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Wave-Optical Computing Based on White-Light Interferometry

Tobias J. Haist, Wolfgang Osten

Published Jul 8, 2015• 0 citations
OpenAlex

Abstract

We introduce a waveoptical computing method based on white-light interferome-try. Problems are solved by 1. the modeling of the problem by optical path lengths, 2. the optical superposition of all possible solutions and 3. the selection of the de-sired solution by interference detection. The method is strongly related to quantum computing but works with purely classical waves. 1

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We introduce a waveoptical computing method based on white-light interferome-try. Problems are solved by 1. the modeling of the problem by optical path lengths, 2. the optical superposition of all possible solutions and 3. the selection of the de-sired solution by interference detection. The method is strongly related to quantum computing but works with purely classical waves. 1
I present a method for optical computing based on white-light interferometry. The problem to be solved is coded by optical path lengths and the superposition of all possible paths that a photon can travel is used for computing the solution. The solution itself is chosen by interference with the reference light. Several gedankenexperiments demonstrate how this method can be used for solving computational hard problems. Especially, I will introduce the basic principle with two maze-type puzzles and then concentrate on how the method can be employed for performing ultra-fast (sub-ps) digital-optical arithmetic with arbitrary precision.
We introduce an optical method based on white light interferometry in order to solve the well-known NP-complete traveling salesman problem. To our knowledge it is the first time that a method for the reduction of non-polynomial time to quadratic time has been proposed. We will show that this achievement is limited by the number of available photons for solving the problem. It will turn out that this number of photons is proportional to N(N) for a traveling salesman problem with N cities and that for large numbers of cities the method in practice therefore is limited by the signal-to-noise ratio. The proposed method is meant purely as a gedankenexperiment.
The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their cumulative effect can become a difficult task. We present an intuitive graph-based method for solving this problem and calculating electric fields within an interferometric setup, classical and quantum. We show how to associate a weighted directed graph with an interferometer and define rules to simplify these associated graphs. Successive application of the rules results in a final graph containing information on the desired field amplitudes. The method is applied to a number of examples in cavity optomechanics and cavity-enhanced interferometers.
The resolution of optical interference is ultimately limited by the wavelength of light, which is known as Rayleigh criterion. Interestingly, this limitation could be surpassed by considering photonic de Broglie wave, and the resulting subwavelength interference is useful for lithography and super-resolving phase measurementsuper-resolving phase measurement. Usually, quantum entangled state is necessary to realize photonic de Broglie wave. Recent advances show that subwavelength interference could also be realized with a classical light through post-selected operation or by considering light-matter interaction. In this work, a new classical source is designed to achieve subwavelength interference without any post-selected operation in a linear scheme.