Directional emission properties of thin film microdisk
Authors: Xu Yu-Xuan , Yao Tai-Yu , Deng Li , Chen Shi-Mei , Xu Chen-Yao , Tang Wen-Xuan ,   School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
Published: February 2024

Based on the directional emission effect of semiconductor deformed microcavities, the fabrication of deformed microcavities in isotropic thin films will provide a new solution for multifunctional and highly integrated photonic active chips. Because the Limacon shaped microcavity has become one of the important configurations of single-mode, low threshold on-chip lasers, the directional emission properties of microdisks fabricated in thin film are investigated. Taking the TE<sub>20,1</sub> mode existing in the Z-cut lithium niobate thin film microdisk for example, according to two-dimensional wave optics theory, the mode distribution, quality factor <i>Q</i>, and directional emission factor <i>D</i> of microdisk variations with deformation factor <inline-formula><tex-math id="M5">\begin{document}$\varepsilon $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M5.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M5.png"/></alternatives></inline-formula> are respectively analyzed through using the wave optics module of COMSOL. Adopting classical scattering theory, Poincaré surfaces of sections under different deformation factors are simulated by optimizing the Dynamical Billards.jl library in Julia. In the simulation realized by Julia, 200 particle collisions are used 200 times to simulate 200 reflections of rays and finally PSOS images are obtained. Simulation results reveal that when the azimuthal quantum number of the light wave mode remains unchanged, although the shape of the microdisk varies, the ratio of the resonant wavelength inside the microdisk to the circumference of the microdisk is approximately a constant, which can predict the microdisk size and resonant wavelength estimation of microcavities. The corresponding PSOS shows that when <inline-formula><tex-math id="M6">\begin{document}$\varepsilon > 0.45$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M6.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M6.png"/></alternatives></inline-formula>, the entire region is covered by chaotic sea area, therefore <inline-formula><tex-math id="M7">\begin{document}$\varepsilon $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M7.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20231754_M7.png"/></alternatives></inline-formula> values of 0, 0.16, 0.24, 0.28, 0.45 are selected to simulate the TE<sub>20,1</sub> mode distribution, far-field radiation flux angle distribution, and PSOS. Theoretical simulation results show that when the deformation factor is greater than 0.24, the microdisk has good unidirectional lasing property, with a <i>Q</i> factor greater than 10<sup>5</sup>. When the deformation factor is greater than 0.4, the PSOS is almost occupied by the chaotic sea area, with a <i>Q</i> factor below 10<sup>3</sup>. Therefore, when the deformation factor of the limacon microdisk in the thin film can be chosen between 0.24 and 0.4, under which circumstance the microdisk not only carries high quality factor (about 10<sup>3</sup>–10<sup>5</sup>), but also forms high laser directionality (about 6.45–8.32). The theoretical simulation results will provide a certain theoretical reference for conducting the experimental research of thin film deformation microcavities.