<title>Vector eigenmodes in a cylindrical laser</title>

Abstract

Eigenmodes characterized by distinct polarization states for the resonator configuration known as the High-Extraction Decentered Annular Ring Resonator (HEXDARR) have been found. The effects of internal annular optical elements (waxicons, reflaxicons, and cones) as well as coatings and mode rotation are included. For a good design, the low-order mode polarization states are nearly circular, with the polarization ellipse orientation and phase angle slightly spatially dependent across the near field of the resonator output. The two lowest-loss eigenmodes are separated by only a small loss which is dependent on the coating properties, one being principally right-hand circularly polarized and the other principally left-hand circularly polarized.

<title>Modeling of rear cone misalignment in the annular resonator</title>

“…E(r,) = E(r,n)exp(inçb), (1) where n is the order of Fourier components. Each Fourier component can be propagated independently for a distance L according to the formula: E' (r' ,n) = E(r,n)J(2 zrr' /AL)rdr, (2) where is the wavelength and J, is the Bessel function of nth order. For convenience, three propagation steps are arranged inside the resonator.…”

“…Due to high Fresnel numbers in the compact leg, it requires a large number of radial sampling points to represent the field, which makes the matrix propagation impractical. However, using the LegendreGardner transformation3, Equation (2) can be converted into a convolution integral which can be evaluated numerically with the fast Fourier transformation (FFT).…”