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

This Review summarizes the simultaneous transmission of several independent spatial channels of light along optical fibres to expand the data-carrying capacity of optical communications. Recent results achieved in both multicore and multimode optical fibres are documented.

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Space-division multiplexing in optical fibres

Sphere Packings, Lattices and Groups

There are two kinds of tutorial articles: those that provide a primer on an established topic and those that let us in on the ground floor of something of emerging importance. The first type of tutorial can have a noted expert who has been gracious (and brave) enough to write a field guide about a particular topic. The other sort of tutorial typically involves researchers who have each been laboring on a topic for some years. Both sorts of tutorial articles are very much desired. But we, as an editorial board for both Systems and Transactions, know that there has been no logical place for them in the AESS until this series was started several years ago. With these tutorials, we hope to continue to give them a home, a welcome, and provide a service to our membership. We do not intend to publish tutorials on a regular basis, but we hope to deliver them once or twice per year. We need and welcome good, useful tutorial articles (both kinds) in relevant AESS areas. If you, the reader, can offer a topic of interest and an author to write about it, please contact us. Self-nominations are welcome, and even more ideal is a suggestion of an article that the editor(s) can solicit. All articles will be reviewed in detail. Criteria on which they will be judged include their clarity of presentation, relevance, and likely audience, and, of course, their correctness and scientific merit. As to the mathematical level, the articles in this issue are a good guide: in each case the author has striven to explain complicated topics in simple-well, tutorial-terms. There should be no (or very little) novel material: the home for archival science is the Transactions Magazine, and submissions that need to be properly peer reviewed would be rerouted there. Likewise, articles that are interesting and descriptive, but lack significant tutorial content, ought more properly be submitted to the Systems Magazine.

What is a tutorial

▓ Local Randomness for True Random Number generators ▓ Non-local Randomness for distribution of Cryptographic Keys ▓ Towards faster, longer distances and cheaper QKD engines ▓ Quantum Repeaters ▓ Device-Independent Quantum Information Processing

Quantum communication

Multi-plane light conversion is a method of performing spatial basis transformations using cascaded phase plates separated by Fourier transforms or free-space propagation. In general, the number of phase plates required scales with the dimensionality (total number of modes) in the transformation. This is a practical limitation of the technique as it relates to scaling to large mode counts. Firstly, requiring many planes increases the complexity of the optical system itself making it difficult to implement, but also because even a very small loss per plane will grow exponentially as more and more planes are added, causing a theoretically lossless optical system, to be far from lossless in practice. Spatial basis transformations of particular interest are those which take a set of spatial modes which exist in the same or similar space, and transform them into an array of spatially separated spots. Analogous to the operation performed by a diffraction grating in the wavelength domain, or a polarizing beamsplitting in the polarization domain. Decomposing the Laguerre-Gaussian, Hermite-Gaussian or related bases to an array of spots are examples of this and are relevant to many areas of light propagation in free-space and optical fibre. In this paper we present our work on designing multi-plane light conversion devices capable or operating on large numbers of spatial modes in a scalable fashion.

/pdf/laguerre-gaussian-mode-sorter-1k3deiur9w.pdf

Laguerre-Gaussian mode sorter.

We transmit over all 30 spatial and polarization modes of a 22.8-km multimode fiber. 15-mode photonic lanterns enabled low-loss coupling into and out of the fiber and a time-multiplexed coherent receiver facilitates measurement of all 30 signals.

30×30 MIMO transmission over 15 spatial modes

We show transmission of a 73.7 Tb/s (96×3×256-Gb/s) DP-16QAM mode-division-multiplexed signal over 119km of few-mode fiber with inline multi-mode EDFA, using 6x6 MIMO digital signal processing. The total demonstrated net capacity is 57.6 Tb/s (SE 12 bits/s/Hz).

/pdf/73-7-tb-s-96x3x256-gb-s-mode-division-multiplexed-dp-16qam-tr9iiqgfzz.pdf

73.7 Tb/s (96X3x256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA

A novel passive integrated optical circuit for mode-multiplexing and demultiplexing six channels, LP01 and LP11 modes in a few-moded fiber, is designed and tested. A push-pull solution is proposed and demonstrated to excite the LP11 modes with a high extinction ratio. The circuit can outperform present bulk-optics solutions through its compactness and stability, and it has the potential advantages of high coupling efficiency and excellent mode crosstalk suppression.

Silicon Photonic Integrated Mode Multiplexer and Demultiplexer

Light's spatial properties represent an infinite state space, making it attractive for applications requiring high dimensionality, such as quantum mechanics and classical telecommunications, but also inherently spatial applications such as imaging and sensing. However, there is no demultiplexing device in the spatial domain comparable to a grating or calcite for the wavelength and polarisation domains respectively. Specifically, a simple device capable of splitting a finite beam into a large number of discrete spatially separated spots each containing a single orthogonal spatial component. We demonstrate a device capable of decomposing a beam into a Cartesian grid of identical Gaussian spots each containing a single Laguerre-Gaussian component. This is the first device capable of decomposing the azimuthal and radial components simultaneously, and is based on a single spatial light modulator and mirror. We demonstrate over 210 spatial components, meaning it is also the highest dimensionality mode multiplexer of any kind.

/pdf/laguerre-gaussian-mode-sorter-1aegh6hkqo.pdf

Haoshuo Chen

Papers

Laguerre-Gaussian mode sorter.

30×30 MIMO transmission over 15 spatial modes

73.7 Tb/s (96X3x256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA

Silicon Photonic Integrated Mode Multiplexer and Demultiplexer

Laguerre-Gaussian mode sorter