Production of azimuthally polarized beam with helical phase by use of the axicons and annular glass cylinder.

In this paper, we proposed a method for producing the azimuthally polarized vector beam experimentally. The experimental setup includes two of the same axicons and one annular glass cylinder. The top angles of the two axicons were placed facing each other and the annular cylinder was set among the two axicons. One circular polarized beam was passed through the first axicon, the annular cylinder, and the second axicon in turn. When the beam incident on the inner surface of the annular cylindrical satisfied the Brewster angle, we obtained the azimuthally polarized beam for the reflected light from the annular cylindrical that only contains the $s$s-polarization component. We have derived that the azimuthally polarized vector beam has the helical phase factor with the helical phase factor of ${\exp}( - {\rm i}\varphi )$exp(-iφ) for the left circularly polarized beam incident and ${\exp}({\rm i}\varphi )$exp(iφ) for the right circularly polarized beam incident.

Generation of propagation-invariant vector beams with square array by use of 2D binary phase mask and pentagonal prism.

In this paper, we realize the generation of propagation-invariant vector beams with square array by use of a 2D binary phase mask and pentagonal prism in a typical Mach-Zehnder optical system. The binary phase mask set in the optical system is perpendicular to the optical axis, and its periodic orientation is 45° relative to the horizontal and vertical directions. One polarizer was used to produce the linearly polarized beam with the angle of 45° relative to the horizontal and vertical directions. One mirror in the Mach-Zehnder optical system was replaced by a pentagonal prism, as the light will be reflected twice inside the pentagonal prism. The intensity distribution of the two branches with the mirror and pentagonal prism have mirror symmetry, and the output optical field of the two branches has an orthogonal polarization state. By adjusting the position of the phase plate accordingly, the total optical field of the two branches can form a vector beam with a square array. The experimental results coincide with the simulation results very well and demonstrate the feasibility of this method.

Double-channel vector spatial light modulator for generation of arbitrary complex vector beams.

We propose an approach for implementation of an arbitrary vector beam based on a vector spatial light modulator (VSLM), which is simply composed by a phase-only spatial light modulator (SLM) and a composed half-wave plate with checkerboard structure. In combination with a four-phase encoding algorithm, the VSLM can transform a linear polarized Gaussian beam or a plane wave into a vector beam with both arbitrary spatial polarization and complex amplitude distributions in two dimensions. It is demonstrated that the VSLM can directly transform pure phase values into two orthogonal polarized complex values with high-diffraction efficiency. Compared with the existing methods for generation of vector beams with SLMs, our approach is on-axis and common-path with simple structure and only involves the zero-order diffraction. The proposed structure is also easier to make an integration and design portable device since it abstains from using optical elements such as special gratings, prisms, and reflectors.

Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators.

A flexible approach is presented to generate vector beams with arbitrary polarization and complex amplitude by means of two cascaded transmissive liquid crystal spatial light modulators (LCSLMs). The configuration of the cascaded LCSLM system and its modulation characteristic are introduced. Theoretical analysis and experimental demonstration prove that the system in combination with a double-pass computer-generated hologram and a black-and-white pattern can generate vector beams with arbitrary polarization and complex amplitude by respectively controlling the complex amplitudes of two orthogonal polarization components of the beams. Using this system, we successfully generate radially polarized vector beams with helical phase distributions and vector Bessel beams with inhomogeneous amplitude distributions in experiments.

Radial Hilbert transform with the spatially variable half-wave plate.

We analyzed the point spread function (PSF) of the typical 4f optical image processing system by use of a spatially variable half-wave plate as the spatial filter and found that the PSF is an elementary vector beam. Theoretical analysis and real experiments show that the optical system can be used for a radially symmetric Hilbert transform that permits two-dimensional edge enhancement as the spiral phase plate. This kind of radial Hilbert transform is useful for image processing because it can enhance the edges of an input image selectively by exerting a polarization analyzer before the output plane. The optical system also can be used for generation of vector beams with arbitrary array and shape in real time conveniently.

Phase-shifting with computer-generated holograms written on a spatial light modulator.

We propose a new computer-controlled phase-shifting method based on computer-generated holograms (CGHs) displayed on a spatial light modulator (SLM). In this method the accurate phase shifts required in phase-shifting digital holography or interferometry are induced by a suitable transformation of the encoding patterns of the CGH displayed on a SLM. Both the theoretical analysis and the experimental results demonstrate the feasibility of this approach. We also discuss possible applications of this method in the field of interferometric null testing of aspheres.

Determination of global phase shifts between interferograms by use of an energy-minimum algorithm.

A new algorithm for precise determination of the global phase shift between two interferograms is introduced. First we calculate the frame difference between the first and the second interferogram; the difference is multiplied by a properly chosen test phase factor, and then we implement a two-dimensional Fourier transform of the frame difference and calculate the energy of the first positive (or negative) diffraction order. An iterative approach is used for the test phase to ensure that the minimum energy is obtained, and then the correct phase shift value is found. This method is called the energy-minimum Fourier transform method, which is accurate and noise insensitive compared with the single-point Fourier transform method. Both the theoretical analysis and experimental results are given.