Resolving spatial modes of lasers via matrix completion.

We explain a technique that recovers the structure and the modal weights of spatial modes of lasers from a limited number of spatial coherence measurements. Our approach interpolates the unobserved spatial coherence measurements via the low-rank matrix completion algorithm based on nuclear norm minimization and then extracts the set of modes via singular value decomposition. Numerical examples are provided on a variety of lasers to demonstrate the effectiveness of the method, and it is shown that the proposed method can further reduce the number of measurements by a factor of 2 for a moderate data size.

Total corneal power estimation: ray tracing method versus gaussian optics formula.

PURPOSE: To evaluate with the use of corneal topographic data the differences between total corneal power calculated using ray tracing (TCP) and the Gaussian formula (GEP) in normal eyes, eyes that previously underwent laser in situ keratomileusis/photorefractive keratectomy (LASIK/PRK), and theoretical models. METHODS: TCP and GEP using mean instantaneous curvature were calculated over the central 4-mm zone in 94 normal eyes, 61 myopic-LASIK/PRK eyes, and 9 hyperopic-LASIK/PRK eyes. A corneal model was constructed to assess the incident angles at the posterior corneal surface for both refracted rays and parallel rays. Corneal models with varying parameters were also constructed to investigate the differences between mean TCP and GEP (4-mm zone), and an optical design software validation was performed. RESULTS: The TCP values tended to be less than GEP in normal and myopic-LASIK/PRK eyes, with the opposite relationship in some hyperopic-LASIK/PRK eyes having the highest anterior surface curvature. The difference between TCP and GEP was a function of anterior surface instantaneous radii of curvature and posterior/anterior ratio in postrefractive surgery eyes but not in normal eyes. In model corneas, posterior incident angles with parallel rays were greater than those with refracted rays, producing an overestimation of negative effective posterior corneal power; differences in magnitude between TCP and GEP increased with decreasing ratio of posterior/anterior radii of curvature, consistent with clinical results. CONCLUSIONS: In eyes after refractive surgery, calculating posterior corneal power using the Gaussian formula and its paraxial assumptions introduces errors in the calculation of total corneal power. This may generate errors in intraocular lens power calculation when using the Gaussian formula after refractive surgery.

Real-time all-optical performance monitoring using optical bit-shape correlation.

A new optical performance monitoring technique of an optical link in real time is experimentally demonstrated. Rather than comparing bit streams or analyzing eye diagrams, we use a novel optical correlator to compare the shapes of the individual received bits to a standard. The all-optical correlator outputs a pulse whose strength directly measures the degradation of the bit during transmission. Results are produced within three bit periods in real time instead of requiring statistical analysis of long data streams. The correlator is based on a simplified White cell-based true-time delay device.

Optical cross-connect system based on the White cell and three-state microelectromechanical system: experimental demonstration of the quartic cell.

We present a proof of concept (design, simulations, and experimental results) for an optical cross-connection device based on the optical White cell and a three-state microelectromechanical system tilting mirror array. We describe in detail the implementation of an underpopulated quartic White cell configuration. We discuss the aberrations associated with the output of the system.

Real-time all-optical quality of service monitoring by use of correlation and a network protocol to exploit it.

We propose to use optical correlation to measure the quality of an optical link in real time, staying completely within the optical domain. We transmit a test signal of 010 and correlate the received (degraded) signal with 010. The strength and shape of the output measure dispersion and attenuation in just 3 bit periods (75 ps at 40 Gb/s) compared with minutes by traditional methods. Correlation becomes feasible owing to the recent development of tapped delay lines with very large numbers of taps. We present simulations showing that this technique can detect attenuation, dispersion, noise, and jitter. With this instantaneous quality-of-service information available to all nodes in a network, new protocols will enable the network to select paths based on quality, allowing service providers to take into account the system's physical impairments when selecting new light paths or when restoring existing ones and to guarantee varying levels of service. We present one such protocol.

Design and demonstration of a switching engine for a binary true-time-delay device that uses a white cell.

Optical true-time-delay devices based on the White cell can be divided into two general types: polynomial cells, in which the number of delays that can be obtained is related to the number of times m that a beam bounces in the cell raised to some power, and exponential cells, in which the number of delays is proportional to some number raised to the power of m. In exponential cells, the topic to be addressed, the spatial light modulator switches between a delay element and a null path on each bounce. We describe an improved design of this switching engine, which contains a liquid-crystal switch and a White cell. We examine astigmatism and corrections for it and present a specific design.

Demonstration of a linear optical true-time delay device by use of a microelectromechanical mirror array.

We present the design and proof-of-concept demonstration of an optical device capable of producing true-time delay(s) (TTD)(s) for phased array antennas. This TTD device uses a free-space approach consisting of a single microelectromechanical systems (MEMS) mirror array in a multiple reflection spherical mirror configuration based on the White cell. Divergence is avoided by periodic refocusing by the mirrors. By using the MEMS mirror to switch between paths of different lengths, time delays are generated. Six different delays in 1-ns increments were demonstrated by using the Texas Instruments Digital Micromirror Device as the switching element. Losses of 1.6 to 5.2 dB per bounce and crosstalk of -27 dB were also measured, both resulting primarily from diffraction from holes in each pixel and the inter-pixel gaps of the MEMS.

Polynomial-based optical true-time delay devices with microelectromechanical mirror arrays.

We previously reported optical true-time delay devices, based on the White cell, to support phased-array radars. In particular, we demonstrated a quadratic device, in which the number of delays obtainable was proportional to the square of the number of times the light beam bounced in the cell. Here we consider the possibilities when a microelectromechanical (MEM) tip/tilt mirror array with multiple stable states is used. We present and compare designs for quadratic, quartic, and octic cells using MEM mirror arrays with two, three, and five micro-mirror tilt angles. An octic cell with a three-state MEM can produce 6,339 different delays in just 17 bounces.

Optical true time delay for phased-array antennas: demonstration of a quadratic White cell.

We have demonstrated a proof-of-concept optical device that can produce true time delays for a phased-array radar. This device combines White cells of differing lengths with a spatial light modulator to select between the paths on multiple bounces of a given beam. The approach can handle thousands of light beams and produce hundreds of different delays. The number of delays is proportional to the square of the number of bounces.