Three-Frequency Nonlinear Heterodyne Detection. 2: Digital Communications and Pulsed Radar

[[abstract]]Part 1 of this paper [Appl. Opt. 14, 666 (1975)] dealt with the cw radar and analog communications uses of three-frequency nonlinear heterodyne detection. In this paper, we evaluate the technique for a number of specific pulsed radar and digital communications applications. Both the vacuum channel and the lognormal turbulent atmospheric channel are considered. It is found that the advantages of the technique in the pulsed/digital system are similar to those obtained in the cw/analog system. Computer generated error probability curves as a function of the input signal-to-noise ratio are presented for a variety of binary receiver parameters and configurations and for various levels of atmospheric turbulence. Orthogonal and nonorthogonal signaling schemes, as well as dependent and independent fading, are considered. When Doppler information is poor, performance is generally superior to that of the conventional heterodyne system.[[booktype]]紙

Photonic circuits for generating modal, spectral, and polarization entanglement

We consider the design of photonic circuits that make use of Ti:LiNbO$_{3}$ diffused channel waveguides for generating photons with various combinations of modal, spectral, and polarization entanglement. Down-converted photon pairs are generated via spontaneous optical parametric down-conversion (SPDC) in a two-mode waveguide. We study a class of photonic circuits comprising: 1) a nonlinear periodically poled two-mode waveguide structure, 2) a set of single-mode and two-mode waveguide-based couplers arranged in such a way that they suitably separate the three photons comprising the SPDC process, and, for some applications, 3) a holographic Bragg grating that acts as a dichroic reflector. The first circuit produces frequency-degenerate down-converted photons, each with even spatial parity, in two separate single-mode waveguides. Changing the parameters of the elements allows this same circuit to produce two nondegenerate down-converted photons that are entangled in frequency or simultaneously entangled in frequency and polarization. The second photonic circuit is designed to produce modal entanglement by distinguishing the photons on the basis of their frequencies. A modified version of this circuit can be used to generate photons that are doubly entangled in mode number and polarization. The third photonic circuit is designed to manage dispersion by converting modal, spectral, and polarization entanglement into path entanglement

Modal, spectral, and polarization entanglement in guided-wave parametric down-conversion

We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear periodically poled two-mode waveguide (one-dimensional planar or two-dimensional circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom-mode number, frequency, or polarization-can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowband or broadband. On the other hand, when the generated photons are distinguished by their frequencies in a type-0 process, modal entanglement turns out to be an efficient alternative to polarization entanglement. Moreover, modal entanglement in type-II down-conversion may be used to generate a doubly entangled state in frequency and polarization

Statistical Correlation of Gain and Buildup Time in APDs And Its Effects on Receiver Performance

This paper reports a novel recurrence theory that enables us to calculate the exact joint probability density function (pdf) of the random gain and the random avalanche buildup time in avalanche photodiodes (APDs) including the effect of dead space. Such calculations reveal a strong statistical correlation between the gain and the buildup time for all widths of the multiplication region. To facilitate the calculation of the photocurrent statistics in the presence of this correlation, the impulse-response function of the APD is approximately modeled by a function of time whose prespecified shape is appropriately parameterized by two random variables: the gain and the buildup time. The evaluation of the variance of the photocurrent under this model leads to the definition of the shot-noise-equivalent bandwidth of the APD, which captures the statistical correlation between the gain and the buildup time. It is shown that the shot-noise-equivalent bandwidth in GaAs APDs is greater, by approximately 30%, than the traditional buildup-time-limited 3-dB bandwidth, which is calculated from the mean of the impulse-response function. A thorough analysis of the performance of APD-based integrate-and-dump digital receivers reveals that the strong correlation between the gain and the buildup time accentuates intersymbol interference (ISI) noise, and thus, adversely affects receiver sensitivity at high transmission rates beyond previously known limits

Impact-ionization and noise characteristics of thin III-V avalanche photodiodes

It is, by now, well known that McIntyre\u27s localized carrier-multiplication theory cannot explain the suppression of excess noise factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and noise characteristics of thin InP, In/sub 0.52/Al/sub 0.48/As, GaAs, and Al/sub 0.2/Ga/sub 0.8/As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-noise-factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess noise factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths

Gain-bandwidth product optimization of heterostructure avalanche photodiodes

A generalized history-dependent recurrence theory for the time-response analysis is derived for avalanche photodiodes with multilayer, heterojunction multiplication regions. The heterojunction multiplication region considered consists of two layers: a high-bandgap Al/sub 0.6/Ga/sub 0.4/As energy-buildup layer, which serves to heat up the primary electrons, and a GaAs layer, which serves as the primary avalanching layer. The model is used to optimize the gain-bandwidth product (GBP) by appropriate selection of the width of the energy-buildup layer for a given width of the avalanching layer. The enhanced GBP is a direct consequence of the heating of primary electrons in the energy-buildup layer, which results in a reduced first dead space for the carriers that are injected into the avalanche-active GaAs layer. This effect is akin to the initial-energy effect previously shown to enhance the excess-noise factor characteristics in thin avalanche photodiodes (APDs). Calculations show that the GBP optimization is insensitive to the operational gain and the optimized APD also minimizes the excess-noise factor

Information-theoretic criterion for the performance of single-photon avalanche photodiodes

A channel-capacity metric is introduced for assessing the performance of single-photon avalanche photodiodes (SPADs) when used as detectors in laser communication systems. This metric is employed to theoretically optimize, with respect to the device structure and operating voltage, the performance of SPADs with simple InP or In/sub 0.52/Al/sub 0.48/As-InP heterojunction multiplication regions. As the multiplication-region width increases, an increase is predicted in both the peak and the full-width at half-maximum of the channel capacity curve versus the normalized excess voltage. Calculations also show the existence of an optimal In/sub 0.52/Al/sub 0.48/As-InP heterojunction multiplication region that maximizes the peak channel capacity beyond that of InP

Optimized Breakdown Probabilities in Al/sub 0.6/Ga/sub 0.4/As-GaAs Heterojunction Avalanche Photodiodes

Recently, it has been shown that the noise characteristics of heterojunction Al/sub 0.6/Ga/sub 0.4/As-GaAs avalanche photodiodes (APDs) can be optimized by proper selection of the width of the Al/sub 0.6/Ga/sub 0.4/As layer. Similar trends have also been shown theoretically for the bandwidth characteristics. The resulting noise reduction and potential bandwidth enhancement have been attributed to the fact that the high bandgap Al/sub 0.6/Ga/sub 0.4/As layer serves to energize the injected electrons, thereby minimizing their first dead space in the GaAs layer. We show theoretically that the same optimized structures yield optimal breakdown-probability characteristics when the APD is operated in Geiger mode. The steep breakdown-probability characteristics, as a function of the excess bias, of thick multiplication regions (e.g., in a 1000-nm GaAs homojunction) can be mimicked in much thinner optimized Al/sub 0.6/Ga/sub 0.4/As-GaAs APDs (e.g., in a 40-nm Al/sub 0.6/Ga/sub 0.4/As and 200-nm GaAs structure) with the added advantage of having a reduced breakdown voltage (e.g., from 36.5 V to 13.7 V)

Effect of stochastic dead space on noise in avalanche photodiodes

A stochastic dead-space model for impact ionization is developed and used to study the effect of the soft nature of the ionization capability of carriers on the excess noise factor of avalanche photodiodes. The proposed model is based on the rationale that the gradual, or soft, transition in the probability density function (PDF) for the distance from birth to impact ionization can be viewed as that resulting from uncertainty in the dead space itself. The resulting soft PDF, which is parameterized by a tunable softness parameter, is used to establish the limitations of the existing hard-threshold ionization models in ultrathin multiplication layers. Calculations show that for a fixed operational gain and fixed average dead space, the excess noise factor tends to increase as a result of the softness in the PDF in very thin multiplication layers (viz, \u3c70 nm), or equivalently, under high applied electric fields (viz., \u3e800 kV/cm). A method is proposed for extracting the softness parameter from noise versus multiplication measurements