A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Modal decomposition of light has been known for a long time, applied mostly to pattern recognition. With the commercialization of liquid-crystal devices, digital holography as an enabling tool has become accessible to all, and with it all-digital tools for the decomposition of light have finally come of age. We review recent advances in unravelling the properties of light, from the modal structure of laser beams to decoding the information stored in orbital angular momentum (OAM)-carrying fields. We show application of these tools to fiber lasers, solid-state lasers, and structured light created in the laboratory by holographic laser beam shaping. We show by experimental implementation how digital holograms may be used to infer the intensity, phase, wavefront, Poynting vector, polarization, and OAM density of some unknown optical field. In particular, we outline how virtually all the previous ISO-standard beam diagnostic techniques may be readily replaced with all-digital equivalents, thus paving the way for unravelling of light in real time. Such tools are highly relevant to the in situ analysis of laser systems, to mode division multiplexing as an emerging tool in optical communication, and for quantum information processing with entangled photons.

Creation and detection of optical modes with spatial light modulators

https://physicstoday.scitation.org/doi/pdf/10.1063/1.3047693

Introduction to the Theory of Coherence and Polarization of Light

We present an optical fiber supporting 36 information bearing orbital angular momentum (OAM) states spanning 9 OAM orders. We introduce design techniques to maximize the number of OAM modes supported in the fiber; while avoiding LP mode excitation. We fabricate such a fiber with an air core and an annular index profile using the MCVD process. We introduce a new technique for shaping OAM beams in free-space to obtain better coupling efficiency with fiber with annular index profiles. We excite 9 orders of OAM in the fiber, using interferometry to verify the OAM state on exiting the fiber. Using polarization multiplexing and both signs for the topological charge, we confirm support of 36 states, exploiting to our knowledge the highest number of OAM modes ever transmitted in optical fiber.

Design, fabrication and validation of an OAM fiber supporting 36 states

We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel–Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel–Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.

/pdf/perfect-vortex-beam-fourier-transformation-of-a-bessel-beam-73jnrjh187.pdf

Perfect vortex beam: Fourier transformation of a Bessel beam.

Two alternative techniques for generating a secondary electromagnetic source with the desired degree of polarization and transverse coherence length are considered and compared. The first technique is based on the changes of coherence and polarization in propagation, while the second one makes use of the coherence and polarization modulation by a random phase screen. The dependence of the results on the employed definition of electromagnetic coherence is discussed.

/pdf/two-techniques-for-generating-a-secondary-electromagnetic-5acpb33uae.pdf

Two techniques for generating a secondary electromagnetic source with desired statistical properties

A technique for experimental determining the coherent-mode structure of vector electromagnetic field is proposed. This technique is based in the method recently reported by F. Ferreira and M. Belsley for a scalar electromagnetic field

Experimental determining the coherent-mode structure of vector electromagnetic field through its decomposition in reference basis

The problem of computer reconstruction of the coherent-mode structure of an optical field with unknown cross-spectral density function is considered. It is proposed the alternative coherent-mode representation of a source which does not involve the solution of the Fredholm integral equation but may be obtained from the results of radiometric measurements. The basic concept is illustrated by the example of the alternative coherent-mode representation calculated for the 1-D Lambertian source.

Computer reconstruction of the coherent-mode structure of and optical field from the radiometric measurements data

Beam shaping by means of Fourier-transforming optical system with partially coherent illumination

The fast algorithm for calculating the image in optical system with partially coherent illumination is proposed. The algorithm is based on the coherent-mode representation of cross-spectral density of illumination. An example of computing is given.

Andrey S. Ostrovsky

Papers

Two techniques for generating a secondary electromagnetic source with desired statistical properties

Experimental determining the coherent-mode structure of vector electromagnetic field through its decomposition in reference basis

Computer reconstruction of the coherent-mode structure of and optical field from the radiometric measurements data

Beam shaping by means of Fourier-transforming optical system with partially coherent illumination

Fast Algorithm for Computational Imaging with Partially Coherent Illumination