Modeling of the whispering gallery mode in microdisk and microgear resonators using a toeplitz matrix formalism for single-photon source

The work presented in this paper develops a new formalism to design microdisks and microgears structures. The main objective is to study the optics and geometrics parameters influence on the microdisks and microgears structures resonance behavior. This study is conducted to choice a resonance structure with height quality factor Q to be associated with Quantum dot to form a single photon source. This new method aims to design resonant structures that are simpler and requires less computing performances than FDTD and Floquet Block methods. This formalism is based on simplifying Fourier transformed and using toeplitz matrix writing. This new writing allows designing all kind of resonance structures with any defect and any modification. In other study we have design a quantum dot emitting a photon at 1550 nm of the fundamental mode, but the quantum dot emits other photons at other wavelengths. The focus of the resonant structure and the quantum dot association is the resonance of the photon at 1550 nm and the elimination of all other photons with others energies. The quantum dot studied in [1] is an InAs/GaAs quantum dot, we design an GaAS microdisk and microgear and we compare the quality factor Q of this two structures and we conclude that the microgear is more appropriated to be associate to the quantum dot and increase the probability P1 to obtain a single photon source at 1550 nm and promotes the obtaining of single photon. The performance improving of the resonant structure is able to increase the success of quantum applications such as quantum gates based on single photon source.