Victor V. Kotlyar

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.

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

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.

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.

Computer-aided design of diffractive optical elements

A number of iterative algorithms for calculating kinoforms are discussed: a multiplicative adaptive algorithm allowing the rate of iterative process to be increased, fast algorithms for interpolating and extrapolating the kinoform phase pixels, an algorithm for calculating kinoforms forming radially symmetrical images and axial light segments, an algorithm for calculating formators of Gauss-Hermite modes in required diffraction orders, and an algorithm for calculating formators of reference wavefronts. The results of computer simulation are given.

An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images

The paper deals with an iterative algorithm for design diffractive optical elements capable of forming light fields with longitudinal periodicity and modal composition. In addition, the conditions are specified under which the beam transverse intensity distribution, which is dependent on the azimuth angle and lacking radial symmetry, undergoes rotation as the beam propagates along the axis, making an integer number of revolutions per period.

Elliptic Laguerre-Gaussian beams

An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at z = 0 and z = infinity the axial intensity is zero. We show that for a beam with a small degree of ellipticity and even order of singularity, two isolated intensity zeroes appear in the Fresnel zone on a straight line at an angle of 45 deg or -45 deg, depending whether the beams spin is right or left. The theoretical conclusions are confirmed by numerical simulation and physical experiments.

Rotating optical fields : experimental demonstration with diffractive optics

Transversally sharply structured optical fields are discussed, which rotate upon propagation without any lateral expansion of the intensity profile. Finite-aperture approximations of such fields, realizable with phase-only and complex-amplitude recording, are demonstrated. Recording of at least some of the amplitude information (rather than neglecting it completely) is shown to improve the field quality considerably, in particular close to the element. Lohmann-coded binary-phase diffractive elements with restricted amplitude recording are fabricated by electron beam lithography and reactive ion etching. The experimental results are in good agreement with theory.

Analysis of the shape of a subwavelength focal spot for the linearly polarized light

By decomposing a linearly polarized light field in terms of plane waves, the elliptic intensity distribution across the focal spot is shown to be determined by the E-vectors longitudinal component. Considering that the Poynting vectors projection onto the optical axis (power flux) is independent of the E-vectors longitudinal component, the power flux cross section has a circular form. Using a near-field scanning optical microscope (NSOM) with a small-aperture metal tip, we show that a glass zone plate (ZP) having a focal length of one wavelength focuses a linearly polarized Gaussian beam into a weak ellipse with the Cartesian axis diameters FWHM(x)=(0.44±0.02)λ and FWHM(y)=(0.52±0.02)λ and the (depth of focus) DOF=(0.75±0.02)λ, where λ is the incident wavelength. The comparison of the experimental and simulation results suggests that NSOM with a hollow pyramidal aluminum-coated tip (with 70° apex and 100 nm diameter aperture) measures the transverse intensity, rather than the power flux or the total intensity. The conclusion that the small-aperture metal tip measures the transverse intensity can be inferred from the Bethe-Bouwkamp theory.