Mark A. Neifeld

The speed of information in a 'fast-light' optical medium.

One consequence of the special theory of relativity is that no signal can cause an effect outside the source light cone, the space-time surface on which light rays emanate from the source. Violation of this principle of relativistic causality leads to paradoxes, such as that of an effect preceding its cause. Recent experiments on optical pulse propagation in so-called ‘fast-light’ media—which are characterized by a wave group velocity υg exceeding the vacuum speed of light c or taking on negative values—have led to renewed debate about the definition of the information velocity υi. One view is that υi = υg (ref. 4), which would violate causality, while another is that υi = c in all situations, which would preserve causality. Here we find that the time to detect information propagating through a fast-light medium is slightly longer than the time required to detect the same information travelling through a vacuum, even though υg in the medium vastly exceeds c. Our observations are therefore consistent with relativistic causality and help to resolve the controversies surrounding superluminal pulse propagation.

Adaptive Waveform Design and Sequential Hypothesis Testing for Target Recognition With Active Sensors

Cognitive radar is a recently proposed approach in which a radar system may adaptively and intelligently interrogate a propagation channel using all available knowledge including previous measurements, task priorities, and external databases. A distinguishing characteristic of cognitive radar is that it operates in a closed loop, which enables constant optimization in response to its changing understanding of the channel. In this paper, we compare two different waveform design techniques for use with active sensors operating in a target recognition application. We also propose the integration of waveform design with a sequential-hypothesis-testing framework that controls when hard decisions may be made with adequate confidence. The result is a system that updates multiple target hypotheses/classes based on measured data, customizes waveforms as the class probabilities change, and draws conclusions when sufficient understanding of the propagation channel is achieved

Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link

A multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM)-carrying beams is studied. We numerically analyze the effects of atmospheric turbulence on the system and find that turbulence induces attenuation and crosstalk among channels. Based on a model in which the constituent channels are binary symmetric and crosstalk is a Gaussian noise source, we find optimal sets of OAM states at each turbulence condition studied and determine the aggregate capacity of the multichannel system at those conditions. OAM-multiplexed FSO systems that operate in the weak turbulence regime are found to offer good performance. We verify that the aggregate capacity decreases as the turbulence increases. A per-channel bit-error rate evaluation is presented to show the uneven effects of crosstalk on the constituent channels.

Distortion management in slow-light pulse delay

We describe a methodology to maximize slow-light pulse delay subject to a constraint on the allowable pulse distortion. We show that optimizing over a larger number of physical variables can increase the distortion-constrained delay. We demonstrate these concepts by comparing the optimum slow-light pulse delay achievable using a single Lorentzian gain line with that achievable using a pair of closely-spaced gain lines. We predict that distortion management using a gain doublet can provide approximately a factor of 2 increase in slow-light pulse delay as compared with the optimum single-line delay. Experimental results employing Brillouin gain in optical fiber confirm our theoretical predictions.

Shannon capacities and error-correction codes for optical atmospheric turbulent channels

Feature Issue on Optical Wireless Communications (OWC) The propagation of an on-off keying modulated optical signal through an optical atmospheric turbulent channel is considered. The intensity fluctuations of the signal observed at the receiver are modeled using a gamma-gamma distribution. The capacity of this channel is determined for a wide range of turbulence conditions. For a zero inner scale, the capacity decreases monotonically as the turbulence strengthens. For non-zero inner scale, the capacity is not monotonic with turbulence strength. Two error-correction schemes, based on low-density parity-check (LDPC) codes, are investigated as a means to improve the bit-error rate (BER) performance of the system. Very large coding gains--ranging from 5.5 to 14 dB, depending on the turbulence conditions--are obtained by these LDPC codes compared with Reed-Solomon error-correction codes of similar rates and lengths.

Spatial correlation and irradiance statistics in a multiple-beam terrestrial free-space optical communication link

By means of numerical simulations we analyze the statistical properties of the power fluctuations induced by the incoherent superposition of multiple transmitted laser beams in a terrestrial free-space optical communication link. The measured signals arising from different transmitted optical beams are found to be statistically correlated. This channel correlation increases with receiver aperture and propagation distance. We find a simple scaling rule for the spatial correlation coefficient in terms of the propagation distance and we are able to predict the scintillation reduction in previously reported experiments with good accuracy. We propose an approximation to the probability density function of the received power of a spatially correlated multiple-beam system in terms of the parameters of the single-channel gamma-gamma function. A bit-error-rate evaluation is also presented to demonstrate the improvement of a multibeam system over its single-beam counterpart.

Feature-specific imaging

We analyze the performance of feature-specific imaging systems. We study incoherent optical systems that directly measure linear projects of the optical irradiance distribution. Direct feature measurement exploit, the multiplex advantage, and for small numbers of projections can provide higher feature-fidelity than those systems that postprocess a conventional image. We examine feature-specific imaging using Wavelet, Karhunen-Loeve (KL), Hadamard, and independent-component features, quantifying feature fidelity in Gaussian-, shot-, and quantization-noise environments. An example of feature-specific imaging based on KL projections is analyzed and demonstrates that within a high-noise environment it is possible to improve image fidelity via direct feature measurement. A candidate optical system is presented and a preliminary implementational study is undertaken.

Optical architectures for compressive imaging

We compare three optical architectures for compressive imaging: sequential, parallel, and photon sharing. Each of these architectures is analyzed using two different types of projection: (a) principal component projections and (b) pseudo-random projections. Both linear and nonlinear reconstruction methods are studied. The performance of each architecture-projection combination is quantified in terms of reconstructed image quality as a function of measurement noise strength. Using a linear reconstruction operator we find that in all cases of (a) there is a measurement noise level above which compressive imaging is superior to conventional imaging. Normalized by the average object pixel brightness, these threshold noise standard deviations are 6.4, 4.9, and 2.1 for the sequential, parallel, and photon sharing architectures, respectively. We also find that conventional imaging outperforms compressive imaging using pseudo-random projections when linear reconstruction is employed. In all cases the photon sharing architecture is found to be more photon-efficient than the other two optical implementations and thus offers the highest performance among all compressive methods studied here. For example, with principal component projections and a linear reconstruction operator, the photon sharing architecture provides at least 17.6% less reconstruction error than either of the other two architectures for a noise strength of 1.6 times the average object pixel brightness. We also demonstrate that nonlinear reconstruction methods can offer additional performance improvements to all architectures for small values of noise.

Optimal pump profile designs for broadband SBS slow-light systems

We describe a methodology for designing the optimal gain profiles for gain-based, tunable, broadband, slow-light pulse delay devices based on stimulated Brillouin scattering. Optimal gain profiles are obtained under system constraints such as distortion, total pump power, and maximum gain. The delay performance of three candidate systems: Gaussian noise pump broadened (GNPB), optimal gain-only, and optimal gain+absorption are studied using Gaussian and super-Gaussian pulses. For the same pulse bandwidth, we find that the optimal gain+absorption medium improves the delay performance by 2.1 times the GNPB medium delay and 1.3 times the optimal gain-only medium delay for Gaussian pulses. For the super-Gaussian pulses the optimal gain-only medium provides a fractional pulse delay 1.8 times the GNPB medium delay.

Digital wavefront reconstruction and its application to image encryption

Phase-shifting digital holography can be used to artificially reconstruct both the amplitude and phase information of a complex object. We apply digital wavefront reconstruction to image encryption. The encrypted wavefront is recorded using a CCD sensor array, facilitating real time transmission of the encrypted message via traditional digital communication methods. Initial experimental results show that high security strength can be obtained with currently available devices.