The ABCD matrix for parabolic reflectors and its application to astigmatism free four-mirror cavities

• We compute the ABCD matrix for parabolic mirrors valid under paraxial approximation.
• An expression for any incident angle for on/off axis parabola is obtained.
• We use it to simulate a four-mirror cavity made of two parabolic mirrors.
• A procedure to align such cavity is proposed and studied numerically.

The ABCD matrix for parabolic reflectors is derived for any incident angles. It is used in numerical studies of four-mirror cavities composed of two flat and two parabolic mirrors. Constraints related to laser beam injection efficiency, optical stability, cavity-mode, beam-waist size and high stacking power are satisfied. A dedicated alignment procedure leading to stigmatic cavity-modes is employed to overcome issues related to the optical alignment of parabolic reflectors.