Trace formula for dielectric cavities. II. Regular, pseudointegrable, and chaotic examples

Abstract

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudointegrable (pentagon), and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic microlasers.

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

“…Bogomolny et al (2011) confirmed the validity of the trace formula for the square, rectangle, ellipse, pentagon, and stadium in numerical simulations and in experiments on organic microlasers (such as in Fig. 11(a)).…”

“…While Wiersig (2003b) and Kudo et al (2013) concluded that rounding the corners increases the Q-factor, Dietrich et al Other dielectric polygonal cavities have been studied as well, such as squares (Chen et al, 2006;Guo et al, 2003;Lohmeyer, 2002;Poon et al, 2001), rectangles (Wiersig, 2006), regular pentagons (Bogomolny et al, 2011;Lebental et al, 2007), equilateral triangles (Lai et al, 2007;Wysin, 2005), regular dodecagons (Nobis et al, 2007), and octahedrons (Korthout et al, 2009).…”

Gain properties of dye-doped polymer thin films

“…The distribution of the lasing frequencies is mostly determined by the resonator shape and is discussed elsewhere [61]. Here, we focus on the envelope, in particular its central wavelength, which depends on the gain medium and is relevant for designing an actual device.…”

Polarization properties of solid-state organic lasers

“…Eventually, the case of whispering gallery modes (WGM) should be considered. In stadium cavities [50], P is close to 1, as in Fabry-Perot lasers, whereas spectral analysis confirm that the lasing modes are indeed WGM [2]. Actually stadium shape leads to chaotic dynamical systems, which could result in a short photon lifetime (∼ 1 ps) [64] and then to a lasing behavior close to the Fabry-Perot cavity.…”

“…We would like to address this issue by way of micronand millimeter-sized lasers of various resonator geometries, which are out of reach of full electromagnetic simulations due to their large scale, but where validity of the semi-classical (or geometrical optics) limit is expected to provide a simplified insight [2]. In this work, we propose to evidence and analyze polarization effects in solid-state organic laser systems, and demonstrate the possibility to modify the out-put polarization by playing on cavity shape or on material related features.…”