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

As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

/pdf/orbital-angular-momentum-origins-behavior-and-applications-1sv8qfuhrs.pdf

Orbital angular momentum: origins, behavior and applications

We propose an interferometric method for measuring the orbital angular momentum of single photons. We demonstrate its viability by sorting four different orbital angular momentum states, and are thus able to encode two bits of information on a single photon. This new approach has implications for entanglement experiments, quantum cryptography and high density information transfer.

/pdf/measuring-the-orbital-angular-momentum-of-a-single-photon-430bag1rrk.pdf

Measuring the orbital angular momentum of a single photon.

We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.

/pdf/efficient-sorting-of-orbital-angular-momentum-states-of-30x8auric6.pdf

Efficient sorting of orbital angular momentum states of light.

Light beams can be engineered to carry orbital angular momentum, with application as, for instance, optical 'spanners' — essentially a 'twisted' variant of the more familiar optical tweezers Here it is shown that it is, in principle, possible to engineer similar behaviour into an electron beam Such a beam could find use in a variety of spectroscopy and microscopy techniques

Generation of electron beams carrying orbital angular momentum

An iterative technique has been developed for calculating phase radial optical elements characterized by a small number of phase gradations and aimed at stretching a minimum diffraction spot. The proof of the algorithm convergence is given and the results of computer simulation are reported.

Phase optical elements for widening a minimum diffraction spot

We discuss finite-energy and infinite-energy Airy beams of the second kind. Similarly to the well-known paraxial Airy beams, these are accelerating beams that can be analytically described in the Fresnel diffraction zone but propagate along a hyperbolic rather than parabolic path over a certain length, with their “gravity center” shifting linearly with distance. The Airy beams of the second kind can be generated near a phase transparency with cubic phase modulation.

Hyperbolic Airy beams

Equations for recovery of the phase of an electromagnetic field

We show by FDTD simulation that a photonic-crystal hyperbolic secant binary microlens in silicon (with the refractive index n=3.47) of size 2 μm × 5 μm with a slit 50 nm wide and 250 nm long can focus a plane TM-wave into a near-surface focal spot of size λ/23 with a 44% diffraction efficiency. The focus intensity is 60 times higher than the incident wave.

Tight light localization in a hyperbolic secant planar slit lens

We propose the use of the photopolymers that have been optimized in our Laboratory to obtain holographic lenses in non-plane substrates. Because photopolymers are self-developing, it is possible to introduce them between two spherical plates of glass which are concentric so that by using the adequate spacers, we generate a uniform layer of photopolymer on the spheric substrates.

Computer generated optical element for detecting the position

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