Mojtaba Mansour Abadi - Optical Communications Research Group (NCRLab), Northumbria University, NE1 8ST, UK
Zabih Ghassemlooy - Optical Communications Research Group (NCRLab), Northumbria University, NE1 8ST, UK
David Smith - Microwave Imaging Research Group, Northumbria University, NE1 8ST, UK
Wai Pang Ng - Optical Communications Research Group (NCRLab), Northumbria University, NE1 8ST, UK

Studying Gaussian beam is a method to investigate laser beampropagation and ABCD matrix is a fast and simple method to simulateGaussian beam propagation in different mediums. Of the ABCD matricesstudied so far, reflection and refraction matrices at various surfaces haveattracted a lot of researches. However, in the previous work the incidentbeam and the principle axis of surface are in parallel. As an extension tothose investigations, a general scheme that the incident beam is oblique isdiscussed here and the full analysis of the reflection and refraction of aGaussian beam at the surface of a tilted concave/convex ellipticparaboloid surface is addressed. Based on the optical phase matching,analytic mathematical equations are derived for the spot size and thewavefront radius of a beam. Expressions are converted into the ABCDmatrices, which are more convenient and practical to use. Finally, apractical case is analyzed by applying the obtained formulas. Thisanalysis is important since paraboloid surfaces in optics or terahertzwaves are used as mirrors or lenses.

Laser Beam،Gaussian Beam،ABCD Matrix،Reflection،Refraction،Tilted Surface،Convex/Concave Elliptic،Paraboloid Surface