# Off-Resonance Control and All-Optical Switching: Expanded Dimensions in Nonlinear Optics
## 6 All-Optical Switching  
The possibility of all-optical switching--in which light is controlled by light--is apparent when a forbidden optical process becomes allowed when subjected to an off-resonant optical input. At the molecular level, this will usually be either one-photon absorption, fluorescence, or resonance energy transfer. For example, a potential set-up (discussed below) based on the latter is shown in Figure 5. All these prospects provide a basis for an all-optical switch since the throughput and absence of the off-resonant signal results in the activation and deactivation of the optical process, respectively. All-optical switching based on dipole transition properties has the distinct advantage of ultrafast operation, compared to most electronic or even optomechanical mechanisms. Moreover, in the ultrafastregime, it is possible to entertain switching that is sustained throughout the duration of an input pulse, rather than requiring the activating input to act as a trigger for a state that will persist beyond the input. When an optical process without the input beam is forbidden, either by the polarization geometry, or by virtue of selection rules, it is notable that both the first and second (interference) terms in Equations (9), (10), and (13) are null. In each case, only the final nonlinear term remains. As discussed earlier, molecules of relatively high symmetry may frequently possess electronic excited states that are accessible by three-quantum, but not single-quantum, transitions. Notably, the selection rules for an electric octupole transition still subsume those for a simple electric dipole [93]. However, in systems where each component of the sample has a common, fixed, orientation--as, for example, in a nematic liquid crystal--then it is possible to arrange experimental conditions such that any specific, single-photon allowed process will be precluded using linearly polarized resonant input whose polarization vector is orthogonal to the conventional transition dipole. Then, the same transition may be allowed through non-zero, off-diagonal components of the transition quasi-hyperpolarizability. This represents a straightforward geometric configuration for effectively switching on or off the associated transition, a simple instance of all-optical switching. Resonance energy transfer can also be prohibited either by a suitable geometric configuration, in which the transition dipole moments of the donor and acceptor and the displacement vector are mutually orthogonal, or by a one-photon symmetry-forbidden electronic transition in the donor or acceptor. To develop an all-optical switch model, using the concepts of the last section, the case of a pair of parallel two-dimensional square-lattice arrays has been studied--with one a donor array and the other an acceptor array, each comprising a set of equally spaced, identical, and optically distinct antennas. The donor species are chemically dissimilar from the acceptors to preclude back-transfer [94], and the two arrays were constructed so that each constituent of the donor array corresponds to a component within the acceptor array. The effective capacity for energy transfer from an emitter in the donor array (assumed at the origin) to be directed to its designated partner in the acceptor array can be quantified by comparing it to the summed efficiencies for transfer to all other molecules within either array, i.e., the cross talk. Presuming typical values for the variables, the aspect ratio (where \(r\) is the distance between the arrays and \(l\) is the lattice constant) can be 0.3 for \(l^{\prime}\)= \(1\times 10^{12}\) W cm\({}^{-2}\) or 0.06 for \(1\times 10^{10}\) W cm\({}^{-2}\) to achieve transfer losses less than 5%. This demonstrates that the irradiance of the off-resonant beam is a major contributing factor in the destination of the donor excitation [53].