Calculation of Higher Order Group Velocity Dispersion in a Grating Pulse Stretcher / Compressor Using Recursion Method

In sub-picosecond Table Top Terawatt laser systems, grating based stretcher and compressor are used for chirped pulse amplification. For such a compressor / stretcher, the analytical expression for the higher order group velocity dispersion (GVD) is obtained using Taylor series method, which involves higher order differentiation. Starting with the same method, we derive here a recursion relation for higher order GVD terms, which eliminates the need of explicit differentiation.