Propagation of elliptical Gaussian beam passing through apertured paraxial optical systems

The propagation of elliptical Gaussian beam passing through paraxial optical systems with aperture is investigated analytically by using tensor method. The approximate formula for propagation of elliptical Gaussian beam through hard apertured optical systems is derived based on the fact that the circ function can be expanded into a finite sum of complex Gaussian functions. The derived formula provides a convenient tool for treating the propagation and transformation of elliptical Gaussian beam through apertured optical systems. As an application example, the propagation properties of elliptical Gaussian beam through apertured fractional Fourier systems are discussed.