Modes of optical cavities containing selecting components

A model of the field mode structure in optical cavities containing selecting components is suggested. The cavity also contains field-attenuating or field-enhancing media where elements of the 4×4 symplectic detour matrix of the cavity become complex. The model makes it possible to determine the stability of the cavity, non-Hermiticity of higher modes, and the complex astigmatism of the eigenmode field. Conditions for unilateral (unidirectional) and bilateral (bidirectional) stability are formulated. A cavity showing unilateral stability at the first transverse mode is described.