Two-Photon Interferometry for High-Resolution Imaging

We discuss the advantages of using non-classical states of light for two aspects of optical imaging: the creation of microscopic images on photosensitive substrates, which constitutes the foundation for optical lithography, and the imaging of microscopic objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and a multi-photon sensitive material or detector, this limit can be surpassed. We give a rigorous quantum mechanical treatment of this problem, address some particularly widespread misconceptions, and discuss turning quantum imaging into a practical technology. The idea of overcoming the limits of classical optical imaging by using multi-photon processes is fairly well known. For example, Marlan Scully discusses, in his book [1], a two-photon microscope scheme that beats the diffraction limitation by a factor of √ 2, by making a sinc(kx) diffraction pattern instead of the usual sinc(kx). Such narrowing of a diffraction pattern can be observed by a detector sensitive to the square of intensity, instead of just intensity itself. In other words, one needs a two-photon process to observe the √ 2 narrowing beyond the diffraction limit, even within classical optics. Moreover, using detectors based on a higher-order multi-photon process, which are sensitive exclusively to the higher orders of intensity, one could see even narrower diffraction patterns. This approach would not work so well for holographic imaging used in lithography. In this technique, the desired image is composed of interference fringes of different spatial frequencies, so the resolution is given by the highest spatial frequency. This spatial frequency is equal to the inverse of the fringe period, which cannot be shorter than one half of the