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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Limits to the efficiency of quantum lithography

Gunnar G. Bjork, C. Kothe, Mohamed Bourennane, Shuichiro Inoue

Published May 1, 2011• 0 citations
Publisher

Abstract

While it is certainly possible to generate sub wavelength patterns with arbitrary resolution, the exposure efficiency will scale in a very unfortunate manner. The photons in fields with the required N photon entanglement diffract independently, and hence spread out over the exposed area, making the event that all N photons hit the same detector element very rare. If the lithographic film consist of 5 independent detecting elements, then the exposure time τ scale as τ = S~N. For a 500 x 500 pixel image, this means that the exposure time will increase with a factor 250 000 when going from N to N+l photons.

DOI
10.1109/cleoe.2011.5943416

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While it is certainly possible to generate sub wavelength patterns with arbitrary resolution, the exposure efficiency will scale in a very unfortunate manner. The photons in fields with the required N photon entanglement diffract independently, and hence spread out over the exposed area, making the event that all N photons hit the same detector element very rare. If the lithographic film consist of 5 independent detecting elements, then the exposure time τ scale as τ = S~N. For a 500 x 500 pixel image, this means that the exposure time will increase with a factor 250 000 when going from N to N+l photons.
Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. However, in the literature, at least two different theoretical descriptions of quantum lithography exist. They differ in the extent to which they predict that the photons retain spatial correlation from generation to absorption, and although both predict the same feature size, they vastly differ in predicting how efficiently a quantum lithographic pattern can be exposed. Until recently, essentially all quantum lithography experiments have been performed in such a way that it is difficult to distinguish between the two theoretical explanations. However, last year an experiment was performed that gives different outcomes for the two theories. We comment on the experiment and show that the model that fits the data unfortunately indicates that the trade-off between resolution and efficiency in quantum lithography is very unfavourable.
Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. However, in the literature, at least two different theoretical descriptions of quantum lithography exist. They differ in the extent to which they predict that the photons retain spatial correlation from generation to absorption, and although both predict the same feature size, they vastly differ in predicting how efficiently a quantum lithographic pattern can be exposed. Until recently, essentially all quantum lithography experiments have been performed in such a way that it is difficult to distinguish between the two theoretical explanations. However, last year an experiment was performed that gives different outcomes for the two theories. We comment on the experiment and show that the model that fits the data unfortunately indicates that the trade-off between resolution and efficiency in quantum lithography is very unfavourable.
We demonstrate a systematic approach to subwavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of $\ensuremath{\lambda}/[2(N+1)]$ by using a particular 2M-photon, multimode entangled state, where N< M,N<~M,N< M, and banks of birefringent plates. By preparing such a statistically mixed state, one can form any pixel pattern on a ${2}^{M\ensuremath{-}N}(N+1)\ifmmode\times\else\texttimes\fi{}{2}^{M\ensuremath{-}N}(N+1)$ pixel grid occupying a square with side ${L=2}^{M\ensuremath{-}N\ensuremath{-}1}\ensuremath{\lambda}.$ Hence, there is a trade off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under nonideal conditions, albeit with somewhat poorer performance.
As demonstrated in Boto et al. [quant-ph/9912052], quantum lithography offers an increase in resolution without an upper bound. This procedure makes use of the entangled state (| n ,0〉+ e inϕ |0, n 〉)/√2. It allows us to write evenly spaced lines with sub-wavelength resolution. Here we generalise this procedure in such a way that it enables us to create arbitrary patterns in one dimension. We distinguish two methods: the ‘Fourier method’ and ‘the superposition method’. The Fourier method is conceptually easier since it depends on Fourier series, but it also involves a minimal finite amount of unwanted exposure of the substrate. The superposition method gets around this problem and gives generally better results, but lacks the intuitive clarity of the Fourier method. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.