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Nonparaxial Propagation of Vectorial Elliptical Gaussian Beams 时间:2017-09-07 22:29 来源:未知作者:admin 点击: 次 Abstract: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 and waist width related parameter has been analyzed. Results show that no matter what value of elliptic coefficient is, when parameter is large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameter 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 is large or small, and the larger the elliptic coefficient is, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.
1. Introduction
With the development of laser technology, research on semiconductor lasers [1], microoptical technologies [2–4], and highly focusing field [5–7] has become deeper. In practical application, the problem that would be confronted is of a beam with large divergence angle or small spot size that is of the order of light wavelength. In this case, the theory of optical propagation and transformation based on paraxial approximation is no longer valid [8], and it needs strict electromagnetic field theory to solve the problem of beam’s nonparaxial propagation. In recent decades, several research methods about solving beam’s nonparaxial propagation have been developed, such as vectorial Rayleigh-Sommerfeld diffraction integral method [9], perturbation power series method [10], transition operators [11], angular spectrum representation [12], and virtual source point technique [13]. And vectorial Rayleigh-Sommerfeld diffraction method has been used to treat various beam’s nonparaxial propagation problems [14–17].
An elliptical Gaussian beam can be radiated and realized by semiconductor diode laser [18]. In the past few years, some nonparaxial propagation properties of vectorial elliptical Gaussian beams have been reported, such as the far-field beam divergence angle [19], diffracted at a circular and a rectangular aperture [20, 21]. Since the semiconductor laser beam has a large divergence angle, it would become necessary to consider the target beam’s nonparaxial propagation. In this work, we use the vectorial Rayleigh-Sommerfeld diffraction integral formulae to solve the nonparaxial propagation of a vectorial elliptical Gaussian beam. Target beam’s nonparaxial propagation analytical expressions are derived and used to investigate its propagation properties, including the evolution of intensity and shape of elliptical Gaussian beam with different elliptic coefficient and different waist width related parameter , and the relationships of elliptical Gaussian beam’s nonparaxial effect and its intensity distributions with elliptic coefficient as well as parameter are analyzed.