Eigen modes of quasiperiodic layered resonators

In presented work, resonance properties of resonators formed by quasiperiodic Bragg reflectors are investigated by solution of some types of eigenvalue problems. In the first eigenvalue problem the values of complex eigenfrequencies are found for the decaying natural oscillations of the "cold" passive resonators. The other eigenvalue problems correspond to undamped oscillations in "hot" structures containing amplifying elements. In the second eigenvalue problem we must find real frequencies and imaginary part of permittivity or permeability (lasing threshold) at fixed value of real part of permittivity and permeability of amplifying layer. In the third case the generation is achieved by introduction of lumped element with negative resistance into structure. In the fourth eigenvalue problem complex eigen permittivities or permeabilities of amplifying layers are found for fixed frequency of oscillations.