Focusing and Energy Dispersion Properties of a Cylindrically Bent Asymmetric Laue Crystal

Elastically bent single-crystal Laue case diffraction crystals provide interesting new opportunities for imaging and spectroscopy applications. The diffraction properties are well understood, however, the ability to easily model the diffracted beams hinders assessment of the focal, phase and energy dispersive properties needed for many applications. This work begins to collect the elements needed to ray trace diffracted beams within bent Laue crystals for the purpose of incorporation into other powerful ray tracing applications such as SHADOW. Specifically, we address the condition in a bent Laue crystal where a cylindrically bent Laue crystal will focus all the polychromatic diffracted beams at a single location when a specific asymmetry angle condition is met for a target x-ray energy - the so-called "magic condition". The focal size of the beam can be minimized, but this condition also results in excellent energy-dispersive properties. The conceptual and mathematical aspects of this interesting focusing and energy dispersive phenomenon is discussed.