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

Cooperative emission from a disordered system: a classical model

Tigran V. Shahbazyan, Mikhail E. Raikh, Zeev Valy Vardeny

Published Dec 1, 1997• 0 citations
Publisher

Abstract

The effect of disorder on the collective emission from a system of classical oscillators is studied theoretically. Three types of disorder are considered: random orientation of dipole moments, finite spread in frequencies of the individual oscillators (diagonal disorder), and dipole- dipole interaction (off-diagonal disorder). We found that for sufficiently high concentration of oscillators the diagonal disorder does not completely destroy the collective character of the emission. We show that the eigenmodes of a cooperative system with disorder comprise a large number of oscillators and, due to cooperative character of the emission, their lifetime is much longer than the lifetime of an individual oscillator. Consequently, the cooperative emission spectrum of the system is not simply broadened by the disorder, but represents a superposition of relatively narrow peaks.

DOI
10.1117/12.284149

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The effect of disorder on the collective emission from a system of classical oscillators is studied theoretically. Three types of disorder are considered: random orientation of dipole moments, finite spread in frequencies of the individual oscillators (diagonal disorder), and dipole- dipole interaction (off-diagonal disorder). We found that for sufficiently high concentration of oscillators the diagonal disorder does not completely destroy the collective character of the emission. We show that the eigenmodes of a cooperative system with disorder comprise a large number of oscillators and, due to cooperative character of the emission, their lifetime is much longer than the lifetime of an individual oscillator. Consequently, the cooperative emission spectrum of the system is not simply broadened by the disorder, but represents a superposition of relatively narrow peaks.
We study theoretically the cooperative light emission from a system of $N\ensuremath{\gg}1$ classical oscillators confined within a volume with spatial scale L much smaller than the radiation wavelength ${\ensuremath{\lambda}}_{0}=2\ensuremath{\pi}c/{\ensuremath{\omega}}_{0}.$ We assume that the oscillator frequencies are randomly distributed around a central frequency ${\ensuremath{\omega}}_{0}$ with some characteristic width $\ensuremath{\Omega}\ensuremath{\ll}{\ensuremath{\omega}}_{0}.$ In the absence of disorder, that is, $\ensuremath{\Omega}=0,$ the cooperative emission spectrum is composed of a narrow subradiant peak superimposed on a wide superradiant band. When $\ensuremath{\Omega}\ensuremath{\ne}0,$ we demonstrate that if N is large enough, the subradiant peak is not simply broadened by the disorder but rather splits into a system of random narrow peaks. We estimate the spectral width of these peaks as a function of N, L, $\ensuremath{\Omega},$ and ${\ensuremath{\lambda}}_{0}.$ We also estimate the amplitude of this mesoscopic structure in the emission spectrum.
Superfluorescent decay in a weakly disordered slab is considered. By solving the Maxwell-Bloch equations we show, that the cooperation number increases with increasing of the mean free path. Superfluorescent impulse is emitted at a small angle to the slab, isotropically in a plane direction. PACS.42.20-Propagation and transmission in inhomogeneous media. PACS.42.20G-Scattering, diffraction and polarization. Introduction. During the spontaneous emission of uncorrelated exited atoms, their dipole moments interact each other via the emitted electromagnetic field. If the lifetime of exited state is long enough, the radiation can induce the correlation between the group of large number Nc (so called cooperation
Coherent emission from two or more classical damped oscillators leads to an apparent violation of conservation of energy if the oscillators are assumed to emit independently. To resolve this apparent paradox, it is necessary to include effects related to cooperative decay, wherein each oscillator modifies the damping rate of the other oscillators. We show how these effects are included for two radiating oscillators and for a line of N oscillators. The relation between cooperative decay, optical coherent transients, and superradiance is discussed.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady state absorption (outside the cavity), transmission spectra (inside the cavity) and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. Effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N), and therefore, the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective NNN) and therefore the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.