Phase modulation in GaAs/AlGaAs double heterostructures. I. Theory

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Abstract
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.