Higher conservation laws associated with the phase-dependent Maxwell-Bloch equations are derived and employed to determine both amplitudes and frequency shifts of the final-state solitons produced in a resonant medium by an initially phase-modulated optical pulse of area $<5\ensuremath{\pi}$. The higher conservation laws are shown to provide a relatively efficient method of relating the parameters of the final pulses to those of the incident pulse. Connection is made to the computer work of Diels and Hahn.
An analysis is made of the propagation of an ultrashort optical radiation pulse under conditions of inhomogeneous broadening of a resonance line. By dispensing with the approximation of a slowly varying complex pulse envelope, constraints on the duration are removed and any phase modulation is automatically taken into account. It is shown that if the boundary conditions determining the attenuation of the pulse at its leading edges are defined, the appropriate reduced Maxwell–Bloch equations can be integrated using the method of the inverse problem of scattering theory. Higher conservation laws, whose existence has been doubted, are found.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
The semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.
We introduce a notion of ``matrix potential'' to nonlinear optical systems. In terms of a matrix potential
g, we present a gauge-field-theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multilevel media. We show that the Bloch part of the equation can be solved identically through
g and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces
G/H. In particular, we associate the nondegenerate two-level system for self-induced transparency with
G/H=SU(2)/U(1) and three-level $\ensuremath{\Lambda}$ or
V systems with
G/H=SU(3)/U(2). We give a detailed analysis for the two-level case in the matrix potential formalism, and address various properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological, and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a different type of pulse stability analysis that explains earlier numerical results.