Svetlana N. Khonina

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.

Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debyes approximation, we demonstrate benefits of using asymmetric to polar angle ϕ binary phase distributions (such as arg[cos ϕ] or arg[sin 2ϕ]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.

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

Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system

An analysis was performed into the possibility of reducing the lateral size and increasing the longitudinal size of a high-aperture focal system focus using a vortex phase transmission function for different types of input polarisation (including the general vortex polarisation). We have shown both analytically and numerically that subwavelength localisation for individual components of the vector field is possible at any polarisation type. This fact can be important when considering the interaction between laser radiation and materials that are selectively sensitive to different components of an electromagnetic field. In order to form substantially subwavelength details in total intensity, specific polarisation types and additional apodisation of pupil function, such as masking by a narrow annular slit, are necessary. The optimal selection of the slit radius allows balance of the trade-off between focus depth and focal spot size.

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.

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.

Polarization conversion when focusing cylindrically polarized vortex beams

Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro- and nano-particles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. The creation of these laser beams is carried out using segmented polarizing plates, subwavelength gratings, interference, or light modulators. Here, we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher-order vortex phase singularity. To simultaneously generate several vortex phase singularities of different orders, we utilized a multi-order diffractive optical element. Both the theoretical and the experimental results regarding the radiation transmitted through the diffractive optical element show that increasing the order of the phase singularity leads to more efficient conversation of the polarization from radial to azimuthal. This demonstrates a close connection between the polarization and phase states of electromagnetic beams, which has important implications in many optical experiments.