A fundamental mode of a nonplanar cavity with even or odd number of mirrors

We research optical multimirror ring-type cavities with a nonplanar contour. In such cavities, the propagation along the contour is accompanied with the rotation of coordinate axes on some angle. In case of odd number of mirrors an additional change of orientation also takes place. For cavities with an alone focusing element (a nonplanar mirror or a lens) we investigate stability conditions and the shape of a stability region in a space of dimensionless parameters. Cases of odd and even number of mirrors appear to be rather different. In case of stability, the cross-sectional distribution of the fundamental mode's field can be expressed in terms of the quadratic form's matrix with positively definite imaginary part. Having applied the method presented in, we obtain explicit analytical formulae for such matrices. There appears that the main directions of the focusing element coincide with such directions of the intensity ellipse or of the phase ellipse in cases of even or odd number of mirrors, respectively.