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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transverse Effects In Swept-Gain Superradiance: Evolution From The Superradiant State

C. M. Bowden, F. P. Mattar

Published Dec 30, 1981• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.932070

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Journal of Applied Physics•Jun 1, 1964•75 citations
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.
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.
The steady-state behavior of amplifiers in which the excitation is swept at the speed of light is discussed in the semiclassical approximation. In the present work we examine the case where the decay time of the population is comparable to that of the polarization. Pulse propagation is shown to obey a generalized sine-Gordon equation which contains the effects of atomic relaxations. The analytical expression of the steady-state pulses (SSP) gives two threshold conditions. In the region of limited gain the SSP is a broad pulse with small area which can be obtained by small signal theory. In the second region of high gain the SSP is the superradiant $\ensuremath{\pi}$ pulse. Its pulse power is not limited as in usual superradiant theory because, as we show, for a swept excitation the cooperation-length limit does not exist.
This paper is devoted to understanding the temporal synchronization of the two-color superfluorescence output powers. Following McCall and Feld et al., the monochromatic superfluorescence can be described in terms of a semi-classical propagational model that shares the same equations as Self-Induced Transparency (SIT). Thus it became important to understand double SIT that was discovered by McCall and Hahn (MH) to correctly interpret co-propagating beams with coherent exchange of energy and nonlinear phase evolution. A further motivation would be to elucidate pump and Stokes synchronization as well as pump depletion effect on Stokes buildup in Raman forward amplifier. In this work, we describe how the diffraction affects the longitudinal and transverse reshaping associated affects the simultaneous resonant propagation of two different-wavelength optical pulses in a three-level medium. The pulse lengths are shorter than any of the relaxation times, thus, the interaction is coherent. The material response has an inertial characteristic, which precludes its description with two instantaneous susceptibilities, and requires instead the density matrix formulism. A semi-classical formulism, as introduced by Konopnicki and Eberly (KE), is adopted in which two paraxial Maxwell field equations are closely intertwined in the generalized three-level Bloch equations.
Recently, Bonifacio, Hopf, Meystre and Scully, using amplifier theory, predicted that under certain conditions, a noise amplifier, pumped by an impulse excitation traveling at the speed of light in the active material, can produce highly nonlinear spacially asymptotic coherent pulses of electromagnetic energy of anomalous intensity and of anomalously short temporal width. The pulse intensities were predicted to increase as the square of the density of the active material, whereas the temporal width should decreased as the inverse of the density. Also, the pulses are characterized by a temporal delay from the pump cutoff to the peak of the pulse evolution. This process has come to be known as swept-gain superradiance. Electromangetic energy having these general characteristics would be useful in application to LADAR systems for propagation, ranging, discrimination and coherent imaging. Other applications would include coupling to plasmas for efficient energy delivery needed for laser induced fusion and for plasma diagnostics. Since the pulses are produced in the amplifier configuration without mirrors, this presents an attractive scheme for production of unidirectional coherent VUV and X-ray radiation.
The dynamical evolution of an excited-state population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the excited states by an externally applied (ccc-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field which is treated quantum mechanically. It is found that stimulated Raman processes can significantly influence the dynamical evolution of population inversion and macroscopic polarization by producing coherence effects among the populations. We examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration. It is shown, using the mean-field approximation, that for uniform pumping and conditions such that the pump Rabi rate ${\ensuremath{\omega}}_{R}$, the characteristic collective radiation time ${\ensuremath{\tau}}_{R}$, and the pump pulse duration ${\ensuremath{\tau}}_{P}$ satisfy the inequalities, ${\ensuremath{\omega}}_{R}>\frac{1}{{\ensuremath{\tau}}_{R}}>\ensuremath{\gamma}$ and ${\ensuremath{\tau}}_{P}\ensuremath{\gtrsim}{\ensuremath{\tau}}_{R}$ ($\ensuremath{\gamma}$ is a characteristic internal dephasing rate for the molecules), the system is left in a state with classical transverse polarization when the pump pulse terminates. The system can evolve collectively from such a state only as superradiant (classical) evolution. For superfluorescent evolution which requires a state of preparation of complete inversion (zero transverse polarization), it is shown that the pump pulse must be effectively of area $\ensuremath{\pi}$ and that ${\ensuremath{\tau}}_{P}<{\ensuremath{\tau}}_{R}$. Our results show that when the former conditions are satisfied the delay time ${\ensuremath{\tau}}_{D}$ for collective free pulse evolution is a function of both ${\ensuremath{\tau}}_{P}$ and ${\ensuremath{\tau}}_{R}$. It is shown further that the pump pulse shape as well as temporal duration significantly affect the final state of preparation. The results of this work are interpreted in connection with recent reported results of experiments in superfluorescence and superradiance.
Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.