Derivation of semiconductor laser mean-field and Swift-Hohenberg equations

J. F. Mercier, Jerome V Moloney

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Bulk and quantum well semiconductor lasers by nature display fundamentally different physical characteristics relative to multilevel gas and solid state lasers. In particular, the refractive index is nonzero at peak gain and the peak gain can shift strongly with varying carrier density or temperature. Moreover, a quantum well laser gain may be strongly asymmetric if more than the lowest subband is populated. Rigorously computed and experimentally validated, gain and refractive index spectra are now available for a variety of quantum well structures emitting from the infrared to the visible. Active devices can be designed and grown such that the gain spectrum remains approximately parabolic for carrier density variations typically encountered in above threshold pumped broad area edge-emitting semiconductor lasers. Under this assumption, we derive a robust optical propagation model that tracks the important peak gain shifts and broadening as long as the gain remains approximately parabolic over the relevant energy range in a running laser. We next derive a multimode model where the longitudinal modes are projected out of the total field. The next stage is to derive a mean-field single longitudinal mode model for a wide aperture semiconductor laser. The mean-field model allows for significant cavity losses and widely different facet reflectivities such as occurs with antireflection- and high-reflectivity-coated facets. The single mode mean-field model is further reduced using an asymptotic expansion of the relevant physical fields with respect to a small parameter. The end result is a complex semiconductor Swift-Hohenberg description of a single longitudinal mode wide aperture laser. The latter should provide a useful model for studying scientifically and technologically important lasers such as vertical cavity surface emitting semiconductor lasers.

Original languageEnglish (US)
Article number036221
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number3
DOIs
StatePublished - Sep 2002

Fingerprint

Swift-Hohenberg Equation
Semiconductor Lasers
Mean Field
derivation
semiconductor lasers
Quantum Well
Laser
Mean-field Model
quantum well lasers
Reflectivity
Facet
Refractive Index
flat surfaces
apertures
refractivity
lasers
reflectance
cavities
Vertical-cavity Surface-emitting Laser (VCSEL)
Solid-state Laser

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Derivation of semiconductor laser mean-field and Swift-Hohenberg equations. / Mercier, J. F.; Moloney, Jerome V.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 66, No. 3, 036221, 09.2002.

Research output: Contribution to journalArticle

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