Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers

TLDR

The refractive index change in GaAs lasers is derived by converting the spontaneous emission spectrum into a gain spectrum and applying a Kramers‑Kronig transformation to obtain the real part as the current increases to threshold. The refractive index change in the GaAs active layer is slightly sublinear with minority carrier density, reaching Δn′ = –0.025±0.005 at threshold (nc ≈ 1.02×10¹⁸ cm⁻³) with a slope of –(1.8±0.4)×10⁻²⁰ cm³, and the real‑to‑imaginary index change ratio is about 6.2 near threshold.

Abstract

The refractive index change caused by changes in the absorption edge of GaAs is determined by analysis of the spontaneous emission spectrum of a buried heterostructure window laser. The spontaneous emission spectrum is converted to a gain spectrum from which changes in the imaginary part of the refractive index can be calculated as the laser is excited from low current up to threshold. The real change in refractive index is then determined by a Kramers-Kronig transformation. The change in refractive index n′ of the GaAs active layer is slightly sublinear with minority carrier density nc. At the laser line, including the calculated contribution of free carriers, Δn′ = −0.025±0.005 and dn′/dnc = −(1.8±0.4)×10−20 cm3 in lasers with carrier densities at threshold estimated as 1.02×1018 cm−3. Near threshold, the ratio of the change in the real index to the change in the imaginary index is about 6.2.