Directional emission properties of limaçon microdisk based on Z-cut and X-cut lithium niobate

In this study, the characteristics of limaçon microdisk based on Z-cut and X-cut Lithium Niobate (LN) is examined under a specific TE mode of $m=20$, such as quality factor $Q$, resonant frequency $f$, directionality $D$, etc., and research finds that refractive index distribution of uniaxial crystal serves as an additional dimension to manipulate emission properties. X-cut microdisk with $\phi =0°$ (the angle of rotation of the principal axis of the refractive index ellipse relative to x-axis) not only exhibits good unidirectionality, but also has higher $Q$ than Z-cut microdisk through numerical calculations, which provides an ideal platform for on-chip light source, when the deformation factor $\epsilon =0.33$. Then perturbation theory under linear transformation is utilized to calculate $f$, simultaneously combined with Poincaré Surface of Section (PSOS) and Husimi function to reveal the difference of $Q$ and $D$ between Z-cut and X-cut microdisks. The research results indicate that the original virtual (OV) space approximation perturbation can accurately calculate the resonant frequency for the X-cut Limacon microdisk, while PSOS and Husimi function in reciprocal virtual (RV) space demonstrate that X-cut microdisk's photons have a higher probability distribution on a more stable orbit than Z-cut microdisk in phase space after $\epsilon \ge 0.33$, resulting in higher $Q$ in X-cut microdisk.