Abstract: Du Fort-Frankel differential format for mode calculation of unstable resonator is presented.A fast finite differential method based on matrix motion and coordinate system transformation is used to calculate output field of a bare cavity and an active cavity.Calculated results are compared with references.It shows that the method is good both in precision and speed in calculating modes of an active unstable resonator with large Fresnel numbers.It can be 20 to 40 times faster compared with a conventional method.With this method,output power of a HF chemical laser is calculated.It shows that the output power increase with decrease of distance between gain medium and concave mirror.This result is valuable to the design of high power DF chemical laser.

Key words: laser technique, unstable resonator, mode calculation, fast finite differential method