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Observing angular deviations in the specular reflection of a light beam


The Law of Reflection of a light ray incident upon a mirror (θin = θout) was first formulated by Euclid around 300 bc in his book Catoptrics1; it has been a tenet of geometrical optics ever since. However, more recently, a small angular deviation of the Law of Reflection has been predicted for a physical light beam when this is regarded as the implementation of a ray2,3,4,5. The deviation is a diffractive consequence of the angular dependence of the reflectivity and should occur for any mirror with less than 100% reflectivity. We report here experimental proof of this angular deviation by determining the direction of an optical beam after reflection from an air–glass interface, using a position detector with nanometre resolution. Our results are relevant for angular metrology in general and cantilever-based surface microscopies in particular. Analogous angular deviations are expected for reflection of acoustic waves and quantum matter waves.

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Figure 1: Schematic representation of non-specular angular reflection.
Figure 2: Experimental set-up.
Figure 3: Angular deviation far from the Brewster angle θB.
Figure 4: Angular deviation near the Brewster angle θB
Figure 5: Verification of the angular nature of the deviation.


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This work was supported by the Netherlands Foundation for Fundamental Research of Matter (FOM) and by the Seventh Framework Programme for Research of the European Commission, under the FET-Open grant agreement HIDEAS, no. FP7-ICT-221906. We acknowledge E.R. Eliel and G.'t Hooft for useful discussions.

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Correspondence to A. Aiello or J. P. Woerdman.

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Merano, M., Aiello, A., van Exter, M. et al. Observing angular deviations in the specular reflection of a light beam. Nature Photon 3, 337–340 (2009).

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