Jose Manuel Rivas-Moscoso

Marginal rays in tapered gradient-index lenses

Marginal rays are used to study the limitations of the spatial and angular extents of light beams by stops and apertures in tapered gradient-index lenses. The results are applied to two kinds of taper functions and compared to selfoc lenses.

Tapered gradient-index media and zone plates

Abstract Light propagation through a tapered gradient-index medium with a zone plate located at the input of the medium for non-uniform and uniform illumination is studied. Evolution of the beam half-width of the zone plate diffraction orders and an analogy with the conventional lens imaging formula are presented. A particular case is analysed.

Tapered gradient-index media and zone plates: Influence of off-axis illumination and finite dimension on light propagation

Abstract The effects of off-axis illumination and finite dimension on the irradiance distribution in a hybrid system formed by a zone plate and a tapered gradient-index (GRIN) medium are investigated. Results are applied to a GRIN medium with a divergent linear taper function and a sinusoidal zone plate of amplitude to show the transverse shift and the diffractional effect.

Focusing of light by zone plates in Selfoc gradient-index lenses.

We study the diffraction fields in a hybrid diffractive-gradient-index element composed of an amplitude zone plate and a quarter-pitch Selfoc gradient-index lens under uniform illumination. Focal positions of the diffractive orders and zone-plate diffraction efficiencies are measured, thereby validating the existing theoretical results.

Zone-plate diffraction patterns in gradient-index media

Diffraction patterns inside gradient-index media in which a complex zone plate is placed at a Fourier transform plane are studied by making use of the optical propagator. The results are illustrated with an example corresponding to a selfoc medium and a Fresnel zone plate of the amplitude and of the phase.

Hybrid refractive-diffractive-gradient-index superresolving focusing device

The focusing properties and resolving power of a device consisting of a tapered gradient-index (GRIN) lens with spherical input and output faces are investigated through the use of the ABCD formalism to achieve minimization of the Airy radius for the device. Diffractive elements, such as zone plates, can, with an appropriate choice of their parameters, increase the resolution of an imaging system compared with a conventional lens. We demonstrate that by combining both elements a hybrid refractive-diffractive-GRIN device can be designed that exhibits improved superresolution characteristics.

Fresnel zones in tapered gradient-index media.

The free propagation of a wave front in an inhomogeneous medium with parabolic refractive-index profile and the division of the wave front into Fresnel zones are studied. We determine the radius and the area of each zone as well as the zone contribution to the total wave at an observation point inside the medium. We find the condition that the optical path must fulfill from each zone to that point so that the disturbance due to successive zones will be in phase opposition. Once this condition is settled the concept of zone plate in gradient-index media is introduced.

Resolving power of a hybrid zone-plate/gradient-index lens system

Following the Rayleigh criterion for resolution, we analyze the resolving power of a hybrid optical structure composed of a zone plate and a gradient-index lens at focal planes inside and outside the lens in terms of the type and number of zones of the zone plate. The Fraunhofer approximation can be invoked to study the irradiance at the Fourier planes inside the lens. In all other cases, the Fresnel diffraction integral must be used, although the resolution defined by the Rayleigh criterion still holds. We compare the limit of resolution for the hybrid structure with the resolution of a lens with the same aperture diameter as a function of the number of zones, stating that both coincide for a large number of zones. Finally, we present irradiance profiles with both approximations at various planes inside the lens and compare the results with those obtained by the use of zone plates in free space.

Zone plates in GRIN media

Zone plate construction in an inhomogeneous medium with parabolic refractive index profile is considered. Ring radii are proven to coincide with the radii of the Fresnel zones into which we divide a wavefront in this medium. From this condition we establish an analogy with the conventional lens imaging formula. Finally, we apply the study to a selfoc medium and a sinusoidal zone plate of the amplitude.

Fresnel zones in GRIN media

The free propagation of a wavefront in an inhomogeneous medium with parabolic refractive index profile and the division of the wavefront into Fresnel zones are studied. We determine the radius and the area of each zone as well as the zone contribution to the total wave at an observation point inside the medium. We find the condition that the optical path must fulfill from each zone to the aforementioned point so that the disturbance due to successive zones will be in phase opposition. Once this condition is settled the concept of zone plate in gradient- index media can be introduced.