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 coefficientαand waist width related parameterfωhas been analyzed. Results show that no matter what value of elliptic coefficientαis, when parameterfωis large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameterfωis 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 parameterfωis large or small, and the larger the elliptic coefficientαis, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.
Nonparaxial propagation of Gaussian beam in arbitrary linearly polarized state
