Description of propagation of a Gaussian beam with general astigmatism by the ray method and application of this method to calculation of the parameters of nonplanar ring cavities

Stability conditions and explicit formulae for basic mode of two classes of rotating two-mirror optical cavities

“…As rotating cavity has the same monodromy matrix as some ring cavity with tetrahedral contour [7], [10], [12], [13], these formulae as well as stability conditions coincide for these two cavities.…”

“…Here A, B, C, D are real 2 × 2 matrices, which may be combined in a symplectic 4 × 4 ray matrix (see, e.g., [7], [8])…”

“…To describe a propagation of the beam in a cavity, following Habraken and Nenhuis, we apply twodimensional generalization (see, e.g., [7]- [14]) of a well-known method of paraxial ray matrices [16], [17]. In this approach, the location and direction of some paraxial ray are determined by twodimensional vectors q(z) and p(z) = q (z).…”

An analytical way of the fundamental cavity mode construction

“…The eigentones of three-dimensional multireflecting cavities were repeatedly considered in the literature (see, e.g., [1], [2]). For a wide class of equations and boundary conditions a wave concentrated in a neighborhood of an axial ray looks like a Gaussian beam u(s, r, k) = v(s, r √ k, k −1/2 )e ik[τ (s)+(Γ(s)r,r)…”