Nonparaxial Propagation of Vectorial Elliptical Gaussian Beams

Based on the vectorial Rayleigh-Sommerfeld diffraction integral formulae, analytical expressions for a vectorial elliptical Gaussian beam's nonparaxial propagating in free space are derived and used to investigate target beam's propagation properties. As a special case of nonparaxial propagation, the target beam's paraxial propagation has also been examined. The relationship of vectorial elliptical Gaussian beam's intensity distribution and nonparaxial effect with elliptic coefficient alpha and waist width related parameter f(omega) has been analyzed. Results show that no matter what value of elliptic coefficient alpha is, when parameter f(omega) is large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameter f(omega) is small, the paraxial approximation of elliptical Gaussian beam is effective. In addition, the peak intensity value of elliptical Gaussian beam decreases with increasing the propagation distance whether parameter f(omega) is large or small, and the larger the elliptic coefficient alpha is, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.