A QUASICLASSICAL ANALYSIS OF SECOND-HARMONIC GENERATION

摘要

We investigate a quantum two-oscillator model for second-harmonic generation. The total Hamiltonian is the sum of two commuting Hamiltonians with eigenvalues E(0) and E(int). The exact determination of these eigenvalues is studied using tridiagonal matrices. We present two general equations in the quasiclassical regime yielding the largest E(int) for a given E(0) and a representation for both eigenvalues in terms of an additional quantum number. Some numerical analysis shows that both equations are fairly consistent for suitably large quantum numbers with the exact quantum results. An approximate analytical expression for the wavefunction is also given. [References: 30]