In order to enhance the energy transfer efficiency in a Cherenkov laser, we propose to use a tapered waveguide with a dielectric thickness properly varied stepwise in the longitudinal direction. With the aid of particle simulation, we investigate the nonlinear characteristics of the Cherenkov laser with the tapered waveguide, demonstrating the effectiveness of our proposal for efficiency enhancement.

The growth characteristics of a two-dimensional Cherenkov laser composed of a planar relativistic electron beam and a parallel plate waveguide one plate of which is loaded with a nonlinear dielectric sheet are analyzed. The permittivity of the nonlinear dielectric sheet becomes inhomogeneous due to the Kerr effect as the electromagnetic wave grows along the waveguide. For the analysis of the electromagnetic fields in the nonlinear dielectric sheet, it is replaced by a number of thin dielectric layers each of which is assumed to be homogeneous. From numerical analysis, it is found that just a few homogeneous layers for the nonlinear dielectric sheet are enough to get the same results as obtained previously by means of the finite element method. This is because the variation of the permittivity across the nonlinear dielectric sheet is as small as within 10% of the linear permittivity of the nonlinear material. Thus the multilayer approximation method is found to be more simple and more efficient for the analysis of the Cherenkov laser loaded with a Kerr-like medium than the finite element method.

The growth and saturation characteristics of an electromagnetic (EM) wave in a Smith-Purcell free-electron laser (FEL) with a Bragg cavity are investigated in detail with the aid of numerical simulation based upon the fluid model of the electron beam. To analyze the problem, a two-dimensional (2-D) model of the Smith-Purcell FEL is considered. The model consists of a planar relativistic electron beam and a parallel plate metallic waveguide, which has a uniform grating carved on one plate. For confinement and extraction of EM waves, a Bragg cavity is formed by a couple of reflector gratings with proper spatial period and length, which are connected at both ends of the waveguide. The results of numerical simulation show that a compact Smith-Purcell FEL can be realized by using a Bragg cavity composed of metallic gratings.

In order to enhance the energy transfer efficiency in a rectangular Cherenkov laser, we propose to vary properly the permittivity of a loaded dielectric in the transverse direction. With the aid of particle simulation, we investigate the amplification characteristics of the rectangular Cherenkov laser with a dielectric permittivity varied in the transverse direction, demonstrating the effectiveness of our proposal for efficiency enhancement.

Nonlinear characteristics of a DBR (Distributed Bragg Reflector) Cherenkov laser are investigated with the aid of particle simulation, allowing for the nonlinear properties of the electron beam. Numerical results show that the EM power extracted from the cavity is considerably suppressed by the nonlinear effect of the electron beam. Additionally, the extracted EM power is found to be critically dependent on the reflection coefficient of the DBR at the output end. Thus the DBRs at both ends of the cavity should be carefully designed in order to extract the EM power from the cavity efficiently.

The characteristics of an open-boundary Cherenkov laser for an electromagnetic wave with a continuous frequency spectrum are numerically analyzed. A given power spectral density for the input wave is found to get concentrated around the frequency where the spatial growth rate is maximum, as it grows along the electron beam. In addition, the frequency for the maximum growth rate is found to shift gradually to higher values. Furthermore, by gradually increasing the permittivity of the dielectric waveguide along it, we can always get the maximum power spectral density at the frequency where the spatial growth rate initially becomes maximum at the input.

The mode analysis of an open-boundary Cerenkov laser is developed in the collective regime. The Cerenkov laser under consideration is composed of a magnetically-confined relativistic electron beam and a dielectric-loaded conducting plane. The electron beam and the dielectric are assumed to be arbitrary in thickness, with an arbitrary spacing allowed between them. For the Cerenkov laser specified above, the following results are obtained. First, an electromagnetic wave mode is coupled with an infinite number of space charge wave modes. In the general case, an electromagnetic wave mode is coupled collectively with space charge wave modes. On the other hand, in the special case where the coupling occurs near the Cerenkov threshold, an electromagnetic wave mode is coupled separately with each of space change wave modes. Second, the characteristics of the growing wave for a magnetically-confined beam are similar to those for an ion-neutralized beam, except that the magnitude of the spatial growth rate becomes somewhat smaller for the former than for the latter.

The interaction between the human eye and electromagnetic (EM) waves in the ISM (industrial, scientific, and medical) frequency bands is investigated with the use of the finite-difference time-domain (FDTD) method. In order to assess possible health hazards, the specific absorption rates (SARs) are calculated and compared with the recommended safety standards. In particular, we calculate temperature rises in the human eye to assess the possibility of microwave-induced cataract formation. The results show that the maximum values of averaged SARs are less than the standard levels. In addition, we observed what is called the 'hot spot' in the region of eye humor at 2.4 GHz but not at 900 MHz and 5.8 GHz. Furthermore, the maximum temperature rise due to the incident EM power density of 5.0 mW/cm2, which is the MPE (maximum permissible exposure) limit for controlled environments, has been found to be at most 0.26 at 5.8 GHz, which is small compared with the threshold temperature rise 3.0 for cataract formation.

With the use of the Fourier-Laplace integral, the impulse response for a two-dimensional model of the Cherenkov-type oscillator is obtained. From the numerical analysis of the impulse response, the temporal evolution of the response is found to have two different phases ini which it grows linearly and exponentially with the distance from the origin where an impulsive excitation is applied.