Research Progress on Photonic Quasicrystals

Abstract

Abstract: Quasicrystals have unique structures with long-range order without periodicity. Photonic quasicrystals have been widely studied because of their excellent ability to control electromagnetic waves and broad application prospects. Photonic quasicrystals not only have general characteristics such as complete bandgap, localization states, negative refraction and near-zero refractive index, but also have advantages in laser and nonlinear frequency conversion due to their unique rotational symmetry. In this paper, the development of photonic quasicrystals in recent years is briefly reviewed, and the main research directions of photonic quasicrystals are introduced from two aspects, theoretical researches, and application ones. At last, the future development trend of photonic quasicrystals is prospected.

Key words: photonic quasicrystal, complete bandgap, localization state, negative refraction, photonic quasicrystal laser, nonlinear photonic quasicrystal

CLC Number:

O734

CHE Zhiyuan, SHI Lei. Research Progress on Photonic Quasicrystals[J]. Journal of Synthetic Crystals, 2021, 50(7): 1248-1258.

References

[1] SHECHTMAN D, BLECH I, GRATIAS D, et al. Metallic phase with long-range orientational order and no translational symmetry[J]. Physical Review Letters, 1984, 53(20): 1951-1953.
[2] 郭可信.五次对称性及Ti-Ni准晶相的发现与研究[J].物理,1989,18(6):344-346.
GUO K X. Discovery and study of quintic symmetry and Ti-Ni quasicrystal phase [J]. Physics, 1989, 18(6): 344-346(in Chinese).
[3] 马鹏辉,刘有延,邹南之,等.二维准晶顶角模型的电子性质[J].物理学报,1990,39(8):1282-1289.
MA P H, LIU Y Y, ZOU N Z, et al. The electronic properties of the vertex model for 2-dimension quasicrystals[J]. Acta Physica Sinica, 1990, 39(8): 1282-1289(in Chinese).
[4] 张富祥,禹日成,秦志成,等.落管中Al-Cu-Fe合金的形核与过冷[J].科学通报,1995,40(1):19-22.
ZHANG F X, YU R C, QIN Z C, et al. Nucleation and supercooling of Al-Cu-Fe alloy in drop tube [J]. Chinese Science Bulletin, 1995, 40(1): 19-22(in Chinese).
[5] 刘永长,杨根仓,刘新宝,等.激光熔凝Al₇₂Ni₁₂Co₁₆中十面体准晶的生长[J].科学通报,2000,45(4):444-447.
LIU Y C, YANG G C, LIU X B, et al. Growth of decahedral quasicrystals in Al₇₂Ni₁₂Co₁₆ by laser melting [J]. Chinese Science Bulletin, 2000, 45(4): 444-447(in Chinese).
[6] 李志强,徐洲,李小平,等.准晶材料的应用研究进展[J].材料导报,2002,16(2):9-11.
LI Z Q, XU Z, LI X P, et al. Progress in research on application of quasicrystalline materials[J]. Materials Review, 2002, 16(2): 9-11(in Chinese).
[7] 郑明毅,吴昆,乔晓光,等.镁系准晶与高性能镁合金[J].材料科学与工艺,2004,12(6):666-671.
ZHENG M Y, WU K, QIAO X G, et al. Quasicrystals containing magnesium and high performance magnesium alloys[J]. Material Science and Technology, 2004, 12(6): 666-671(in Chinese).
[8] 冯志芳,刘荣鹃,李志远.十二重准晶中的方向缺陷[J].物理学报,2009,58(3):1948-1953.
FENG Z F, LIU R J, LI Z Y. Directional defect modes in twelve-fold-symmetry quasicrystal[J]. Acta Physica Sinica, 2009, 58(3): 1948-1953(in Chinese).
[9] LEVINE D, STEINHARDT P J. Quasicrystals: a new class of ordered structures[J]. Physical Review Letters, 1984, 53(26): 2477-2480.
[10] DE BRUIJN N G. Algebraic theory of Penrose’s non-periodic tilings of the plane. I[J]. Indagationes Mathematicae (Proceedings), 1981, 84(1): 39-52.
[11] DUNEAU M, KATZ A. Quasiperiodic patterns[J]. Physical Review Letters, 1985, 54(25): 2688-2691.
[12] SOCOLAR J E S, STEINHARDT P J, LEVINE D. Quasicrystals with arbitrary orientational symmetry[J]. Physical Review B, 1985, 32(8): 5547-5550.
[13] TSUNETSUGU H, FUJIWARA T, UEDA K, et al. Electronic properties of the Penrose lattice. I. Energy spectrum and wave functions[J]. Physical Review B, 1991, 43(11): 8879-8891.
[14] GOLDMAN A I, KELTON R F. Quasicrystals and crystalline approximants[J]. Reviews of Modern Physics, 1993, 65(1): 213-230.
[15] JEONG H C, STEINHARDT P J. Cluster approach for quasicrystals[J]. Physical Review Letters, 1994, 73(14): 1943-1946.
[16] STEINHARDT P J, JEONG H C. A simpler approach to Penrose tiling with implications for quasicrystal formation[J]. Nature, 1996, 382(6590): 431-433.
[17] STEINHARDT P J, JEONG H C, SAITOH K, et al. Experimental verification of the quasi-unit-cell model of quasicrystal structure[J]. Nature, 1998, 396(6706): 55-57.
[18] YAN Y F, PENNYCOOK S J, TSAI A P. Direct imaging of local chemical disorder and columnar vacancies in ideal decagonal Al-Ni-co quasicrystal[J]. Physical Review Letters, 1998, 81(23): 5145-5148.
[19] BEN-ABRAHAM S I, GÄHLER F. Covering cluster description of octagonal MnSiAl quasicrystals[J]. Physical Review B, 1999, 60(2): 860-864.
[20] JOANNOPOULOS J D, JOHNSON S G, WINN J N, et al. Photonic crystals[M]. New Jersey: Princeton University Press, 2011.
[21] YABLONOVITCH E. Photonic band-gap structures[J]. Josa B, 1993, 10(2): 283-295.
[22] JOANNOPOULOS J D, VILLENEUVE P R, FAN S H. Photonic crystals: putting a new twist on light[J]. Nature, 1997, 386(6621): 143-149.
[23] KOHMOTO M, SUTHERLAND B, IGUCHI K. Localization of optics: quasiperiodic media[J]. Physical Review Letters, 1987, 58(23): 2436-2438.
[24] DAL NEGRO L, BORISKINA S V. Deterministic aperiodic nanostructures for photonics and plasmonics applications[J]. Laser & Photonics Reviews, 2012, 6(2): 178-218.
[25] VARDENY Z V, NAHATA A, AGRAWAL A. Optics of photonic quasicrystals[J]. Nature Photonics, 2013, 7(3): 177-187.
[26] JANOT C, PAUFLER P. Quasicrystals. A primer[M]. 2nd Ed. Oxford: Clarendon Press, 1994.
[27] LUBIN S M, HRYN A J, HUNTINGTON M D, et al. Quasiperiodic moiré plasmonic crystals[J]. ACS Nano, 2013, 7(12): 11035-11042.
[28] CHE Z Y, ZHANG Y B, LIU W Z, et al. Polarization singularities of photonic quasicrystals in momentum space[J]. Physical Review Letters, 2021, 127(4): 043901.
[29] CHAN Y S, CHAN C T, LIU Z Y. Photonic band gaps in two dimensional photonic quasicrystals[J]. Physical Review Letters, 1998, 80(5): 956-959.
[30] ZHANG X D, ZHANG Z Q, CHAN C T. Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals[J]. Physical Review B, 2001, 63(8): 081105.
[31] ZOOROB M E, CHARLTON M D B, PARKER G J, et al. Complete photonic bandgaps in 12-fold symmetric quasicrystals[J]. Nature, 2000, 404(6779): 740-743.
[32] RECHTSMAN M C, JEONG H C, CHAIKIN P M, et al. Optimized structures for photonic quasicrystals[J]. Physical Review Letters, 2008, 101(7): 073902.
[33] FLORESCU M, TORQUATO S, STEINHARDT P J. Complete band gaps in two-dimensional photonic quasicrystals[J]. Physical Review B, 2009, 80(15): 155112.
[34] JIA L, BITA I, THOMAS E L. Impact of geometry on the TM photonic band gaps of photonic crystals and quasicrystals[J]. Physical Review Letters, 2011, 107(19): 193901.
[35] MAN W N, MEGENS M, STEINHARDT P J, et al. Experimental measurement of the photonic properties of icosahedral quasicrystals[J]. Nature, 2005, 436(7053): 993-996.
[36] SCHWARTZ T, BARTAL G, FISHMAN S, et al. Transport and Anderson localization in disordered two-dimensional photonic lattices[J]. Nature, 2007, 446(7131): 52-55.
[37] LEVI L, RECHTSMAN M, FREEDMAN B, et al. Disorder-enhanced transport in photonic quasicrystals[J]. Science, 2011, 332(6037): 1541-1544.
[38] FUJIWARA T, YAMAMOTO S, TRAMBLY DE LAISSARDIÈRE G. Band structure effects of transport properties in icosahedral quasicrystals[J]. Physical Review Letters, 1993, 71(25): 4166-4169.
[39] WANG K. Light wave states in two-dimensional quasiperiodic media[J]. Physical Review B, 2006, 73(23): 235122.
[40] KANG W. Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study[J]. Physical Review B, 2007, 76(8): 085107.
[41] LIN C, STEINHARDT P J, TORQUATO S. Light localization in local isomorphism classes of quasicrystals[J]. Physical Review Letters, 2018, 120(24): 247401.
[42] JEON S Y, KWON H, HUR K. Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal[J]. Nature Physics, 2017, 13(4): 363-368.
[43] FENG Z F, ZHANG X D, WANG Y Q, et al. Negative refraction and imaging using 12-fold-symmetry quasicrystals[J]. Physical Review Letters, 2005, 94(24): 247402.
[44] DONG J W, CHANG M L, HUANG X Q, et al. Conical dispersion and effective zero refractive index in photonic quasicrystals[J]. Physical Review Letters, 2015, 114(16): 163901.
[45] NOTOMI M, SUZUKI H, TAMAMURA T, et al. Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice[J]. Physical Review Letters, 2004, 92(12): 123906.
[46] MAHLER L, TREDICUCCI A, BELTRAM F, et al. Quasi-periodic distributed feedback laser[J]. Nature Photonics, 2010, 4(3): 165-169.
[47] NOZAKI K, BABA T. Quasiperiodic photonic crystal microcavity lasers[J]. Applied Physics Letters, 2004, 84(24): 4875-4877.
[48] KIM S K, LEE J H, KIM S H, et al. Photonic quasicrystal single-cell cavity mode[J]. Applied Physics Letters, 2005, 86(3): 031101.
[49] ZHU S N, ZHU Y Y, MING N B. Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice[J]. Science, 1997, 278(5339): 843-846.
[50] ZHU S N, ZHU Y Y, QIN Y Q, et al. Experimental realization of second harmonic generation in a fibonacci optical superlattice of LiTaO₃[J]. Physical Review Letters, 1997, 78(14): 2752-2755.
[51] CLAUSEN C B, KIVSHAR Y S, BANG O, et al. Quasiperiodic envelope solitons[J]. Physical Review Letters, 1999, 83(23): 4740-4743.
[52] LIFSHITZ R, ARIE A, BAHABAD A. Photonic quasicrystals for nonlinear optical frequency conversion[J]. Physical Review Letters, 2005, 95(13): 133901.
[53] FREEDMAN B, BARTAL G, SEGEV M, et al. Wave and defect dynamics in nonlinear photonic quasicrystals[J]. Nature, 2006, 440(7088): 1166-1169.
[54] FREEDMAN B, LIFSHITZ R, FLEISCHER J W, et al. Phason dynamics in nonlinear photonic quasicrystals[J]. Nature Materials, 2007, 6(10): 776-781.