Absorption and optimal plasmonic resonances for small ellipsoidal particles in lossy media

Abstract

A new simplified formula is derived for the absorption cross section of small dielectric ellipsoidal particles embedded in lossy media. The new expression leads directly to a closed form solution for the optimal conjugate match with respect to the surrounding medium, i.e., the optimal permittivity of the ellipsoidal particle that maximizes the absorption at any given frequency. This defines the optimal plasmonic resonance for the ellipsoid. The optimal conjugate match represents a metamaterial in the sense that the corresponding optimal permittivity function may have negative real part (inductive properties), and can not in general be implemented as a passive material over a given bandwidth. A necessary and sufficient condition is derived for the feasibility of tuning the Drude model to the optimal conjugate match at a single frequency, and it is found that all the prolate spheroids and some of the (not too flat) oblate spheroids can be tuned into optimal plasmonic resonance at any desired center frequency. Numerical examples are given to illustrate the analysis. Except for the general understanding of plasmonic resonances in lossy media, it is also anticipated that the new results can be useful for feasibility studies with e.g., the radiotherapeutic hyperthermia based methods to treat cancer based on electrophoretic heating in gold nanoparticle suspensions using microwave radiation.

On the quasistatic optimal plasmonic resonances in lossy media

“…The maximal absorption of a small dielectric ellipsoid under the quasistatic approximation can readily be calculated as follows, see also 11,12 . Consider a small, homogeneous and isotropic dielectric ellipsoid with relative permittivity which is embedded in a lossy dielectric background medium with relative permittivity b .…”

“…To this end, it is also interesting to observe that the limit of (11) as (Im{ }, Im{ b }) → (0, 0) will depend on how this limit is taken. In particular, (12) is obtained for fixed (Im{ } > 0) as Im{ b } → 0 and (12) is then unbounded as Im{ } approaches zero. On the other hand, (11) approaches zero for fixed Im{ b } > 0 as Im{ } → 0 (and Re{ } = 0).…”

“…However, there are many application areas of plasmonics where the exterior losses must be taken into account. One potential application in medicine is the localized electrophoretic heating of a bio-targeted and electrically charged gold nanoparticle (GNP) suspension as a radiotherapeutic hyperthermia based method to treat cancer, cf., [8][9][10][11][12] or with the related plasmonic photothermal therapy as proposed in 13 . Other potential application areas include plasmon waveguides, aperture arrays, extraordinary transmission, superlenses, artificial magnetism, negative refractive index, and surface-enhanced biological sensing with molecular monolayer spectroscopy, etc., see e.g., 3 .…”

“…We are also considering only a single electric dipole resonance, and we are discarding any possibilities of having an unbounded absorption due to multiple mode super resolution effects, etc., see e.g., [21][22][23] . A quasistatic theory has been developed in 11,12 giving the optimal plasmonic dipole resonance of small dielectric ellipsoids in terms of an optimal conjugate match with respect to the background loss. However, an important limitation of this theory is that it does not give the correct physical answers when the background becomes lossless or has very small losses.…”

Optical theorems and physical bounds on absorption in lossy media

“…There is a number of application areas where the surrounding losses clearly cannot be neglected. This includes typically medical applications such as localized electrophoretic heating of a bio-targeted and electrically charged gold nanoparticle suspension as a radiotherapeutic hyperthermia-based method to treat cancer, cf., [8][9][10]37,46 . Corresponding applications in the optical domain are concerned with light in biological tissue 11 , and the use of gold nanoparticles for plasmonic photothermal therapy 19 .…”