Quantum well shape tailoring via inverse spectral theory: optimizing resonant second-harmonic generation

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Abstract
A procedure for the design of quantum well structures optimized as regards intersubband double-resonant second-harmonic generation is proposed. It relies on the inverse spectral theory, allowing one to start from an arbitrary potential and shift its levels to the positions required for a particular application, in this case such that they become equispaced. The free parameters that appear, and determine the shape of the modified potential, are then varied in order to find the optimal potential shape that maximizes the nonlinearity, while level energies are automatically fixed throughout this variation. Furthermore, the procedure is adapted to handle cases of variable effective mass, unlike the conventional inverse spectral theory. The use of this procedure is demonstrated by the designing of a graded AlGaAs ternary alloy quantum well optimized for second-order nonlinearity at . Starting with a truncated parabolic potential, the final optimized quantum well potential is obtained, with nonlinearity exceeding values previously obtained in the literature.