# Off-Resonance Control and All-Optical Switching: Expanded Dimensions in Nonlinear Optics
## 4 Laser-Modified Fluorescence  
Following electronic excitation of a molecule--and in the absence of phosphorescence arising from inter-system crossing--there are usually two major relaxation routes: One is fluorescent emission, the subject of this section, and the other is energy transfer to a second 'acceptor' molecule (discussed in Section 5). Since, in terms of quantum electrodynamics, light emission is simply time-reversed absorption, the passing of off-resonant laser light of sufficient intensity through an excited molecular system can evidently enhance or suppress the fluorescent emission in an analogous fashion to its effect on absorption. When no light is present, i.e., when the resonant radiation responsible for the initial excitation has left the system, fluorescence once again involves a single photon-molecule interaction that relates to the first term of Equation (4). However, this is not the case when the system is irradiated by the off-resonant beam. Here again, three concerted photon-molecule couplings arise, as shown by Figure 2(b), corresponding to the third term of Equation (4). This contrasts with stimulated emission, which involves the delivery of radiation with a frequency that must match the fluorescence. The intensity of fluorescence (power per unit solid angle [46]), \(I(\Omega)\), is the Fermi emission rate multiplied by the energy of a fluorescent photon, \(\hbar ck\), so that the leading contributions are given by [54]  
\[ \begin{array}{ll}I(\Omega)&=\left(\frac{c\xi^{4}}{8\pi^{2}\epsilon_{0}} \right)\vec{e}\cdot\vec{e}\left[\mu_{i}^{(0)\alpha}\overline{\mu}_{j}^{(0) \alpha}+(I^{\prime}/c\epsilon_{0})\mu_{i}^{(0)\alpha}\overline{\mu}_{j}^{(2) \alpha}(\omega^{\prime})\right.\\ &\left.+\left(I^{\prime 2}/4c^{2}\epsilon_{0}^{2}\right)\mu_{i}^{(2)\alpha}( \omega^{\prime})\overline{\mu}_{j}^{(2)\alpha\alpha}(\omega^{\prime})\right] \end{array}  \tag{10}\]  
which can be interpreted as emission associated with the effective fluorescence-decay (second-order) transition moment \(\mu_{i}^{(2)\alpha}(\omega^{\prime})\equiv\vec{e^{\prime}}_{j}e^{\prime}_{k} \theta_{ijk}^{\alpha\alpha}(\omega;-\omega^{\prime},\omega^{\prime})\), where the explicit form of the hyperpolarizability \(\beta_{ijk}\) is similar to that of laser-modified absorption [56]. Again, it is the quantum interference term (the second one, linearly dependent on \(I^{\prime}\)) that represents the leading correction to the emission intensity without the throughput beam. The term that is quadratically dependent on \(I^{\prime}\) relates to a special condition that we return to in Section 6. Most often, it will prove negligible compared to the first two terms in Equation (10). Nonetheless, for both terms involving \(I^{\prime}\), pre-resonance enhancement is again possible: Judicious choice of wavelength for the throughput beam may enhance the magnitude of the second-order transition moment through its dependence on the dispersion properties of the pseudo-hyperpolarizability tensor. This possibility is shown in Figure 3c,d. A quantity known as the fluorescence anisotropy, \(r\), is an important element in many fluorescence studies. This is determined from the general expression \(r=\left(I_{\parallel}-I_{\perp}\right)/\left(I_{\parallel}+2I_{\perp}\right)\), where \(I_{\parallel}\) and \(I_{\perp}\) are fluorescence intensities measured through polarizers oriented parallel and perpendicular, respectively, to the polarization of the excitation beam. When the laser-modified interaction comes into play, the effect on the fluorescence anisotropy becomes significantly more intricate, but it may be simplified to an experimentally tractable form based on a two-level approximation.