Evolution of paraxial field——Heggens transform

The large scale (ten/tens meters) quasiconcentric cavity used in high average output power farinfrared FEL and the shortpulse effects require that the numerical simulation must involve evolution in both space and time, which means huge quantity of calculating. To decrease quantity of calculating and keep accuracy, an new calculating method named "Heggens transform" was developed which is an integral expression similar to the KirchhoffFresnel expression and can be applied out of undulator．