. Zhang . Moiré circuits: Engineering magic-angle behavior. Phys. Rev. B, 2021, 104(20): L201408
CrossRef
ADS
Google scholar
|
[38] |
P. Wang , Y. Zheng , X. Chen , C. Huang , Y. Kartashov , L. Torner , V. Konotop , F. Ye . Localization and delocalization of light in photonic moiré lattices. Nature, 2020, 577(7788): 42
CrossRef
ADS
Google scholar
|
[39] |
Z. Chen , X. Liu , J. Zeng . Electromagnetically induced moiré optical lattices in a coherent atomic gas. Front. Phys., 2022, 17(4): 42508
CrossRef
ADS
Google scholar
|
[40] |
X. R. Mao , Z. K. Shao , H. Y. Luan , S. L. Wang , R. M. Ma . Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol., 2021, 16(10): 1099
CrossRef
ADS
Google scholar
|
[41] |
Z. Zhang , D. Liu , Y. Huo , T. Ning . Ultralow-level all-optical self-switching in a nanostructured moiré superlattice. Opt. Lett., 2022, 47(20): 5260
CrossRef
ADS
Google scholar
|
[42] |
H. Z. Zhang , H. Y. Qin , W. X. Zhang , L. Huang , X. D. Zhang . Moiré graphene nanoribbons: Nearly perfect absorptions and highly efficient reflections with wide angles. Opt. Express, 2022, 30(2): 2219
CrossRef
ADS
Google scholar
|
[43] |
P. Hong , L. Xu , C. Ying , M. Rahmani . Flatband mode in photonic moiré lattice for boosting second-harmonic generation with monolayer van der Waals crystals. Opt. Lett., 2022, 47(9): 2326
CrossRef
ADS
Google scholar
|
[44] |
S. Ha , N. H. Park , H. Kim , J. Shin , J. Choi , S. Park , J. Y. Moon , K. Chae , J. Jung , J. H. Lee , Y. Yoo , J. Y. Park , K. J. Ahn , D. I. Yeom . Enhanced third-harmonic generation by manipulating the twist angle of bilayer graphene. Light Sci. Appl., 2021, 10(1): 19
CrossRef
ADS
Google scholar
|
[45] |
F. Y. Yang , W. S. Song , F. H. Meng , F. C. Luo , S. Lou , S. R. Lin , Z. L. Gong , J. H. Cao , E. S. Barnard , E. Chan , L. Yang , J. Yao . Tunable second harmonic generation in twisted bilayer graphene. Matter, 2020, 3(4): 1361
CrossRef
ADS
Google scholar
|
[46] |
L. J. Du , Y. Y. Dai , Z. P. Sun . Twisting for tunable nonlinear optics. Matter, 2020, 3(4): 987
CrossRef
ADS
Google scholar
|
[47] |
T. Ning , X. Li , Y. Zhao , L. Yin , Y. Huo , L. Zhao , Q. Yue . Giant enhancement of harmonic generation in all-dielectric resonant waveguide gratings of quasi-bound states in the continuum. Opt. Express, 2020, 28(23): 34024
CrossRef
ADS
Google scholar
|
[48] |
K. Koshelev , Y. Tang , K. Li , D. Y. Choi , G. Li , Y. Kivshar . Nonlinear metasurfaces governed by bound states in the continuum. ACS Photonics, 2019, 6(7): 1639
CrossRef
ADS
Google scholar
|
[49] |
D. E. Aspnes , A. A. Studna , Dielectric functions , optical parameters of Si . InAs, and InSb from 1.5 to 6.0 eV. Phys. Rev. B, 1983, 27(2): 985
CrossRef
ADS
Google scholar
|
[50] |
C. Schinke , P. Christian Peest , J. Schmidt , R. Brendel , K. Bothe , M. R. Vogt , I. Kröger , S. Winter , A. Schirmacher , S. Lim , H. T. Nguyen , D. MacDonald . Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon. AIP Adv., 2015, 5(6): 067168
CrossRef
ADS
Google scholar
|
[51] |
L. Huang , W. Zhang , X. Zhang . Moiré quasibound states in the continuum. Phys. Rev. Lett., 2022, 128(25): 253901
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |