Elimination of variables in simple laser equations

C. Z. Ning, H. Haken

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (γ≫γ, κ) and case 2 (γ, γ≫κ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (γ, κγ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (κ). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.

Original languageEnglish (US)
Pages (from-to)117-120
Number of pages4
JournalApplied Physics B Photophysics and Laser Chemistry
Issue number2
StatePublished - Aug 1 1992
Externally publishedYes


  • 02
  • 42.55
  • 42.65

ASJC Scopus subject areas

  • General Engineering


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