Effects of Propagation, Transverse Mode Coupling and Diffraction on Nonlinear Light Pulse Evolution

C. M. Bowden, F. P. Mattar

Results of numerical calculations are presented and analyzed for pulse generation and subsequent stabilization in large propagation distance z , for a collection of two-level absorbers which are swept-excited by an impulse inversion along the z-direction at the speed of light in the medium. The calculation is performed using the coupled Maxwell-Bloch formalism and for the conditions that T2 = T1 , T2 > ιc, g/κ > > 1, where T2 is macroscopic dipole moment dephasing time, T1 is the longitudinal relaxation time for the absorber, ιc is the characteristic superradiant cooperation time among the absorbers and g/κ is the linear gain, g , to diffraction loss, κ, ratio. Results of the calculation for nonlinear pulse evolution and propagation for one spacial dimension (planar case) is compared with the results for the comparable case where transverse mode coupling is included.

W. J. Firth

Charles M. Bowden, Farrès P. Mattar

Results of numerical calculations are presented and analyzed for pulse generation and propagation in one-and two-spacial dimensions in a medium consisting of a collection of two-level atoms which are resonantly swept-excited by an impulse excitation traveling at the speed of light in the medium. The conditions imposed for the calculation in one-spacial dimension are that T1 = T2, where T1 and T2 are the single atom relaxation and dephasing times, respectively, and that the gain, g, to loss, κ , ratio g/κ >> 1 , which determines the non-linear regime for pulse evolution. In addition, we impose that T2 >> τc, where τc is the characteristic superradiance cooperation time, so that the pulse evolves from conditions appropriate for superradiant pulse generation for sufficiently small values for the propagation distance z . We report and analyze calculational results for the transient regime of pulse buildup through the asymptotic regime of large propagation distance z where the pulse generated exhibits steady-state behavior with regard to pulse area, energy and intensity profile. Additional results of computations are presented which incorporate transverse effects and diffraction using a Gaussian radial gain profile for the initial condition and under imposed conditions comparable with those of the corresponding one-spacial dimension calculations. The results of the two sets of calculations are compared and discussed. We demonstrate and give predictive requirements for swept-gain pulse evolution from the superradiant state.

V. S. Grigor'ian, Andrei I. Maimistov, Iu. M. Skliarov

F. P. Mattar, C. M. Bowden

A model is presented for the dynamical evolution of superfluorescence from an optically pumped three-level system. The full propagation, transverse, and diffraction effects are taken into account. With the use of a previously developed algorithm, a computational simulation was constructed from this model and results are presented and discussed. In particular, it is shown that the injected coherent pump-pulse initial characteristics, such as on-axis area, temporal and radial width and shape, can have significant deterministic effects on the superfluorescent pulse delay time, peak intensity, temporal width, and shape. Thus, by specifying certain initial properties of the injected pump pulse, the superfluorescent pulse can be shaped and altered. The results predict the conditions under which an injected light pulse of a given frequency can be used to generate, shape, and control a second light pulse of a different frequency via a nonlinear medium, thus demonstrating a new aspect of the phenomenon of light control by light.

Eli A. Mishkin