Malvin C. Teich

Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes

The effect of dead space on the statistics of the gain in a double-carrier-multiplication avalanche photodiode (APD) is determined using a recurrence method. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. Recurrence equations are derived for the first moment, the second moment, and the probability distribution function of two random variables that are related, in a deterministic way, to the random gain of the APD. These equations are solved numerically to produce the mean gain and the excess noise factor. The presence of dead space reduces both the mean gain and the excess noise factor of the device. This may have a beneficial effect on the performance of the detector when used in optical receivers with photon noise and circuit noise. >

Power-law shot noise

The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1/f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1/f/sup alpha / shot noise for alpha in the range 0 >

Fractal character of the neural spike train in the visual system of the cat.

We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGCs) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The continuing statistics reveal 1/f-type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted form one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

Role of Entanglement in Two-Photon Imaging

The use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever the strength of the correlations between the two photons. We consider a two-photon imaging system in which one photon is used to probe a remote (transmissive or scattering) object, while the other serves as a reference. We discuss the role of entanglement versus correlation in such a setting, and demonstrate that entanglement is a prerequisite for achieving distributed quantum imaging.

Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for α. The discrepancy between the desired and achieved values of α is shown to arise from finite data size and from the character of the point-process generation mechanism. In the context of point-process simulation, reduction of this discrepan...

Binomial states of the quantized radiation field

We introduce the binomial state of the quantized radiation field, which is a state that yields a binomial counting probability distribution. It reduces to the coherent state and to the number state in different limits. The binomal state is quantum mechanical in nature, and we show that it produces light that is antibunched, sub-poissonian, and squeezed for certain parameter ranges. A mixed binomial state is also defined. Particular attention is devoted to the mixed Bernoulli state which is an important special case. The properties of this mixed state indicate that squeezing might be present in individual atomic emissions.

Demonstration of dispersion-canceled quantum-optical coherence tomography.

We present an experimental demonstration of quantum-optical coherence tomography. The technique makes use of an entangled twin-photon light source to carry out axial optical sectioning. It is compared to conventional optical coherence tomography. The immunity of the quantum version to dispersion, as well as a factor of 2 enhancement in resolution, is experimentally demonstrated.

ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES

We investigate the properties of fractal stochastic point processes (FSPPs). First, we define FSPPs and develop several mathematical formulations for these processes, showing that over a broad range of conditions they converge to a particular form of FSPP. We then provide examples of a wide variety of phenomena for which they serve as suitable models. We proceed to examine the analytical properties of two useful fractal dimension estimators for FSPPs, based on the second-order properties of the points. Finally, we simulate several FSPPs, each with three specified values of the fractal dimension. Analysis and simulation reveal that a variety of factors confound the estimate of the fractal dimension, including the finite length of the simulation, structure or type of FSPP employed, and fluctuations inherent in any FSPP. We conclude that for segments of FSPPs with as many as 106 points, the fractal dimension can be estimated only to within ±0.1.

Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology

We applied multiresolution wavelet analysis to the sequence of times between human heartbeats (

Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera

R\ensuremath{-}R