A rigorous method for finding the best-connected orthogonal communication channels, modes, or degrees of freedom for scalar waves between two volumes of arbitrary shape and position is derived explicitly without assuming planar surfaces or paraxial approximations. The communication channels are the solutions of two eigenvalue problems and are identical to the cavity modes of a double phase-conjugate resonator. A sum rule for the connection strengths is also derived, the sum being a simple volume integral. These results are used to analyze rectangular prism volumes, small volumes, thin volumes in different relative orientations, and arbitrary near-field volumes: all situations in which previous planar approaches have failed for one or more reasons. Previous planar results are reproduced explicitly, extending them to finite depth. Depth is shown not to increase the number of communications modes unless the volumes are close when compared with their depths. How to estimate the connection strengths in some cases without a full solution of the eigenvalue problem is discussed so that estimates of the number of usable communications modes can be made from the sum rule. In general, the approach gives a rigorous basis for handling problems related to volume sources and receivers. It may be especially applicable in near-field problems and in situations in which volume is an intrinsic part of the problem.

/pdf/communicating-with-waves-between-volumes-evaluating-1hnvpw192e.pdf

Communicating with waves between volumes: evaluating orthogonal spatial channels and limits on coupling strengths.

Publisher Summary This chapter discuses the principles and design of optical arrays. Arrays of optical elements can be found in nature, such as the compound eyes of insects, and in everyday life, such as the corner-cube arrays on cars and bicycles or on road signs. The chapter describes the most unusual new phenomena associated with arrays—that is, the non-Gaussian imaging property of GRIN (gradient index) rod arrays and the pseudo phase conjugation phenomenon of corner-cube arrays. The chapter reviews the essential features of the 2 × 2 ray transfer matrix method. The augmented 4 × 4 matrix introduced to describe the optical behavior of a misaligned optical element is derived. The chapter examines how an array may be treated in terms of a 2 × 2 matrix, which accounts for imaging properties, phase conjugation properties, and some other new properties of arrays. Some examples of arrays that possess interesting properties are given. The problem of the quality of synthesized images is treated by analyzing the additional aberrations of the arrays, and interference fringe formation, with particular regard to the conditions under which they can be eliminated.

III Principles and Design of Optical Arrays

Tailored physical systems were recently exploited to rapidly solve hard computational challenges, such as spin simulators, combinatorial optimization, and focusing through scattering media. Here, we address the phase retrieval problem where an object is reconstructed from its scattered intensity distribution. This is a key problem in many applications, ranging from x-ray imaging to astrophysics, and currently, it lacks efficient direct reconstruction methods: The widely used indirect iterative algorithms are inherently slow. We present an optical approach based on a digital degenerate cavity laser, whose most probable lasing mode rapidly and efficiently reconstructs the object. Our experimental results suggest that the gain competition between the many lasing modes acts as a highly parallel computer that could rapidly solve the phase retrieval problem. Our approach applies to most two-dimensional objects with known compact support, including complex-valued objects, and can be generalized to imaging through scattering media and other hard computational tasks.

https://advances.sciencemag.org/content/advances/5/10/eaax4530.full.pdf

Rapid laser solver for the phase retrieval problem

A laser which self-corrects for distortions introduced into the laser beam wavefronts by aberrations and time-varying phenomena internal to the laser. The improved laser includes a partially transmissive first reflecting element, an aperture stop, a lasing medium and a nonlinear phase conjugate reflecting device as the second reflecting element. During laser operation, aberrated wavefronts impinging upon the second reflecting element are reflected as the phase conjugate waveform thereof. The aperture stop restricts laser operation to the fundamental mode which allows only corrected, unaberrated waves to pass through the aperture stop and to subsequently exit the laser. Four embodiments are described utilizing stimulated Brillouin scattering (SBS), four-wave mixing, three-wave mixing and photon echo devices as the second reflecting element.

Laser having a nonlinear phase conjugating reflector

Adaptive Optical Techniques for Wave-Front Correction

The feasibility of compensating for intracavity phasefront distortions using a multidither zonal COAT system has been demonstrated insided an unstable resonator cavity using a CO2 electric discharge laser. Experimental data are presented that verify that intracavity-induced degradation of the near-field and far-field intensity distributions can be corrected and the extracted output power improved by using adaptive resonator techniques.

H R Garcia

Papers

Adaptive laser resonator.