Аннотация:Using the spectral method, the boundary problem of the spatiotemporal dynamics of the formation and propagation of spectrally singular modes generated by propagating short (sub-picosecond) optical pulse within a dispersive PT-symmetric 1D photonic crystal is solved. The spectral amplitudes of transmitted and reflected spectrally singular waves tend to infinity. It is shown that for a certain photonic crystal thickness, when the Bragg condition is satisfied, two waves in each direction have not only the same frequencies and different projections of wave vectors, but also the equal amplitude modules and opposite signs. The sum of such waves has a standing envelope of the traveling wave amplitudes (a traveling wave with zero group velocity of the envelope). The traveling component of this wave is amplified as it propagates along the gain-loss photonic crystal; its intensity is proportional to the square of the incident pulse duration. The amplitudes of singular modes decay slowly with a lifetime inversely proportional to the mode spectrum width. Excitation of singular modes leads to a radical change in the intensity, shape, and dynamics of the excitation pulse itself. The leading edge of the pulses is formed by the spectral components of the incident pulse, and the slowly decaying trailing edge is determined by the long lifetime of the spectrally singular mode. Increasing the duration of the incident pulse leads to the emission of amplified extended pulses in the forward and diffracted directions at the frequency of spectral singularity with an almost stepped envelope profile.
