Future Trends in Microelectronics: Up the Nano Creek

Is There a Linewidth Theory for Semiconductor Lasers?

Boris Spivak

Dept. of Physics, University of Washington, Seattle, WA 98195, U.S.A.

Serge Luryi

Dept. of Electrical and Computer EngineeringSUNY–Stony Brook, Stony Brook, NY 11794, U.S.A.

1.   Introduction

Laser linewidth theory was pioneered by Schawlow and Townes¹ and further developed in Refs. 2 and 3. In this chapter, we will discuss the status of the Schawlow-Townes-Lax-Henry (STLH) theory of laser linewidth in the instance of semiconductor injection lasers. At injection levels I below threshold I < I_C, one can introduce two spectra g(ω,I) and σ(ω,I), see Fig. 1 (a), describing respectively the material gain and the loss at cavity mirrors of the electromagnetic field intensity. The gain g(ω,I) is generally an increasing function of I. At I = I_C, the two spectra touch each other, g(ω₀,I) = σ(ω₀), and the generation begins. The STLH theory of laser linewidth is based on the assumption that in the mean-field approximation (i.e. without fluctuations), the laser generation remains singular in frequency for I > I_C, i.e. above threshold. In the framework of this approach, the laser line acquires a finite width Γ entirely due to fluctuations. In an ideal laser these fluctuations are due to the random discrete nature of spontaneous emission.

We shall refer to the property of the two spectral curves g(ω,I) and σ(ω) touching each other at a singular frequency for I > I_C as rigidity, see Fig. 1(b). In principle, however, scenarios ...