Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors--Analysis

We present an analytical treatment of the reflection of femtosecond pulses from broad-band multiple-layer dielectric mirrors. In particular, closed-form expressions are given for the reflected pulse amplitude which includes the dispersive effect of the cubic phase term. It is shown that this term is still insufficient to accurately describe certain experimental results obtained with 20-fs optical pulses. We introduce an alternative technique which describes the phase branches analytically and yields accurate closed-form expressions for the reflected pulse amplitude in terms of complementary error functions having real or complex arguments.