Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

Abstract

The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

Decomposed entropy and estimation of output power in deformed microcavity lasers

“…o 6 t j m U t q u q J v b n + p S p F D T J z G f Y p L w s w o Z 3 2 2 j S Y x t e v e e i b + Z j I 1 q / c s y 0 3 x r m 9 J A 3 Z / j n M e t I 7 K 7 n G 5 c l E p V c + y U e e x h 3 0 c 0 j x P U E U N d T T J e 4 h H P O H Z q l m h l V p 3 n 6 l W L t P s 4 t u y H j 4 A 8 a q Q H Q = = < / l a t e x i t > H T < l a t e x i t s h a 1 _ b a s e 6 4 = " q 9 x Q + S i h x s 6…”

“…Deformed microcavity lasers [1,2] have been widely studied up to now owing to the existence of models for investigating various physical phenomena, such as scar [3,4], tunneling [5,6], exceptional point [7,8], and ray-way correspondence [9,10]. They have also attracted considerable attention owing to their potential for optical applications [11].…”

Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard

“…The value of O L 0.0 at = 0.0 comes from the condition that one unperturbed mode (with p c 0.82) must be placed above the t = 4 : r = 1 resonance chain with P t=4:r=1 = cos(πr/t) = 1/ √ 2 0.707 while another one (with p c 0.67) must be placed below the P t=4:r=1 so that RAT can occur. Here, the P t=4:r=1 corresponds to the adiabatically invariant curve interpolating through the nonlinear resonance [41]. The increased value of the O L can be due to the increased coupling strength by increased area of separatrix of the resonance chain.…”

Decomposed Entropy and Estimation of Output Power in Deformed Microcavity Lasers

“…Deformed microcavity lasers [ 1 , 2 ] have been widely studied up to now owing to the existence of models for investigating various physical phenomena, such as scar [ 3 , 4 ], tunneling [ 5 , 6 ], exceptional point [ 7 , 8 ], and ray–wave correspondence [ 9 , 10 ]. They have also attracted considerable attention owing to their potential for optical applications [ 11 ].…”