Modulation depth and bandwidth analysis of planar thermo-optic diamond actuators

Thermo-optic actuators based on bulk materials are considered too slow in applications such as laser frequency control. The availability of high-quality optical materials that have extremely fast thermal response times, such as diamond, present an opportunity for increasing performance. Here, diamond thermal actuators are investigated for configurations that use a planar thermal resistive layer applied to a heat-sinked rectangular prism. A general analytical formulation is obtained which simplifies substantially for high thermal conductivity such as diamond. Expressions for modulation depth, bandwidth and power requirements are obtained as functions of modulator dimensions and heat-transfer coefficients. For a 1 mm × 1 mm cross-section diamond at wavelength of 1 µm, around 450 W of applied heat power is needed to achieve a π phase shift at a modulation frequency of 2 kHz.