Real-Time Fourier Transformer System Using Transmissive Fiber Gratings

The duality between the equations that describe the paraxial diffraction of light beams in free space and the temporal dispersion of narrowband pulses in dielectrics allows one to deduce a time-domain equivalent to the spatial Fraunhofer approximation. This equivalence is used to design real-time optical Fourier transformer systems, which are shown to be realizable by using linearly chirped intermodal couplers (transmissive fiber gratings) as the dispersive media. In particular, the design of an intermodal coupler to carry out Fourier transformations is presented and it is shown that this design exhibits very good correlation between theoretical and simulated results.