Exact transparent boundary condition for the multidimensional Schrödinger equation in hyperrectangular computational domain.

In this paper an exact transparent boundary condition for the multidimensional Schrödinger equation in a hyperrectangular computational domain is proposed. It is derived as a generalization of exact transparent boundary conditions for two-dimensional (2D) and 3D equations reported before. An exact fully discrete (i.e., derived directly from the finite-difference scheme used) 1D transparent boundary condition is also proposed. Several numerical experiments using an improved unconditionally stable numerical implementation in the 3D space demonstrate propagation of Gaussian wave packets in free space and penetration of a particle through a 3D spherically asymmetrical barrier. The application of the multidimensional transparent boundary condition to the dynamics of the 2D system of two noninteracting particles is considered. The proposed boundary condition is simple, robust, and can be useful in the field of computational quantum mechanics, when an exact solution of the multidimensional Schrödinger equation (including multiparticle problems) is required.

Exact transparent boundary condition for the three-dimensional Schrödinger equation in a rectangular cuboid computational domain.

We report an exact transparent boundary condition (TBC) on the surface of a rectangular cuboid for the three-dimensional (3D) time-dependent Schrödinger equation. It is obtained as a generalization of the well-known TBC for the 1D Schrödinger equation and of the exact TBC in the rectangular domain for the 3D parabolic wave equation, which we reported earlier. Like all other TBCs, it is nonlocal in time domain and relates the boundary transverse derivative of the wave function at any given time to the boundary values of the same wave function at all preceding times. We develop a discretization of this boundary condition for the implicit Crank-Nicolson finite difference scheme. Several numerical experiments demonstrate evolution of the wave function in free space as well as propagation through a number of 3D spherically symmetrical and asymmetrical barriers, and, finally, scattering off an asymmetrical 3D potential. The proposed boundary condition is simple and robust, and can be useful in computational quantum mechanics when an accurate numerical solution of the 3D Schrödinger equation is required.

Exact transparent boundary condition for the parabolic equation in a rectangular computational domain.

In this paper, an exact three-dimensional transparent boundary condition for the parabolic wave equation in a rectangular computational domain is reported. It is a generalization of the well-known two-dimensional Basakov-Popov-Papadakis transparent boundary condition. It relates the boundary transversal derivative of the wave field at any given longitudinal position to the field values at all preceding computational steps. Several examples demonstrate propagation of light along simple structured optical fibers as well as in x-ray guiding structures. The proposed condition is simple and robust and can help to reduce the size of the computational domain considerably.

Extreme ultraviolet spectroscopy diagnostics of low-temperature plasmas based on a sliced multilayer grating and glass capillary optics.

New extreme ultraviolet (EUV) spectroscopic diagnostics of relatively low-temperature plasmas based on the application of an EUV spectrometer and fast EUV diodes combined with glass capillary optics is described. An advanced high resolution dispersive element sliced multilayer grating was used in the compact EUV spectrometer. For monitoring of the time history of radiation, filtered fast EUV diodes were used in the same spectral region (>13 nm) as the EUV spectrometer. The radiation from the plasma was captured by using a single inexpensive glass capillary that was transported onto the spectrometer entrance slit and EUV diode. The use of glass capillary optics allowed placement of the spectrometer and diodes behind the thick radiation shield outside the direction of a possible hard x-ray radiation beam and debris from the plasma source. The results of the testing and application of this diagnostic for a compact laser plasma source are presented. Examples of modeling with parameters of plasmas are discussed.

Fabrication of x-ray zone plates by surface-plasma chemical vapor deposition.

A new cost-efficient sputter-slice technology for hard x-ray (10-30 keV) Fresnel zone plates fabrication, imposing no limitation to aspect ratio, is proposed. By means of a plasma chemical process, SiO(2)/Si(1-x)Ge(x)O(2) glassy film multilayer structures are deposited on a lateral surface of a silica rod, outermost layers being as thin as 100 nm. It has been shown by numerical simulation that for x=0.2 germanium fraction, 100-300 microm zone plate thickness and the number of zones of about 1000, first order diffraction efficiency as high as 20%-30% at the energy of approximately 20 keV can be achieved.