Propagation Equation Of Gaussian Beams Research Articles

Propagation equation of Gaussian beams through apertured focusing systems and parametric study of focal shift.

Diffraction of a Gaussian beam passing through a circular aperture subsequently focused by a lens is investigated. An expression is derived for the amplitude distribution beyond the lens. With the aid of the axial intensity and encircled energy, the effect of the aperture-lens separation on the focal shift is obtained, and the quantitative influence of the truncation parameter and Fresnel number on the focal shift is also presented.

Propagation properties of Gaussian beams through cat eye optical lens with center shelter

Based on the method of matrix decomposition and expanding the aperture function into a sum of finite complex Gaussian functions, the analytical propagation equations of Gaussian beams through cat eye optical lens with center shelter are derived. Through numerical calculation, the laws governing the variation of the intensity distribution of the cat eye reflected light with the center shelter ratio and the diameter of the detector at the focal plane are given. The results show that the diffraction series and the intensity of the cat eye reflected light depend strongly on the center shelter ratio. As a further extension, it is found that the eye optical lens can be interpreted as a spatial filter, and different filter effect can be obtained by changing the pinhole size.

Rotating the intensity distribution of Gaussian beams propagating through paraxial ABCD systems with parallelogram apertures

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of Gaussian beams through a paraxial ABCD optical system with parallelogram apertures are derived and illustrated with numerical examples. It is found that the intensity distribution pattern rotates round the propagation axis during the propagation.

Approximate analytical propagation equations of Gaussian beams through hard-aperture optics

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of Gaussian beams through a paraxial multi-apertured ABCD optical system are derived and illustrated with numerical examples. The numerical results find an agreement with those by straightforward integral of the Collins formula, but the computing time is strongly reduced.

Studies on the analytical propagation equations of Gaussian beams through a mult i-apertured imaging system of B=0

By using the method of matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian functions, the closed-form propagation equ ations of Gaussian beams through a multi-apertured imaging system of B=0 are der ived and are illustrated with a few typical numerical examples. The advantages o f our treatment are pointed out.

Propagation of Gaussian beams through an astigmatic lens

Summary Based on the generalized Huygens-Fresnel diffraction integral and in consideration of astigmatism introduced by a lens, a closed-form propagation equation of Gaussian beams passing through the astigmatic lens is derived, which enables us to discuss the focusing properties of astigmatic Gaussian beams both analytically and numerically. Furthermore, the beam propagation factor ( M 2 -factor) and power in the bucket (PIB) are chosen as the criteria, the beam quality of astigmatic Gaussian beams is analyzed. It is shown that the effects of astigmatic lens on the irradiance distribution and PIB are determined by a combined parameter C 5 2 + C 6 2 , and the astigmatism results in a decrement of the PIB.