Jeffrey P. Wilde

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Transmitter-based adaptive optics and receiver-based single-mode filtering are combined to compensate modal dispersion in multimode fiber (MMF). A liquid-crystal spatial light modulator controls the launched field pattern for ten 10-Gb/s nonreturn-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C-band. Error-free transmission through 2.2 km of 50-mum graded-index MMF is achieved for launch offsets up to 10 mum and for worst-case launched polarization. A ten-channel transceiver based on parallel integration of electronics and photonics is employed.

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We have conducted measurements of the linear electro‐optic coefficient (r41) and electrogyratory coefficient (η41) in Bi12TiO20 at 633 nm. A precise knowledge of these coefficients is important for evaluating the holographic recording properties of this photorefractive material. We have employed both transverse and longitudinal electric field geometries. For each geometry, we present the results of dc as well as ac techniques. Based on these results we find r41=5.75±0.10 pm/V and ‖η41‖≤0.30±0.05 pm/V. We critically examine our measurements and discuss their relative accuracy. Our findings are compared to those previously reported by other investigators.

10 Gb/s DWDM Transmission Through 2.2-km Multimode Fiber Using Adaptive Optics

We develop a method for synthesis of a desired intensity profile at the output of a multimode fiber (MMF) with random mode coupling by controlling the input field distribution using a spatial light modulator (SLM) whose complex reflectance is piecewise constant over a set of disjoint blocks. Depending on the application, the desired intensity profile may be known or unknown a priori. We pose the problem as optimization of an objective function quantifying, and derive a theoretical lower bound on the achievable objective function. We present an adaptive sequential coordinate ascent (SCA) algorithm for controlling the SLM, which does not require characterizing the full transfer characteristic of the MMF, and which converges to near the lower bound after one pass over the SLM blocks. This algorithm is faster than optimizations based on genetic algorithms or random assignment of SLM phases. We present simulated and experimental results applying the algorithm to forming spots of light at a MMF output, and describe how the algorithm can be applied to imaging.

Measurement of electro‐optic and electrogyratory effects in Bi12TiO20

Single-crystal Sr0.61Ba0.39Nb2O6 (SBN:61) is a very attractive candidate for a number of optical and acoustical applications. Boules grown by the Czochralski (CZ) method can provide crystals of the required size and quality. The main difficulty in applying the CZ growth technique to SBN stems from an instability of the crystal diameter that is primarily attributed to faceted radial growth. The instability is a principal limiting factor in obtaining large, constant diameter boules. However, this problem can be overcome by weighing the crystal in real time and using a computer to provide temperature-based automatic diameter control (ADC). In this paper a number of important issues concerning unstable growth and its control are addressed. First, the radial growth process is analyzed for the purpose of modeling the corresponding weight signal. In doing so, the standard equations governing the meniscus dynamics (neglecting heat balance) have been modified to accommodate a situation of rapidly-varying diameter. Next, a digital ADC algorithm is presented along with a discussion of noise sources and filtering techniques. Finally, typical results for growth of SBN are given.

Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling

The readout diffraction efficiency of a photorefractive hologram stored in single-crystal strontium barium niobate (SBN) is shown to depend strongly on a uniform electric field applied along the c axis. The effect is observed in the vicinity of the diffuse ferroelectric phase transition that occurs near room temperature for SBN:75. Measurements of the nonlinear electro-optic and dielectric properties of SBN verify a simple model describing the origin of the field-dependent diffraction.

Diameter stabilization of Czochralski-grown Sr0.61Ba0.39Nb2O6 (SBN) crystals using real-time computer control

Abstract Single-crystal Sr 0.61 Ba 0.39 Nb 2 O 6 (SBN:61) fibers of high optical quality have been grown by the laser-heated pedestal growth (LHPG) method. Strontium barium niobate, based on its photorefractive properties, is a promising medium for holographic data storage. The use of a fiber bundle in this application is particularly attractive because each individual fiber can store many (10–30) independent holograms with little cross-talk between adjacent fibers. For this purpose, fibers that are oriented with the c -axis perpendicular to the pulling direction are preffered because they provide a significant increase in photorefractive performance when compared to fibers grown along the c -axis. In this paper we report, to our knowledge, the first stable growth of SBN fibers along the [100] and [110] crystallographic axes. Previous attempts to grow bulk crystals with these orientations using the Czochralski technique have been generally unsuccessful because of diameter instability. We do not encounter this problem with the LHPG method and instead find that [100] and [110] fibers can be readily pulled. Growth conditions, morphology and crystal quality are discussed.

Electric-field-controlled diffraction in photorefractive strontium barium niobate

A novel architecture for a reconfigurable optical routing switch using photorefractive crystals with nondestructive readout is presented. This design reduces the order of complexity from n2 to n for a general two-wavelength n × n holographic interconnection network. The packing capacity of the network is discussed and is calculated to be of the order of 1000 × 1000 for an ideal volume holographic recording material. In practice, we show that the actual value is constrained by the number of gratings that can be multiplexed in a single photorefractive crystal. A 2 × 3 switch is demonstrated by using a Bi12GeO20 crystal with 514-nm writing beams and 633-nm signal (readout) beams.

Growth of Sr0.61Ba0.39Nb2O6 fibers: new results regarding orientation

Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode coupling, and minimizes the number of ports required to accommodate a given traffic volume. When a pure mode is present at the input, modal transmission and coupling coefficients are mode-dependent and may be computed using a simple mode-clipping model. When multiple modes are present, interference between modes alters the transmission and coupling coefficients, shifting the passband center frequency and changing its bandwidth. Mode-coupling matrices are used to compute mixed modes having the narrowest or widest bandwidths, or having the largest center-frequency offsets. In a specific design for graded-index fiber, five mode groups and 50-GHz channel spacing, the one-sided bandwidth may change up to ±3.6 GHz. In a system with many cascaded switches and strong mode coupling, the end-to-end response per switch may be characterized by a mode-averaged transmission coefficient.

Two-wavelength photorefractive dynamic optical interconnect

We explore theoretically and experimentally how application of an electric field to a photorefractive crystal affects the recording and the readout of holograms. We consider, for the first time to our knowledge, the effects of fringe bending caused by nonlinear two-wave mixing on the change in Bragg condition and diffraction efficiency as a function of the applied electric field. Practical performance limitations for holographic data storage and image amplification are discussed.

Wavelength-Selective Switches for Mode-Division Multiplexing: Scaling and Performance Analysis

Rayleigh scattering (λ=488 nm) is observed in single‐crystal Sr0.61Ba0.39Nb2O6 (SBN:61). In particular, the scattered intensity is measured as a function of temperature across the ferroelectric–paraelectric phase transition. The results show that the scattered intensity can vary by as much as two orders of magnitude in passing through the transition. The particular form of the intensity‐vs‐temperature curve is found to depend on the poling history of the crystal. The unpoled crystal exhibits a rapid change from strong scattering below the transition (ferroelectric state) to weak scattering above the transition (paraelectric state). The measured inflection point is near 63 °C upon heating and near 58 °C upon cooling. In this case the scattering is predominantly attributed to the presence of high‐density ferroelectric domains, which vanish above the transition. If the crystal is thermally poled (by cooling through the transition with an electric field applied), it shows no measurable domain scattering but does exhibit strong central‐peak behavior at 65 °C upon heating and 59 °C upon cooling. Despite repeated cycling through the transition, the previously thermally poled crystal consistently displays central‐peak behavior. The results suggest that thermal poling in SBN followed by thermal depoling produces a significant increase in the average ferroelectric domain size when compared to the unpoled crystal.