Fresnel-Gaussian shape invariant for optical ray tracing

Abstract

We propose a technique for ray tracing, based in the propagation of a Gaussian shape invariant under the Fresnel diffraction integral. The technique uses two driving independent terms to direct the ray and is based on the fact that at any arbitrary distance, the center of the propagated Gaussian beam corresponds to the geometrical projection of the center of the incident beam. We present computer simulations as examples of the use of the technique consisting in the calculation of rays through lenses and optical media where the index of refraction varies as a function of position.

Experimental profiling of a non-truncated focused Gaussian beam and fine-tuning of the quadratic phase in the Fresnel Gaussian shape invariant

“…The process of propagation is calculated by means of an iterative set of equations for each FGSI, and is described in [8,10]; for convenience a brief description follows. These equations are used to calculate the propagation of each FGSI from the n-th plane up to (n 1 + )-th plane which are separated a distance z.…”

“…From Eqs. (15) and (18) [8,10]. It is now necessary to introduce new equations to adequately describe the plot given in Fig.…”

“…For optical systems there is commercially available dedicated software as ASAP s or FRED s to perform this task [5,6]. In particular, we have previously reported the possibility of representing an optical field by means of a superposition of Gaussian functions following a Rayleigh-like criterion [7][8][9][10]. In this criterion each Gaussian function is placed such that its center coincides with the e 1/ value of its right and left neighbor functions.…”

“…In a following report we have proposed a Fresnel Gaussian shape invariant (FGSI) method to calculate the propagation of a field through an optical system. FGSI is similar to a ray tracing method and is based on a set of iterative equations [8]. FGSI carries the overall information of the field: linear and quadratic phases and the complex amplitude.…”

Refractive index and geometrical thickness measurement of a transparent pellicle in air by Gaussian beam defocusing

“…For simplicity in the description of our proposal this is not necessary; it is sufficient to begin our description by considering the beam distribution just after the lens. For this, let us consider a circular amplitude distribution of the Gaussian just at the back surface of the lens as [8],…”