The new types of photonic switching systems based on the newly developed fundamentally new 4x4-switching cell are presented. Using this cell instead well-known 2x2-switching cell allows us to signifi- cantly improve the characteristics of switching systems. The double-stage 16x16-switching system and 256x256-switching system are described in detail for the first time. The expressions for the numbers of stages and basic elements on the number of inputs for the developed schemes are obtained for the first time also. Numerical calculations and comparison with well-known schemes is carried out.