Attribution of Fano resonant features to plasmonic particle size, lattice constant, and dielectric wavenumber in square nanoparticle lattices
Spotlight summary: If you’re a regular reader of Spotlight on Optics, you’ve seen a lot about optical resonances. Many materials can support energy levels above their ground states, whether the energy is vibrational, rotational, photonic, or electronic. In most cases, physicists model energy states as harmonic oscillators, similar to a mass on a spring. If we try to drive a mass-spring energy system by oscillating it, we find that it only accepts energy at a narrow range of frequencies. If we drive it too quickly or too slowly, the spring never builds up a strong oscillation. The range of frequencies over which a spring will store energy depends on the mass, the stiffness of the spring, and the damping – that is, the rate at which energy is lost to the environment as heat or sound. Generally, more damping implies a wide range of possible excitation frequencies, which we refer to as a broad resonance, and less damping conversely implies a narrow resonance, which only accepts a thin band of frequencies.
If we graph the response of an oscillator like a spring versus the driving frequency, we always end up with a peaked function called a Lorentzian, which is fully described by its center location, its height, and its width. But in 1961, Ugo Fano found that in some cases, a broad resonance can overlap with a narrow resonance, and the two Lorentzian lineshapes interfere with one another. The result is a characteristically asymmetric response that dips down on one side. These so-called Fano resonances can be useful, because they tend to be very sensitive to their environment. By tracking the location and shape of a Fano resonance, systems can be used as sensitive detectors, for example.
The presence of Fano resonances has been well known in atomic systems for a long time. In that case, the resonances are electronic: electrons can only be excited to higher energy levels at certain frequency bands. If multiple excitations are attempted at the same time, the resonances can interfere and produce Fano lineshapes. But recently, Fano resonances have been observed in arrays of nanoscopic metal particles, called plasmonic arrays. The particles are typically tens of nanometers in diameter and can take on any shape, but spheres and discs are common, since they are relatively easy to fabricate and model mathematically. While Fano resonances have been observed in these arrays, it is not clear exactly how to design arrays to exhibit specific resonance behavior, due to the complexity of the calculation.
In this paper, DeJarnette et al. model arrays of spherical nanoparticles, leaving the diameter and spacing of the particles as free parameters, as well as the medium in which they are immersed. They make the calculation easier by combining analytical methods (in which the equations for the optical response of materials is written out as a function) and numerical methods (in which the problem is laid out as a series of single calculations with no functions and carried out approximately). This combination of two methods can be extremely powerful for nano-sized systems, since they often straddle the boundary between classical and quantum physics, and combine distances scales between microns and nanometers.
The authors find that not all arrays support Fano resonances, but that there are certain ranges of parameters that do. In particular, they reach four major conclusions. First, the presence and frequencies of Fano resonances are affected strongly by the material in which the nanoparticles are suspended. Second, the higher the index of refraction of the materials, the lower energy the Fano resonances, and the broader they become. Third, the Fano resonance is much more sensitive to the refractive index than other kinds of material resonances. Specifically, they compared it to plasmonic (electronic) resonances, and dipole (optical) resonances, and found it to be about 15 times more sensitive to the refractive index. Finally, they find that their method has the ability to maximize Fano sensitivity. That is, by choosing parameters correctly, they believe they can design arrays that will act as sensors with excellent sensitivity.
ToC Category: Plasmonics
|OCIS Codes:||(290.5850) Scattering : Scattering, particles|
|(050.1755) Diffraction and gratings : Computational electromagnetic methods|
|(230.5298) Optical devices : Photonic crystals|
|(250.5403) Optoelectronics : Plasmonics|
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