Directional couplers nonlinear

Numerics has been used intensively in the field of integrated optics (10) since its early days, simply due to the fact that even the basic example of the slab waveguide requires the solution of a transcendental equation in order to calculate the propagation constants of the slab- guided modes. Of course, the focus was directed to analytical methods, primarily, as long as the power of a desktop computer did allow for a few coupled equations and special functions only e.g. to describe the nonlinear directional coupler in a coupled mode theory (CMT) picture. During the years, lots of analytic and semi-analytic approaches to solve the wave equation have been developed in order... 

The nonlinear directional coupler is potentially a useful device because it has four ports, two input and two output, and because the outputs can be manipulated with either one or two inputs. Optimally the two channels are identical, and the coupling occurs through field overlap between the two channels. As a result, when only one of the channels is excited with low powers at the input, the power oscillates between the two channels with a beat length Lb, just like what occurs in a pair of weakly coupled identical pendulii. As the input power is increased, a mismatch is induced in the wavevectors of the two channels, which decreases the rate of the power transfer with propagation distance. This leads to an increase in the effective beat length. There is a critical power associated with this device, for which an infinitely long, lossless NLDC acts as a 50 50 splitter, that is, Lb oo. 

At this time, many of the parameters listed above have not been measured for nonlinear organic materials. Measurement will be necessary for an assessment of the full potential of such materials. To date, only a nonlinear directional coupler has been implemented in a nonlinear polymer, (poly-4BCMU). For this device at 1060 nm, the nonlinear response was dominated by two-photon absorption, and some limited switching attributable to absorption changes was observed (27). More recent work at 1030 nm appeared to show switching attributable to refractive nonlinearities (28). Clearly there is much progress to be made. 

Figure 11. Power-dependent nonlinear coupling at a nonlinear directional coupler.

Figure 12. Schematica 1 structure of the nonlinear directional coupler.

Although many all-optical devices have been proposed, I will concentrate on the nonlinear directional coupler. This device has been studied extensively by theory and simulation, and has been realized for the case of dual-core optical fibers. ° The basic device (Figure 1) consists of two parallel channels of an NLO material, spaced so that light propagating through one channel is coupled to the second through the overlap of the light s evanescent... 

Stegeman et al [37] have proposed a figure of merit T=2pX/n2 for a nonlinear directional coupler, with T values < 1 implying useful materials. In the case of poly(di-n-hexylsilane), our lower bound estimate on n2 yields a T value ranging from 0.1 - 1.0 for the wavelength range 580-650 nm. 

Fig. 4.27 Nonlinear waveguide device geometries and their response characteristics (a) nonlinear Mach-Zehnder interferometer (b) nonlinear directional coupler.

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