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Physical Review Letters

Quantum Lithography with Classical Light

Philip Hemmer, Ashok Muthukrishnan, Marlan O. Scully, Muhammad Suhail Zubairy

Published Apr 28, 2006• 83 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.96.163603

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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.
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.
I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber or coincidence detection. Using the same nonclassical states of light as those for quantum lithography, the proposed method requires only optical intensity measurements, followed by image postprocessing, to produce the same complex quantum interference patterns as those in quantum lithography. The method is expected to be experimentally realizable using current technology.
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.
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.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.