Metal nanoparticles can effectively convert local changes of refractive index into frequency shifts of their localized surface plasmon resonances. Thus, metal nanoparticles have been successfully applied to achieving high-sensitivity refractive-index sensing. In contrast to the fruitful development in experimental studies, there is a long-standing theoretical unsolved problem attached to the resonance shift of metal nanoparticles induced by small perturbations. The difficulty mainly arises from the absence of a solid theoretical framework being able to handle the computation of the resonance modes of metal nanoparticles. Therefore in the past, theoretical studies of plasmonic sensing have mainly relied on tedious and repeated fully-vectorial electromagnetic simulations.
In the present work [1], we derive a simple albeit intuitive analytical formula to predict accurately both the frequency shift and the broadening of the spectral width of localized surface plasmon resonances induced by small perturbing objects. If we denote by Em and ωres as the resonance mode and complex eigenfrequency of a bare metallic nanoparticle, and denote by Eapp≈Em a slightly modified version of Em that takes into account local field corrections, the expression for complex-valued resonance shift Δωres due to a local permittivity change Δε, can be derived as
Δωres=-ωres∫ΔεEapp• Em dV
where the integral runs over the volume of the perturbing object. Once the resonance mode Em and the complex eigenfrequency ωres are calculated, based on a solid theoretical framework for the modes of lossy resonators [2,3], the shift is known analytically for any shape, size, position or permittivity of the perturbation.
Note that there are several radical differences between the current work and earlier theoretical works. A fundamental one resides in the integrand used, an E•E product instead of an E•E* product. The latter is valid only for very high-Q resonators composed of non-lossy materials, such as photonic crystal cavities, but it cannot be used for metallic nanoresonators with a strong absorption.
At the conference, the high accuracy of the equation for metal resonators of various shapes and sizes, and for perturbations of different sizes and materials or at different locations will be presented.
[1] J.Yang, H.Giessen and P.Lalanne, (under review).
[2] C. Sauvan, et al., Phys. Rev. Lett. 110, 237401 (2013).
[3] Bai, Q. et. al., Opt. Exp. 21, 27371 (2013).
Philippe.Lalanne@institutoptique.fr