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Dynamic coupling and instability in a resonant superfluorescence

Igor V. Mel’nikov

Published Jan 1, 1995• 1 citation
OpenAlex

Abstract

The instability of superfluorescent decay is found for the sample whose size is comparable with or greater than the resonant wavelength. This instability is associated with the coupling of counterpropagating waves, can inhibit forward emission in the direction of the pump pulse, and even cause the forward emission to be switched off. The semiclassical theory is employed to take into account the effects of phase dynamics for a resonant emitter and without slow envelope approximation.

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The instability of superfluorescent decay is found for the sample whose size is comparable with or greater than the resonant wavelength. This instability is associated with the coupling of counterpropagating waves, can inhibit forward emission in the direction of the pump pulse, and even cause the forward emission to be switched off. The semiclassical theory is employed to take into account the effects of phase dynamics for a resonant emitter and without slow envelope approximation.
On working beyond the slowly varying envelope approximation, the instability of superfluorescent decay is investigated for the case in which the sample size is greater than or comparable to the resonant wavelength. The instability is associated with coupling between counterpropagating waves and can inhibit emission in the direction of the pump pulse. In particular, it is shown that tiny changes of the sample length can cause the forward emission to be switched off, suggesting that the optical analog of a directing antenna may be experimentally accessible.
Correlation of the parameters (delay times, peak intensities) of counterpropagating superfluorescence pulses is studied within the framework of a one-dimensional theoretical model depending on the sharpness of boundaries of the excitation region. The concentration N 0 of the initially excited active centers is described by a smoothed profile (decaying to zero within the h − and h + wide intervals at the left-and right-hand ends of the sample, respectively), rather than by a rectangular profile. It is established that variation of the excitation region boundary widths h ± does not eliminate the observed correlations. Moreover, the correlations can significantly increase for the samples with a length of L = n λ/2, where n is any natural number and λ is the resonance light wavelength. The oscillating dependence of the parameters of counterpropagating superfluorescence pulses on the h ± values and a significant asymmetry of these pulses for h − ≠ h + are discussed.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.
Spontaneous decay is a phenomenon that has been described for the first time by Dirac, Wigner and Weisskopf, at the early ages of the development of quantum electrodynamics. The theory is applicable to a multi-body system only when atoms don’t interact during their decay. Dicke introduces in his seminal paper the case where this assumption doesn’t hold. The results he obtains not only tell that the system emits pulses, but the pulse duration now depends on 1/N, where N is the number of participating atoms to the process. The pulses temporal profile is described by a squared hyperbolic secant function. The resulting emission intensity scales as N^2. The atomic system radiates more intensively than the ordinary fluorescent emission, this is the reason why the process is called superradiance, or by a generalization to extended systems, superfluorescence. The superradiant emission has preferential escape directions, depending on the atomic sample shape. Superradiance is a collective process and it takes place when the group of excited atoms is left unper- turbed during the formation of of the macroscopic dipole. A fundamental difference compared to the spontaneous and stimulated emission processes is that all atoms act together as a single entity and it isn’t possible to identify single atoms involved. This remarkable behaviour is manifest when the atomic coherence of the system, while influenced by environmental interactions that cause dephasing in atoms, persists for a sufficient interval of time. Typical dephasing mechanisms, such as collisions in gases or lattice phonon interactions in crystals, make its experimental observation difficult. A possible solution to this problem is the use of optical crystals doped with rare-earths that are characterized by long and narrow levels lifetimes.
The coupling of forward and backward propagating waves is studied theoretically in the transition region between superfluorescence (SF) and amplified spontaneous emission (ASE). To accomplish this a computer code has been written that solves Maxwell's equations in time and two spatial dimensions and accounts for counter-propagation, diffraction, and temporal coherence in the Bloch equations. Diffraction is ignored in the present calculations. In the SF regime the coupling is generally weak, as found by others; however, I have found a randomly occurring shot-to-shot coupling that is quite significant in cases where one wave, forward or backward, becomes established from quantum noise first in the amplified rod. In this case the wave that arises second is strongly coupled to the first. In the ASE regime the propagation shows strong forward-backward coupling and the characteristic spatial profile of the inversion that tends to zero at either end and to the small signal value of one in the middle of the amplifier. In the transion region the propagation shows mixed SF and ASE behavior.