Broadening of short light pulses by many reflections from multilayer dielectric coatings

The broadening of short light pulses which are reflected from multilayer dielectric mirror coatings is calculated. The case when a pulse is reflected many times is treated in detail. The quarter-wave stack is the design for minimal pulse broadening. The broadening after many reflections is mainly due to the phase variations close to the edge of the reflection band of the coating. The shortest output pulses are obtained if only the center part of the reflection band of the mirror is used; an input pulse which contains only this part of the spectrum produces a much shorter output pulse than a delta-function input. Output pulses as short as 10(-13) sec are possible for typical mirror coatings and one-thousand reflections. The influence of errors in the fabrication of a coating on the calculated results is discussed.