Normalized pulsed energy thresholding in a nonlinear optical loop mirror.

We demonstrate for the first time, to the best of our knowledge, that a Sagnac interferometer can threshold the energies of pulses. Pulses below a given threshold T are suppressed, while those above this threshold are normalized. The device contains an in-loop tunable isolator and 10.4 m of a highly doped silica fiber. We derive an analytical model of the nonlinear optical loop mirror's pulse energy transfer function and show that its energy transfer function approximates a step function for very high phase shifts (>π). We reveal some limitations of this approach, showing that a step-function transfer function necessarily results in pulse distortion in fast, nonresonant all-optical devices.

Improving the privacy of optical steganography with temporal phase masks.

Temporal phase modulation of spread stealth signals is proposed and demonstrated to improve optical steganography transmission privacy. After phase modulation, the temporally spread stealth signal has a more complex spectral-phase-temporal relationship, such that the original temporal profile cannot be restored when only dispersion compensation is applied to the temporally spread stealth signals. Therefore, it increases the difficulty for the eavesdropper to detect and intercept the stealth channel that is hidden under a public transmission, even with a correct dispersion compensation device. The experimental results demonstrate the feasibility of this approach and display insignificant degradation in transmission performance, compared to the conventional stealth transmission without temporal phase modulation. The proposed system can also work without a clock transmission for signal synchronization. Our analysis and simulation results show that it is difficult for the adversary to detect the existence of the stealth transmission, or find the correct phase mask to recover the stealth signals.

A compact nonlinear fiber-based optical autocorrelation peak discriminator.

We experimentally demonstrate a nonlinear fiber-based optical autocorrelation peak discriminator. The approach exploits four-wave mixing in a 37-cm highly-nonlinear bismuth-oxide fiber that provides a passive and compact means for rejecting cross-correlation peaks. The autocorrelation peak discriminator plays an important role in improving the detection of optical CDMA signals. Eye diagrams and bit-error rates are measured at different power ratios. Significant receiver sensitivity improvements are obtained and error-floors are removed. The experimental results show that the autocorrelation peak discriminator works well even when the amplitudes of individual cross-correlation peaks are higher than that of the autocorrelation peak.

Generalized performance parameter for single-threshold detection systems.

A new generalized performance parameter for single-threshold detection systems is investigated that provides a more consistent measure of system performance than the conventional signal-to-noise ratio (SNR). It is shown explicitly that this parameter decreases monotonically as the Bayes risk and probability of error increase, and that it reduces to the SNR under appropriate conditions. An example is presented in which this parameter is monotonic with system performance, but the SNR is not. The analysis, which utilizes normalizing transformations, is also useful in the direct calculation of the Bayes risk, probability of error, and sensitivity, as is considered in detail subsequently (P. R. Prucnal, Applied Optics19, 3606 (1980)).

Receiver performance evaluation using photocounting cumulants with application to atmospheric turbulence.

A new technique for evaluating optical communication system performance directly from the photocounting cumulants is presented. This technique is most useful in situations where exact, explicit, closed form solutions exist for the photocounting cumulants, but do not exist for the photocounting distribution, such as in the generalized case of communication through lognormal atmospheric turbulence. Using this technique, theoretical probability of error curves are presented for communication through lognormal atmospheric turbulence, for a superposed coherent-in-chaotic signal, embedded in additive independent Poisson noise, with arbitrary ratio of sampling time to source coherence time, arbitrary ratio of coherent to chaotic component, arbitrary mean frequencies of the coherent and chaotic components, and where the chaotic component need not be stationary and may have arbitrary spectral distribution. Since no solution exists for the photocounting distribution itself in this generalized case, the corresponding performance calculation has not previously been possible. The case described applies to the detection of radiation originating from a multimode laser or scattered from a rough target, and passing through atmospheric turbulence. A special case of these results is shown to be in excellent agreement with previous calculations [Rosenberg and Teich, Applied Optics12, 2625 (1973)] for a lognormally modulated coherent signal.

Transformation of image-signal-dependent noise into image-signal-independent noise.

A point transformation, the normalizing transform, is presented, which, when applied to a measured noisy image, renders its noise signal independent. The transform is suitable for arbitary noise-to-signal dependence. We demonstrate its applicability and its limitations by using, as an example, noisy signals that belong to a family of gamma-distributed random variables with power-law variance-to-mean dependence. Its normalizing and variance-stabilizing properties are studied.

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications.

A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [IEEE Trans. Inf. Theory IT-25, (March, 1979)].

Efficient optical packet-generation and -compression scheme.

An efficient optical packet-generation and -compression scheme is proposed. Packet compression is achieved when the packet is sent through a series of semiconductor optical amplifiers, which have either a transmitting or an absorbing state. The proposed scheme requires no fast electronics and uses exceptionally simple devices such as a tapped series of D flip-flops and frequency dividers. A detailed performance analysis on the system size limitations is also provided by the consideration of pulse-spreading effects and semiconductor optical-amplifier noise.

Multiplication noise in the human visual system at threshold: 2. Probit estimation of parameters.

A mathematical technique is described that relates detection model parameters to stimulus magnitude and experimental probability of detection. The normalizing transform is used to make the response statistics approximately Gaussian. Conventional probit analysis is then applied. From measurements at M stimulus levels, a system of M equations is solved and estimates of M unknown parameters of the detection model are obtained. The technique is applied to a threshold vision model based on additive and multiplicative Poisson noise. Results are obtained for the parameter estimates for individual subjects, and for the standard deviation of the estimates, for various values of the stimulus energy and number of trials. A frequency-of-seeing experiment is performed using a point-source stimulus that randomly assumes 3 energy levels with 200 trials per level. With a central efficiency of 50%, the estimated ocular quantum efficiency for our four subjects lies between 12% and 23%, the average dark count at the retina lies between 8 and 36 counts, and the threshold count for our (low false-report rate) data lies between 11 and 32. The theoretical results reduce to those obtained by Barlow (J. Physiol. London 160, 155-168, 1962), in the absence of dark light and multiplication noise.

Exact variance-stabilizing transformations for image-signal-dependent Rayleigh and other Weibull noise sources.

Variance-stabilizing transforms for families of Rayleigh and, more generally, for Weibull random variables are derived and shown to be exact. These transforms, when applied to appropriate noisy images, render signal-dependent noise signal-independent. Their utility is that, after applying the transforms, classical estimation procedures devised for additive, signal-independent noise can be brought to bear. The results are expected to find use in image filtering, in photon counting, and in the processing of optical field magnitudes and intensities generated by chaotic sources.

Bit-level packet-switching all-optical multihop shuffle networks with deflection routing.

We propose an all-optical packet-switching scheme in multihop shuffle networks in which deflection routing is used as its contention-resolution principle. In our scheme only partial address information in the packet header is read before a routing decision is made. Because the new scheme does not involve a time-consuming look-up table, extremely low latency operation is possible at each node. Moreover, because the number of demultiplexers at each node can be kept constant even though the network size changes, cost-effective design of a node is possible.

All-optical switching in an asymmetric silicon Fabry-Perot étalon based on the free-carrier plasma effect.

We demonstrate all-optical switching at 1.3 and 1.5 µm in the reflection mode of an asymmetric silicon Fabry-Perot étalon by a control beam at 0.85 µm. Both switch-on and switch-off operations are demonstrated at different locations of the etalon. Based on the free-carrier plasma effect, a modulation depth as large as 10% is obtained and a frequency response as high as 0.5 GHz is achieved.

Asymmetric optical loop mirror: analysis of an all-optical switch.

We present an analysis of the optical loop mirror in which a nonlinear optical element is asymmetrically placed in the loop. This analysis provides a general framework for the operation of a recently invented ultrafast all-optical switch known as the terahertz optical asymmetric demultiplexer. We show that a loop with small asymmetry, such as that used in the terahertz optical asymmetric demultiplexer, permits low-power ultrafast all-optical sampling and demultiplexing to be performed with a relatively slow optical nonlinearity. The size of the loop is completely irrelevant to switch operation as long as the required degree of asymmetry is accommodated. This is therefore the first low-power ultrafast all-optical switch that can be integrated on a single substrate.

Fabrication of precision fiber-optic time delays with in situ monitoring for subpicosecond accuracy.

We have developed a technique to produce precise fiber-optic time delays with subpicosecond accuracy and <0.1-dB loss by heating and stretching optical fiber in a fusion splicer. A fiber Mach-Zehnder interferometer allows in situ measurement of these precise delays using a simple alignment process and requiring only a weak optical signal. To demonstrate this capability, we assembled a six-stage feed-forward delay line that can be used to generate 64 optical pulses with 9.5 +/- 0.8-ps pulse spacings and 4.8-dB total insertion loss.

Comparison of Sagnac and Mach-Zehnder ultrafast all-optical interferometric switches based on a semiconductor resonant optical nonlinearity.

We present a theoretical analysis of recently demonstrated ultrafast all-optical interferometric switching devices (based on Sagnac and Mach-Zehnder interferometers) that use a large optical nonlinearity in a resonant regime. These devices achieve ~10-ps switching windows and do not require high-energy optical control pulses. We theoretically analyze and compare one Sagnac and two Mach-Zehnder switching configurations.

Nonlinear-index-of-refraction measurement in a resonant region by the use of a fiber Mach-Zehnder interferometer.

The nonlinear index of refraction in a resonant region has been determined by the use of a fiber-based Mach--Zehnder interferometer to measure the temporal fringe shift between two signals. The measurement technique is direct and does not require additional amplitude information for the extraction of the nonlinear index of refraction. This technique has been used to measure the temporal response of an InGaAsP semiconductor optical amplifier at 1.313 µm.

Interactions of bound multiple solitons in strongly birefringent fibers.

We report the observation of the interaction of bound multiple solitons generated by orthogonally polarized, highamplitude pulses in strongly birefringent fibers. For the birefringence used, the threshold amplitude for the interaction is higher than that of the onset of second-order solitons on each axis. The characteristics of the output pulses are in good agreement with the results of a numerical simulation of this interaction. A general investigation of this effect is carried out at high values of birefringence, and it is found numerically that, even though the system is nonintegrable, the description of its evolution appears to be reduceable to a finite number of effective degrees of freedom.

Multiplication noise in the human visual system at threshold: 1. Quantum fluctuations and minimum detectable energy.

We have carried out a series of frequency-of-seeing experiments similar to those performed by Hecht, Shlaer, and Pirenne [J. Gen. Physiol. 25, 819-840 (1942)], using an Ar+ laser operated at 514.5 nm as the source of light. In certain blocks of trials, our subjects were encouraged to report as seen those trials in which the stimulus might have been present. It was determined that sensitivity and reliability were traded against each other over a broad range: for our subjects, the detection of 147 photons at the cornea with 60% frequency of seeing entailed, on the average, a 1% false-positive rate (FPR), whereas the detection of 34 photons at the cornea with 60% frequency of seeing was accompanied by a 33% FPR. A new neural-counting model has been developed in the framework of signal-detection theory. It combines Poisson stimulus fluctuations with additive and multiplicative neural noise, both of which are known to be present in the visual system at threshold. The resulting probability-of-detection curves, derived from the Neyman Type-A counting distribution, are in good accord with our experimental frequency-of-seeing data for sensible values of the model parameters. We deduce that, on the average, our four subjects are able to detect a single photon at the retina with 60% frequency of seeing, at the expense of a 55% FPR. In Part 2 of this set of papers [P.R. Prucnal and M.C. Teich, Biol. Cybern. 43, 87-96 (1982)], we use the normalizing transform, together with probit analysis, to provide improved estimates of threshold parameters, whereas in Part 3 [M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, and W.J. McGill, submitted to Biol. Cybern.], we consider the effects of non-Poisson quantum fluctuations.

Multiplication noise in the human visual system at threshold. 3. The role of non-Poisson quantum fluctuations.

Several kinds of light used in vision experiments produce photon statistics that are distinctly non-Poisson. Representative examples are light from a cathode-ray tube and an image-intensifier device. For the class of vision experiments in which the photon statistics play an important role, excess fluctuations produced by such light sources can alter the observed results and obscure the visual mechanisms being studied. They must therefore be accounted for in a proper way. We use the results of a Hecht-Shlaer-Pirenne type experiment, carried out with modulated Poisson light, to illustrate the point. Sensitivity and modulation depth, as well as sensitivity and reliability, are shown to be traded against each other. Finally, we demonstrate that number-state light, which is comprised of photons of an ideal kind, provides the ultimate tool for extracting information about the intrinsic noise distribution in the visual system at threshold. The state of the art in producing such light is discussed.

Simple method to start and maintain self-mode-locking of a Ti:sapphire laser.

By periodically moving one of the end mirrors of a Ti:sapphire laser using a shaker, we have been able to start and maintain self-mode-locking of the laser. The resulting laser is stable over a long period with low-amplitude noise (3.3%) and low random timing jitter (4.8 ps). In addition, there is a deterministic timing variation on the order of subnanoseconds, caused by the moving mirror, which can be reduced by employing a feedback system. Pulses as short as 43 fs have been obtained.