Abstract: For a new crystal LiNbO₃ detector, a new theoretic calculating method is presented for the first time. In this method, the phase retardation is directly related to the radiation field without the standardization of quadratic equation under the arbitrary field. Taking into account of the distribution of the field and group velocity mismatch we also give the optimized size of the new detector.

Key words: ultra fast electromagnetic radiation, electro-optic sampling detection, LiNbO₃ microstrip antenna, principal axis system, non-uniform phase retardatio