Search results for "Ray transfer matrix analysis"
showing 4 items of 4 documents
Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes
2007
We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.
Teaching stable two-mirror resonators through the fractional Fourier transform
2009
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…
Study of periodic Dielectric Frequency-Selective Surfaces under 3D plane wave incidence
2016
A periodic Dielectric Frequency-Selective Surface (DFSS) is studied under 3D plane-wave incidence, whose unit cell in the periodic direction is composed of a dielectric grating and a homogeneous dielectric layer. The structure is excited by a linearly polarized plane-wave. The procedure for computing the Brillouin diagram of the structure under 2D plane-wave incidence with TE or TM polarization was already described by the authors, and the extension to the 3D incidence case has been performed in a similar way. Following the same formalism, it has been obtained the Generalized Scattering Matrix (GSM) of one period of the infinite periodic lattice. This requires the knowledge of the modal spe…
Chromatic compensation of broadband light diffraction: ABCD-matrix approach
2004
Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spati…