Localized Structures in Dissipative Nonlinear Systems - Abstract
Amiranashvili, Shalva
Propagation of ultrashort optical pulses in fibers is discussed. We demonstrate that derivation of a first-order propagation model can be interpreted as a transformation to a Hamiltonian representation of the underlying Maxwell equations. The resulting model posses similarity to a well known envelope equation, but applies to electric field directly without using the envelope and the slowly varying envelope approximation (SVEA). The electric field is represented in the form of two classical complex fields referring to the quantum creation and annihilation operators. For the unidirectional propagation the complex electric field is equivalent to so-called analytic signal. Furthermore, if the SVEA applies, the complex electric field is naturally related to the pulse envelope. The Hamiltonian point of view is further applied to derive integrals of motion for the pulse propagation and to characterize solitary solutions.