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Quantum Lithography

Pieter Kok, Samuel L. Braunstein, Agedi N. Boto, Daniel S. Abrams, Colin P. Williams, Jonathan P. Dowling

Published Feb 24, 2006• 0 citations

Abstract

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.

DOI: 10.1007/0-306-47114-0_59

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We review our progress toward implementing the proposal of Boto et al. (Phys. Rev. Lett. 85, 2733-2736, 2000) for using entangled photons to increase the spatial resolution of the process of interferometric photolithography beyond that of the standard Rayleigh limit.

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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.

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.

Summary form only given. Recently, Boto et al. (see Phys. Rev. Lett., vol. 85, p. 2773, 2000) showed that using N entangled photons and an N-photon responsive lithographic recording medium, one could potentially write lithographic gratings with a resolution that is N times better than the classical Rayleigh criterion. An anticipated experimental difficulty is that such beams are weak, yet strong fields are needed to excite the N-photon absorption process. For the case of N=2, which was described in detail by Boto et al., we propose a method to overcome this problem. We also propose to use this idea "in reverse" to perform microscopy with better resolution than aloowed by the Rayleigh limit.

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.

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.