I still fondly remember the first time I learned of the connection between Snell’s law of refraction, and Fermat’s principle of least time. From that day forth, I looked at Snell’s law in a new and more general light, namely as one of many manifestations of extremum principles in physics.

Upon reading the Spotlighted article by Courtial and Tyc, together with the associated references, I find myself again learning to see Snell’s law in a new and more general light, namely as a subset of the “generalized laws of refraction” mentioned in the title to the paper.

The authors consider the generalized law of refraction in the setting of the constraints which wave optics places upon ray optics. Away from phase singularities, a monochromatic scalar electromagnetic wave with well-behaved phase phi (proportional to the ray eikonal S) will be locally planar, with the unit-vector light direction s given by the gradient of the eikonal. Taking the curl of the resulting expression s = grad S leads to the result that the ray-field s is curl-free; ray-fields s which meet this condition are termed “wave-optically allowed light-ray fields”. Conversely, “wave-optically forbidden light-ray fields” are those which violate the condition that the ray field s be curl free.

The intriguing possibility of generalized laws of refraction which do not preserve the zero curl of s is raised, in the context of earlier work in this field, together with the possible utility of the concept of generalized refraction to the important technological problem of how to couple light both into and out of silicon. Connections are drawn between these ideas and the concept of metamaterials in optics. This article has opened my mind, for example, to the idea of refraction between media with the same refractive index n which are separated by a planar interface, with plane waves incident upon such interfaces being refracted through non-zero angles and the associated phase fronts being discontinuous across the said interface. To learn about these and other intriguing possibilities in the world of generalized refraction, I warmly recommend this important and stimulating article to your attention.

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