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Physical Review A

Quantum lithography with classical light: Generation of arbitrary patterns

Qingqing Sun, Philip Hemmer, Muhammad Suhail Zubairy

Published Jun 27, 2007• 34 citations
Publisher

Abstract

Based on our previous scheme [Hemmer et al., Phys. Rev. Lett. 96, 163603 (2006)] we show the procedures to obtain any one- or two-dimensional pattern by multiple exposures. A key modification to the resonance condition is made to achieve subwavelength pattern resolution. The level separation of the substrate does not pose an upper limit to the frequency summation. So the fundamental frequency can be high and the number of Fourier terms can be large, making our scheme very suitable for subwavelength arbitrary patterns.

DOI
10.1103/physreva.75.065803

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Based on our previous scheme [Hemmer et al., Phys. Rev. Lett. 96, 163603 (2006)] we show the procedures to obtain any one- or two-dimensional pattern by multiple exposures. A key modification to the resonance condition is made to achieve subwavelength pattern resolution. The level separation of the substrate does not pose an upper limit to the frequency summation. So the fundamental frequency can be high and the number of Fourier terms can be large, making our scheme very suitable for subwavelength arbitrary patterns.
The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.
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.
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.
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.
The resolution of an interferometric optical lithography system is about the half wavelength of the illumination light. We proposed a method based on Doppleron resonance to achieve a resolution beyond half wavelength [Phys. Rev. Lett. 96, 163603 (2006)]. Here, we analyze a possible experimental demonstration of this method in the negatively charged silicon-vacancy (${\mathrm{SiV}}^{\ensuremath{-}}$) system by considering realistic experimental parameters. Our results show that quarter wavelength resolution and beyond can be achieved in this system even in room temperature without using perturbation theory.