Wave guides for x-rays and neutrons: A scalar model.

摘要

Planar and cylindrical dielectric wave guides for x-rays and neutrons are studied. The theory is developed for scalar waves. For x-rays this is only an approximation, albeit a good one. The theory developed here shares many features with theories that describe dielectric guides for infrared and visible light. However, the small value of the dielectric susceptibility for x-rays, and the extreme difference of scale between the wavelength and the typical dimensions of guides allows approximations that result in considerable simplification of the theory.; The dimensions of the cylindrical guides are chosen to model the glass capillaries currently used in x-ray optics. Under many experimental conditions, the guide opening is illuminated by a divergent incoherent beam, and the standard methods of geometrical optics yield satisfactory results. However, current technology allows illumination by highly collimated coherent beams. In this case, geometrical optics approximations fail and wave effects become crucially important.; Our problem is tackled in three steps. First we study the propagation along the guide. This involves finding the guided field modes, their phase velocities, and their attenuation by absorption along the guide. Next we calculate the probabilities for the excitation of each mode by a plane wave incident at the guide entrance. Finally, the emergence of the guided modes out into vacuum is treated as the Fraunhofer diffraction of a nontrivial wave (a superposition of guided modes) incident on an aperture in a screen (the exit opening of the guide).; We find that absorption is nearly nonexistent because the modes penetrate very little into the dielectric but that the differences in phase velocities for the various modes can have appreciable effects on the emerging diffracted intensity distribution. The excitation of essentially a single mode can be achieved by a sufficiently well collimated incident beam. For a plane wave of 8 keV x-rays incident parallel to a planar guide with a gap of 10 microns, we find that as much as 81% of the incoming energy is channeled into the fundamental mode. For a cylindrical guide with a diameter of 10 microns the excitation of the fundamental mode is still a remarkable 69%.