We systematically investigate the field distribution of the transverse electric modes in X-cut lithium niobate disks as an example of circular microcavities with anisotropic refractive index. A conserved quantity is discovered, which indicates the absence of chaos that generally exists in deformed microcavities and leads to a nontrivial directional emission. The emission directionality was theoretically investigated and experimentally verified by exciting high-order modes of an X-cut lithium niobate microresonator assisted with second harmonics. The field distribution analysis can enrich the knowledge in designing photonic devices that need precise control of field distribution, such as phase matching in nonlinear processes. Furthermore, the discovered emission phenomenon is momentous in enhancing and controlling communications between on-chip photonic devices.