Modeling lasing of a chalcogenide glass microcylinder

Abstract

Theoretical modeling of the interaction between electromagnetic radiation and microresonators in the shape of homogeneous microcylinders has shown that the morphology of the microresonators affects the transformation of optical radiation in the microlaser modes. We established that in a laser with microresonators of cylindrical symmetry made from chalcogenide glass, two-mode lasing regimes can be realized in modes of different orders for gain-to-loss ratios <1. The region of existence for two-mode lasing is determined by the gain-to-loss ratio and the magnitude of the electromagnetic fi eld for the spatial structure of morphological resonances. Introduction. Currently microresonators have been at the center of extensive research due to the possibility of using them as a convenient object for realization of miniature devices based on single dielectric microspheres and microfi bers. This is connected with the fact that weakly absorbing dielectric microparticles act as optical resonators, and morphological resonances are realized in them. A microresonator based on a dielectric microparticle of a certain symmetry (spherical, cylindrical, ellipsoidal, etc.) has additional advantages, including signifi cant lowering of the threshold for realization of various nonlinear phenomena, strong focusing of radiation, low sensitivity to fracture and overheating due to the strength scale effect, and convenient matching between microspheres or microcylinders and optical fi bers. One of the fi rst investigations of modes in a dye-impregnated cylindrical microlaser and their use for measuring the parameters of microresonators are described in (1, 2). Microfi bers enable nearly lossless excitation of high-Q modes in optical cavities, which are extremely sensitive to a change in the environment and can also be used as sensors (3, 4). Optical processes in cylindrical microresonators are the object of active experimental studies (5-8). However, these papers basically just demonstrate potential ways such systems may be used. At the same time, optical phenomena observed in this case need theoretical substantiation; in particular, the characteristic features of the effect of the spatial structure of the electromagnetic fi eld on the process of low-threshold stimulated emission have not yet been suffi ciently studied. Fabrication of chalcogenide glass microcylinders is of special interest (9). This material is widely used in spectroscopy for fast processing of optical signals in fi ber-optic communication lines, video camera tubes, and also for recording holograms. The high refractive index of chalcogenide glass (2.2-2.7) lets it be used for fabrication of microresonators, strongly concentrating the radiation within the microcylinders. This is why the corresponding theoretical studies were done using microcylinders made of chalcogenide glass. Theoretical Model. In microresonators of cylindrical symmetry, certain sets of eigenmodes are realized. Each mode is characterized by a certain frequency and Q factor, which depend both on the diffraction parameter (ρ = 2πR/λ, R is the radius of the microcylinder, λ is the wavelength of the laser radiation) for the microcylinder and on the optical constants of the microcylinder material. Along with the Q factor, an important electrodynamic characteristic of a microresonator is the spatial structure of the electromagnetic fi eld inside it, which is formed by summing the spatial structures of the fi elds for the eigenmodes. Methods for obtaining and solving the equations for determining the frequencies of the eigenmodes are well known and discussed in detail in (10). We should point out that each equation has an infi nite number of solutions. Each solution is characterized by the mode number l, which determines the number of peaks in the intensity distribution of the internal fi eld as the polar angle j varies from 0 to 180°, and the order s, equal to the number of peaks in the fi eld intensity distribution for