The first article by Turunen and Friberg deals with a class of fields with propagation-invariant properties such as the optical intensity distribution. Coherent and partially coherent stationary and pulsed solutions are treated in view of scalar and electromagnetic approaches. Approximations of ideal propagation-invariant fields and methods for their generation are discussed. Finally, some application areas are covered.

Propagation-Invariant Optical Fields

An optical system having a first positive optical element having an aspherical surface; and a second positive optical element having an aspherical surface. The first and second optical elements are arranged in a Keplerian configuration. The aspheric surface of the second optical element is related to the aspheric surface of the first optical element by a ray-tracing function that maps substantially all of an input light beam that is incident to the first optical element to a collimated output light beam that is output from the second optical element. The input light beam has a first axially-symmetric intensity distribution, such as a Gaussian intensity distribution, and the output light beam has a second axially-symmetric intensity distribution, such as a continuous, sigmoidal intensity distribution. Preferably, the output light beam has a Fermi-Dirac intensity distribution, and the ray-tracing function maps the input light beam to the output beam to a 1/e 6 intensity radius of the input light beam.

Refractive optical system that converts a laser beam to a collimated flat-top beam

We demonstrate the annular flattop beam shaping technique with dual phase only liquid crystal spatial light modulators (LC-SLM) based on the refractive laser beam shaping systems. One LC-SLM redistributes the intensity distribution, and the other restores the initial underlying wave front. Differing from the conventional annular beam shaping technique, the wave front of the output beam can be maintained. The influences of deviations of beam waist and beam shape on the output beam profile are discussed in detail. Experimental results show that approximate 71% of the power is enclosed in a region with less than 7% rms intensity variation. The 4.1mm diameter near-diffraction-limited beam retains an annular flattop intensity distribution without significant diffraction peaks for a working distance of more than 24cm in the near field.

Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators

An optical beam transformation system includes a first and a second optical element, each of which has a non-reentrant surface. The system transforms a substantially non-uniform optical input beam (such as a Gaussian) to a substantially uniform output beam. The first and second optical elements are arranged in either a Keplerian or Galilean configuration. The aspheric surface of the second optical element is related to the aspheric surface of the first optical element by a ray-tracing function that maps substantially all of an input light beam that is incident on the first optical element to a collimated output light beam that is output from the second optical element. Preferably, the output light beam has a Fermi-Dirac intensity distribution, and the ray-tracing function maps the input light beam to the output beam out to the (1/e)6 intensity radius of the input light beam.

System for converting optical beams to collimated flat-top beams

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.

Simple lens axicon

A refracting system consisting of two lenses is designed to transform an annular Gaussian laser beam into a circular Bessel beam. The slopes of the input and output surfaces fit well with a sixth-order polynomial. A smooth variation of the radii of curvature of the resulting aspheric surfaces is very attractive for easy machining of the surfaces. The diffraction-free length for the designed system is 59.4735 m at 633 nm.

Two-element refracting system for annular Gaussian-to-Bessel beam transformation

A refracting system is designed for transforming an annular Gaussian laser beam into a circular Bessel beam. The slope of the input and output surfaces fitted well with a sixth-order polynomial. The radii of curvature of the resulting aspheric surfaces are found to vary smoothly over the surface. The diffraction-free length for this system is found to be 59.4735 m at 633 nm.

Meer M. Hossain

Papers

Two-element refracting system for annular Gaussian-to-Bessel beam transformation

Refracting System for Annular Gaussian-to-Bessel Beam Transformation.