PHASE MODULATION IN GAAS ALGAAS DOUBLE HETEROSTRUCTURES .1. THEORY

This work aims at a systematic study of phase modulation in GaAs/AlGaAs double-heterostructure waveguides with different doping profiles. Both theoretical (part I) and experimental (part II) aspects are investigated, leading to interesting new results. Phase modulation is the sum of a linear electro-optic term, a quadratic electro-optic term, and a free-carrier term. The carrier term is shown to be the sum of a plasma term, an intervalence-band term (for holes only), a band-filling term, and a band-shrinkage term, the latter being due to many-body effects. A new analytic expression for the band-filling term is derived which shows that the band-filling effect does not depend on the carrier effective mass. We prove that the band-shrinkage term is approximately half of the band-filling term, but has opposite sign. The phase modulation is computed using an overlap integral between the optical intensity and the local refractive-index difference. We also report an analytic expression for the modulation efficiency of a p-i-n junction double-heterostructure modulator. This expression is very accurate and only requires knowledge of the depletion width and the guiding parameters.