Substrate radiation losses in GaAs heterostructure lasers

Abstract

Double-heterostructure (DH) diode lasers with a thin Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> As layer between the active GaAs region and the GaAs substrate or superstrate are analyzed. In these devices power flows through the thin Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> As layer and is radiated into the substrate or superstrate. Three methods for computing the laser thresholds are developed and compared. The first is an analytic perturbation technique, which yields accurate results in many cases of practical interest. The second and third are rapidly convergent numerical iteration techniques. The former utilizes overlap integrals to compute absorption losses and thresholds; the latter includes all losses and gains directly in the formulation. We show that conventional DH diode lasers can be designed with thick active GaAs layers and still achieve lowest order TE-mode operation. These devices will produce better collimated, higher power output beams than do similar devices with thinner active regions. Transverse-mode control is achieved because all higher order modes have increased penetration through the thin Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> As , and therefore exhibit inereased radiation losses into the substrate or superstrate. A design example is included in which it is shown that with proper choice of the Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> As-layer thickness the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -mode threshold increases by 5 percent compared with a 110-percent increase in the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> threshold. These results are virtually independent of the substrate power-absorption coefficient. Threshold current densities are computed for a set of diodes studied experimentally by Casey and Panish and the results are shown to be in excellent agreement.