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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 474–488

Steady-state ab initio laser theory for N-level lasers

Alexander Cerjan, Yidong Chong, Li Ge, and A. Douglas Stone  »View Author Affiliations

Optics Express, Vol. 20, Issue 1, pp. 474-488 (2012)

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We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the type solved by the SALT algorithm. This mapping yields excellent agreement with more computationally demanding N-level time domain solutions for the steady state.

© 2011 OSA

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Lasers and Laser Optics

Original Manuscript: September 27, 2011
Revised Manuscript: November 21, 2011
Manuscript Accepted: November 22, 2011
Published: December 21, 2011

Alexander Cerjan, Yidong Chong, Li Ge, and A. Douglas Stone, "Steady-state ab initio laser theory for N-level lasers," Opt. Express 20, 474-488 (2012)

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  1. H. Haken, Light: Laser Dynamics (North-Holland Phys. Publishing, 1985), Vol. 2.
  2. W. E. Lamb, “Theory of an optical maser,” Phys. Rev.134, A1429 (1964). [CrossRef]
  3. A. E. Siegman, Lasers (University Science Books, 1986).
  4. A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag.46, 334–340 (1998). [CrossRef]
  5. K. S. Yee, “Numerical solution of the initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans Antennas Propag. 14, 302–307 (1966). [CrossRef]
  6. H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A74, 043822 (2006). [CrossRef]
  7. H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A76, 013813 (2007). [CrossRef]
  8. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science320, 643–646 (2008). [CrossRef] [PubMed]
  9. L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A82, 063824 (2010). [CrossRef]
  10. H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A38, 10497–10535 (2005). [CrossRef]
  11. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284, 1819–1821 (1999). [CrossRef] [PubMed]
  12. S. Chua, Y. D. Chong, A. D. Stone, M Soljac̆ić, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express19, 1539 (2011). [CrossRef] [PubMed]
  13. 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,” Science280, 1556–1564 (1998). [CrossRef] [PubMed]
  14. Ge Li, Yale PhD thesis, 2010.
  15. L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express16, 16895 (2008). [CrossRef] [PubMed]
  16. The equations are written for the TM case, the modifications for TE are straightforward.
  17. The observation that coherent and incoherent pumping are nearly equivalent for most systems, is invalid when the coherent pumping is supplied at a similar frequency to the atomic lasing transition and thus interactions between the lasing field and pumping field must be taken into account.
  18. H. Fu and H. Haken, “Multifrequency operations in a short-cavity standing-wave laser,” Phys. Rev. A43, 2446–2454 (1991). [CrossRef] [PubMed]
  19. Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).
  20. B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Meth. Partial Differential Equations19, 284–300 (2003). [CrossRef]
  21. For any 1D cavity which is uniformly pumped the TCF states for solving SALT can also be found using a transfer matrix method which does not require discretizing space. We use a more general TCF solver in the calculations presented here which does discretize space.
  22. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett.85, 70 (2000). [CrossRef] [PubMed]
  23. X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B69, 104202 (2004). [CrossRef]
  24. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

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