Parameter-dependent resonant third-order susceptibility contributed by inter-band transitions in image quantum wells

The resonance enhancement of the third-order nonlinear optical susceptibility χ(3) for degenerated four-wave mixing, due to the transition between valence band and conduction band, in InGaN/GaN multi-quantum wells have been calculated. The band structures of valence bands and conduction bands and the wave functions are calculated by the theory of effective mass. The contributions of the subbands of holes (heavy holes, light holes and the spin-orbit split-off bands) to χ(3) in the different directions are discussed. The correlations between χ(3) in the different directions and the width of the quantum wells, and the constituents of the quantum wells are obtained.