Abstract

The lowest threshold lasing mode in a rounded D-shape microcavity is theoretically analyzed and experimentally demonstrated. To identify the lowest threshold lasing mode, we investigate threshold conditions of different periodic orbits by considering the linear gain condition due to the effective pumping region and total loss consisting of internal and scattering losses in ray dynamics. We compare the ray dynamical result with resonance mode analysis, including gain and loss. We find that the resonance modes localized on the pentagonal marginally unstable periodic orbit have the lowest threshold in our fabrication configuration. Our findings are verified by obtaining the path lengths and far-field patterns of lasing modes.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

C.-H. Yi, J.-W. Lee, J. Ryu, J.-H. Kim, H.-H. Yu, S. Gwak, K.-R. Oh, J. Wiersig, and C.-M. Kim, “Robust lasing of modes localized on marginally unstable periodic orbits,” Phys. Rev. A 101(5), 053809 (2020).
[Crossref]

2019 (2)

V. S. Pereira and S. Blawid, “Drift-diffusion simulation of leakage currents in unintentionally doped organic semiconductors with non-uniform interfaces,” J. Comput. Electron. 18(1), 120–129 (2019).
[Crossref]

Y. Sun, X. Kang, Y. Zheng, J. Lu, X. Tian, K. Wei, H. Wu, W. Wang, X. Liu, and G. Zhang, “Review of the recent progress on GaN-based vertical power Schottky barrier diodes (SBDs),” Electronics (Basel, Switz.) 8(5), 575 (2019).
[Crossref]

2018 (2)

2017 (3)

2016 (2)

I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24(3), 2253–2258 (2016).
[Crossref]

J. Kullig and J. Wiersig, “Frobenius–perron eigenstates in deformed microdisk cavities: non-hermitian physics and asymmetric backscattering in ray dynamics,” New J. Phys. 18(1), 015005 (2016).
[Crossref]

2013 (1)

E. G. Altmann, J. S. E. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85(2), 869–918 (2013).
[Crossref]

2012 (1)

2011 (4)

J.-W. Ryu and M. Hentschel, “Designing coupled microcavity lasers for high-Q modes with unidirectional light emission,” Opt. Lett. 36(7), 1116–1118 (2011).
[Crossref]

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108(15), 5976–5979 (2011).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref]

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
[Crossref]

2009 (3)

C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95(14), 141107 (2009).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79(1), 013830 (2009).
[Crossref]

2008 (4)

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92(13), 131110 (2008).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref]

J. Wiersig and J. Main, “Fractal weyl law for chaotic microcavities: Fresnel’s laws imply multifractal scattering,” Phys. Rev. E 77(3), 036205 (2008).
[Crossref]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008).
[Crossref]

2007 (2)

S. Sunada and T. Harayama, “Design of resonant microcavities: application to optical gyroscopes,” Opt. Express 15(24), 16245–16254 (2007).
[Crossref]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref]

2006 (2)

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 (2006).
[Crossref]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E 73(3), 036207 (2006).
[Crossref]

2005 (1)

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72(1), 013803 (2005).
[Crossref]

2004 (3)

2003 (6)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref]

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
[Crossref]

A. I. Rahachou and I. V. Zozoulenko, “Effects of boundary roughness on a Q factor of whispering-gallery-mode lasing microdisk cavities,” J. Appl. Phys. 94(12), 7929–7931 (2003).
[Crossref]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5(1), 53–60 (2003).
[Crossref]

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond,” Europhys. Lett. 62(5), 636–642 (2003).
[Crossref]

1996 (2)

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69(17), 2456–2458 (1996).
[Crossref]

D. Garbuzov, L. Xu, S. R. Forrest, R. Menna, R. Martinelli, and J. C. Connolly, “1.5 μm wavelength, SCH-MQW InGaAsP/InP broadened-waveguide laser diodes with low internal loss and high output power,” Electron. Lett. 32(18), 1717–1719 (1996).
[Crossref]

1994 (1)

T. Namegaya, N. Matsumoto, N. Yamanaka, N. Iwai, H. Nakayama, and A. Kasukawa, “Effects of well number in 1.3-μm GaInAsP/InP GRIN-SCH strained-layer quantum-well lasers,” IEEE J. Quantum Electron. 30(2), 578–584 (1994).
[Crossref]

1990 (1)

T. R. Chen, L. E. Eng, Y. H. Zhuang, and A. Yariv, “Experimental determination of transparency current density and estimation of the threshold current of semiconductor quantum well lasers,” Appl. Phys. Lett. 56(11), 1002–1004 (1990).
[Crossref]

1980 (1)

M. Hatzakis, B. J. Canavello, and J. M. Shaw, “Single-step optical lift-off process,” IBM J. Res. Dev. 24(4), 452–460 (1980).
[Crossref]

Aloïsi, P.

P. Aloïsi, Power MOSFET Transistors (John Wiley & Sons, Ltd, 2010), chap. 1, pp. 1–56.

Altmann, E. G.

E. G. Altmann, J. S. E. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85(2), 869–918 (2013).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79(1), 013830 (2009).
[Crossref]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref]

Beak, Y.-S.

S. H. Oh, J.-U. Shin, Y.-J. Park, S. Park, S.-B. Kim, H.-K. Sung, Y.-S. Beak, and K.-R. Oh, “Fabrication of WDM-PON OLT source using external cavity laser,” in COIN-NGNCON 2006 - The Joint International Conference on Optical Internet and Next Generation Network (2006), pp. 217–219.

Belkin, M. A.

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).
[Crossref]

Ben-Messaoud, T.

Blawid, S.

V. S. Pereira and S. Blawid, “Drift-diffusion simulation of leakage currents in unintentionally doped organic semiconductors with non-uniform interfaces,” J. Comput. Electron. 18(1), 120–129 (2019).
[Crossref]

Canavello, B. J.

M. Hatzakis, B. J. Canavello, and J. M. Shaw, “Single-step optical lift-off process,” IBM J. Res. Dev. 24(4), 452–460 (1980).
[Crossref]

Capasso, F.

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).
[Crossref]

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69(17), 2456–2458 (1996).
[Crossref]

Cerjan, A.

Chang, R. K.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21(5), 923–934 (2004).
[Crossref]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Chen, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108(15), 5976–5979 (2011).
[Crossref]

Chen, T. R.

T. R. Chen, L. E. Eng, Y. H. Zhuang, and A. Yariv, “Experimental determination of transparency current density and estimation of the threshold current of semiconductor quantum well lasers,” Appl. Phys. Lett. 56(11), 1002–1004 (1990).
[Crossref]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Cho, A. Y.

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69(17), 2456–2458 (1996).
[Crossref]

Cho, J.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92(13), 131110 (2008).
[Crossref]

Choi, M.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93(16), 164102 (2004).
[Crossref]

Chong, Y.

Connolly, J.

L. Xu, D. Garbuzov, S. Forrest, R. Menna, R. Martinelli, and J. Connolly, “Very low internal loss, 1.5 μm wavelength SCH-MQW InGaAsP/InP laser diodes with broadened-waveguides,” in Conference Proceedings LEOS’96 9th Annual Meeting IEEE Lasers and Electro-Optics Society, vol. 1 (1996), pp. 352–353.

Connolly, J. C.

D. Garbuzov, L. Xu, S. R. Forrest, R. Menna, R. Martinelli, and J. C. Connolly, “1.5 μm wavelength, SCH-MQW InGaAsP/InP broadened-waveguide laser diodes with low internal loss and high output power,” Electron. Lett. 32(18), 1717–1719 (1996).
[Crossref]

Diehl, L.

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).
[Crossref]

Edamura, T.

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Y. Kawashima, S. Shinohara, S. Sunada, and T. Harayama, “Self-adjustment of a nonlinear lasing mode to a pumped area in a two-dimensional microcavity,” Photonics Res. 5(6), B47–B53 (2017).
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J.-W. Lee, C.-H. Yi, M.-W. Kim, J. Ryu, K.-R. Oh, and C.-M. Kim, “Unidirectional emission of high-Q scarred modes in a rounded D-shape microcavity,” Opt. Express 26(26), 34864–34871 (2018).
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J. Ryu, J.-W. Lee, C.-H. Yi, J.-H. Kim, I.-G. Lee, H.-S. Kim, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Chirality of a resonance in the absence of backscatterings,” Opt. Express 25(4), 3381–3386 (2017).
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C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
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J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E 73(3), 036207 (2006).
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Kim, J. H.

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92(13), 131110 (2008).
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Kim, J.-H.

C.-H. Yi, J.-W. Lee, J. Ryu, J.-H. Kim, H.-H. Yu, S. Gwak, K.-R. Oh, J. Wiersig, and C.-M. Kim, “Robust lasing of modes localized on marginally unstable periodic orbits,” Phys. Rev. A 101(5), 053809 (2020).
[Crossref]

J.-W. Lee, C.-H. Yi, I.-G. Lee, J.-H. Kim, H.-H. Yu, K.-R. Oh, and C.-M. Kim, “Extremely high Q and unidirectional laser emission due to combination of the Kolmogorov-Arnold-Moser barrier and the chaotic sea in a dielectric microdisk,” Opt. Lett. 43(24), 6097–6100 (2018).
[Crossref]

J. Ryu, J.-W. Lee, C.-H. Yi, J.-H. Kim, I.-G. Lee, H.-S. Kim, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Chirality of a resonance in the absence of backscatterings,” Opt. Express 25(4), 3381–3386 (2017).
[Crossref]

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108(15), 5976–5979 (2011).
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Kim, K. S.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
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J.-W. Lee, C.-H. Yi, M.-W. Kim, J. Ryu, K.-R. Oh, and C.-M. Kim, “Unidirectional emission of high-Q scarred modes in a rounded D-shape microcavity,” Opt. Express 26(26), 34864–34871 (2018).
[Crossref]

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
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Kim, S.-B.

J. Ryu, J.-W. Lee, C.-H. Yi, J.-H. Kim, I.-G. Lee, H.-S. Kim, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Chirality of a resonance in the absence of backscatterings,” Opt. Express 25(4), 3381–3386 (2017).
[Crossref]

I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24(3), 2253–2258 (2016).
[Crossref]

S. H. Oh, J.-U. Shin, Y.-J. Park, S. Park, S.-B. Kim, H.-K. Sung, Y.-S. Beak, and K.-R. Oh, “Fabrication of WDM-PON OLT source using external cavity laser,” in COIN-NGNCON 2006 - The Joint International Conference on Optical Internet and Next Generation Network (2006), pp. 217–219.

Kim, W.

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
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S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
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Kwon, T.-Y.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93(16), 164102 (2004).
[Crossref]

Lee, C.-W.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
[Crossref]

Lee, H.

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108(15), 5976–5979 (2011).
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Lee, I.-G.

Lee, J.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92(13), 131110 (2008).
[Crossref]

Lee, J.-M.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
[Crossref]

Lee, J.-W.

Lee, S. H.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92(13), 131110 (2008).
[Crossref]

Lee, S.-Y.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84(4), 041803 (2011).
[Crossref]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E 73(3), 036207 (2006).
[Crossref]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93(16), 164102 (2004).
[Crossref]

M. S. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29(23), 2758–2760 (2004).
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Liu, X.

Y. Sun, X. Kang, Y. Zheng, J. Lu, X. Tian, K. Wei, H. Wu, W. Wang, X. Liu, and G. Zhang, “Review of the recent progress on GaN-based vertical power Schottky barrier diodes (SBDs),” Electronics (Basel, Switz.) 8(5), 575 (2019).
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Y. Sun, X. Kang, Y. Zheng, J. Lu, X. Tian, K. Wei, H. Wu, W. Wang, X. Liu, and G. Zhang, “Review of the recent progress on GaN-based vertical power Schottky barrier diodes (SBDs),” Electronics (Basel, Switz.) 8(5), 575 (2019).
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Lu, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108(15), 5976–5979 (2011).
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D. Garbuzov, L. Xu, S. R. Forrest, R. Menna, R. Martinelli, and J. C. Connolly, “1.5 μm wavelength, SCH-MQW InGaAsP/InP broadened-waveguide laser diodes with low internal loss and high output power,” Electron. Lett. 32(18), 1717–1719 (1996).
[Crossref]

L. Xu, D. Garbuzov, S. Forrest, R. Menna, R. Martinelli, and J. Connolly, “Very low internal loss, 1.5 μm wavelength SCH-MQW InGaAsP/InP laser diodes with broadened-waveguides,” in Conference Proceedings LEOS’96 9th Annual Meeting IEEE Lasers and Electro-Optics Society, vol. 1 (1996), pp. 352–353.

Matsumoto, N.

T. Namegaya, N. Matsumoto, N. Yamanaka, N. Iwai, H. Nakayama, and A. Kasukawa, “Effects of well number in 1.3-μm GaInAsP/InP GRIN-SCH strained-layer quantum-well lasers,” IEEE J. Quantum Electron. 30(2), 578–584 (1994).
[Crossref]

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D. Garbuzov, L. Xu, S. R. Forrest, R. Menna, R. Martinelli, and J. C. Connolly, “1.5 μm wavelength, SCH-MQW InGaAsP/InP broadened-waveguide laser diodes with low internal loss and high output power,” Electron. Lett. 32(18), 1717–1719 (1996).
[Crossref]

L. Xu, D. Garbuzov, S. Forrest, R. Menna, R. Martinelli, and J. Connolly, “Very low internal loss, 1.5 μm wavelength SCH-MQW InGaAsP/InP laser diodes with broadened-waveguides,” in Conference Proceedings LEOS’96 9th Annual Meeting IEEE Lasers and Electro-Optics Society, vol. 1 (1996), pp. 352–353.

Nakayama, H.

T. Namegaya, N. Matsumoto, N. Yamanaka, N. Iwai, H. Nakayama, and A. Kasukawa, “Effects of well number in 1.3-μm GaInAsP/InP GRIN-SCH strained-layer quantum-well lasers,” IEEE J. Quantum Electron. 30(2), 578–584 (1994).
[Crossref]

Namegaya, T.

T. Namegaya, N. Matsumoto, N. Yamanaka, N. Iwai, H. Nakayama, and A. Kasukawa, “Effects of well number in 1.3-μm GaInAsP/InP GRIN-SCH strained-layer quantum-well lasers,” IEEE J. Quantum Electron. 30(2), 578–584 (1994).
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Oh, K. R.

Oh, K.-R.

C.-H. Yi, J.-W. Lee, J. Ryu, J.-H. Kim, H.-H. Yu, S. Gwak, K.-R. Oh, J. Wiersig, and C.-M. Kim, “Robust lasing of modes localized on marginally unstable periodic orbits,” Phys. Rev. A 101(5), 053809 (2020).
[Crossref]

J.-W. Lee, C.-H. Yi, I.-G. Lee, J.-H. Kim, H.-H. Yu, K.-R. Oh, and C.-M. Kim, “Extremely high Q and unidirectional laser emission due to combination of the Kolmogorov-Arnold-Moser barrier and the chaotic sea in a dielectric microdisk,” Opt. Lett. 43(24), 6097–6100 (2018).
[Crossref]

J.-W. Lee, C.-H. Yi, M.-W. Kim, J. Ryu, K.-R. Oh, and C.-M. Kim, “Unidirectional emission of high-Q scarred modes in a rounded D-shape microcavity,” Opt. Express 26(26), 34864–34871 (2018).
[Crossref]

S. H. Oh, J.-U. Shin, Y.-J. Park, S. Park, S.-B. Kim, H.-K. Sung, Y.-S. Beak, and K.-R. Oh, “Fabrication of WDM-PON OLT source using external cavity laser,” in COIN-NGNCON 2006 - The Joint International Conference on Optical Internet and Next Generation Network (2006), pp. 217–219.

Oh, S. H.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
[Crossref]

S. H. Oh, J.-U. Shin, Y.-J. Park, S. Park, S.-B. Kim, H.-K. Sung, Y.-S. Beak, and K.-R. Oh, “Fabrication of WDM-PON OLT source using external cavity laser,” in COIN-NGNCON 2006 - The Joint International Conference on Optical Internet and Next Generation Network (2006), pp. 217–219.

Özdemir, S. K.

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref]

Park, M.-H.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
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Park, S.

S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
[Crossref]

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Appl. Phys. Lett. (6)

C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95(14), 141107 (2009).
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C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).
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Electron. Lett. (1)

D. Garbuzov, L. Xu, S. R. Forrest, R. Menna, R. Martinelli, and J. C. Connolly, “1.5 μm wavelength, SCH-MQW InGaAsP/InP broadened-waveguide laser diodes with low internal loss and high output power,” Electron. Lett. 32(18), 1717–1719 (1996).
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Electronics (Basel, Switz.) (1)

Y. Sun, X. Kang, Y. Zheng, J. Lu, X. Tian, K. Wei, H. Wu, W. Wang, X. Liu, and G. Zhang, “Review of the recent progress on GaN-based vertical power Schottky barrier diodes (SBDs),” Electronics (Basel, Switz.) 8(5), 575 (2019).
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Europhys. Lett. (1)

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond,” Europhys. Lett. 62(5), 636–642 (2003).
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IBM J. Res. Dev. (1)

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IEEE J. Quantum Electron. (1)

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S. H. Oh, C.-W. Lee, J.-M. Lee, K. S. Kim, H. Ko, S. Park, and M.-H. Park, “The design and the fabrication of monolithically integrated GaInAsP MQW laser with butt-coupled waveguide,” IEEE Photonics Technol. Lett. 15(10), 1339–1341 (2003).
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J. Appl. Phys. (1)

A. I. Rahachou and I. V. Zozoulenko, “Effects of boundary roughness on a Q factor of whispering-gallery-mode lasing microdisk cavities,” J. Appl. Phys. 94(12), 7929–7931 (2003).
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J. Comput. Electron. (1)

V. S. Pereira and S. Blawid, “Drift-diffusion simulation of leakage currents in unintentionally doped organic semiconductors with non-uniform interfaces,” J. Comput. Electron. 18(1), 120–129 (2019).
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J. Opt. A: Pure Appl. Opt. (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5(1), 53–60 (2003).
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J. Opt. Soc. Am. B (1)

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
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Nat. Nanotechnol. (1)

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
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Nature (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
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New J. Phys. (1)

J. Kullig and J. Wiersig, “Frobenius–perron eigenstates in deformed microdisk cavities: non-hermitian physics and asymmetric backscattering in ray dynamics,” New J. Phys. 18(1), 015005 (2016).
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Opt. Express (5)

Opt. Lett. (3)

Optica (1)

Photonics Res. (1)

Y. Kawashima, S. Shinohara, S. Sunada, and T. Harayama, “Self-adjustment of a nonlinear lasing mode to a pumped area in a two-dimensional microcavity,” Photonics Res. 5(6), B47–B53 (2017).
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Phys. Rev. A (5)

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 (2006).
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E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79(1), 013830 (2009).
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C.-H. Yi, J.-W. Lee, J. Ryu, J.-H. Kim, H.-H. Yu, S. Gwak, K.-R. Oh, J. Wiersig, and C.-M. Kim, “Robust lasing of modes localized on marginally unstable periodic orbits,” Phys. Rev. A 101(5), 053809 (2020).
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T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72(1), 013803 (2005).
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Phys. Rev. E (2)

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E 73(3), 036207 (2006).
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J. Wiersig and J. Main, “Fractal weyl law for chaotic microcavities: Fresnel’s laws imply multifractal scattering,” Phys. Rev. E 77(3), 036205 (2008).
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Phys. Rev. Lett. (2)

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Figures (6)

Fig. 1.
Fig. 1. An RDS semiconductor microcavity laser. (a) is a schematic of our RDS microcavity with $\phi =80^{\circ }$ and $r=0.5R$. A linear section between the smaller arcs is highlighted by red color. (b) shows a stack layer diagram of an InP-based semiconductor laser along the vertical cross-section. (c) is an SEM image of a fabricated RDS microcavity laser. (d) is a zoomed image of the red square region in (c) showing the $3$ $\mu$m inward gap between the contact region and the sidewall. (e) shows a vertical cross-section of RDS embedding an SCH-MQW active layer marked by a red band. Green bars in (d) and (e) represent the length of $\lambda$.
Fig. 2.
Fig. 2. Ray dynamical simulation of the RDS cavity. (a) is CRD, which shows chaotic saddles possessing marginally unstable periodic orbits (red) and unstable periodic orbits (green). (b) is normalized SPD in a logarithmic scale. Three dotted circles around $S/S_{\textrm {max}}=0.4$, $0.8$, and $1.0$ indicate emission windows.
Fig. 3.
Fig. 3. Semi-logarithmic plots of survival probability time distributions (discrete symbols) and their linear fittings (straight curves) for each periodic orbit. (a) $p_{1,3}$MUPO, (b) $p_{1,4}$MUPO, (c) $p_{1,4}$UPO, (d) $p_{1,5}$MUPO, (e) $p_{1,5}$UPO, and (f) $p_{1,6}$MUPO. From the slopes of the fitting curves, the decaying exponent $\alpha _{s}$ with respect to the effective propagation time of the propagation length with a constant velocity of rays is obtained.
Fig. 4.
Fig. 4. Passive resonance modes for the RDS cavity. (a) is the eigenvalue distribution of $p_{1,3}$ (blue triangle), $p_{1,4}$ (cyan square), $p_{1,5}$ (red pentagram), and $p_{1,6}$ MUPO (black circle) and $p_{1,4}$ (green diamond) and $p_{1,5}$ UPO (purple hexagram) in the region $n_{e}kR\sim 396$. The eigenvalues of representative modes marked with dotted-red boxes are $120.2018-i3.8006\times 10^{-5}$ for $p_{1,3}$ MUPO, $119.0782-i3.4248\times 10^{-5}$ for $p_{1,4}$ MUPO, $119.7007-i3.2675\times 10^{-5}$ for $p_{1,5}$ MUPO, $119.7075-i3.1429\times 10^{-5}$ for $p_{1,6}$ MUPO, $119.8308-i3.4238\times 10^{-5}$ for $p_{1,4}$ UPO, and $119.1448-i3.1848\times 10^{-5}$ for $p_{1,5}$ UPO. (b) is the spatial wave patterns and their Husimi distributions of representative modes. We overlap the Husimi distribution on the periodic orbits in CRD to make clear the mode localization.
Fig. 5.
Fig. 5. Threshold parameters depending on the length of the inward gap between the sidewall and the effective pumping region at the gain layer. (a) and (b) are threshold parameters of $p_c$ and $p_w$, respectively, which are defined by the classical excited length and the ratio of the sum of wave function inside the cavity and the sum of the overlapped wave function. Both results show a range of 0.7 $\mu$m < $l_{g}$ < 1.8 $\mu$m for the lowest threshold parameter of $p_{1,5}$ MUPO. The insets are the magnified graphs, which show the lowest threshold parameters of $p_{1,5}$ MUPO.
Fig. 6.
Fig. 6. Experimental results of the RDS semiconductor microcavity laser. (a) shows the total output power (red) and major peak intensity (blue) as functions of injection current. A vertical dotted line shows a threshold of lasing at $44$ mA. (b) shows the line width $w$ of the major peak $\lambda =\lambda _c$ (black) fitted by Gaussian curve (red) at the threshold current. The spectra in (c), (d), and (e) are measured at $44$ mA, $47$ mA, and $51$ mA, respectively. Two mode groups in the spectra are marked by dashed-red lines (Group 1) and dashed-green lines (Group 2). (f) is the far-field pattern from the ray dynamical simulation, (g) is the average far-field pattern from the resonance modes localized on $p_{1,5}$ MUPO, and (h) is the far-field pattern from the experiments. All of the far-field patterns indicate three emission directions around $\theta =10^{\circ }$, $70^{\circ }$, and $150^{\circ }$.

Tables (1)

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Table 1. Path lengths of periodic orbits for our RDS microcavity

Equations (9)

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L I l 10 log I N / I 0 l = 10 log ( 1 N n N r n ) l α s l   ,
α s = d L I d l   .
G > α i + α s = α i + 1 L p log 1 R   ,
G th = L e L p × G th = Γ g L e L p ( J th J 0 ) = α i + α s   ,
J th = J 0 + L p / L e Γ g ( α i + α s ) = J 0 + C 1 p c   ,
W th = n e 2 γ 2 π ρ κ 2 Im ( k ) + β Re ( k ) D d x d y | ψ ( x , y ) | 2 D d x d y | ψ ( x , y ) | 2 Θ ( x , y ) = C 2 p w   ,
A eff = I 0 q ρ μ 1 ( E t E b ) ( 1 x / d ) + E b = A c 1 + ( A c / A e 1 ) ( 1 x / d )   ,
α i + α s = 2 π n e λ Q 7.36  cm 1 α i 6.1  cm 1 .
L p = 1 N 1 i = 1 N 1 [ ( λ i + λ i + 1 ) / 2 ] 2 n g Δ λ   ,