Abstract

We introduce a simplified version of the steady-state ab initio laser theory for calculating the effects of mode competition in continuous wave lasers using the passive cavity resonances. This new theory harnesses widely available numerical methods that can efficiently calculate the passive cavity resonances, with negligible additional computational overhead. Using this theory, we demonstrate that the pump profile of the laser cavity can be optimized both for highly multi-mode and single-mode emission. An open source implementation of this method has been made available.

© 2016 Optical Society of America

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References

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  1. N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
    [Crossref]
  2. T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
    [Crossref] [PubMed]
  3. L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
    [Crossref]
  4. S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
    [Crossref]
  5. S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
    [Crossref]
  6. L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30,049 (2015).
    [Crossref]
  7. L. Ge, H. Cao, and A. D. Stone, “Condensation of thresholds in multimode microlasers,” arXiv:1607.08204, in submission.
  8. B. Bidégaray, “Time discretizations for maxwell-bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
    [Crossref]
  9. Y. Huang and S. Ho, “Computational model of solid-state, molecular, or atomic media for fdtd simulation based on a multi-level multi-electron system governed by pauli exclusion and fermi-dirac thermalization with application to semiconductor photonics,” Opt. Express 14, 3569–3587 (2006).
    [Crossref] [PubMed]
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    [Crossref]
  11. Y. Huang and S.-T. Ho, “Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices,” Opt. Quantum Electron. 40, 337–341 (2008).
    [Crossref]
  12. A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
    [Crossref]
  13. H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043,822 (2006).
    [Crossref]
  14. L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
    [Crossref]
  15. A. Cerjan, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory for complex gain media,” Opt. Express 23, 6455–6477 (2015).
    [Crossref] [PubMed]
  16. S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
    [Crossref]
  17. A. Cerjan, “Resonance SPA-SALT,” github (2016) [retrieved 26 August 2016], https://github.com/acerjan/comsol_spasalt .
  18. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
    [Crossref]
  19. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
    [Crossref] [PubMed]
  20. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
    [Crossref]
  21. H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
    [Crossref]
  22. A. Sommerfeld, Partial Differential Equations in Physics (Academic Press, 1949).
  23. S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
    [Crossref]
  24. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Incorporated, 2005).
  25. A. Goetschy, A. Cerjan, and A. D. Stone, “Analytic statistical theory of random lasers in the non-linear regime,” in preparation.
  26. B. Redding, M. A. Choma, and H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
    [Crossref] [PubMed]
  27. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
    [Crossref] [PubMed]
  28. B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
    [Crossref] [PubMed]
  29. L. Bunimovich, “Ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1979).
    [Crossref]
  30. S. Ree and L. Reichl, “Classical and quantum chaos in a circular billiard with a straight cut,” Phys. Rev. E 60, 1607–1615 (1999).
    [Crossref]
  31. M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38, 3858–3861 (2013).
    [Crossref] [PubMed]
  32. B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
    [Crossref] [PubMed]
  33. B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

2015 (5)

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30,049 (2015).
[Crossref]

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

A. Cerjan, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory for complex gain media,” Opt. Express 23, 6455–6477 (2015).
[Crossref] [PubMed]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

2014 (4)

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

2013 (3)

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38, 3858–3861 (2013).
[Crossref] [PubMed]

2012 (2)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref] [PubMed]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

2011 (1)

2010 (1)

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
[Crossref]

2008 (2)

K. Böhringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. i. theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[Crossref]

Y. Huang and S.-T. Ho, “Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices,” Opt. Quantum Electron. 40, 337–341 (2008).
[Crossref]

2006 (2)

2005 (1)

H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]

2003 (1)

B. Bidégaray, “Time discretizations for maxwell-bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]

1999 (2)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

S. Ree and L. Reichl, “Classical and quantum chaos in a circular billiard with a straight cut,” Phys. Rev. E 60, 1607–1615 (1999).
[Crossref]

1998 (1)

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

1997 (1)

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

1979 (1)

L. Bunimovich, “Ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1979).
[Crossref]

Adachi, M.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Andreasen, J.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

Bachelard, N.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

Bidégaray, B.

B. Bidégaray, “Time discretizations for maxwell-bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]

Bixler, J. N.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Böhringer, K.

K. Böhringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. i. theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[Crossref]

Bunimovich, L.

L. Bunimovich, “Ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1979).
[Crossref]

Cao, H.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38, 3858–3861 (2013).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref] [PubMed]

H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

L. Ge, H. Cao, and A. D. Stone, “Condensation of thresholds in multimode microlasers,” arXiv:1607.08204, in submission.

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Capasso, F.

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

Cerjan, A.

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

A. Cerjan, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory for complex gain media,” Opt. Express 23, 6455–6477 (2015).
[Crossref] [PubMed]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

A. Cerjan, “Resonance SPA-SALT,” github (2016) [retrieved 26 August 2016], https://github.com/acerjan/comsol_spasalt .

A. Goetschy, A. Cerjan, and A. D. Stone, “Analytic statistical theory of random lasers in the non-linear regime,” in preparation.

Chang, R. P. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Cho, A. Y.

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

Choma, M. A.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref] [PubMed]

Chong, Y. D.

A. Cerjan, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory for complex gain media,” Opt. Express 23, 6455–6477 (2015).
[Crossref] [PubMed]

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
[Crossref]

Collier, B.

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043,822 (2006).
[Crossref]

Davidson, N.

Dyer, P. N.

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Esterhazy, S.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Faist, J.

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

Friesem, A. A.

Fukushima, T.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Ge, L.

L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30,049 (2015).
[Crossref]

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
[Crossref]

L. Ge, H. Cao, and A. D. Stone, “Condensation of thresholds in multimode microlasers,” arXiv:1607.08204, in submission.

Gigan, S.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

Gmachl, C.

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

Goetschy, A.

A. Goetschy, A. Cerjan, and A. D. Stone, “Analytic statistical theory of random lasers in the non-linear regime,” in preparation.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Incorporated, 2005).

Harayama, T.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Hess, O.

K. Böhringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. i. theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[Crossref]

Hisch, T.

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Ho, S.

Ho, S. T.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Ho, S.-T.

Y. Huang and S.-T. Ho, “Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices,” Opt. Quantum Electron. 40, 337–341 (2008).
[Crossref]

Hokr, B. H.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Huang, X.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

Huang, Y.

Johnson, S. G.

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Lee, M. L.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

Liertzer, M.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Liew, S. F.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

Liu, D.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Makris, K. G.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Malik, O.

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

Melenk, J. M.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Mintert, F.

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Narimanov, E. E.

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

Nixon, M.

Nöckel, J. U.

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

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

Noojin, G. D.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Pick, A.

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

Pogany, D.

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Redding, B.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38, 3858–3861 (2013).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Ree, S.

S. Ree and L. Reichl, “Classical and quantum chaos in a circular billiard with a straight cut,” Phys. Rev. E 60, 1607–1615 (1999).
[Crossref]

Reichl, L.

S. Ree and L. Reichl, “Classical and quantum chaos in a circular billiard with a straight cut,” Phys. Rev. E 60, 1607–1615 (1999).
[Crossref]

Rockwell, B. A.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Rotter, S.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Schmidt, M. S.

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Scully, M. O.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Sebbah, P.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

Seelig, E. W.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Shinohara, S.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Sivco, D. L.

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

Solomon, G. S.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Partial Differential Equations in Physics (Academic Press, 1949).

Stone, A. D.

A. Cerjan, A. Pick, Y. D. Chong, S. G. Johnson, and A. D. Stone, “Quantitative test of general theories of the intrinsic laser linewidth,” Opt. Express 23, 28,316–28,340 (2015).
[Crossref]

A. Cerjan, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory for complex gain media,” Opt. Express 23, 6455–6477 (2015).
[Crossref] [PubMed]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043,822 (2006).
[Crossref]

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

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

L. Ge, H. Cao, and A. D. Stone, “Condensation of thresholds in multimode microlasers,” arXiv:1607.08204, in submission.

A. Goetschy, A. Cerjan, and A. D. Stone, “Analytic statistical theory of random lasers in the non-linear regime,” in preparation.

Sunada, S.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Incorporated, 2005).

Thomas, R. J.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Türeci, H. E.

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043,822 (2006).
[Crossref]

Wang, Q. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Yakovlev, V. V.

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

Zhao, Y. G.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Appl. Phys. Lett. (1)

S. F. Liew, B. Redding, L. Ge, G. S. Solomon, and H. Cao, “Active control of emission directionality of semiconductor microdisk lasers,” Appl. Phys. Lett. 104, 231,108 (2014).
[Crossref]

Commun. Math. Phys. (1)

L. Bunimovich, “Ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1979).
[Crossref]

J. Phys. A (1)

H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]

Nat. Photonics (2)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref] [PubMed]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

Nature (1)

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

Numer. Meth. Partial Differential Equations (1)

B. Bidégaray, “Time discretizations for maxwell-bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

Y. Huang and S.-T. Ho, “Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices,” Opt. Quantum Electron. 40, 337–341 (2008).
[Crossref]

Phys. Rev. A (5)

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043,822 (2006).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063,824 (2010).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043,828 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Phys. Rev. E (1)

S. Ree and L. Reichl, “Classical and quantum chaos in a circular billiard with a straight cut,” Phys. Rev. E 60, 1607–1615 (1999).
[Crossref]

Phys. Rev. Lett. (3)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett. 109, 033,903 (2012).
[Crossref]

T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111, 023902 (2013).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U. S. A. (2)

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. U. S. A. 112, 1304–1309 (2015).
[Crossref] [PubMed]

B. H. Hokr, J. N. Bixler, G. D. Noojin, R. J. Thomas, B. A. Rockwell, V. V. Yakovlev, and M. O. Scully, “Single-shot stand-off chemical identification of powders using random raman lasing,” Proc. Natl. Acad. Sci. U. S. A. 111, 12320–12324 (2014).
[Crossref] [PubMed]

Prog. Quantum Electron. (1)

K. Böhringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. i. theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[Crossref]

Science (1)

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

Other (6)

A. Cerjan, “Resonance SPA-SALT,” github (2016) [retrieved 26 August 2016], https://github.com/acerjan/comsol_spasalt .

L. Ge, H. Cao, and A. D. Stone, “Condensation of thresholds in multimode microlasers,” arXiv:1607.08204, in submission.

B. H. Hokr, M. S. Schmidt, J. N. Bixler, P. N. Dyer, G. D. Noojin, B. Redding, R. J. Thomas, B. A. Rockwell, H. Cao, V. V. Yakovlev, and M. O. Scully, “A narrow-band speckle-free light source via random Raman lasing,” arXiv: 1505.07156 (2015).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Incorporated, 2005).

A. Goetschy, A. Cerjan, and A. D. Stone, “Analytic statistical theory of random lasers in the non-linear regime,” in preparation.

A. Sommerfeld, Partial Differential Equations in Physics (Academic Press, 1949).

Supplementary Material (1)

NameDescription
» Code 1       Repository for code.

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Figures (3)

Fig. 1
Fig. 1

(a–c) Plot of the modal intensity Iμ as a function of the pump parameter D0 for D-shaped cavities with R = 5μm, n = 3.5, filled with a gain medium with a central wavelength of λa = 1μm, and width γ = 30nm. Different choices of r0 are shown in each plot, (a) r0 = 0.3R, (b) r0 = 0.5R, and (c) r0 = 0.7R. Solid lines show the direct calculation using full SALT simulations, while dashed lines show resonance SPA-SALT results. The SALT simulations were performed using 100 CF basis states, and were run to ∼6 lasing modes. In (b), the SALT simulations terminate after seven lasing modes when the simulations became too memory intensive to continue. (d–f) Plots of the generalized modal competition parameter, λ, given in Eq. (11), for the same cavity. Different choices of r0 are shown in each plot, (d) r0 = 0.3R, (e) r0 = 0.5R, and (f) r0 = 0.7R.

Fig. 2
Fig. 2

Plot of the non-interacting (dashed lines) and interacting (solid lines) modal thresholds for the first 10 lasing modes for a D-shaped cavity with R = 5μm, n = 3.5, filled with a gain medium with a central wavelength of λa = 1μm, and width γ = 10nm using different pump profiles calculated using SPA-SALT with the passive cavity resonances generated by COMSOL Multiphysics. The thresholds for the uniform pump are shown in red and those generated using a genetic algorithm to minimize Eq. (16) are in green. For the inhomogeneous pumping scheme, there are 12 independent electrical contacts which divide the cavity radially in two, and angularly in eight.

Fig. 3
Fig. 3

Plots of the modal intensities, Iμ, given in Eq. (15), for a D-shaped cavity with R = 4μm, r0 = 2μm, n = 3.5, filled with a gain medium with a central wavelength of λa = 1μm, and width γ = 10nm. Solid lines show the direct calculation using full SALT simulations, while dashed lines show the SPA-SALT results generated using passive cavity information generated by COMSOL Multiphysics. (Left panel) Uniformly pumped D-shaped cavity, as indicated in the inset. (Right panel) Inhomogeneously pumped D-shaped cavity, as indicated in the inset. Here, the pump profile has been optimized using Eq. (17) to increase the range of single mode operation while maintaining the same threshold pump as the uniformly pumped cavity. There are 23 electrical contacts here, which divide the cavity radially in three, and angularly in ten.

Equations (17)

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[ ( × × ) ( ε c ( x ) + χ g ( x , ω μ , D 0 ) ) ω μ 2 c 2 ] Ψ μ ( x ) = 0 , x C , [ ( × × ) n 0 2 ω μ 2 c 2 ] Ψ μ ( x ) = 0 . x C ,
χ g ( x , ω , D 0 ) = γ D 0 ( x ) ω ω a + i γ ( 1 1 + ν N L Γ ν | Ψ ν ( x ) | 2 ) .
lim r r d 1 2 ( c r i ω μ ) Ψ μ ( x ) = 0 ,
[ ( × × ) ( ε c ( x ) + ε abs ( x ) ) ω ˜ m 2 c 2 ] φ m ( x ) = 0 ,
C ε c ( x ) φ μ ( x ) φ μ ( x ) d x = 1 .
D ( μ ) = | ( Re [ ω ˜ μ ] ω a + i γ γ ) ( ω ˜ μ 2 Re [ ω ˜ μ ] 2 Re [ ω ˜ μ ] 2 ) | ( 1 f μ ¯ ) ,
f μ ¯ = | C f ( x ) φ μ 2 ( x ) d x | ,
D 0 D 0 ( μ ) 1 = ν Γ ν I ν χ μ ν ,
χ μ ν = | C φ μ ( x ) ε c ( x ) φ μ ( x ) | φ ν ( x ) | 2 d x | .
D int ( μ ) = 1 1 λ μ D ( μ ) ,
λ μ = ν = 1 N L A μ ν ( c ν D ( μ ) b ν ) 1 ν = 1 N L A μ ν b ν ,
A μ ν = Γ ν χ μ ν ,
b μ = ν = 1 N L ( A 1 ) μ ν ,
c μ = ν = 1 N L ( A 1 ) μ ν D ( ν ) .
I μ = c μ D 0 b μ .
F ( { p i } ) = n = 1 N L D adap , int ( n ) D uni ( 1 ) ,
F ( { p i } ) = D adap ( 1 ) D adap , int ( 2 ) + | 1 D adap ( 1 ) D uni ( 1 ) | .

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