Abstract

A coherent combination of emission power from an array of coupled semiconductor lasers operating on the same chip is of fundamental and technological importance. In general, the nonlinear competition among the array supermodes can entail incoherence and spectral broadening, leading to a spatiotemporally unstable and multimode emission pattern and thus poor beam quality. Here, by harnessing notions from supersymmetric (SUSY) quantum mechanics, we report that the strategic coupling between a class III-V semiconductor microring laser array with its dissipative superpartner can be used to limit the number of supermodes available for laser actions to one. We introduce a novel approach based on second-order SUSY transformation in order to drastically simplify the superpartner array engineering. Compared to a conventional laser array, which has a multimode spectrum, a SUSY laser array is observed to be capable of operating in a single (transverse) supermode. Enhancement of the peak output intensity of the SUSY laser array has been demonstrated with high efficiency and lower lasing threshold, compared with a single laser and a conventional laser array. Our experimental findings pave the way towards broad-area and high-power light generation in a scalable and stable fashion.

© 2019 Chinese Laser Press

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References

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  1. M. Drees, R. Godbole, and P. Roy, Theory and Phenomenology of Sparticles (World Scientific, 2004).
  2. M. Dine, Supersymmetry and String Theory: Beyond the Standard Model (Cambridge University, 2007).
  3. S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
    [Crossref]
  4. G. Junker, Supersymmetric Methods in Quantum and Statistical Physics (Springer, 1996).
  5. S. Longhi, “Invisibility in non-Hermitian tight-binding lattices,” Phys. Rev. A 82, 032111 (2010).
    [Crossref]
  6. M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
    [Crossref]
  7. B. Midya, W. Walasik, N. M. Litchinitser, and L. Feng, “Supercharge optical arrays,” Opt. Lett. 43, 4927–4930 (2018).
    [Crossref]
  8. M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
    [Crossref]
  9. R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
    [Crossref]
  10. W. Walasik, B. Midya, L. Feng, and N. M. Litchinitser, “Supersymmetry-guided method for mode selection and optimization in coupled systems,” Opt. Lett. 43, 3758–3761 (2018).
    [Crossref]
  11. D. Botez and D. R. Scifres, eds., Diode Laser Arrays (Cambridge University, 1994).
  12. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
    [Crossref]
  13. M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
    [Crossref]
  14. D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
    [Crossref]
  15. D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
    [Crossref]
  16. E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
    [Crossref]
  17. A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
    [Crossref]
  18. E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. 9, 125–127 (1984).
    [Crossref]
  19. J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2013).
  20. H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
    [Crossref]
  21. L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
    [Crossref]
  22. J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
    [Crossref]
  23. D. Brunner and I. Fischer, “Reconfigurable semiconductor laser networks based on diffractive coupling,” Opt. Lett. 40, 3854–3857 (2015).
    [Crossref]
  24. S. Longhi and L. Feng, “Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling,” APL Photon. 3, 060802 (2018).
    [Crossref]
  25. M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

2018 (3)

2015 (2)

D. Brunner and I. Fischer, “Reconfigurable semiconductor laser networks based on diffractive coupling,” Opt. Lett. 40, 3854–3857 (2015).
[Crossref]

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

2014 (2)

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

2013 (2)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

2010 (1)

S. Longhi, “Invisibility in non-Hermitian tight-binding lattices,” Phys. Rev. A 82, 032111 (2010).
[Crossref]

2005 (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

2003 (1)

A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
[Crossref]

1988 (1)

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

1984 (1)

1983 (1)

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
[Crossref]

1981 (1)

S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
[Crossref]

1979 (1)

D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
[Crossref]

1978 (1)

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
[Crossref]

1975 (1)

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[Crossref]

Brunner, D.

Burnham, R.

D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
[Crossref]

Burnham, R. D.

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
[Crossref]

Christodoulides, D. N.

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

Dimopoulos, S.

S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
[Crossref]

Dine, M.

M. Dine, Supersymmetry and String Theory: Beyond the Standard Model (Cambridge University, 2007).

Drees, M.

M. Drees, R. Godbole, and P. Roy, Theory and Phenomenology of Sparticles (World Scientific, 2004).

El-Ganainy, R.

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

Feng, L.

S. Longhi and L. Feng, “Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling,” APL Photon. 3, 060802 (2018).
[Crossref]

W. Walasik, B. Midya, L. Feng, and N. M. Litchinitser, “Supersymmetry-guided method for mode selection and optimization in coupled systems,” Opt. Lett. 43, 3758–3761 (2018).
[Crossref]

B. Midya, W. Walasik, N. M. Litchinitser, and L. Feng, “Supercharge optical arrays,” Opt. Lett. 43, 4927–4930 (2018).
[Crossref]

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

Fischer, I.

D. Brunner and I. Fischer, “Reconfigurable semiconductor laser networks based on diffractive coupling,” Opt. Lett. 40, 3854–3857 (2015).
[Crossref]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

García-Ojalvo, J.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

Ge, L.

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

Glova, A. F.

A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
[Crossref]

Godbole, R.

M. Drees, R. Godbole, and P. Roy, Theory and Phenomenology of Sparticles (World Scientific, 2004).

Heinrich, M.

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

Hokmabadi, M. P.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

Junker, G.

G. Junker, Supersymmetric Methods in Quantum and Statistical Physics (Springer, 1996).

Kapon, E.

Katz, J.

E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. 9, 125–127 (1984).
[Crossref]

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
[Crossref]

Khajavikhan, M.

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

Litchinitser, N. M.

Longhi, S.

S. Longhi and L. Feng, “Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling,” APL Photon. 3, 060802 (2018).
[Crossref]

S. Longhi, “Invisibility in non-Hermitian tight-binding lattices,” Phys. Rev. A 82, 032111 (2010).
[Crossref]

Ma, R. M.

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

Margalit, S.

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
[Crossref]

Midya, B.

Mirasso, C. R.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

Miri, M.-A.

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

Nolte, S.

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

Nye, N. S.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2013).

Philipp-Rutz, E. M.

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[Crossref]

Raby, S.

S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
[Crossref]

Roy, P.

M. Drees, R. Godbole, and P. Roy, Theory and Phenomenology of Sparticles (World Scientific, 2004).

Scifres, D.

D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
[Crossref]

Scifres, D. R.

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
[Crossref]

Soriano, M. C.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

Streifer, W.

D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
[Crossref]

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
[Crossref]

Stützer, S.

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

Szameit, A.

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

Walasik, W.

Wang, S. S.

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

Wang, Y.

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

Wilczek, F.

S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
[Crossref]

Winful, H. G.

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

Wong, Z. J.

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

Yariv, A.

E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. 9, 125–127 (1984).
[Crossref]

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
[Crossref]

Zhang, X.

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

APL Photon. (1)

S. Longhi and L. Feng, “Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling,” APL Photon. 3, 060802 (2018).
[Crossref]

Appl. Phys. Lett. (4)

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–556 (1983).
[Crossref]

H. G. Winful and S. S. Wang, “Stability of phase locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
[Crossref]

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[Crossref]

IEEE J. Quantum Electron. (1)

D. Scifres, W. Streifer, and R. Burnham, “Experimental and analytic studies of coupled multiple stripe diode lasers,” IEEE J. Quantum Electron. 15, 917–922 (1979).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

Nat. Commun. (1)

M. Heinrich, M.-A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (2)

R. El-Ganainy, L. Ge, M. Khajavikhan, and D. N. Christodoulides, “Supersymmetric laser arrays,” Phys. Rev. A 92, 033818 (2015).
[Crossref]

S. Longhi, “Invisibility in non-Hermitian tight-binding lattices,” Phys. Rev. A 82, 032111 (2010).
[Crossref]

Phys. Rev. D (1)

S. Dimopoulos, S. Raby, and F. Wilczek, “Supersymmetry and the scale of unification,” Phys. Rev. D 24, 1681–1683 (1981).
[Crossref]

Phys. Rev. Lett. (1)

M.-A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013).
[Crossref]

Quantum Electron. (1)

A. F. Glova, “Phase locking of optically coupled lasers,” Quantum Electron. 33, 283–306 (2003).
[Crossref]

Rev. Mod. Phys. (1)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

Science (1)

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346, 972–975 (2014).
[Crossref]

Other (6)

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2013).

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” arXiv:1812.10690 (2018).

D. Botez and D. R. Scifres, eds., Diode Laser Arrays (Cambridge University, 1994).

G. Junker, Supersymmetric Methods in Quantum and Statistical Physics (Springer, 1996).

M. Drees, R. Godbole, and P. Roy, Theory and Phenomenology of Sparticles (World Scientific, 2004).

M. Dine, Supersymmetry and String Theory: Beyond the Standard Model (Cambridge University, 2007).

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Figures (4)

Fig. 1.
Fig. 1. Fundamental concept behind the single (transverse) supermode lasing. (a) A single laser supports multiple longitudinal cavity modes (vertical black lines) separated by free spectral range. When N such rings are coupled, N closely spaced transverse supermodes emerge with equal threshold (middle panel). In the presence of gain, a suitable pump can induce simultaneous lasing of all the supermodes. The global mode coupling with a dissipative superpartner in a SUSY laser array, schematically shown in (b), can increase the threshold of undesired modes (shown in vertical purple lines in the bottom panel), enforcing a lasing of a single supermode that lacks a superpartner counterpart. (c) Second-order SUSY transformation for the superpartner design.
Fig. 2.
Fig. 2. SUSY laser array linear mode analysis. (a) Design parameter of a SUSY microring laser array containing nine coupled lasers. (b), (c) Linear eigen spectrum and corresponding modal intensities (only the cross-sectional view is shown), respectively. The spectrum shows that the fundamental mode of the SUSY array has the least threshold. All other modes of the conventional laser array split into symmetric and anti-symmetric pairs Ω±. Here ω˜=0, γ0=0.005k, γ=k/6, and k=1 are considered.
Fig. 3.
Fig. 3. Device and spectrum. (a) Scanning electron microscope images of the fabricated SUSY microring laser array. The image was taken before the transfer of the sample into a silica substrate. (b) Evolution of the photon emission spectrum from photoluminescence to amplified spontaneous emission and then to supermode lasing at the wavelengths of about 1544 nm and 1568 nm, when pumping is increased. The two lasing peaks, separated by 24 nm, belong to two longitudinal modes in a single microring laser [see Fig. 4(a)].
Fig. 4.
Fig. 4. Comparison of measured spectra. (a) Output spectra for a single laser, a conventional laser array, and the SUSY laser array when 2.46  GW/m2 pump intensity is considered. The conventional array is seen to be highly multimoded (as evident from the magnified spectrum shown in the inset). The spectra of a single laser and the SUSY laser array are almost indistinguishable. The enhancement of lasing output peak intensity is seen in the SUSY laser array. The nearfield images of lasing emissions are also shown. (b) Light–light curve showing the lowering of the threshold and enhancement of lasing output in a SUSY laser array compared to a single microring laser.