Design procedure for the active region of current\ud pumped quantum cascade laser is proposed, so to achieve maximal gain. Starting with an arbitrary smooth potential, a family of isospectral Hamiltonians with predefined energy spectrum is generated using the inverse spectral theory. By varying the relevant control parameter the potential shape is varied, inducing changes\ud in transition dipole moments and electron–phonon scattering\ud times, and the optimal potential which gives the largest gain is thus found. For purpose of realization, a simple step quantum-well structure with just a few layers is then designed so that in the post-growth heating-induced layer interdiffusion, it will acquire a shape as close as possible to the optimal smooth potentia
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