# Off-Resonance Control and All-Optical Switching: Expanded Dimensions in Nonlinear Optics
## 1 Introduction  
Nonlinear optics is one of the most remarkable and pervasive fields to emerge from the development of the laser over 50 years ago. Optically parametric processes, such as second and third harmonic generation (SHG and THG), are the preeminent means of converting laser output to a shorter wavelength. The basic theoretical principles of nonlinear optics were rapidly established and consolidated, notably in an early treatise by [PERSON] in 1965 [1]. More modern introductions to the field include prominent texts by [PERSON] [2], [PERSON] [3], [PERSON] and [PERSON] [4], [PERSON] [5], [PERSON] [6], [PERSON] [7], [PERSON], [PERSON] [8], and [PERSON] [9], among many others. Conventionally, nonlinear processes involve the concurrent absorption of multiple off-resonant photons--meaning that the associated rate depends on the square, or a higher order, of the corresponding input laser intensity. In resonant processes, this typically produces local dipole transitions to a higher energy (most often electronically excited) state. In non-resonant parametric processes, each fundamental interaction results in the promotion of the active material to a virtual intermediate state, which then returns to the ground state via emission into an optical mode or modes that differs, usually in frequency, from the laser input. Largely overlooked is the fact that a moderately intense off-resonant laser beam (\(\sim\)10\({}^{11}\)-10\({}^{12}\) W cm\({}^{-2}\)) may provide a controlling effect on a resonant process such as fluorescence--acting as a stimulus with an optical frequency at which the molecule is transparent. In such a case, the beam is unaltered by the light-matter interactions that occur. To this extent, 'optical catalyst' is anapt name for the effect, since the beam is unchanged before and after the process. The terms is also used in a different connection relating to beam splitting. Here, optical catalysts have been extensively studied [10; 11; 12; 13] and suggested as a method for improved performance of continuous-variable quantum key distribution systems [14]. Moreover, in connection to the photolysis of isolated phenol molecules, a strong off-resonant infrared electromagnetic field has recently been shown to lower the activation barrier to photolysis via a dynamic Stark shift [15], signifying a form of optical catalysis whose effect is also analogous those detailed in this review. Applying the off-resonant beam to a conventional optically resonant process results in an unconventional nonlinear optical effect. The outcome is the possibility of an increased or decreased rate compared to the resonant process without the ancillary beam. The capacity for the stimulus beam to be under direct experimental control confers numerous advantages, especially compared with the commonly known capacity of a neighboring surface plasmon to enhance the rate of many optical processes [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. Moreover, if the resonant process is forbidden by virtue of selection rules or another symmetry constraint, it is possible that it can become entirely activated by the input beam, since the resultant nonlinear process may then be allowed. This is the potential basis for an all-optical switch. Here, the realm of application may extend to control circuitry in signal propagation and waveguide networks for optical communication [42]. In this review, we first recap on the formulation for conventional nonlinear optics, serving to introduce a quantum electrodynamical framework that is equally valid for the newer effects that will be our focus. The approach is concisely illustrated for the process of second harmonic generation (Section 2). Sections 3 and 4 provide an analysis of the effect of an off-resonant beam on absorption and fluorescence. These processes are known as laser-modified absorption and fluorescence.