Supersymmetric quantum-well shape optimization for intersubband bound-continuum second harmonic generation

maximizing the second-order susceptibilities relevant for second harmonic g eneration. The possibility is explored of obtaining resonantly enhanced non linear optical susceptibilities in quantum wells with two bound states and a continuum resonance state as the dominant third state. The method relies on applying the isospectral (energy structure preserving) transformations t o an initial Hamiltonian in order to generate a parameter-controlled family of Hamiltonians. By changing the values of control parameters one changes the potential shape and thus the values of matrix elements relevant to susc eptibility to be maximized. The method was used for the design of Al(x)Gal( 1-x)As-based QWs. The results indicate the possibility of employing continu um states in resonant second harmonic generation at higher photon energies, (h) over bar omega = 200-300 meV. (C) 2000 Academic Press.