Abstract
Many ray-optics models have been proposed to describe the propagation of paraxial Gaussian beam. However, those paraxial ray-optics models are inapplicable to the beams that violate the paraxial condition. In this paper, we present a skew line ray (SLR) based model to represent the propagation properties of nonparaxial Gaussian beam under the oblate spheroidal coordinates. The free-space evolution of complex wavefront of the light beam including amplitude and phase is derived via this model. Our analysis demonstrates that the SLR model is available for both nonparaxial and paraxial conditions, and can be used to precisely describe the propagation of complex wavefront. Furthermore, this model changes the transverse density of rays while propagating. The behavior influences the transverse intensity distribution and makes the optical rays become concentrated towards the center. We believe that this ray-optics model can be further developed to describe other kind of structured beams such as Laguerre-Gauss and Bessel-Gauss beams.
Highlights
Gaussian beams are widely used in optical imaging [1, 2], optical communications [3, 4] and optical manipulations [5, 6]
Since the skew lines are regarded as trajectories of light rays, the geometrical optical field of nonparaxial Gaussian beam, including amplitude and phase, is traveling along these rays
The optical field deduced by nonparaxial skew line ray (SLR) model is consistent with that obtained from the wave equation
Summary
Gaussian beams are widely used in optical imaging [1, 2], optical communications [3, 4] and optical manipulations [5, 6]. A ray-optics model of nonparaxial Gaussian beam offers a rather convenient way to reveal the beam’s propagation behaviors. In the spirit of SLR model, here we present a SLR model of nonparaxial Gaussian beam This model is based on skew lines of one-sheet hyperboloid in the oblate spheroidal coordinates. Since the skew lines are regarded as trajectories of light rays, the geometrical optical field of nonparaxial Gaussian beam, including amplitude and phase, is traveling along these rays. Our SLR model enables precise description of the propagation behaviors of nonparaxial light fields without explicit diffraction calculations, and provides new insight into the physics of structured light beams.
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