Necessary Condition for Temporal Self Imaging in a Linear Dispersive Medium

We demonstrate the nonreciprocal propagation of optical pulses in a linear dispersive medium with a time-varying refractive index. The change of refractive index with time breaks the time-translation symmetry of the spatially homogeneous medium compelling it to be inherently nonreciprocal. A time-reversal asymmetric field ratio of the counter-propagating optical pulses along with a frequency shift leading to spectral nonreciprocity in such dynamic media have been observed. The findings have emerged a new avenue to realize nonreciprocal light flow in dynamically tuned integration-feasible photonic systems.

Chapter 3 - Group-velocity dispersion

Sensitivity to interaural time differences (ITDs) in high-frequency bandpass-filtered periodic and aperiodic (jittered) pulse trains was tested at a nominal pulse rate of 600 pulses per second (pps). It was found that random binaurally-synchronized jitter of the pulse timing significantly increases ITD sensitivity. A second experiment studied the effects of rate and place. ITD sensitivity for jittered 1200-pps pulse trains was significantly higher than for periodic 600-pps pulse trains, and there was a relatively small effect of place. Furthermore, it could be concluded from this experiment that listeners were not solely benefiting from the longest interpulse intervals (IPIs) and the instances of reduced rate by adding jitter, because the two types of pulse trains had the same longest IPI. The effect of jitter was studied using a physiologically-based model of auditory nerve and brainstem (medial superior olive neurons). It was found that the random timing of the jittered pulses increased firing synchrony in the auditory periphery, which caused an improved rate-ITD tuning for the 600-pps pulse trains. These results suggest that a recovery from binaural adaptation induced by temporal jitter is possibly related to changes in the temporal firing pattern, not spectral changes.

The electronic structures of the Floquet states of the dynamic Wannier-Stark ladder (DWSL) are examined, where the DWSL is formed by driving the biased superlattices (SLs) by the periodic pulse train (PPT) with the electric field $F(t)$---with time $t$---and the temporal period $2\ensuremath{\pi}∕\ensuremath{\omega}$. For a strong $F(t)$, interminiband interactions, namely, the ac-Zener tunneling (ac-ZT), are predominantly caused in the DWSL. Such a system is termed the interacting DWSL. In order to understand the details of the Floquet states and the modulation patterns by alteration of a couple of the PPT laser parameters, the linear absorption spectra, ${\ensuremath{\alpha}}_{\mathit{abs}}({\ensuremath{\omega}}_{p};\ensuremath{\omega})$, of optical interband transitions invoked by the monochromatic probe laser ${f}_{p}(t)$ with the frequency ${\ensuremath{\omega}}_{p}$ are calculated, where the spectra are not only linear in ${f}_{p}(t)$ but also nonlinear in $F(t)$. The exciton effect is not included for the sake of simplicity. For the PPT driving with unit-pulse shapes largely deviated from the square and saw-toothed profiles, the spectra show unexpected dent structures, differing a great deal from the corresponding ac-ZT-free spectra basically similar to those of the original SLs just showing the ascending steplike structure. To deepen the understanding of this anomaly, the spectra of ${\ensuremath{\alpha}}_{\mathit{abs}}^{0}({\ensuremath{\omega}}_{p};\ensuremath{\omega})\ensuremath{\propto}\ensuremath{\partial}{\ensuremath{\alpha}}_{\mathit{abs}}({\ensuremath{\omega}}_{p};\ensuremath{\omega})∕\ensuremath{\partial}{\ensuremath{\omega}}_{p}$ are also calculated, whereby the dent structures become spectral dips showing the negative absorption. It is found that such anomalous behavior is attributed to the ac-ZT between different minibands that accompanies emission/absorption of the nonzero net number of photons with $J\ensuremath{\omega}$ (with $J$ a nonzero integer). This anomaly also shows the unusual time dependence in the dual-time optical susceptibility associated with ${\ensuremath{\alpha}}_{\mathit{abs}}^{0}({\ensuremath{\omega}}_{p};\ensuremath{\omega})$. Moreover, the possibility of existence of the negative absorption in the more realistic excitonic spectra is speculated.

Poor sensitivity to the interaural time difference (ITD) constrains the ability of human bilateral cochlear implant users to listen in everyday noisy acoustic environments. ITD sensitivity to periodic pulse trains degrades sharply with increasing pulse rate but can be restored at high pulse rates by jittering the interpulse intervals in a binaurally coherent manner (Laback and Majdak. Binaural jitter improves interaural time-difference sensitivity of cochlear implantees at high pulse rates. Proc Natl Acad Sci USA 105: 814-817, 2008). We investigated the neural basis of the jitter effect by recording from single inferior colliculus (IC) neurons in bilaterally implanted, anesthetized cats. Neural responses to trains of biphasic pulses were measured as a function of pulse rate, jitter, and ITD. An effect of jitter on neural responses was most prominent for pulse rates above 300 pulses/s. High-rate periodic trains evoked only an onset response in most IC neurons, but introducing jitter increased ongoing firing rates in about half of these neurons. Neurons that had sustained responses to jittered high-rate pulse trains showed ITD tuning comparable with that produced by low-rate periodic pulse trains. Thus, jitter appears to improve neural ITD sensitivity by restoring sustained firing in many IC neurons. The effect of jitter on IC responses is qualitatively consistent with human psychophysics. Action potentials tended to occur reproducibly at sparse, preferred times across repeated presentations of high-rate jittered pulse trains. Spike triggered averaging of responses to jittered pulse trains revealed that firing was triggered by very short interpulse intervals. This suggests it may be possible to restore ITD sensitivity to periodic carriers by simply inserting short interpulse intervals at select times.

Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media

The complex geometrical optics (CGO) was applied for the spatiotemporal evolution of arbitrary number of 3D mutually incoherent (with different carrier frequencies) Gaussian wave packets (GWPs) interacting and propagating in a nonlinear medium of Kerr type. The CGO reduced description of the propagation of the beam, the pulse and the wave packet to complex ordinary differential equations (ODE) This leads to exceptionally fast numerical algorithms. We observed high efficiency of the CGO method to compute interactions of arbitrary number of 3D Gaussian wave packets propagating in a nonlinear (anomalous) dispersive medium of the Kerr type. The derived CGO equations were compared with equations obtained by the variational method. CGO described the Gaussian beam propagation in free space as well as the Gaussian pulse spreading in the linear anomalous dispersive medium more illustratively than both the Fourier transform method and the Fresnel diffraction integral method. The spatiotemporal CGO has been proven to be a method more practical than the spectral analysis, the variational method, the method of moments and the method of the generalized eikonal approximation. Complementary to the presented results, an on-line CGO solver, implemented in Javascript, is freely available at the authors' website: http://slawek.ps.pl/odelia.html.

Some signals are transmitted as periodic pulse trains. If more than one pulse train is transmitted over the same communication channel, a challenge is to separate them for source identification at the receiver. This is known as pulse train deinterleaving and is clearly a fundamental problem in the study of discrete-event systems. Frequently, the only relevant information at the receiver is the time of arrival (TOA) data, which is usually contaminated by jitter noise. Perhaps there are also missing or overlapping pulses. In this paper, we present an approach for deinterleaving pulse trains and estimating their periods using an extended Kalman filter (EKF). A naive application of EKF theory is not attractive because of discontinuities in the signal model. Here, a form of smoothing of the discontinuities is proposed so that the EKF approach becomes attractive. The advantage of this EKF approach is that it is less computationally expensive than most previously proposed methods, which are of order N/sup 2/, where N is the number of pulses being processed. The computation required here is of order N. The method proposed appears to give useful results for up to seven or so pulse trains, particularly when there is some a priori information on the pulse frequencies, which can be obtained using computations of order N log N.

Different from second-order temporal ghost imaging usually realized by means of second-order correlation measurement, in this paper, we investigate theoretically temporal imaging with temporally thermal light via first-order field correlation based on a Mach-Zehnder interferometer. The paraxial wave equation describing the diffraction of light and the differential equation characterizing the dispersion of light pulse are given. Based on the similarity between these equations, the duality between the paraxial diffraction of the light in the spatial domain and the dispersion of the temporal narrow-band pulse in the dispersive medium (i.e. the space-time duality) is obtained, and the impulse response functions in the time domain for several optical systems are also presented. Then in terms of the space-time duality, we design the scheme for temporal imaging via first-order thermal field correlation based on a Mach-Zehnder interferometer and obtain the intensity expression for first-order temporal imaging according to the temporal impulse response functions, and discuss the influences of the source pulse width and coherence time on the image visibility and resolution. The result shows that the temporal signal can be reconstructed through temporal first-order temporal imaging. Furthermore, when the source’s coherence time is fixed, the image visibility decreases as the pulse width increases. However, the image resolution increases. When the source’s pulse width is fixed, the image visibility increases as the coherence time increases. And yet the image resolution decreases. Specially, when the source’s pulse width is 100 ps and the coherence time is 0.5 ps, the image quality (taking both the visibility and resolution into account) of a temporally rectangular object is satisfactory. In the simulation, the distance and width of the temporal rectangular object are 20 ps and 8 ps, respectively. It is shown that there is a dilemma between the visibility and resolution of first-order temporal imaging which is similar to the result of second-order ghost imaging. Our result discussed herein could be valuable in the reconstruction and detection of temporal signal via first-order temporal ghost imaging with temporally thermal light.

Five experiments on the identifiability of synthetic vowels masked by wideband sounds are reported. In each experiment, identification thresholds (signal/masker ratios, in decibels) were measured for two versions of four vowels: a vibrated version, in which FO varied sinusoidally around 100 Hz; and a steady version, in which F0 was fixed at 100 Hz. The first three experiments were performed on naive subjects. Experiment 1 showed that for maskers consisting of bursts of pink noise, vibrato had no effect on thresholds. In Experiment 2, where the maskers were periodic pulse trains with an F0 randomly varied between 120 and 140 Hz from trial to trial, vibrato slightly improved thresholds when the sound pressure level of the maskers was 40 dB, but had no effect for 65-dB maskers. In Experiment 3, vibrated rather than steady pulse trains were used as maskers; when these maskers were at 40 dB, the vibrated versions of the vowels were slightly less identifiable than their steady versions; but, as in Experiment 2, vibrato had no effect when the maskers were at 65 dB. Experiment 4 showed that the unmasking effect of vibrato found in Experiment 2 disappeared in subjects trained in the identification task. Finally, Experiment 5 indicated that in trained listeners, vibrato had no influence on identification performance even when the maskers and the vowels had synchronous onsets and offsets. We conclude that vibrating a vowel masked by a wideband sound can affect its identification threshold, but only for tonal maskers and in untrained listeners. This effect of vibrato should probably be considered as a Gestalt phenomenon originating from central auditory mechanisms.

It is suggested that the quantum uncertainty of cavity radiation is measurable via Aharonov-Bohm effects for electrons in a ring which is threaded by the magnetic cavity flux. When the electrons follow this oscillatory flux nearly adiabatically, and dissipation is negligible, the noise in the ring current should provide a quantum-nondemolition measure of the flux uncertainty. Unlike standard photodetection, such measurements should reveal the scaling of the flux uncertainty with the diamagnetic or dielectric index of the cavity medium, depending on the dimensions of the electron ring.

A number of different FDTD methods used to model electromagnetic propagation in linear dispersive media have been published. We introduce a new FDTD method for general linear dispersive media (dielectrics and non-magnetized cold plasmas) based on exponential fitting of the auxiliary difference equation. We show that the recursive convolution method, developed by Luebbers et al. (1990, 1991) is exactly equivalent to a particular discretization in the context of our new method. Using this alternate formulation of the recursive convolution method, we apply a new analysis technique to compare the accuracy of the recursive convolution method and the exponential fitting method, as well as other formulations based on straightforward difference approximations of the governing differential equations.

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.

This paper presents an example of power analysis in parallel resonant circuit excited by current defined as periodic pulse train. The cyclostationary methodology being developed into approach to the electric power analysis, which consists in exploiting a standard set of cyclostationary characteristics such as cross correlation function and its frequency counterpart – cross spectral correlation density (CSCD). These characteristics make it possible to calculate all commonly used power quantitative measures including instantaneous, apparent and average power, power factor and others. The harmonic power distribution is investigated for the chosen low-Q resonant case. The expression for components of CSCD via current and voltage Fourier series coefficients is obtained using the known frequency response of the circuit under study.

The oscillators star-coupled by one resistor exhibit the phase-shift synchronization and there exist many different steady phase patterns according to their initial states. Therefore we have suggested that these systems can be use as structural elements of neural networks and large scale memories. In such cases, to get appropriate phase patterns, controlling the phase patterns should be an important problem. In this study, we propose the Wien-bridge oscillators star-coupled by one resistor driven by the periodic pulse train. In this system, the phase pattern switching is caused by the stimulation of the pulse. From the results, we suggest that the pulse stimulation is one of the ways to control the phase patterns in coupled oscillators systems.