Coherent emission

An alternative approach to obtaining microwave spectroscopy is Fourier transfonn microwave (FTMW) spectroscopy in a molecular beam [10], This may be considered as the microwave analogue of Fourier transfonn NMR spectroscopy. The molecular beam passes into a Fabry-Perot cavity, where it is subjected to a short microwave pulse (of a few milliseconds duration). This creates a macroscopic polarization of the molecules. After the microwave pulse, the time-domain signal due to coherent emission by the polarized molecules is detected and Fourier transfonned to obtain the microwave spectmm. 

The photon thus induced to be emitted has the same phase relationship as the inducing photon. Further amplification of this coherent emission is brought about in a resonant optical cavity containing two highly reflecting mirrors, one of which allows the amplified beam to come out, either through a pin-hole or by a little transmission (Section 10.4). 

F. Auzel, Coherent emission in rare-earth materials 507... 

Section IV is devoted to excitons in a disordered lattice. In the first subsection, restricted to the 2D radiant exciton, we study how the coherent emission is hampered by such disorder as thermal fluctuation, static disorder, or surface annihilation by surface-molecule photodimerization. A sharp transition is shown to take place between coherent emission at low temperature (or weak extended disorder) and incoherent emission of small excitonic coherence domains at high temperature (strong extended disorder). Whereas a mean-field theory correctly deals with the long-range forces involved in emission, these approximations are reviewed and tested on a simple model case the nondipolar triplet naphthalene exciton. The very strong disorder then makes the inclusion of aggregates in the theory compulsory. From all this study, our conclusion is that an effective-medium theory needs an effective interaction as well as an effective potential, as shown by the comparison of our theoretical results with exact numerical calculations, with very satisfactory agreement at all concentrations. Lastly, the 3D case of a dipolar exciton with disorder is discussed qualitatively. 

The analysis of (4.12) shows that in the general case as well, we have a threshold Ac = gcr (with gc 1) above which no coherent emission can build up only an incoherent emission of isolated domains is then possible. Below the threshold (An < Ac), the coherent state has y linear in A — Ac [the function... 

Figure 4.2. Variation of the radiative width y, or coherent emission rate, of a 2D disordered exciton as a function of the disorder strength A. For A > g,r, the emission becomes incoherent. For all distributions, including the gaussian distribution, there is threshold behavior with a sudden takeoff of the coherent emission.

Figure 4.5. Wave vectors around the center of the excitonic Brillouin zone for which coherent emission [solution of equations 4.10 and 4.25] is possible according to the disorder critical value Ac. We notice that r0 is the imaginary eigenvalue for K = 0 (emission normal to the lattice plane) and that K" and K1 indicate, respectively, components of K parallel and perpendicular to the transition dipole moment, assumed here to lie in the 2D lattice. The various curves for constant disorder parameter Ac determine areas around the Brillouin-zone center with (1) subradiant states (left of the curve) and (2) superradiant states (right of the curve). We indicate with hatching, for a large disorder (A,. r ), a region of grazing emission angles and superradiant states for a particular value of A.

According to Section IV.A.3, for each wave vector K such that gcTK > A , there is an imaginary solution of (4.25). Thus, since localized states have a projection on every K> state, a very fast photon emission occurs (coherent emission) in the direction determined by K. In second-order perturbation theory124 126 (Fermi s golden rule"), / K takes values between 0 and x for... 

K 0/c (Fig. 3.7). Then, coherent emission is always possible for sufficiently grazing emission angles, in directions normal to the transition dipole (see Fig. 4.5). For a normal or nearly normal emission (K = 0), the transition to the coherent emission regime takes place for A = gcr0. If our model of static disorder may be extrapolated to dynamical disorder induced by thermal fluctuations, this transition should be observable as a function of temperature. A similar buildup of superradiance below a critical temperature in the condensed phase has been recently reported by Florian et al.154... 

Because the effects of VER are contained in the incoherent anti-Stokes signal (2), any coherent emission resulting from coupling between the pump and probe pulses may be regarded as an artifact. Coherent coupling artifacts are well known in pump-probe measurements of population dynamics (78). In the IR-Raman experiment, the dominant artifact in the anti-Stokes... 

Up to now/ the dimer laser system has been described alone in terms of population inversion between suitable energy levels/ and for this description the condition S2 > A 2 is indeed the only necessary condition for cw laser oscillation/ as long as the thermal population density in the lower laser level remains negligibly low. However/ as this optically pumped laser system is a coherently excited three level system/ the coherent emission can also be described as stimulated Raman scattering/ which is resonantly enhanced by the common level 3 of the pump and laser transitions. This coupled two photon or Raman process does not require a population inversion between levels 3 and 2 and introduces qualitatively new aspects which appreciably influence and change the normal laser behaviour. For a detailed and deeper description of the coherently excited three level dimer... 

Field emission from carbon nanotubes may be more complex than implied by the analysis above since, in contrast to metal tips, the Fermi wavelengths are comparable to the tip size and consequently electronic states exist, which extend over the entire tip [152,168]. Emission is therefore not from individual atoms but from these tip states such that the emission is coherent. The field emission patterns from individual MWNTs in fact carry the signature of coherent emission from the tip states [168] (see Fig. 36). SWNTs have been imaged as well and the patterns correspond with calculated nanotube charge densities [152]. 

The coherent emission property has recently been demonstrated and utilized to produce electron holography images [173]. This is an important result since the coherence was much higher than from standard tungsten tips so that nanotube tips may replace tungsten tips in high resolution electron microscopy applications. 

All these phenomena can occur simultaneously within the same material, as illustrated by the spectral response of an oriented polymer doped with DCM dye (4-dicyanomethylene-2-methyl-6-p-dimethylamino-styryl-4H-pyran) under 1.06 iJ,m laser irradiation (Figure 1.1). The two sharp signals at 532 and 354 nm are coherent emission induced by SHG and THG, whereas the broad band is incoherent emission of two-photon excited fluorescence (TPEF). 

For many molecules of interest there exist radiationless transitions that couple the levels of an electronically excited surface to a dense manifold of quasidegenerate levels on one or more other electronic surfaces, and these latter levels have vanishingly small transition dipole matrix elements with the initial level on the ground state surface. As shown in the preceding section, exponential decay of the amplitude of a wavepacket on an excited state surface via, say, a radiationless process, reduces the amplitude of a coherent emission signal but does not destroy the coherence. 

Fig. 5. Pulsed-nozzle FT microwave measurements. A molecule-radiation interaction occurs when the gas pulse is between mirrors forming a Fabry-Perot cavity. If the transient molecule has a rotational transition of frequency vm falling within the narrow band of frequencies carried into the cavity by a short pulse (ca. 1 (is) of monochromatic radiation of frequency v, rotational excitation leads to a macroscopic electric polarization of the gas. This electric polarization decays only slowly (half-life T2 = 100 (is) compared with the relatively intense exciting pulse (half-life in the cavity t 0.1 (is). If detection is delayed until ca. 2 (is after the polarization, the exciting pulse has diminished in intensity by a factor of ca. 106 but the spontaneous coherent emission from the polarized gas is just beginning. This weak emission can then be detected in the absence of background radiation with high sensitivity. For technical reasons, the molecular emission at vm is mixed with some of the exciting radiation v and detected as a signal proportional to the amplitude of the oscillating electric vector at the beat frequency v - r , as a function of time, as in NMR spectroscopy Fourier transformation leads to the frequency spectrum [reproduced with permission from (31), p. 5631.

Obviously, the resonant-cavity must conform to a frequency mode of emission of our crystal. To build such a cavity, we find that we must carefully control its physical dimensions so that a specific wavelength of emission will build in Intensity and control the wavelength of coherent emission. To do this, we insert mirrors (first surface) at both ends of the crystal so that many reflections of a photon can occur tluroii the crystal, as illustrated in the following diagram, given as 5.8.68. on the next page. 

You will note that diode lasers cover a wide range of coherent emission wavelengths, from the visible to the far infrared. Also, the same materials used as for LED s are employed here except that a resonant laser chamber equipped with totally reflecting mirror and an output mirror of... 

The coherent emission intensity of an ensemble of N molecules is therefore N times stronger than the incoherent emission. This result is due to the N(N— 1) cross-terms in the expansion as first shown by Dicke. A closer look at this enhanced spontaneous emission shows that the coherent emission is also highly directional, in fact in a sample of macroscopic size the constructive interference effects only occur in the direction of the exciting laser beam. 

In a recent paper by Burland, Carmona, and Cuellar the first OFID measurements on an organic radical, duryl in a durene host ciystal, were reported. At low temperature T2 was found to be 212 78 ns, which is substantial shorter than half the fluorescence lifetime (530 ns). The authors concluded that in this system also the nuclear spin-flip processes determine the OFID decay. We note here that in these multilevel systems the coherence bandwidth of the exciting laser will have a profound effect on the coherent emission. 

Light amplification by stimulated emission of radiation was first demonstrated by Maiman in 1960, the result of a population inversion produced between energy levels of chromium ions in a ruby crystal when irradiated with a xenon flashlamp. Since then population inversions and coherent emission have been generated in literally thousands of substances (neutral and ionized gases, liquids, and solids) using a variety of incoherent excitation techniques (optical pumping, electrical discharges, gas-dynamic flow, electron-beams, chemical reactions, nuclear decay). 

---