We investigate superradiant lasing in 1D photonic crystal taking into account both homogeneous and inhomogeneous
broadening in a two-level active medium. The latter may be based on, e.g., the quantum-well heterostructures and the
fibers activated by color centers where Bragg structure can be fabricated artificially by means of a periodic modulation
of the cladding layers. The truncated Maxwell-Bloch equations for the counter-propagating waves, the polarization and
inversion of an inhomogeneously broadened two-level medium are used to analyze numerically the interplay between the
back-scattering, amplification, dispersion, and de-phasing of waves. It is found that, if the photonic band gap is less than
the coherent amplification bandwidth, there is a wide range of the pumping and relaxation parameters of a two-level medium
where superradiant lasing exists and results in generation of a quasi-periodic and/or chaotic series of powerful and
short pulses similar to those of Dicke superfluorescence. It is the cavity mode selection due to distributed feedback
caused by the resonant Bragg structure which is responsible for the existence of superradiant lasing. Typical parameters
of superradiant photonic-crystal lasers, including lengths, photonic band gaps and relaxation rates, are indicated.
We show that a two-level active sample of one-dimensional photonic crystal can generate chaotic sequence of extremely short pulses in the absence of mirrors. Numerical analysis and optimization of this promising superradiant laser is presented.
A theoretical model of a waveguide free-electron laser is developed which includes the mismatches of group and cavity synchronism conditions as well as the waveguide dispersion. Under the assumption of a high quality resonator, a parabolic equation for the evolution of the profile of electromagnetic pulse is derived. The condition
of self-excitation and the parameters of stationary generation are found. It is shown that the waveguide dispersion makes it possible the operation of free-electron laser not only under positive but also under negative mismatch between the period of electron bunch injection and the period of electromagnetic pulse round trip. The transient and nonlinear stages of the free-electron laser operation are analyzed, and the optimal mismatches of group and cavity synchronism conditions are found, ensuring, in particular, utmost efficient generation of the terahertz pulses.
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