Brief comment: Dicke Superradiance and Superfluorescence Find Application for Remote Sensing in Air

Brief comment: Dicke Superradiance and Superfluorescence Find Application for Remote Sensing in Air D. C. Dai* Physics Department, Durham University, South Road, Durham DH1 3LE, United Kingdom *Corresponding author: dechang.dai@durham.ac.uk Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX This letter briefly introduces the concepts of Dicke superradiance (SR) and superfluorescence (SF), their difference to amplified spontaneous emission (ASE), and the hints for identifying them in experiment. As a typical example it analyzes the latest observations by Dogariu et al. (Science 331, 442, 2011), and clarifies that it is SR. It also highlights the revealed potential significant application of SR and SF for remote sensing in air. © 2011 Optical Society of America OCIS Codes: 020.1670, 270.1670, 260.7120, 010.0280, 280.1350 In 1954 Dicke predicted the cooperative emission from a dense excited two-level system of gaseous atoms or molecules in population inversion in the absence of a laser cavity [1], soon after, Bonifacio and Lugiato termed it into two distinct forms [2]: Dicke Superradiance (SR) and Superfluorescence (SF). In a simplified picture, SR is from such an energy level prepared directly by laser into a quantum state which has an initial macroscopic dipole (coherence); whereas SF is from an initially incoherent energy level, which later on spontaneously builds-up a macroscopic dipole, in this case the system is started by normal fluorescent emission (FL), then gives rise to SF pulse, having a characteristic induction time (τD) for the coherence development [2,3]. Both SR and SF are greatly limited by an opposed factor, the dephasing time (T2 or T2*, defined by the inverse of linewidth of a corresponding optical transition containing homogeneous broadening only or inhomogeneous broadening respectively), which always acts to destroy the coherence [2,3].

Fig. 1. (Color online) Illustration of SR (a), SF (b) and ASE (c) in a four-energy-level system in laser physics. Here, E3 has relatively longer lifetime than E4 and E2, the fast relaxation from E4 to E3 leads to population accumulation on E3 and results in a population inversion between E3 and E2. The property of emission from E3 is determined by its dephasing time (T2*), for example, in (a) if T2*« τp it is not SR but ASE. In contrast to SR and SF, amplified spontaneous emission (ASE) is the collective emission from such a similar but purely incoherent system. In ASE process, all the modes of spontaneous emission within gain can be amplified by stimulated emission in a single pass through the excitation volume, yet among them the mode with the maximum gain gradually wins others by competition effect, and finally results in coherent output at the end [3]. Fig. 1 illustrates three cases above.
In experiments, the phenomena of ASE, SR and SF are all appeared as stimulated emission or mirror-less lasing, their behaviors are quite similar to each other: they share the observable features based upon a clear threshold determined by population inversion, such as spectral line narrowing, exponentially growing intensity as pump power, and drastically shortened emission lifetime, directionality and polarization of emission beam etc, these usually bring much confusion to researcher in a test to identify a specific case of SR or SF from the more common cases of ASE [3]. Given the facts that SR and SF have been successfully observed predominantly in gaseous systems [4], since the first report in HF gas in 1973 [5], some hints are summarized here: in frequency domain, (i) doing energy level analyses as shown in Fig. 1, SR is from such an energy level resonantly populated by a pump laser, (ii) checking exponential index by fitting pump power dependent intensity growth, both SR and SF have an explicit index of 2.0 by definition in the case of single photon excitation, or 4.0 in two-photon excitation, for ASE it could be any number; then in time domain, (iii) looking for any quantum effect for SR and SF, such as the interference effect, quantum beats and ringing, which are the characteristics of the emission from coherent states, whereas ASE lacks of these; (iv) trying to resolve a time delay, τD, between normal FL and lasing with a short pulse duration of pump laser, τp. This τD is unique for SF, yet absent in both SR and ASE; (v) checking T2* and comparing it to τp, if τp is apparently longer than T2*, the emission is most possibly ASE rather than SR or SF; (vi) specifically, SF intensity exhibits quantum noise due to its triggering mechanism, and has other quantitative measures and criteria [6].
time (τD) (a) E4 E3 E2 E1 laser (τp) E4 E2 E3 E1 FL E2 E1 E4 E3 SF E4 E3 E2 E1 laser (τp) E4 E2 E3 E1 ASE (c ) (b) laser (τp) SR E3 E2 E1 E4 time (τD) (a) E4 E3 E2 E1 laser (τ

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