Theory of an electro-optic modulator based on quantum wells in a semiconductor étalon

We present the design of an electro-optic modulator which is based on the quantum- confined Stark effect (QCSE) in GaAs quantum wells contained within the central layer of a Fabry-Perot étalon. The étalon mirrors are quarter wave stacks of Ga_0.7Al_0.3As and AlAs, eliminating the need for the application of anti-reflection coatings. p-i-n-doping is employed with the undoped QW stack sandwiched between coped mirrors, enabling electric fields of the order of 10⁵Vcm^-1 to be readily developed across the quantum wells. Placing a multiple quantum well structure within an étalon resonant cavity gives flexibility of design in terms of operating wavelength and mode: Light incident perpendicular to the QW stack is modulated through the operation of the QCSE on the GW excitons, either electro- refractively by a change in the real part of the GW refractive index producing a wavelength modulation of the narrow-band Fabry-Perot transmission resonance or in electro-absorptive mode. The semi-empirical theory uses conventional multilayer optical matrix methods together with a recent theory of the GCSE which has been tested against the results of electro-reflectance experiments. In electro-absorption mode we find a ratio of 19:1 on:off at 857.5nm for 8 quantum wells. In electro-refractive mode, using 32 wells, we predict modulation from 10% to 76% reflection at 883nm. These figures exclude substrate effects. Extension of the theory to other materials systems is readily accomplished. We present the reflectivity spectrum of a high quality etalon in In_0.53Ga_0.47As/InP and find good agreement with the predictions of the optical matrix model.