Abstract

Whispering-gallery-mode (WGM) hexagonal optical micro-/nanocavities can be utilized as high-quality (Q) resonators for realizing compact-size low-threshold lasers. In this paper, the progress in WGM hexagonal micro-/nanocavity lasers is reviewed comprehensively. High-Q WGMs in hexagonal cavities are divided into two kinds of resonances propagating along hexagonal and triangular periodic orbits, with distinct mode characteristics according to theoretical analyses and numerical simulations; however, WGMs in a wavelength-scale nanocavity cannot be well described by the ray model. Hexagonal micro-/nanocavity lasers can be constructed by both bottom-up and top-down processes, leading to a diversity of these lasers. The ZnO- or nitride-based semiconductor material generally has a wurtzite crystal structure and typically presents a natural hexagonal cross section. Bottom-up growth guarantees smooth surface faceting and hence reduces the scattering loss effectively. Laser emissions have been successfully demonstrated in hexagonal micro-/nanocavities synthesized with various materials and structures. Furthermore, slight deformation can be easily introduced and precisely controlled in top-down fabrication, which allows lasing-mode manipulation. WGM lasing with excellent single-transverse-mode property was realized in waveguide-coupled ideal and deformed hexagonal microcavity lasers.

© 2019 Chinese Laser Press

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2019 (1)

M. Tang, Y. D. Yang, H. Z. Weng, J. L. Xiao, and Y. Z. Huang, “Ray dynamics and wave chaos in circular-side polygonal microcavities,” Phys. Rev. A 99, 033814 (2019).
[Crossref]

2018 (7)

Y. D. Yang, H. Z. Weng, Y. Z. Hao, J. L. Xiao, and Y. Z. Huang, “Square microcavity semiconductor lasers,” Chin. Phys. B 27, 114212 (2018).
[Crossref]

C. X. Xu, F. F. Qin, Q. X. Zhu, J. F. Lu, Y. Y. Wang, J. T. Li, Y. Lin, Q. N. Cui, Z. L. Shi, and A. G. Manohari, “Plasmon-enhanced ZnO whispering-gallery mode lasing,” Nano Res. 11, 3050–3064 (2018).
[Crossref]

J. W. Wang, Y. Yin, Q. Hao, S. Z. Huang, E. S. G. Naz, O. G. Schmidt, and L. B. Ma, “External strain enabled post-modification of nanomembrane-based optical microtube cavities,” ACS Photon. 5, 2060–2067 (2018).
[Crossref]

J. W. Wang, Y. Yin, Q. Hao, Y. D. Yang, S. Valligatla, E. S. G. Naz, Y. Li, C. N. Saggau, L. B. Ma, and O. G. Schmidt, “Curved nanomembrane-based concentric ring cavities for supermode hybridization,” Nano Lett. 18, 7261–7267 (2018).
[Crossref]

F. J. Shu, X. F. Jiang, G. M. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7, 1455–1460 (2018).
[Crossref]

H. Z. Weng, Y. D. Yang, J. L. Xiao, Y. Z. Hao, and Y. Z. Huang, “Spectral engineering for circular-side square microlasers,” Opt. Express 26, 9409–9414 (2018).
[Crossref]

F. L. Wang, Y. D. Yang, Y. Z. Huang, Z. X. Xiao, and J. L. Xiao, “Single-transverse-mode waveguide-coupled deformed hexagonal resonator microlasers,” Appl. Opt. 57, 7242–7248 (2018).
[Crossref]

2017 (9)

X. F. Jiang, L. B. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. H. Gong, M. Loncar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358, 344–347 (2017).
[Crossref]

S. Longhi and L. Feng, “Unidirectional lasing in semiconductor microring lasers at an exceptional point,” Photon. Res. 5, B1–B6 (2017).
[Crossref]

X. C. Chen, C. S. Fenrich, M. Y. Xue, M. Y. Kao, K. Zang, C. Y. Lu, E. T. Fei, Y. S. Chen, Y. J. Huo, T. I. Kamins, and J. S. Harris, “Tensile-strained Ge/SiGe multiple quantum well microdisks,” Photon. Res. 5, B7–B14 (2017).
[Crossref]

J. Y. Ma, X. S. Jiang, and M. Xiao, “Kerr frequency combs in large-size, ultra-high-Q toroid microcavities with low repetition rates,” Photon. Res. 5, B54–B58 (2017).
[Crossref]

Q. X. Zhu, F. F. Qin, J. F. Lu, Z. Zhu, H. Y. Nan, Z. L. Shi, Z. H. Ni, and C. X. Xu, “Synergistic graphene/aluminum surface plasmon coupling for zinc oxide lasing improvement,” Nano Res. 10, 1996–2004 (2017).
[Crossref]

H. Z. Weng, Y. Z. Huang, Y. D. Yang, X. W. Ma, J. L. Xiao, and Y. Du, “Mode Q factor and lasing spectrum controls for deformed square resonator microlasers with circular sides,” Phys. Rev. A 95, 013833 (2017).
[Crossref]

M. Tang, Y. Z. Huang, Y. D. Yang, H. Z. Weng, and Z. X. Xiao, “Variable-curvature microresonators for dual-wavelength lasing,” Photon. Res. 5, 695–701 (2017).
[Crossref]

Z. X. Xiao, Y. Z. Huang, Y. D. Yang, J. L. Xiao, and X. W. Ma, “Single-mode unidirectional-emission circular-side hexagonal resonator microlasers,” Opt. Lett. 42, 1309–1312 (2017).
[Crossref]

R. Medishetty, J. K. Zareba, D. Mayer, M. Samoc, and R. A. Fischer, “Nonlinear optical properties, upconversion and lasing in metal-organic frameworks,” Chem. Soc. Rev. 46, 4976–5004 (2017).
[Crossref]

2016 (7)

Z. Y. Gu, K. Y. Wang, W. Z. Sun, S. Liu, N. Zhang, S. M. Xiao, and Q. H. Song, “Triangular lasing modes in hexagonal perovskite microplates with balanced gain and loss,” RSC Adv. 6, 64589–64594 (2016).
[Crossref]

Y. D. Yang and Y. Z. Huang, “Mode characteristics and directional emission for square microcavity lasers,” J. Phys. D 49, 253001 (2016).
[Crossref]

Y. Y. Lai, Y. H. Chou, Y. P. Lan, T. C. Lu, S. C. Wang, and Y. Yamamoto, “Crossover from polariton lasing to exciton lasing in a strongly coupled ZnO microcavity,” Sci. Rep. 6, 20581 (2016).
[Crossref]

H. J. He, E. Ma, Y. J. Cui, J. C. Yu, Y. Yang, T. Song, C. D. Wu, X. Y. Chen, B. L. Chen, and G. D. Qian, “Polarized three-photon-pumped laser in a single MOF microcrystal,” Nat. Commun. 7, 11087 (2016).
[Crossref]

Y. Y. Wang, C. X. Xu, M. M. Jiang, J. T. Li, J. Dai, J. F. Lu, and P. L. Li, “Lasing mode regulation and single-mode realization in ZnO whispering gallery microcavities by the Vernier effect,” Nanoscale 8, 16631–16639 (2016).
[Crossref]

X. F. Jiang, C. L. Zou, L. Wang, Q. H. Gong, and Y. F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

L. Wang, D. Lippolis, Z. Y. Li, X. F. Jiang, Q. H. Gong, and Y. F. Xiao, “Statistics of chaotic resonances in an optical microcavity,” Phys. Rev. E 93, 040201 (2016).
[Crossref]

2015 (9)

Y. D. Yang, J. L. Xiao, B. W. Liu, and Y. Z. Huang, “Mode characteristics and vertical radiation loss for AlGaInAs/InP microcylinder lasers,” J. Opt. Soc. Am. B 32, 439–444 (2015).
[Crossref]

Y. D. Yang, H. Z. Weng, B. W. Liu, J. L. Xiao, and Y. Z. Huang, “Localized-cavity-loss-induced external mode coupling in optical microresonators,” J. Opt. Soc. Am. B 32, 2376–2381 (2015).
[Crossref]

S. S. Sui, M. Y. Tang, Y. D. Yang, J. L. Xiao, Y. Du, and Y. Z. Huang, “Investigation of hybrid microring lasers adhesively bonded on silicon wafer,” Photon. Res. 3, 289–295 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

G. Y. Zhu, J. T. Li, Z. S. Tian, J. Dai, Y. Y. Wang, P. L. Li, and C. X. Xu, “Electro-pumped whispering gallery mode ZnO microlaser array,” Appl. Phys. Lett. 106, 021111 (2015).
[Crossref]

H. Long, Y. Z. Huang, X. W. Ma, Y. D. Yang, J. L. Xiao, L. X. Zou, and B. W. Liu, “Dual-transverse-mode microsquare lasers with tunable wavelength interval,” Opt. Lett. 40, 3548–3551 (2015).
[Crossref]

Y. Y. Zhang, X. H. Zhang, K. H. Li, Y. F. Cheung, C. Feng, and H. W. Choi, “Advances in III-nitride semiconductor microdisk lasers,” Phys. Status Solidi A 212, 960–973 (2015).
[Crossref]

T. Kouno, S. Suzuki, K. Kishino, M. Sakai, K. Yamano, A. Yanagihara, and K. Hara, “Optical properties of arrays of hexagonal GaN microdisks acting as whispering-gallery-mode-type optical microcavities,” Phys. Status Solidi A 212, 1017–1020 (2015).
[Crossref]

X. F. Liu, S. T. Ha, Q. Zhang, M. de la Mata, C. Magen, J. Arbiol, T. C. Sum, and Q. H. Xiong, “Whispering gallery mode lasing from hexagonal shaped layered lead iodide crystals,” ACS Nano 9, 687–695 (2015).
[Crossref]

2014 (10)

Q. Zhang, S. T. Ha, X. F. Liu, T. C. Sum, and Q. H. Xiong, “Room-temperature near-infrared high-Q perovskite whispering-gallery planar nano lasers,” Nano Lett. 14, 5995–6001 (2014).
[Crossref]

T. Kouno, M. Sakai, K. Kishino, and K. Hara, “Optical microresonant modes acting in thin hexagonal GaN microdisk,” Jpn. J. Appl. Phys. 53, 072001 (2014).
[Crossref]

C. X. Xu, J. Dai, G. P. Zhu, G. Y. Zhu, Y. Lin, J. T. Li, and Z. L. Shi, “Whispering-gallery mode lasing in ZnO microcavities,” Laser Photon. Rev. 8, 469–494 (2014).
[Crossref]

C. Tessarek, R. Roder, T. Michalsky, S. Geburt, H. Franke, R. Schmidt-Grund, M. Heilmann, B. Hoffmann, C. Ronning, M. Grundmann, and S. Christiansen, “Improving the optical properties of self-catalyzed GaN microrods toward whispering gallery mode lasing,” ACS Photon. 1, 990–997 (2014).
[Crossref]

C. Tessarek, M. Heilmann, and S. Christiansen, “Whispering gallery modes in GaN microdisks, microrods and nanorods grown by MOVPE,” Phys. Status Solidi C 11, 794–797 (2014).
[Crossref]

H. Baek, J. K. Hyun, K. Chung, H. Oh, and G. C. Yi, “Selective excitation of Fabry–Perot or whispering-gallery mode-type lasing in GaN microrods,” Appl. Phys. Lett. 105, 201108 (2014).
[Crossref]

D. Xu, W. Xie, W. H. Liu, J. Wang, L. Zhang, Y. L. Wang, S. F. Zhang, L. X. Sun, X. C. Shen, and Z. H. Chen, “Polariton lasing in a ZnO microwire above 450 K,” Appl. Phys. Lett. 104, 082101 (2014).
[Crossref]

J. Wang, T. R. Zhan, G. S. Huang, P. K. Chu, and Y. F. Mei, “Optical microcavities with tubular geometry: properties and applications,” Laser Photon. Rev. 8, 521–547 (2014).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photon. Res. 2, 177–181 (2014).
[Crossref]

Y. D. Yang, Y. Zhang, Y. Z. Huang, and A. W. Poon, “Direct-modulated waveguide-coupled microspiral disk lasers with spatially selective injection for on-chip optical interconnects,” Opt. Express 22, 824–838 (2014).
[Crossref]

2013 (14)

Y. F. Xiao, X. F. Jiang, Q. F. Yang, L. Wang, K. B. Shi, Y. Li, and Q. H. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51–L54 (2013).
[Crossref]

Q. F. Yang, X. F. Jiang, Y. L. Cui, L. B. Shao, and Y. F. Xiao, “Dynamical tunneling-assisted coupling of high-Q deformed microcavities using a free-space beam,” Phys. Rev. A 88, 023810 (2013).
[Crossref]

X. F. Jiang, Y. F. Xiao, Q. F. Yang, L. B. Shao, W. R. Clements, and Q. H. Gong, “Free-space coupled, ultralow-threshold Raman lasing from a silica microcavity,” Appl. Phys. Lett. 103, 101102 (2013).
[Crossref]

Z. P. Liu, X. F. Jiang, Y. Li, Y. F. Xiao, L. Wang, J. L. Ren, S. J. Zhang, H. Yang, and Q. H. Gong, “High-Q asymmetric polymer microcavities directly fabricated by two-photon polymerization,” Appl. Phys. Lett. 102, 221108 (2013).
[Crossref]

L. B. Shao, L. Wang, W. J. Xiong, X. F. Jiang, Q. F. Yang, and Y. F. Xiao, “Ultrahigh-Q, largely deformed microcavities coupled by a free-space laser beam,” Appl. Phys. Lett. 103, 121102 (2013).
[Crossref]

J. T. Lin, Y. X. Xu, J. X. Song, B. Zeng, F. He, H. L. Xu, K. Sugioka, W. Fang, and Y. Cheng, “Low-threshold whispering-gallery-mode microlasers fabricated in a Nd:glass substrate by three-dimensional femtosecond laser micromachining,” Opt. Lett. 38, 1458–1460 (2013).
[Crossref]

S. Mehrabani and A. M. Armani, “Blue upconversion laser based on thulium-doped silica microcavity,” Opt. Lett. 38, 4346–4349 (2013).
[Crossref]

L. N. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev. 7, 60–82 (2013).
[Crossref]

V. D. Ta, R. Chen, L. Ma, Y. J. Ying, and H. D. Sun, “Whispering gallery mode microlasers and refractive index sensing based on single polymer fiber,” Laser Photon. Rev. 7, 133–139 (2013).
[Crossref]

Q. Q. Duan, D. Xu, W. H. Liu, J. Lu, L. Zhang, J. Wang, Y. L. Wang, J. Gu, T. Hu, W. Xie, X. C. Shen, and Z. H. Chen, “Polariton lasing of quasi-whispering gallery modes in a ZnO microwire,” Appl. Phys. Lett. 103, 022103 (2013).
[Crossref]

Y. Y. Lai, Y. P. Lan, and T. C. Lu, “Strong light–matter interaction in ZnO microcavities,” Light: Sci. Appl. 2, e76 (2013).
[Crossref]

C. Tessarek, G. Sarau, M. Kiometzis, and S. Christiansen, “High quality factor whispering gallery modes from self-assembled hexagonal GaN rods grown by metal-organic vapor phase epitaxy,” Opt. Express 21, 2733–2740 (2013).
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Q. H. Song, L. Ge, J. Wiersig, and H. Cao, “Formation of long-lived resonances in hexagonal cavities by strong coupling of superscar modes,” Phys. Rev. A 88, 023834 (2013).
[Crossref]

H. H. Fang, R. Ding, S. Y. Lu, Y. D. Yang, Q. D. Chen, J. Feng, Y. Z. Huang, and H. B. Sun, “Whispering-gallery mode lasing from patterned molecular single-crystalline microcavity array,” Laser Photon. Rev. 7, 281–288 (2013).
[Crossref]

2012 (9)

G. Y. Zhu, C. X. Xu, Y. Lin, Z. L. Shi, J. T. Li, T. Ding, Z. S. Tian, and G. F. Chen, “Ultraviolet electroluminescence from horizontal ZnO microrods/GaN heterojunction light-emitting diode array,” Appl. Phys. Lett. 101, 041110 (2012).
[Crossref]

S. F. Li and A. Waag, “GaN based nanorods for solid state lighting,” J. Appl. Phys. 111, 071101 (2012).
[Crossref]

W. Xie, H. X. Dong, S. F. Zhang, L. X. Sun, W. H. Zhou, Y. J. Ling, J. Lu, X. C. Shen, and Z. H. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref]

Q. H. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
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R. Chen, V. D. Ta, and H. D. Sun, “Single mode lasing from hybrid hemispherical microresonators,” Sci. Rep. 2, 244 (2012).
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M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J. M. Gerard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Hofling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett. 100, 031111 (2012).
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X. F. Jiang, Y. F. Xiao, C. L. Zou, L. N. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. H. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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Y. C. Liu, Y. F. Xiao, X. F. Jiang, B. B. Li, Y. Li, and Q. H. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A 85, 013843 (2012).
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2011 (11)

J. K. Kitur, V. A. Podolskiy, and M. A. Noginov, “Stimulated emission of surface plasmon polaritons in a microcylinder cavity,” Phys. Rev. Lett. 106, 183903 (2011).
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J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415–11421 (2011).
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Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol. 29, 2754–2760 (2011).
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2010 (5)

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Y. D. Yang, S. J. Wang, and Y. Z. Huang, “Investigation of mode radiation loss for microdisk resonators with pedestals by FDTD technique,” Chin. Opt. Lett. 8, 502–504 (2010).
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Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 130902 (2010).
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2009 (7)

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80, 041807 (2009).
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Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral-triangle-resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron. 45, 1529–1536 (2009).
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2008 (5)

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Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75, 013817 (2007).
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Y. D. Yang and Y. Z. Huang, “Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators,” Phys. Rev. A 76, 023822 (2007).
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Y. D. Yang and Y. Z. Huang, “Mode analysis and Q-factor enhancement due to mode coupling in rectangular resonators,” IEEE J. Quantum Electron. 43, 497–502 (2007).
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2006 (6)

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, “Mode characteristics for equilateral triangle optical resonators,” IEEE J. Sel. Top. Quantum Electron. 12, 59–65 (2006).
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2005 (2)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Optical modes in 2-D imperfect square and triangular microcavities,” IEEE J. Quantum Electron. 41, 857–862 (2005).
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T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005).
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2004 (4)

T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93, 103903 (2004).
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2003 (5)

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L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett. 83, 825–826 (2003).
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2001 (2)

A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001).
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2000 (4)

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1998 (2)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
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1997 (2)

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1993 (2)

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1992 (1)

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Armani, D. K.

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett. 83, 825–826 (2003).
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M. Lebental, N. Djellali, C. Arnaud, J. S. Lauret, J. Zyss, R. Dubertrand, C. Schmit, and E. Bogomolny, “Inferring periodic orbits from spectra of simply shaped microlasers,” Phys. Rev. A 76, 023830 (2007).
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Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93, 133902 (2004).
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J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev. 5, 553–570 (2011).
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S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Optical modes in 2-D imperfect square and triangular microcavities,” IEEE J. Quantum Electron. 41, 857–862 (2005).
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Y. D. Yang, J. L. Xiao, B. W. Liu, and Y. Z. Huang, “Mode characteristics and vertical radiation loss for AlGaInAs/InP microcylinder lasers,” J. Opt. Soc. Am. B 32, 439–444 (2015).
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J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Single transverse whispering-gallery mode AlGaInAs/InP hexagonal resonator microlasers,” IEEE Photon. J. 3, 756–764 (2011).
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J. L. Xiao, C. G. Ma, Z. X. Xiao, Y. D. Yang, and Y. Z. Huang, “Random bit generation in dual transverse mode microlaser without optical injection or feedback,” in IEEE International Semiconductor Laser Conference ISLC (2018), pp. 171–172.

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Figures (12)

Fig. 1.
Fig. 1. (a) Schematic diagram and (b) symmetry operators of a 2D hexagonal microcavity. (c) The hexagonal periodic orbits and (d) the triangular periodic orbits in the hexagonal microcavity. The solid lines and dashed lines indicate, respectively, the ray trajectories connecting the midpoints of the sides and the other ray trajectories in the same orbit family with the same incident angles.
Fig. 2.
Fig. 2. (a) Simulated TE modes in the hexagonal microcavity with refractive indices of 3.2/1. (b)–(d) The magnetic-field amplitude distributions of the modes marked by A, B, and C.
Fig. 3.
Fig. 3. (a) Mode Q factors versus normalized frequency for TE modes in the hexagonal microcavity with refractive indices of 3.2/1.54. (b) Simulated mode Q factors of modes A and B as functions of ni/no.
Fig. 4.
Fig. 4. Mode Q factors of (a) TE and (b) TM modes in a wavelength-scale hexagonal nanocavity with refractive indices of 3.2/1 as functions of angular mode number. The insets show, respectively, the magnetic- and electric-field amplitude distributions of the TE and TM modes.
Fig. 5.
Fig. 5. Mode Q factors of (a) TE and (b) TM modes in the wavelength-scale hexagonal nanocavity as functions of ni/no.
Fig. 6.
Fig. 6. Cross-section and top-down SEM images of ZnO nanodisks with diameters of (a) 842 nm, (c) 612 nm, and (e) 491 nm. (b), (d), and (f) Corresponding lasing spectra collected at increasing pump powers. Inset: PL intensity versus pump power. (g) Room temperature lasing threshold versus disk diameter. Reproduced from Ref. [80].
Fig. 7.
Fig. 7. (a) Emission spectra of a ZnO microrod with a diagonal of 6.67 μm when excited with a Nd:YAG laser at different excitation power densities. Inset: far-field emission image of the lasing ZnO microrod taken with a digital camera. (b) Output lasing intensity versus excitation power density. Reproduced from Ref. [84].
Fig. 8.
Fig. 8. PL mapping along the ZnO tapered arm for (a) TE and (b) TM polarized modes. Reproduced from Ref. [119].
Fig. 9.
Fig. 9. SEM images of (a) the bird’s-eye view and (b) the top view of a GaN hexagonal microdisk. (c) Bird’s-eye-view SEM image of the GaN hexagonal microdisk cut with an FIB. (d) Schematic diagram of hexagonal and triangular periodic orbits (called WGM and quasi-WGM here). Reproduced from Ref. [87].
Fig. 10.
Fig. 10. (a) Schematic diagram of ray path in on-chip nanopillars. (b) FDTD-simulated field profile of a WGM with an angular mode number of 6 in the hexagonal plane. (c) First-order and (d) higher-order transverse modes in the vertical direction. (e) SEM image of a subwavelength device. [(f)–(h)] SEM images and experimental emission patterns of nanopillars. Reproduced from [128].
Fig. 11.
Fig. 11. (a) Applied voltage and fiber-coupled output power versus continuous-wave injection current, and (b) lasing spectra at different injection currents for a hexagonal microcavity laser with a side length of 10 μm and a 1.5-μm-wide output waveguide. The inset in (a) shows a microscopic image of the hexagonal microcavity laser.
Fig. 12.
Fig. 12. (a) SEM image of a deformed hexagonal microlaser after inductively coupled plasma etching. (b) Microscopic image of a deformed hexagonal microcavity laser. (c) Applied voltage and fiber-coupled output power versus continuous-wave injection current. (d) Lasing spectra at injection currents of 2.5, 14, and 23 mA. (e) Small-signal responses for the circular-side hexagonal resonator at bias currents of 6, 8, 14, and 21 mA. Reproduced from Ref. [91].

Tables (1)

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Table 1. Character Table of Point Group C6v

Equations (5)

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θi={θb,2π/3θb,θbπ/3;π/3<θb<π/2θb,π/3θb,2π/3θb;π/6<θb<π/3θb,π/3θb,π/3+θb;0<θb<π/6.
δ(θ)=2arctan(βni2sin2θno2nicosθ),
Re(33nika)+6δ(π3)=2lπ,
Re(9nika)+6δ(π6)=2lπ.
2ψ(x,y)=n2(x,y)ω2c2ψ(x,y),

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