A QUASI-CLASSICAL ANALYSIS OF 2ND-HARMONIC GENERATION

We investigate a quantum two-oscillator model for second-harmonic gene ration. The total Hamiltonian is the sum of two commuting Hamiltonians with eigenvalues E(0) and E(int). The exact determination of these ei genvalues is studied using tridiagonal matrices. We present two genera l equations in the quasiclassical regime yielding the largest E(int) f or 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 wit h the exact quantum results. An approximate analytical expression for the wavefunction is also given.