Glass capillary X-ray waveguides

The theory describing the performance of narrow cylindrical glass capillaries as waveguides for x rays is developed. Some aspects of the theory resemble theories that describe dielectric waveguides for visible light. However, the small value of the dielectric susceptibility for x rays allows approximations that result in considerable simplifications.; The modes of the electromagnetic field that propagate along the guide are studied. One obtains both the distribution of the fields and their polarizations. Circular-polarized modes correspond to definite values of the spin angular momentum. Here one obtains modes with definite orbital as well as spin angular momentum. Perhaps surprisingly these modes can be superposed into linearly polarized modes showing that both circular and linear polarization is conserved as the x rays propagate along the waveguide.; The intensity losses due to photoelectric absorption and due to scattering from surface roughness are calculated and found to be minimal for the lowest order modes.; The degree to which various linearly polarized modes are excited by a plane linearly-polarized wave incident at the entrance of the waveguide are calculated as a function of incidence angle. It is possible to achieve conditions which closely approach single mode excitation: for 8 keV x rays incident parallel to the axis of the waveguide with diameter of 10 μm as much as 70% of the incident energy is deposited into the fundamental mode.; Finally, a new approach to vector diffraction theory is proposed and used to calculate the Fraunhofer diffraction patterns produced from a superposition of linearly polarized modes as the x rays leave the waveguide exit. This new diffraction theory is inspired by an asymptotic form of the reciprocity theorem, which has been found useful in a variety of other problems of electromagnetic wave generation and scattering. It is physically equivalent to the usual theory based on the vector Kirchhoff diffraction formula but its application to non-trivial incident waves (the Bessel modes instead of plane waves) is considerably simpler.