Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method

Abstract

The axicon-based-Bessel-Gauss resonator (ABGR) has been proposed for the production of Bessel-Gauss beams. To analyze eigenfields of the ABGR with a plane or spherical output coupler, we present and demonstrate the transfer-matrix method. Since the method is slow to converge to eigenmodes of the ABGR by use of the Fox and Li iterative algorithm, in this paper the Huygens-Fresnel diffraction integral equations associated with ray matrices are converted into finite-sum matrix equations, and mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of the laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. Moreover, eigenfields across arbitrary interfaces between the axicon and the output coupler, and the propagation of output beams, are simulated by using the fast-Fourier transform (FFT). The calculation results reveal that because of the ABGR's poor transverse mode discrimination the ABGR should be improved to produce good-quality Bessel-Gauss beams.

Phase fluctuations of optical waves in the case of cone focusing in turbulent atmosphere

“…The equivalent procedure of passive or active laser beam transformation with the aim of formation of a conical optical wave can lead to similar results [1,3,4]. A conical optical wave so formed is, on the one hand like a nondiffraction Bessel beam, and on the other hand has important features of the optical radi ation amplitude and phase distribution.…”

“…In view of this, the study of properties of optical beams keeping their functional form during propagation in a homogeneous medium is of interest [1,2]. Among such beams is distinguished a small (but very important) group of nondiffraction beams [1][2][3][4]: cosine, Bessel, Matie, and parabolic beams. Bessel beams take the leading place among them, because they are not as elementary as cosine beams and not so complicated as Matie and parabolic beams.…”

Investigation of Quasi-Optical Bessel-Gauss Resonator at Mm- And Submm-Wavelengths

“…How to generate effectively Bessel-Gauss beams is an important subject that is worth studying. Several different methods in optics have been proposed to generate the Bessel-Gauss beams [6,[12][13][14][15][16]. To our knowledge, no method has yet been proposed to generate these beams at mm-and sub mm-wavelengths.…”

Multiple vortex with different topological charge generated by means of SLM

“…The HA is used to generate diffraction-free laser Bessel beams, and the SPP is able to generate optical vortices and perform the radial Hilbert transform [2][3][4]. Interest in the potential uses of the HA and SPP [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] has markedly quickened in the recent years. This is because the improved quality of fabrication of spatial light modulators (SLM) has made them suitable for generating diffractive optical elements, including the HA and SPP.…”

“…The theoretical analysis of the paraxial Fresnel and Fraunhofer diffraction by the SPP was conducted for the incident Gaussian beam [16], unbounded plane wave [2,12], bounded plane wave [5,13], and elliptical beam [17]. Diffraction by the HA was theoretically studied for the unbounded plane wave [14] and the Gaussian beam [18]. Interest in the studies of the HA and SPP is also due to the potential for optical micromanipulation they show [5,14,19].…”