Jacek Sochacki

Nonparaxial design of generalized axicons

The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

Phase retardation of the uniform-intensity axilens

A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication [Opt. Lett. 16, 523 (1991)]. Within the presented formulation good agreement is achieved between the geometrical-optics prediction and the numerically evaluated diffraction integral.

Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions

We show that the apodized annular-aperture logarithmic axicon preserves excellent uniformity of the on-axis intensity, energy flow, and lateral resolution. Numerical evaluation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions. Once again the geometrical law of energy conservation turns out to be a useful tool in designing axicons.

Accurate reconstruction of the refractive-index profile of fibers and preform rods from transverse interferometric data

A closed-form strict correlation between the interference fringe shift and the ray deflection function is derived which enables an accurate determination of the refractive-index distribution in fibers, preform rods, and GRIN-rod lenses to be performed by transverse interferometric methods. The refraction of the probing rays as well as the defocusing effect are entirely compensated and the immersion-object index mismatch is also taken into account. The comprehensive analysis presented proves that nondestructive transverse interferometry can be utilized as a reliable tool in the examination of both GRIN and step-index fibers and rods with low as well as with high numerical apertures.

Imaging and transforming capabilities of GRIN rods with noncylindrical surfaces of constant index: a family of exact solutions

Following the previously derived results a general condition is formulated which determines a family of the exact solutions for GRIN rod lenses with perfect (within the paraxial approximation) imaging and transforming capabilities. Using this condition a new index profile is closely evaluated, and the detailed analysis of this construction is presented.

New method for designing the stigmatically imaging gradient-index lenses of spherical symmetry

The general solution presented here yields smooth, continuous, and monotonic refractive-index profiles for Luneburg-Morgan lenses with a boundary index of N > 1. The new formula incorporates an original apparent-immersing method as well as the continuous-deflection-function concept recently developed by one of the authors for the description of waveguide lenses.

Reliability in reconstruction of the axisymmetric refractive index profiles from transverse interferograms. Accurate versus approximate methods: A comparative study

Abstract A mathematical formalism related to the approximate as well as the accurate interferometric data reduction schemes is briefly outlined and subsequently applied in the reconstruction of the assumed (Luneburg) axisymmetric refractive index distribution. The presented comparative analysis confirms the generally held opinion that the approximate methods (“straight-line” and Kokubun-Iga approaches) may provide quite reasonable results in the examination of refractively inhomogeneous disturbances characterized by weak gradient and moderate index variation. On the other hand, the accurate scheme for transverse interferometric data interpretation and reduction, based on the close-form correlation between the fringe shift and the deflection function, [1] remains the only method for reliable reconstruction of strongly refracting index profiles, independently of magnitude of refraction and ambiguity of the fringes. This fact is of considerable importance for transverse interferometry of fibers (preform rods...

Nonfull-aperture Luneburg lenses: a novel solution

A new formula for the refractive-index distribution for nonfull-aperture Luneburg lenses is proposed. It yields smooth index profiles and provides an explicit description of the index in the outer shell.

Perfect geodesic lens designing.

A new treatment for the problem of perfectly imaging geodesic lenses is presented that provides a uniform mathematical description for full aperture as well as for nonfull aperture media. A family of the existing particular solutions is surveyed and completed with novel results. The proposed formulation is in some aspects similar to the mathematical description of the Luneburg lens, which may be of some convenience for those familiar with the Luneburg lens theory.

Design of gradient-index microlenses for stacked planar optics

The refractive-index profiles of planar matrix microlenses that result from the Luneburg lens theory turn out to yield considerable aberrations. The presented modification of the design process enables satisfactory suppression of the focusing errors.