Simulation of Stress-Optic Microresonator Modulator
Photonic integrated circuits (PIC) play important roles in contemporary optical communication systems. Incorporating functional materials into PICs equips passive photonic devices with active modulation capabilities, unleashing great potentials in optical signal processing, quantum information computing, radio frequency synthesizing, and laser frequency stabilization. Recently, there is a thrust in developing piezoelectric actuated optical modulators based on stress-optic effect recently [1], [2], [3]. It involves heterogeneous integration of piezoelectric material and electrodes with optical microresonators. Such a device needs the interplay between photonics, solid mechanics, and electrostatics. However, the complexity of multi-physics hinders the numerical modeling of the devices. Despite several successful experimental demonstrations, there lacks a systematic procedure in designing and optimizing the piezo-actuated stress-optic microresonator modulators. In this work, we developed a multiphysics modeling approach to simulate the piezoelectric optical modulator by using COMSOL Multiphysics®. We adopt the structure geometry from Ref. [1] as an example and establish a 2D axisymmetric microresonator modulator model with the Al/AlN/Mo piezo-actuation film stacks on top and the SiO2/Si3N4/SiO2 photonic waveguide structure on the bottom, as shown in Fig. 1 Material properties are assigned to each domain per the requirements of the involved physics. Then we define variable refractive indices of each material which correlating stress and refractive indices by stress-optic coefficient. We first perform mode analysis in to obtain the azimuthal optical mode number (m) of a ring cavity with the help of the RF module. Fig. 2 shows the TE mode of waveguide. The azimuthal mode number is derived from the equation 2πRn_eff=mλ, and is fixed in the eigenfrequency study to track the specific resonance. Then, stress-optic simulation is performed to correlate the mechanical stress with applied voltage by using the Electrostatics and Solid Mechanics modules. Fig. 3 shows the stress of z component on the device. A deformed geometry physics is inserted in the model to link the mechanical displacement with optical constants. By sweeping the applied voltage across the Al and the Mo layers, the eigenfrequency at the fixed azimuthal mode number is solved. Finally, we obtain the modulation efficiency from the slope of the curve of the resonant frequency and the applied voltage. In this example, the device has a modulation efficiency of 0.0257 pm/V as shown in Fig. 4. Given the difference of material parameters, the simulation results of the model are quite close to the experimental results (about 0.02 pm/V) [4], which shows the high accuracy of the model. The demonstrated simulation procedure provides a useful tool to accurately model and analyze the performance of piezo-actuated heterogeneously integrated microresonator modulators, which may not only deepen the understanding of multi-physical mechanisms but also improve the production yield.
