Abstract

Breaking the spatial symmetry in optical systems has become a key approach to the study of nonlinear dynamics, wave chaos, and non-Hermitian physics. Moreover, it enables tailoring of the spatiotemporal properties of such systems. Breaking the circular symmetry of lasers yields a more uniform light intensity profile within the optical aperture and makes uniform the spectral distribution of the optical states (modes). Those effects are known to enhance spontaneous as well as stimulated emission and consequently suppress undesired nonradiative recombination in the active region, but their importance for laser emission is not fully understood so far. In this paper, using the example of vertical-cavity surface-emitting lasers, we show that intentionally deformed optical apertures induce a more uniform light intensity distribution within the optical aperture, related to wave chaos, and a higher density of optical states, enhancing stimulated emission as predicted by quantum electrodynamics theory. These two phenomena contribute to increasing the optical output power by more than 60% and quantum efficiency by more than 10%. The results of this study are of significant importance for a variety of lasers, showing a clear link between the fundamentals of their operation and quantum electrodynamics and providing a general, robust method of enhancing emitted power for high-power broad-area lasers.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

  • View by:

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  34. P. Moser, J. A. Lott, and D. Bimberg, “Energy efficiency of directly modulated oxide-confined high bit rate 850-nm VCSELs for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 19, 1702212 (2013).
    [Crossref]
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  36. C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
    [Crossref]
  37. S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
    [Crossref]
  38. K. Becker, I. Fischer, and W. Elsäßer, “Spatio-temporal emission dynamics of VCSELs: modal competition in the turn-on behavior,” Proc. SPIE 5452, 452–461 (2004).
    [Crossref]
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    [Crossref]

2019 (3)

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]

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
[Crossref]

2018 (1)

S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
[Crossref]

2015 (1)

W. Wei, X. Zhang, X. Yan, and X. Ren, “Observation of enhanced spontaneous and stimulated emission of GaAs/AlGaAs nanowire via the Purcell effect,” AIP Adv. 5, 087148 (2015).
[Crossref]

2014 (2)

2013 (3)

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
[Crossref]

P. Moser, J. A. Lott, and D. Bimberg, “Energy efficiency of directly modulated oxide-confined high bit rate 850-nm VCSELs for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 19, 1702212 (2013).
[Crossref]

M. Lorke, T. Suhr, N. Gregersen, and J. Mørk, “Theory of nanolaser devices: rate equation analysis versus microscopic theory,” Phys. Rev. B 87, 205310 (2013).
[Crossref]

2012 (1)

Q. 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]

2011 (2)

2009 (2)

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode VCSELs via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[Crossref]

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref]

2008 (1)

M. Djiango, T. Kobayashi, and W. J. Blau, “Cavity-enhanced stimulated emission cross section in polymer microlasers,” Appl. Phys. Lett. 93, 143306 (2008).
[Crossref]

2007 (2)

S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E 75, 036216 (2007).
[Crossref]

D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
[Crossref]

2006 (1)

H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

2005 (1)

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

2004 (2)

H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
[Crossref]

K. Becker, I. Fischer, and W. Elsäßer, “Spatio-temporal emission dynamics of VCSELs: modal competition in the turn-on behavior,” Proc. SPIE 5452, 452–461 (2004).
[Crossref]

2003 (1)

A. Barchanski, T. Gensty, C. Degen, I. Fischer, and W. Elsäßer, “Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization,” IEEE J. Quantum Electron. 39, 850–858 (2003).
[Crossref]

2000 (1)

S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
[Crossref]

1999 (2)

M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
[Crossref]

C. Degen, I. Fischer, and W. Elsäßer, “Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects,” Opt. Express 5, 38–47 (1999).
[Crossref]

1997 (3)

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

H. Wenzel and H.-J. Wunsche, “The effective frequency method in the analysis of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1156–1162 (1997).
[Crossref]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

1996 (1)

J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

1992 (1)

L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

1991 (1)

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[Crossref]

1989 (1)

H. Yokoyama and S. D. Brorson, “Rate equation analysis of microcavity lasers,” J. Appl. Phys. 66, 4801 (1989).
[Crossref]

1985 (1)

S. Uchiyama and K. Iga, “Two-dimensional array of GaInAsP/lnP surface-emitting lasers,” Electron. Lett. 21, 162–164 (1985).
[Crossref]

1963 (1)

H. Kroemer, “A proposed class of hetero-junction injection lasers,” Proc. IEEE 51, 1782–1783 (1963).
[Crossref]

1961 (1)

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering gallery modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[Crossref]

Altug, H.

H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

Barchanski, A.

A. Barchanski, T. Gensty, C. Degen, I. Fischer, and W. Elsäßer, “Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization,” IEEE J. Quantum Electron. 39, 850–858 (2003).
[Crossref]

Bava, G. P.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

Becker, K.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

K. Becker, I. Fischer, and W. Elsäßer, “Spatio-temporal emission dynamics of VCSELs: modal competition in the turn-on behavior,” Proc. SPIE 5452, 452–461 (2004).
[Crossref]

Bellancourt, A.-R.

D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
[Crossref]

Bhattacharya, A.

J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

Bimberg, D.

P. Moser, J. A. Lott, and D. Bimberg, “Energy efficiency of directly modulated oxide-confined high bit rate 850-nm VCSELs for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 19, 1702212 (2013).
[Crossref]

Binder, R.

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

Bittner, S.

S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
[Crossref]

Blau, W. J.

M. Djiango, T. Kobayashi, and W. J. Blau, “Cavity-enhanced stimulated emission cross section in polymer microlasers,” Appl. Phys. Lett. 93, 143306 (2008).
[Crossref]

Bond, W. L.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering gallery modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[Crossref]

Botez, D.

J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

Brorson, S. D.

H. Yokoyama and S. D. Brorson, “Rate equation analysis of microcavity lasers,” J. Appl. Phys. 66, 4801 (1989).
[Crossref]

Burak, D.

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

Campillo, A. J.

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[Crossref]

Cao, H.

S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
[Crossref]

Q. 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]

Chang, Y.-C.

C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
[Crossref]

Chembo, Y. K.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode VCSELs via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[Crossref]

Chien, C.-H.

C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
[Crossref]

Christodoulides, D. N.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346, 975–978 (2014).
[Crossref]

Colet, P.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode VCSELs via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[Crossref]

Collodo, M. C.

Connolly, J. C.

J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

Debernardi, P.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

Degen, C.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

A. Barchanski, T. Gensty, C. Degen, I. Fischer, and W. Elsäßer, “Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization,” IEEE J. Quantum Electron. 39, 850–858 (2003).
[Crossref]

C. Degen, I. Fischer, and W. Elsäßer, “Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects,” Opt. Express 5, 38–47 (1999).
[Crossref]

DeMarco, L.

J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

Di Falco, A.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
[Crossref]

Djiango, M.

M. Djiango, T. Kobayashi, and W. J. Blau, “Cavity-enhanced stimulated emission cross section in polymer microlasers,” Appl. Phys. Lett. 93, 143306 (2008).
[Crossref]

Ebeling, K. J.

M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
[Crossref]

El-Ganainy, R.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

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H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
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A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
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J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
[Crossref]

Feng, L.

Fischer, I.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode VCSELs via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[Crossref]

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

K. Becker, I. Fischer, and W. Elsäßer, “Spatio-temporal emission dynamics of VCSELs: modal competition in the turn-on behavior,” Proc. SPIE 5452, 452–461 (2004).
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A. Barchanski, T. Gensty, C. Degen, I. Fischer, and W. Elsäßer, “Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization,” IEEE J. Quantum Electron. 39, 850–858 (2003).
[Crossref]

C. Degen, I. Fischer, and W. Elsäßer, “Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects,” Opt. Express 5, 38–47 (1999).
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C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
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J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
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C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering gallery modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
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Q. 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).
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T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, “Wave chaos in real-world vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 94, 233901 (2005).
[Crossref]

A. Barchanski, T. Gensty, C. Degen, I. Fischer, and W. Elsäßer, “Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization,” IEEE J. Quantum Electron. 39, 850–858 (2003).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
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T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
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S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E 75, 036216 (2007).
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H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346, 975–978 (2014).
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H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
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S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
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H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346, 975–978 (2014).
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M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
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S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
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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).
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S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
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M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
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C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
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A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
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C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
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J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
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M. Lorke, T. Suhr, N. Gregersen, and J. Mørk, “Theory of nanolaser devices: rate equation analysis versus microscopic theory,” Phys. Rev. B 87, 205310 (2013).
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P. Moser, J. A. Lott, and D. Bimberg, “Energy efficiency of directly modulated oxide-confined high bit rate 850-nm VCSELs for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 19, 1702212 (2013).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
[Crossref]

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Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode VCSELs via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[Crossref]

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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
[Crossref]

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J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
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L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
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H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346, 975–978 (2014).
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S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
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Molinari, D.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
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M. Lorke, T. Suhr, N. Gregersen, and J. Mørk, “Theory of nanolaser devices: rate equation analysis versus microscopic theory,” Phys. Rev. B 87, 205310 (2013).
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P. Moser, J. A. Lott, and D. Bimberg, “Energy efficiency of directly modulated oxide-confined high bit rate 850-nm VCSELs for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 19, 1702212 (2013).
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J. Mawst, A. Bhattacharya, J. Lopez, D. Botez, D. Z. Garbuzov, L. DeMarco, J. C. Connolly, M. Jansen, F. Fang, and R. F. Nabiev, “8 W continuous wave front-facet power from broad-waveguide Al-free 980 nm diode lasers,” Appl. Phys. Lett. 69, 1532–1534 (1996).
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Ngo, T. H.-B.

C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
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J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
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M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

Oh, S. S.

S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
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S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
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C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7, 473–478 (2013).
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L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Pu, X. Y.

Redding, B.

Q. 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).
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W. Wei, X. Zhang, X. Yan, and X. Ren, “Observation of enhanced spontaneous and stimulated emission of GaAs/AlGaAs nanowire via the Purcell effect,” AIP Adv. 5, 087148 (2015).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
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H. Schomerus, J. Wiersig, and M. Hentschel, “Optomechanical probes of resonances in amplifying microresonators,” Phys. Rev. A 70, 012703 (2004).
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S. Sekiguchi, T. Miyamoto, T. Kimura, G. Okazaki, F. Koyama, and K. Iga, “Improvement of current injection uniformity and device resistance in long-wavelength vertical-cavity surface-emitting laser using a tunnel junction,” Jpn. J. Appl. Phys. 39, 3997–4001 (2000).
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T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
[Crossref]

S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E 75, 036216 (2007).
[Crossref]

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L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

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Q. 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).
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J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
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M. Lorke, T. Suhr, N. Gregersen, and J. Mørk, “Theory of nanolaser devices: rate equation analysis versus microscopic theory,” Phys. Rev. B 87, 205310 (2013).
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S. Uchiyama and K. Iga, “Two-dimensional array of GaInAsP/lnP surface-emitting lasers,” Electron. Lett. 21, 162–164 (1985).
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D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88, 493–497 (2007).
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M. Grabherr, M. Miller, R. Jager, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, “High-power VCSELs: single devices and densely packed 2-D-arrays,” IEEE J. Sel. Top. Quantum Electron. 5, 495–502 (1999).
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H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
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Wang, Q. J.

S. Bittner, S. Guazzotti, Y. Zeng, X. Hu, H. Yılmaz, K. Kim, S. S. Oh, Q. J. Wang, O. Hess, and H. Cao, “Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities,” Science 361, 1225–1231 (2018).
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W. Wei, X. Zhang, X. Yan, and X. Ren, “Observation of enhanced spontaneous and stimulated emission of GaAs/AlGaAs nanowire via the Purcell effect,” AIP Adv. 5, 087148 (2015).
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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).
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Wu, S.-H.

C.-H. Chien, S.-H. Wu, T. H.-B. Ngo, and Y.-C. Chang, “Interplay of Purcell effect, stimulated emission, and leaky modes in the photoluminescence spectra of microsphere cavities,” Phys. Rev. Appl. 11, 051001 (2019).
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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).
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Supplementary Material (1)

NameDescription
Supplement 1       Supplementary information, tables,and figures

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. First column, schematic top view of five different VCSEL mesa shapes; further columns, near-field images of spontaneous emission for VCSELs with different aperture shapes including ball (first row), ping-pong (second row), padel (third row), squash (fourth row), and tennis (fifth row). The numbers correspond to the diameter of the side mesa for each racket (see Supplement 1, Section S1). Colored frames indicate configurations analyzed from Fig. 2(b) onwards.
Fig. 2.
Fig. 2. (a) Maximal emitted optical power versus oxide aperture area for all tested devices, and (b) emitted optical power versus injected current for the devices indicated by colored frames in Fig. 1 and collected in Table 1. The colors represent ball (black), ping-pong (magenta), padel (blue), squash (green), and tennis (red). The numbers in (a) indicate the diameters of the circular side mesas (see Supplement 1, Section S1). The black line in (a) intersects ${P_{{\max}}} = {{0}}$, $s = {{0}}$, and the black point corresponding to ball indicates in an approximate manner the proportionality between the emitted power and the surface area of the circular oxide aperture VCSEL.
Fig. 3.
Fig. 3. Emission spectra and near-field distributions of the dominant modes for (a) ball, (b) ping-pong30, (c) padel30, (d) squash40, and (e) tennis40 VCSEL devices. The label “total” indicates the distribution of the total spatial light intensity for the given current.
Fig. 4.
Fig. 4. (a) Total light intensity ($I$) in the left circle-shaped part of the VCSEL apertures averaged over the angle (see Fig. 3); the relative radius $r_0$ is determined based on the light intensity distribution corresponding to half the maximum; (b) quantum efficiency; (c) maximal output power versus the integral of the near-field light intensity. The integral profile of the light intensity is normalized to 1.
Fig. 5.
Fig. 5. (a) Wavelengths of all registered modes in the experimental spectra of the ball and a polynomial fit (dashed line) of the wavelength versus CW bias current for the 10 modes with the longest wavelengths. Relative wavelengths ($\Delta \lambda$) of all registered modes in the experimental spectra of (b) ball; (c) ping-pong30; (d) padel30; (e) squash40; and (f) tennis40, for CW bias currents ($I$) ranging from the proximity of threshold to the LI rollover. The colors represent the intensity of the modes (on a logarithmic scale) relative to the dominant mode in the emission spectrum at a given current.
Fig. 6.
Fig. 6. (a) Spectral density of modes (${\rho _m}$) versus bias current based on the experimental spectra of the VCSELs. ${\rho _m}$ was averaged over 20 consecutive spectra; (b) quantum efficiency; (c) maximal output power versus the maximal density of modes for the considered VCSELs.
Fig. 7.
Fig. 7. Cumulative nearest-neighbor eigenvalue spacing $P(\sigma)$ (left axis) and Lorentzian function $L(\sigma)$ with different values of $\Delta E$ (right axis).

Tables (1)

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Table 1. Surface Area of the Oxide Aperture ( s ), Threshold Current ( I t h ), Maximal Quantum Efficiency ( η Q E m a x ), and Maximal Emitted Power ( P max ) for the Studied VCSELs

Equations (1)

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L ( σ ) = 1 1 + ( σ Δ E ) 2 ,

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