Enhancement of optical Kerr effect in quantum-cascade lasers with multiple resonance levels

In this paper, we investigated the optical Kerr lensing effect in quantum-cascade lasers with multiple resonance levels. The Kerr refractive index n₂ is obtained through the third-order susceptibility at the fundamental frequency χ⁽³⁾ (ω; ω, ω,-ω). Resonant two-photon processes are found to have almost equal contributions to χ⁽³⁾(ω; ω, ω,-ω) as the single-photon processes, which result in the predicted enhancement of the positive nonlinear (Kerr) refractive index, and thus may enhance mode-locking of quantum-cascade lasers. Moreover, we also demonstrate an isospectral optimization strategy for further improving n₂ through the band-structure design, in order to boost the multimode performance of quantum-cascade lasers. Simulation results show that the optimized stepwise multiple-quantum-well structure has n ₂≈ 10^-8 Cm²/W, a twofold enhancement over the original flat quantum-well structure. This leads to a refractive-index change Δn of about 0.01, which is at the upper bound of those reported for typical Kerr medium. This stronger Kerr refractive index may be important for quantum-cascade lasers ultimately to demonstrate self-mode-locking.