The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main feat...

In the previous three chapters, we built up the foundation for our study of waves. In the remainder of this book, we’ll investigate various types of waves, such as waves on a string, sound waves, electromagnetic waves, water waves, quantum mechanical waves, and so on. In Chapters 4 through 6, we’ll discuss the properties of the two basic categories of waves, namely dispersive waves, and non-dis...

The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One example is dispersive wave generation, the optical analog of Cherenkov radiation. These waves have an essential role in fiber spectral broadeners that are routin...

We analyze a quantum trajectory model given by a steady-state hydrodynamic system for quantum fluids with positive constant temperature in bounded domains for arbitrary large data. The momentum equation can be written as a dispersive thirdorder equation for the particle density where viscous effects are incorporated. The phenomena that admit positivity of the solutions are studied. The cases, o...

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov–type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...

In this paper, we study a class of nonlinear Schrödinger equations (NLS) which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H, and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we...

In this paper we have simulated and evaluated the performance of WCDMA uplink system for mobile communications over dispersive channel. We have built a simple simulator for WCDMA for UMTS systems. Achievement of simulation has been done by the use of MATLAB. It is found that the dispersive channel affects the system performance drastically, especially by the increase of number of users.

A highly-dispersive mirror with the unprecedented group delay dispersion of -10000 fs2 in the wavelength range of 1025-1035 nm is reported. Reproducible production of a coating with such a high dispersion was possible due to the recently developed robust synthesis technique. Successful employment of the new highly-dispersive mirror in an oscillator is demonstrated.

We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general.