ABCD Matrix for Reflection and Refraction of Laser Beam at Tilted Concave and Convex Elliptic Paraboloid Interfaces and Studying Laser Beam Reflection from a Tilted Concave Parabola of Revolution

ARTICLE HISTORY: Received 04 March 2015 Revised 22 March 2015 Accepted 22 March 2015 Studying Gaussian beam is a method to investigate laser beam propagation and ABCD matrix is a fast and simple method to simulate Gaussian beam propagation in different mediums. Of the ABCD matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. However, in the previous work the incident beam and the principle axis of surface are in parallel. As an extension to those investigations, a general scheme that the incident beam is oblique is discussed here and the full analysis of the reflection and refraction of a Gaussian beam at the surface of a tilted concave/convex elliptic paraboloid surface is addressed. Based on the optical phase matching, analytic mathematical equations are derived for the spot size and the wavefront radius of a beam. Expressions are converted into the ABCD matrices, which are more convenient and practical to use. Finally, a practical case is analyzed by applying the obtained formulas. This analysis is important since paraboloid surfaces in optics or terahertz waves are used as mirrors or lenses.