We have shown experimentally, in a real-world setting, that it is possible to use two beams of incoherent radio waves, transmitted on the same frequency but encoded in two different orbital angular momentum states, to simultaneously transmit two independent radio channels. This novel radio technique allows the implementation of, in principle, an infinite number of channels in a given, fixed bandwidth, even without using polarization, multiport or dense coding techniques. This paves the way for innovative techniques in radio science and entirely new paradigms in radio communication protocols that might offer a solution to the problem of radio-band congestion.

https://iopscience.iop.org/article/10.1088/1367-2630/14/3/033001/pdf

Encoding many channels on the same frequency through radio vorticity: first experimental test

Publisher Summary The widespread availability of spatially and temporally coherent laser sources makes the production of optical vortices inevitable in any experiment involving scattered laser light. The realization of quantized vortices is not specific to optics: these objects occur in all spatial scalar fields. Although optical vortices are often referred to as “points of phase singularity within a cross section of the field,” physical optical fields extend over three dimensions, and the phase singularities are actually lines of perfect destructive interference that are embedded in the volume filled by the light. Optical vortices are examples of the singularity lines within all complicated scalar fields. By comparison, electromagnetic vector fields do not generally have nodes in all components simultaneously. However, vector fields possess singularities associated with the parameterization of elliptical and partial polarization rather than phase. Polarization singularities are present in many situations, ranging from sunlight to the light transmitted by birefringent materials. Their descriptors are more complicated than their scalar counterpart in that they have both handedness and additional categorization. The study of optical vortices and orbital angular momentum has led to a recognition that the energy flow—characterized by the Poynting vector—has features not immediately apparent from the intensity alone, nor from global properties of a beam.

Singular optics: optical vortices and polarization singularities

We present a new method for recording digital holograms under incoherent illumination. Light is reflected from a 3D object, propagates through a diffractive optical element (DOE), and is recorded by a digital camera. Three holograms are recorded sequentially, each for a different phase factor of the DOE. The three holograms are superposed in the computer, such that the result is a complex-valued Fresnel hologram. When this hologram is reconstructed in the computer, the 3D properties of the object are revealed.

/pdf/digital-spatially-incoherent-fresnel-holography-57h7q6mcom.pdf

Digital spatially incoherent Fresnel holography.

Chapter 5 - Optical vortices and vortex solitons

Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index

The quantum theory of light.

Experimental and numerical techniques allowed us to predict and verify the existence of a robust phase singularity in the spatial coherence function when a vortex is present. Though observed in the optical domain, this phenomenon may occur in any partially coherent vortex wave.

https://www.cis.rit.edu/~grovers/Doc/Publications/PRL_Palacios2004.pdf

Spatial correlation singularity of a vortex field.

Spatial correlation vortex dipoles may form in the four-dimensional mutual coherence function when a partially coherent light source contains an optical vortex. Analytical and numerical investigations are made in near- and far-field regimes.

https://www.cis.rit.edu/~grovers/Doc/Publications/Maleev_JOSAB_04.pdf

Spatial correlation vortices in partially coherent light: theory

The scalar Huygens-Fresnel principle is reformulated to take into account the vector nature of light and its associated directed electric and magnetic fields. Based on Maxwell's equations, a vector Huygens secondary source is developed in terms of the fundamental radiating units of electromagnetism: the electric and magnetic dipoles. The formulation is in terms of the vector potential from which the fields are derived uniquely. Vector wave propagation and diffraction formulated in this way are entirely consistent with Huygens's principle. The theory is applicable to apertures larger than a wavelength situated in dark, perfectly absorbing screens and for points of observation in the right half-space at distances greater than a wavelength beyond the aperture. Alternatively, a formulation in terms of the fields is also developed; it is referred to as a vector Huygens-Fresnel theory. The proposed method permits the determination of the diffracted electromagnetic fields along with the detected irradiance.

Vector diffraction theory for electromagnetic waves

The complete Rayleigh–Sommerfeld scalar diffraction formula contains (1-ikR) in the integrand Usually the wavelength is small compared with the distance of the observation point from the aperture and (1-ikR) is approximated by -ikR alone Other approximations usually made in the Rayleigh–Sommerfeld formula are addressed as well Closed-form solutions, without approximations, are possible wherein interesting consequences of these approximations become apparent

On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory.

It is well known that the intensity interferometry of Hanbury Brown and Twiss measures the square of the absolute value of the normalized coherence function and that the phase of the function is lost. We show that the cosine and the sine of the phase can be determined using triple- and quadruple-intensity correlations. This information is used to derive the intensity distribution of the object. The procedure for the phase reconstruction described depends on the starting values of the phase function for the least separation of the mirrors or for the nearest neighbors in the two perpendicular directions of the array of mirrors. These starting values are determined by means of an amplitude correlation experiment, such as the Young's two-slit type. The procedure of intensity correlations is then used for all other separations throughout the array. Computer simulation of the proposed procedure and a simple example of reconstruction of object intensity distribution are shown.

Arvind S. Marathay

Papers

Spatial correlation singularity of a vortex field.

Spatial correlation vortices in partially coherent light: theory

Vector diffraction theory for electromagnetic waves

On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory.

Phase function of spatial coherence from second-, third-, and fourth- order intensity correlations