Wave-Optical Computing Based on White-Light Interferometry

The basic idea of the method [1] is best demonstrated with a simple problem that already is given in terms of paths. Fig. 1 depicts how we can solve a typical maze problem. The maze is equipped with mirrors so that light entering the maze simultaneously runs through all possible paths. Interference will be detected if the optical path lengths (OPD) of the two interferometer arms are equal. Therefore one increases the delay of the reference arm until interference is detected. Now the input to the interference detector is moved (by an optical fiber) back into the maze to the last junction of the maze. The reference path length will be decreased by the same distance so that we still detect interference. Therefore we can test (by holding the fiber to all possible arms of the junction) from where the “correct” (meaning interfering) light comes. We repeat the process until we reach the input of the maze. For solving the maze we have to make K measurements where K is proportional to the number of junctions along the solution path. The computational cost of the solution therefore increases proportional to N if we denote the size of the maze by N x N . This should be compared with traditional computer-based algorithms where we have an increase proportional to N. This improvement is not obtained for free because the number of photons that are needed for the measurements increases exponentially with N . A detailed analysis shows that for 1 W of power at λ = 1μm and a signal-to-noise ratio of 1 we could in principle solve mazes with about 70 junctions along the solution path. Depending on the type of maze this corresponds to a lateral maze size of some hundred elemental cells. The interference-based detection is helpful since it leads to a better signal-to-noise behavior of the method. In principle it would also be possible to perform the experiment with (short) light pulses. In this case we would detect the time when a pulse arrives at the exit of the maze.