We discuss the production of induced noise by a pulse and the propagation of the noise in a dispersive medium. We present a simple model where the noise is the sum of pulses and where the mean of each pulse is random. We obtain explicit expressions for the standard deviation of the spatial noise as a function of time. We also formulate the problem in terms of a time-frequency phase space approa...

In "imaging the biomechanical properties of tissues," a number of approaches analyze shear wave propagation initiated by a short radiation force push. Unfortunately, it has been experimentally observed that the displacement-versus-time curves for lossy tissues are rapidly damped and distorted in ways that can confound simple tracking approaches. This article addresses the propagation, decay and...

As interest in photonic crystals and metamaterials expands, it is becoming increasingly clear that these materials often exhibit strong spatial dispersion. Understanding spatial dispersion and its consequences is essential to understanding these materials. It has long been known that temporal dispersion alters the expression for the electromagnetic energy density of a material. Similarly, it is...

The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized w...

The estimation of instantaneous frequency (IF) method is introduced to compensate for the group velocity of electromagnetic wave in dispersive medium. The location of the reflected signal can be obtained by using the time-frequency cross correlation (TFCC), following which it is used to extract the transmitted signal from the total signal acquired. The signal propagated in the dispersive medium...

We study longitudinal elastic strain waves in a one-dimensional periodically layered medium, alternating between two materials with different densities and stress-strain relations. If the impedances are different, dispersive effects are seen due to reflection at the interfaces. When the stress-strain relations are nonlinear, the combination of dispersion and nonlinearity leads to the appearance...

We consider Synthetic Aperture Radar (SAR) image formation in the situation when the propagation medium is random and dispersive. The propagation model is the Klein-Gordon equation with a random index of refraction and a random dispersive term. We show via a multiscale analysis how the medium heterogeneities and the dispersion affect the image. In fact, in the situation with a strong source chi...

A Finite Difference Time Domain (FDTD) scheme used to model the wave propagation in biological dispersive media has been proposed in this paper. FDTD scheme based on the direct solution of time domain Maxwell’s equations has developed and these solutions were approximated by time based linear functions. We are applied FDTD scheme for different dispersive media models such as Cole-Cole, Cole-Dav...