Elimination of variables in simple laser equations |
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Authors: | C Z Ning H Haken |
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Institution: | (1) Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57/4, W-7000 Stuttgart 80, Fed. Rep. Germany |
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Abstract: | 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 (, ) and case 2 (, ), 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 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities. |
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Keywords: | 42 55 42 65 02 |
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