Theory of the linewidth of semiconductor lasers

Abstract

A theory of the spectral width of a single-mode semiconductor laser is presented and used to explain the recent measurements of Fleming and Mooradian on AlGaAs lasers. They found the linewidth to be inversely proportional to power and to have a value of 114 MHz at 1 mW per facet. This value is 30 times greater than can be explained by existing theories. The enhanced linewidth is attributed to the variation of the real refractive index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n'</tex> with carrier density. Spontaneous emission induces phase and intensity changes in the laser field. The restoration of the laser to its steady-state intensity results in changes in the imaginary part of the refractive index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta n"</tex> . These changes are accompanied by changes in the real part of the refractive index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta n'</tex> , which cause additional phase fluctuations and line broadening. The linewidth enhancement is shown to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 + \alpha^{2}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha = \Delta n'/\Delta n"</tex> . A value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha \approx 5.4</tex> , needed to explain the observed linewidth, is close to the experimental values of a of 4.6 and 6.2.