Second-harrnonic generation efficiencies in germanium-doped planar waveguides: a normal-mode analysis

摘要

Second-harmonic generation (StJG) in gerrnanium-doped silica planar waveguides seeded by a fundamental wave and its second harmonic is investigated using normal-mode analysis. The effects of self- and cross-phase modulation are included in this analysis. A set of two coupled equations that describe the evolution of the amplitude of the writing second-harmonic beam along the direction of propagation is obtained. The solution to these coupled equations is used to write the effective grating. This grating is then used to determine the second-harmonic power generated when the beam is read with only a fundamental wave propagating in a particular waveguiding mode. Due to diffraction, the conversion efficiency saturates as a function of waveguide length. It is also found that if the reading fundamental wave is in the same mode as the writing fundamental wave, relatively significant SHG is obtained with the generated second-harmonic wave propagating primarily in the same mode as the seed second-harmonic wave. The power generated in any of the higher order modes is of the same order as that for the lowest order mode.