## Abstract

The design of the active region of a current-pumped quantum-cascade laser to achieve maximal gain is proposed. Starting with an arbitrary smooth potential, a family of isospectral Hamiltonians with a predefined energy spectrum is generated by use of the inverse spectral theory. By varying the relevant control parameter, one varies the potential shape, inducing changes in transition dipole moments and electron–phonon scattering times, and thus finds the potential that gives the largest gain. As an example, a simple step quantum-well structure with just a few layers is then designed such that, in postgrowth heating-induced layer interdiffusion, it will acquire a shape that is as close as possible to that of the optimal smooth potential.

© 2002 Optical Society of America

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