Reflection of attosecond x-ray free electron laser pulses

In order to utilize hard x-ray free electron lasers (XFEL's) when they are extended to attosecond pulse lengths, it is necessary to choose optical elements with minimal response time. Specular grazing-incidence optics made of low-Z materials are popular candidates for reflectors since they are likely to withstand x-ray damage and provide sufficiently large reflectivities. Using linear-optics reflection theory, we calculated the transient reflectivity of a delta-function electric pulse from a homogenous semi-infinite medium as a function of angle of incidence for s- and p-polarized light. We specifically considered the pulse response of beryllium, diamond, silicon carbide, and silicon, all of which are of relevance to the XFEL's that are currently being built. We found that the media emit energy in a damped oscillatory way, and that the impulse-response times are shorter than 0.3 fs for normal incidence. For grazing incidence, the impulse-response time is substantially shorter, making grazing-incidence mirrors a good choice for deep subfemtosecond reflective optics.