Abrupt discontinuity in the broad band density of states in a photonic crystal near PBG and low group velocity can have practical impact in many exiting applications of photonic crystals, for example, optical transistor, tunable filters, chromatic dispersion compensators and pulse compression. However it is difficult to excite EM modes in the photonic crystal at frequency close to its PBG by external beam because of tremendous group index mismatch. To solve this problem we propose an idea of a transition interface with a smooth group index profile. Firstly, the idea has been investigated in general using a multi-layer stack as a “toy” model. Then, general trends have been verified for 2D photonic crystals with infinite thickness and slab photonic crystals with one-dimensional periodicity. It has been shown that if there is no interface, reflection/back-diffraction from the photonic crystal at the frequency in the transmission window near its edge is close to 100%. However in case of transition interfaces the transmission increases and abrupt edge of the broad band transmission spectrum takes place. The thicker transition interface - the more abrupt transmission spectrum. It has been shown that not only thickness, but also the group velocity profile in the transition interface is essential.