Frequency crystal

Pulse filtering through a medium with infinite periodic structure in transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose widths of transmitting and absorbing windows are equal. The second, named anharmonic frequency crystal (AHFC), has narrow absorption peaks separated by wide transmission windows. AHFC of moderate optical thickness demonstrates properties quite similar to those of high finesse atomic frequency comb (AFC) with limited number of the absorption peaks, which produce a few pulses from a short input pulse. On the contrary, HFC transforms the input pulse into a train of pulses whose maximum amplitudes follow a wide bell-shaped envelope. HFC allows to find an exact universal analytical solution, which describes transformation of a broadband pulse into a train of short pulses, slow light propagation for a pulse whose spectral width fits one of the transparency windows of the crystal, and absorption typical for a single line absorber if the pulse spectrum falls into one of the absorption peaks. Potential applications of HFC are discussed.