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arXiv:quant-ph/0411163 · Optics Express

Quantum lithography by coherent control of classical light pulses

Avi Pe’er, Barak Dayan, Marija Vucelja, Yaron R. Silberberg, Asher A. Friesem

Published Jan 1, 2004• 55 citations
arXivHTMLPDF

Abstract

The smallest spot in optical lithography and microscopy is generally limited by diffraction. Quantum lithography, which utilizes interference between groups of N entangled photons, was recently proposed to beat the diffraction limit by a factor N. Here we propose a simple method to obtain N photons interference with classical pulses that excite a narrow multiphoton transition, thus shifting the "quantum weight" from the electromagnetic field to the lithographic material. We show how a practical complete lithographic scheme can be developed and demonstrate the underlying principles experimentally by two-photon interference in atomic Rubidium, to obtain focal spots that beat the diffraction limit by a factor of 2.

DOI
10.1364/opex.12.006600

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The smallest spot in optical lithography and microscopy is generally limited by diffraction. Quantum lithography, which utilizes interference between groups of N entangled photons, was recently proposed to beat the diffraction limit by a factor N. Here we propose a simple method to obtain N photons interference with classical pulses that excite a narrow multiphoton transition, thus shifting the "quantum weight" from the electromagnetic field to the lithographic material. We show how a practical complete lithographic scheme can be developed and demonstrate the underlying principles experimentally by two-photon interference in atomic Rubidium, to obtain focal spots that beat the diffraction limit by a factor of 2.
Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.
We have learnt in Chapter 5 how to reduce fluctuations of an electromagnetic (EM) field below the quantum (Heisenberg) limit imposed by the quantum nature of light. It has been shown that the quantum limit can be beaten using non-classical squeezed light of reduced fluctuations. Another issue of significant interest in quantum optics is to beat the diffraction limit imposed on the resolution of measured objects by the wave nature of light. In this chapter, we will illustrate how one can beat the diffraction limit by using the quantumnature of entangled light beams.We shall see that entangled light can lead us to a new domain of quantum optics in which detectors can resolve two closely spaced objects or spectral lines with the minimal resolvable limit significantly reduced or even completely suppressed. This subject is generally known as quantum optical lithography and could be described in short as the ability to print patterns onto certain materials using non-classical light. The developments in this area are of fundamental interest, and they hold promise for advances in optical interferometry and in applications such as quantummetrology and gravitational wave studies.
The working principle of quantum lithography has been demonstrated a few years ago: entangled N-photon systems can improve the spatial resolution of an imaging system by a factor of N, despite the classical Rayleigh limit. Recently, a number of experiments successfully simulated certain features of quantum imaging and two-photon interference-diffraction by using chaotic light in coincidence detection experiments. Can classical light simulate the effect of imaging type quantum lithography? This article attempts to provide an answer to this currently debated question.
We show how to achieve subwavelength diffraction and imaging with classical light, previously thought to require quantum fields. By correlating wave vector and frequency in a narrow band, multiphoton detection process that uses Doppleron-type resonances, we show how to achieve arbitrary focal and image plane patterning with classical laser light at submultiples of the Rayleigh limit, with high efficiency, visibility, and spatial coherence. A frequency-selective measurement process thus allows one to simulate, semiclassically, the path-number correlations that distinguish a quantum entangled field.