| Summary: | Investigating the behavior of an atom in response to the applied electric field when the
latter frequency is in resonance with the natural frequency of the atom is an interesting subject. Near resonance, some of the most interesting optical phenomena such as dispersion, and absorption are more pronounced. Moreover, considering resonant and near
resonant interaction of light with two-level atoms, uncovers fascinating physical phenomena
such as area theorem and self-induced transparency describing stable pulse propagation
regimes in which the pulses maintain their identity. Existence of these optical structures
in on-resonance optical media has not been investigated in detail. In this thesis, the on-resonance interaction of optical field with atoms is considered and the formation of several
novel self-similar and kink waves in linear and nonlinear resonant media is discovered and
theoretically explored.
First, self-similar pulse formation in homogeneous broadened linear amplifiers in a
vicinity of an optical resonance is analyzed. It is demonstrated that the self-similar pulses
serve as universal asymptotics of any near resonance short pulses propagating in coherent
linear amplifiers. Second, ultrashort self-similar pulse propagation in coherent linear absorbers near optical resonance is investigated. Third, existence of self-similar optical waves with kink structure in resonant optical systems is discovered. Fourth, it is found that self-induced transparency quadratic solitons are realizable in the media with quadratic optical nonlinearities, doped with resonant impurities. Finally, stable spatial similaritons supported by homogeneous conservative optical media with quintic nonlinearities are explored.
To experimentally realize the presented results, physical models are presented for all
systems under consideration. The stability of the proposed near resonance optical systems
is demonstrated through a series of numerical case studies.
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