Abstract

We analyze Lang and Kobayashi equations for a semiconductor laser subject to optical feedback. Using asymptoptic methods, we derived in [1] a third order delay-differential equation for the phase of the laser field: (*) where ξ, Δ, Λ and θ are scaled parameters proportionals to the laser damping coefficient, the angular frequency of the solitary laser (mod 2π), the feedback rate and the delay of the feedback, respectively. Time s is measured in units of the laser relaxation oscillations period. We have shown that Eq. (*) admits multiple branches of time-periodic states in agreement with the numerical bifurcation diagram of the original laser equations. Our analysis assumed that the delay θ is an 0(1) quantity but in many experiments θ is numerically larger. We have modified the analysis in [1] and have found that large delays may lead to a secondary bifurcation to quasiperiodic intensity oscillations. This bifurcation has been suspected in earlier studies but has never been investigated analytically. We show that these quasiperiodic oscillations are characterized by two distinct frequencies: ω₁ ≈ 1 and ω₂ proportional to 1/θ. We analyze the bifurcation both analytically and numerically.

© 1996 IEEE