Pulses In Dispersive Media Research Articles

Electromagnetic cosine non-uniformly correlated pulses in dispersive media

A new class of electromagnetic pulse with cosine non-uniform correlation is introduced. The analytical expression for the elements of the mutual coherence matrix of such pulses propagating through the dispersive media is derived. It is found that this pulsed field exhibits self-focusing effect and temporal shift of the intensity maximum. The self-focusing effect can be enhanced by adjusting the parameter characterizing the modulation of cosine function and the chirp coefficient. The evolution of on-axis degree of polarization is more complex than the case of the electromagnetic non-uniformly correlated pulse. Moreover, the temporal degree of polarization of the pulse has asymmetric distribution being distinct from that of pulses with temporally uniform correlation.

High accuracy analytical presentation of the propagation of chirped super-Gaussian pulses in dispersive media

Chirped and non-chirped Super Gaussians (SG) are very common in pulse modeling for optical communications. However, unlike Gaussian pulses, the propagation (and distortions) of SG pulses in dispersive media cannot be expressed in closed-form analytical expression, nor can its Fourier transform, i.e. its spectrum. In this paper, it is shown that analytical smooth rectangular can be utilized to formulate analytically (in both time and frequency domains) with high accuracy the propagation of chirped SG pulses in dispersive medium. The paper also elaborates on chirped pulses cascading and on the propagation of asymmetric SG pulses.

Propagation of chirped rectangular pulses in dispersive media: analytical analysis.

Analytical smooth rectangular (ASR) pulses have shown to be useful in optical communications. ASR pulses can be cascaded, and therefore they can be very useful in non-return-to-zero communication protocols. Moreover, unlike super-Gaussian (SG) pulses, the propagation of ASR pulses in dispersive media can be expressed in analytical forms (in both time and frequency domains). However, the propagation of chirped ASR as well as chirped SG pulses, which are common in direct-modulation channels, cannot be expressed analytically. It is shown that by utilizing the similarity between ASR and SG pulses and applying analytical continuation, chirped ASR pulses can be rewritten in a form that does have an analytical expression in both time and spectral domains.

Second-order Talbot self-imaging effect in the time domain

Different from classical Talbot self-imaging, second-order spatial Talbot effect is a kind of second-order imaging, in which the self-imaging of an object is observed through intensity correlation measurement. Here, in terms of space-time duality, we investigate the temporal counterpart of second-order Talbot self-imaging with temporally incoherent light. Our work shows that second-order Talbot effect in the time domain is related to the joint dispersion of light pulse in dispersive medium. Particularly, based on the discrete Fourier transformation, the fractional Talbot self-imaging via intensity correlation doesn't generally possess a definite fractional period, which contradicts some articles' results. Our results may be useful for implementing the repetition-rate-multiplication technique and remotely transmitting the periodic temporal signals robustly.

Analytical Solutions for the Propagation of UltraShort and UltraSharp Pulses in Dispersive Media

Ultrashort pulses are severely distorted even by low dispersive media. While the mathematical analysis of dispersion is well known, the technical literature focuses on pulses, Gaussian and Airy pulses, which keep their shape. However, the cases where the shape of the pulse is unaffected by dispersion is the exception rather than the norm. It is the objective of this paper to present a variety of pulse profiles, which have analytical expressions but can simulate real-physical pulses with great accuracy. In particular, the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones (and vice versa) are presented. Besides the usage of this paper as a handbook of analytical expressions for pulse propagations in a dispersive medium, there are several new findings. The main findings are the analytical expressions for the propagation of chirped rectangular pulses, which converge to extremely short pulses; an analytical approximation for the propagation of super-Gaussian pulses; the propagation of the Nyquist-Sinc Pulse with smooth spectral boundaries; and an analytical expression for a physical realization of an attenuation compensating Airy pulse.

Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media

A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

Propagation properties of stochastic electromagnetic non-uniformly correlated partially coherent pulses in dispersive media

The scalar model of non-uniformly correlated partially coherent pulses is extended to the full electromagnetic domain and the realizability conditions of stochastic electromagnetic non-uniformly correlated partially coherent (SENUC) pulse sources in the frequency domain are derived. It is shown that the evolution properties of the intensity and degree of polarization (DOP) of the SENUC pulse in dispersive media in the frequency domain are much different from those of an SENUC pulse in the temporal domain. And the distribution of the intensity and DOP of the pulse on propagation is dependent on its spectral coherence width, shift parameters of the spectral correlation maximum and second-order dispersion coefficient.

Pulse propagation and windowed wave functions

We apply quasi-distribution methods developed for quantum mechanics to the propagation of pulses in dispersive media with attenuation. We show that a Schrödinger type equation follows for propagation of the pulse for each mode. One then transforms the equation to obtain an equation of evolution in the phase space of position and wavenumber. In this paper we emphasize windowed wave functions and their corresponding phase space quasi-distributions. We obtain the time evolution equation, discuss possible approximations, and compare to the Wigner distribution approximation previously derived by Loughlin and Cohen by different methods.

Generic pattern formation of sharp-boundaries pulses propagation in dispersive media

In optical communication, pulses have approximately a rectangular shape with smooth boundaries. In order to understand the dynamics of these pulses: (A) the generic dynamics of singular quantum mechanics’ wave functions was applied to sharp-boundaries pulses propagation in short dispersive medium and (B) an analytical expression for the propagation of a smooth rectangular pulse in dispersive medium was derived. This analytical expression consists of a couple of complex error functions and can be applied in good approximation to most rectangular pulses propagations in dispersive medium. (C) An analytical approximation was derived for the propagation of any pulse with sharp boundaries. This approximation, despite being analytical, can be applied to any sharp-boundaries pulse with any given shape. These exact expressions and approximations can be used in other systems where the Schrodinger dynamics hold, such as the paraxial approximation.

Microwave source of multigigawatt peak power based on a relativistic backward-wave oscillator and a compressor

The effect of passive compression of frequency-modulated pulses in dispersive media is used to raise the microwave radiation peak power to a multigigawatt level. A waveguide with a helically corrugated surface is applied as a dispersive medium, and a relativistic 3-cm backward-wave oscillator with an accelerating voltage decaying within the pulse duration serves as a source of frequency-modulated pulses. The compression of pulses to an FWHM of 2.2 ns attended by a rise in the peak power by a factor of 4.5 (to 3.2 GW) is demonstrated with a SINUS-6 accelerator.

Changes in the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic pulses in dispersive media

Based on the theory of coherence and polarization of stochastic electromagnetic pulses, the analytical expression for the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic pulses propagating in dispersive media is derived. Numerical calculations are performed to show the dependence of spectral degree of polarization on the spatial correlation length, temporal coherence length, pulse duration, pulse frequency, and medium dispersion. The results are interpreted physically.

Fidelity and fidelity susceptibility of pulses in dispersive media

Motivated by the growing importance of the fidelity and fidelity susceptibility (FS) in quantum critical phenomena, we use these concepts to describe the pulse propagation inside the dispersive media. It is found that there is a dramatic change in the fidelity and the FS of the pulse at a critical propagation distance inside a dispersive medium, and whether such a dramatic change for a light pulse occurs or not strongly depends on both the dispersive strength of the media and the pulse property. We study in detail about the changes in the fidelity and the FS for both a smooth and a truncated Gaussian pulse through the abnormal and normal dispersive media, where the group velocities are well defined. Our results show that both the fidelity and the FS could be very useful to determine whether the pulse is completely distorted or not at the critical distance; therefore it would be very helpful to find the maximal effective propagation region of the pulse's group velocity, in terms of the changes in the pulse's fidelity and FS.

Controlling the carrier-envelope phase of few-cycle focused laser beams with a dispersive beam expander

We report on a procedure to focalize few-cycle laser pulses in dispersive media with controlled waveform. Stationarity of the carrier-envelope phase for extended depth of focus is attained by shaping the spatial dispersion of the ultrashort beam. An adjustable group velocity is locally tuned in order to match a prescribed phase velocity at focus. A hybrid diffractive-refractive lens system is proposed to drive the wavefield to an immersion microscope objective under convenient broadband modulation. Numerical simulations demonstrate robustness over positioning of this dispersive beam expander.

Measured Electromagnetic Pulses Verify Asymptotics and Analysis for Linear, Dispersive Media

Electromagnetic precursors and other pulses in dispersive media have been studied theoretically since 1914. Yet a recent National Research Council study [1, pp. 73–75] found few measurements that verify the relevant theories. Verification is useful because, where independent theories and measurements agree, the results are highly reliable. This report describes two laboratory verifications of transient-electromagnetic theory that I completed recently.

Measurement of Net Group and Reshaping Delays for Optical Pulses in Dispersive Media

We experimentally demonstrate the direct measurement of net group and reshaping delays for arbitrary optical pulses in dispersive media, verifying the earlier prediction of Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)]. Incoherent pulse propagation in an absorptionless system is well described by net group delay; even the medium causes a great deal of deformation in the transmitted pulse. However, in the case of phase modulated chirping pulses in a resonant absorber, the so-called superluminal or subluminal propagation velocity is strongly influenced by the reshaping delay.

Analysis of Propagation of Ultrasonic Pulses in Dispersive Media Using Group Delay Concept

A new analytical technique of the propagation of ultrasonic pulses in dispersive or nondispersive media is proposed. First, on the basis of the concept of group delay, we develop the theory as follows: (1) group delay is deduced directly from the Fourier transform of waveforms, and (2) cross-correlation theory is extended to a total measurement system which may include, for example, a sensor, couplant, amplifier, and A/D converter. Then, a fundamental result that the group delay between wave motions generated in a medium is exactly the same as that of corresponding waveforms observed by an observer is obtained. Next, this result is applied to improve the conventional pulse-echo method, and it is shown that by preparing two specimens of the same material but with different thicknesses, correct group delay in propagation can be obtained even though no physical or mechanical constants of the couplant or sensor may be known. In order to apply the results to the pulse-echo method, measurements of phase and group velocity in synthetic fused silica were also attempted.

Causality and acoustic group velocity in dispersive media

This talk examines two specific issues related to causality and the group velocity of acoustic pulses in dispersive media. First, the causal prediction of group velocity from attenuation with finite-bandwidth Kramers-Kronig (K-K) relations is discussed. Without extrapolating beyond the measurement bandwidth, the causal linkages of resonant-type data are established using expressions derived from the acoustic K-K relations to predict group velocity and slope of attenuation (frequency derivative of attenuation). These predictions provide a stricter test of causal consistency than the determination of the phase velocity and attenuation coefficient due to their shape-invariance with respect to subtraction constants. Secondly, conditions under which the group velocity is the velocity of the peak in the envelope of a acoustic pulse are described. The spatial and temporal signatures of acoustic pulses with arbitrarily large (e.g., superluminal) and negative group velocities are also demonstrated. These signatures are shown to be consistent with both simple and relativistic causality.

Angular dispersion of diffraction-free optical pulses in dispersive medium

The comprehensive analysis of angular dispersion of diffraction-free optical pulsed beams in linear dispersive medium is carried out. It is shown that properties of an angular dispersion curve essentially depend on its behavior at zero point of pulse group-velocity dispersion in the medium. As an example, the angular dispersion curves in transparency region of fused silica are presented. It is demonstrated that the radius of diffraction-free pulsed beams exhibits a strong dependence on angular dispersion.

Linear and nonlinear propagation of sinh-Gaussian pulses in dispersive media possessing Kerr nonlinearity

This paper presents an investigation on linear and nonlinear propagation of sinh-Gaussian pulses in a dispersive medium possessing Kerr nonlinearity. First, the effects of group velocity dispersion and nonlinearity have been treated separately, and then, the dynamic interplay between group velocity dispersion and nonlinearity induced self phase modulation have been discussed. In both normal and anomalous dispersive media, these pulses broaden due to GVD at a much slower rate in comparison to Gaussian pulses. With the increase in the value of sinh factor Ω 0 , the broadening decreases for both chirped and unchirped pulses. It has been found that the self phase modulated spectra are associated with considerable internal structure. For small value of Ω 0 , the number of peaks in the spectrum is less, whereas, for large value of Ω 0 , number of internal peaks is more in comparison to Gaussian pulses. Moreover, number of internal peaks increases with the increase in the value of Ω 0 . When the pulse power is appropriate, they can propagate as antisymmetric solitons in anomalous dispersive media. Linear stability analysis shows that such solitons are stable. The dynamic behavior of these pulses, when magnitude of nonlinearity and dispersion are not same, has been also discussed.

Localized subluminal envelope pulses in dispersive media

The existence and properties of propagative nondispersive and nondiffracting localized envelope waves in dispersive transparent media, with either normal or anomalous group-velocity dispersion, showing subluminal group velocities and strong spatial localization are pointed out. Nonparaxial effects may lead to group-velocity reduction of several orders of magnitude. Numerical simulations are given for wave propagation in sapphire.