PHYSICAL REVIEW A 99, 033814 (2019) Ray dynamics and wave chaos in circular-side polygonal microcavities MinTang, Yue-De Yang, * Hai-Zhong Weng, Jin-Long Xiao, and Yong-Zhen Huang † State Key Laboratory of Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China and Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China (Received 11 November 2018; published 6 March 2019) We systematically study mode characteristics in circular-side polygonal microcavities (CSPMs), particularly in these cavities with chaotic ray dynamics, in order to gain insights into the wave chaos in the CSPMs. The circular sides could improve the light confinement of the CSPMs as concave mirrors, in that regular islands are formed around the stable fixed points in the Poincaré surface of sections (SOS). However, the fixed points become unstable under some specific deformations, and global chaos with quasistable “star islands” appears around these fixed points in the Poincaré SOS accordingly. The phenomenon can be well explained by the ray dynamic analysis under the second-order approximation, and the results show that the high-order terms play an important role in the motions of light rays and destroy the regular islands in the phase space leading to chaotic ray dynamics. The destruction of regular islands results in degradation of mode quality factors and dispersed mode field distributions according to the finite-element method simulation of the confined modes. Furthermore, an unusual variation of mode quality factor is observed by varying the refractive index of the outside media for the CSPM with chaotic ray dynamics. DOI: 10.1103/PhysRevA.99.033814 I. INTRODUCTION Whispering-gallery mode (WGM) optical microcavities, which confine light rays by continuous total internal reflec- tions (TIRs) at the cavity boundaries, have attracted great attention in both fundamental physics studies and practical device applications [1–4]. By storing optical energy in small volumes, the WGM microcavities could greatly enhance the light-matter interactions [5–7] and the phonon-photon cou- pling [8–10]. Among the WGM microcavities with various shapes, circular microcavities with a circularly symmetric ge- ometry have achieved the most successes in the demonstration of ultralow-threshold microlasers, thanks to their ultrahigh- quality (Q) WGMs [11,12]. However, the circular rotational symmetry results in homogeneous lasing emission along the cavity rim, which limits the practical applications of the cir- cular microcavity lasers in photonic integration. Especially for the semiconductor microcavities, the Q factors of the WGMs are typically limited by both the material absorption and the vertical radiation losses [13]. Thus designing a cavity shape to properly break the rotational symmetry is required to achieve efficient in-plane directional emission with moderately high Q factor [14]. Various asymmetric resonant cavities (ARCs), including spiral-shaped cavity [15], limaçon cavity [16], and the “Face” cavity [17], have been proposed and demonstrated experimen- tally for realizing directional emission. The mechanism of di- rectional emission for the ARCs is explained as chaos-assisted tunneling (CAT) and unstable manifolds escape, which is the heart of quantum chaos and nonlinear dynamics in an * yyd@semi.ac.cn † yzhuang@semi.ac.cn open system [18–22]. Chao-assisted channeling (CAC) was proposed and proved to realize directional emission from the chaotic microcavities with long-lived resonances [23]. Besides realizing directional emission, the chaotic ARCs were also demonstrated to achieve broadband and fast momentum transformation [24], enhance energy storage [25], and sup- press spatiotemporal instabilities [26]. In addition, the wave chaos in ARCs affected the competition between the lasing modes and resulted in single-mode operation [27,28]. Apart from the ARCs with smooth boundaries, WGM microcavities with regular polygonal shapes have also been investigated intensively due to their special mode properties [29–37]. Recently, we proposed and demonstrated circular- side square microcavity semiconductor lasers to enhance the mode Q factors and the transverse mode interval simulta- neously, and suppress the undesired high-order transverse modes [38,39]. The circular sides introduce an additional degree of freedom for manipulating the WGMs in circular- side polygonal microcavities (CSPMs), and may lead to novel applications of these microcavities. However, there is still a lack of a global understanding for the regulation mechanism of the WGMs in the CSPMs. In this paper, we systematically study the ray dynamics and the corresponding wave solutions for the CSPMs, particularly the cavities with chaotic ray dynamics. The orbits connecting the midpoints of the sides are inherent periodic orbits (POs) of the CSPMs, which appear as fixed points in the Poincaré surface of sections (SOSs). Based on the analyses of the ray dynamics, the circular sides of the CSPMs typically lead to regular islands around the stable fixed points in the Poincaré SOSs. The size of the islands varies with the deformation parameter. Interestingly, a transition of POs from stable to unstable is observed under a few specific deformations, and global chaos appears as the regular islands degrade to quasistable “star islands.” The 2469-9926/2019/99(3)/033814(9) 033814-1 ©2019 American Physical Society