Victor A. Soifer

The Phase Rotor Filter

Abstract We report creation by photolithography techniques of the phase rotor filter, an optical element whose complex transmittance depends in a linear fashion on the azimuth angle. Relationships are given that describe the scalar diffraction of coherent light by the rotor filter. The results of the numerical simulation and experiments are discussed.

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularitys integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

Diffraction of a plane, finite-radius wave by a spiral phase plate

We derive analytical expressions containing a hypergeometric function to describe the Fresnel and Fraunhofer diffraction of a plane wave of circular and ringlike cross section by a spiral phase plate (SPP) of an arbitrary integer order. Experimental diffraction patterns generated by an SPP fabricated in resist through direct e-beam writing are in good agreement with the theoretical intensity distribution.

An analysis of the angular momentum of a light field in terms of angular harmonics

Abstract This paper proposes an optical interpretation for the Lie algebras symmetry operators of the paraxial wave equation. In particular, the angular momentum operator is used to derive a relation for the expression of the angular momentum of an arbitrary light field in terms of angular harmonics. Furthermore, experimental results are presented demonstrating a filter that extracts angular harmonics from different Gauss-Laguerre modes.

Gauss-Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element

Multilevel surface-relief-type diffractive optical elements are designed which are capable of generating a large number of Gauss-Laguerre modes with arbitrary mode indices in different diffraction orders of the element. Some such elements are fabricated by electron beam lithography, proportional reactive ion etching in SiO , and hot embossing in PMMA. Good 2

Investigation of computer-generated diffractive beam shapers for flattening of single-modal CO 2 laser beams

A full cycle was realized of the photolithographic development and detailed testing of a diffractive optical element that transforms the diverging Gaussian beams of CO(2) lasers into a uniformly filled-in rectangle. The zone feature size of the beam shaper, the diffractive efficiency and accuracy, the focus depth, and the stability with respect to the size and the divergence of incident Gaussian beams are studied by computer modeling. Calculated flattop intensity distributions are presented in the same form of gray-level pictures and three-dimensional plots as the corresponding results measured by an IR camera.

Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 microm.

Design of DOEs for wavelength division and focusing

We propose a technique for calculating the color separation gratings aimed at separating plane light beams of different wavelengths into different diffraction orders. The technique is based on a special-type optimization criterion. With this criterion, the problem of calculating the piecewise-constant grating profile is reduced to sequentially solving independent problems of optimization of the step heights. We derived an analytical expression for the profile of a color separation grating that generalizes the familiar analytical solutions. The criterion introduced is used to design a diffractive optical element (DOE) that generates required light beams when it is illuminated by different wavelengths. Design of color separation gratings able to separate three and five different wavelengths and DOEs to demultiplex and focus the two- and three-wavelength beams is presented.

A method of designing diffractive optical elements focusing into plane areas

We propose a numerical method for designing phase function of diffractive optical elements (DOEs) aimed at focusing into a plane area of complex shape. The method is applied to factorable intensity distribution in the domain of focusing and factorable illuminating beam of arbitrary cross-section. The diffraction analysis of a direct problem of focusing into the plane region is carried out. Based on a specially developed software, the numerical experiment was carried out, which allowed us to find that the theoretical power efficiency of typical DOEs is no less than 85%.

Rotation of microparticles with Bessel beams generated by diffractive elements

Abstract We show that imaging a non-diverging Bessel beam by a spherical lens leads to the generation of a diverging Bessel beam. Expressions for the projections of the Umov-Poynting vector for a two-dimensional TE-polarized Bessel beam and a three-dimensional paraxial linearly polarized Bessel beam are derived. A fifth-order Bessel beam is produced using a single optical element-a 16-level phase-only diffractive helical axicon fabricated using electron beam lithography. This beam was successfully used to trap and rotate 5-10 μm diameter yeast particles and polystyrene beads of diameter 5 μm.