Plasmonic metamaterials for ultra-sensitive sensing: topological darkness

Extinction of the reflection of the p-polarized wave by the surface of a semi-infinite transparent medium is a well-known phenomenon exploited in Brewster angle microscopy. For absorbing media, however, described by a complex refractive index of refraction, the Brewster extinction condition does not exist anymore since the real and imaginary parts of the reflection coefficient cannot be canceled simultaneously. The exact zero reflection condition can be restored if a thin film of suitable complex index is deposited on top of a semi-infinite substrate. In such case, whatever the accuracy of the experimental setup, the existence of a true perfect cancelation of the reflection is guaranteed by the Jordan topological theorem. In the immediate vicinity of the zero reflection point, the phase of the reflected wave undergoes an extremely steep variation that enables ultra-sensitive sensing. The existence of a topological darkness condition and its application to the detection of dilute biological molecules were first demonstrated on plasmonic meta-surfaces made of two-dimensional arrays of gold nanopillars deposited on a glass substrate by electron beam lithography. The effective complex refractive index of the homogenized equivalent film indeed satisfies the topological darkness condition. In this paper, we show that several plasmonic systems prepared by the physical chemistry methods of colloids exhibit topological darkness and may provide good substrates for ultra-sensitive sensing at lower cost.