We use a quantum mechanical model to study electron energy-loss spectroscopy (EELS) from
crystalline noble metal films, revealing intrinsic features associated with their crystallographic orientation.
Within the random-phase approximation, we employ a 1-D potential across the film that captures the main
features of the electronic band structure of such different surfaces, including the electron-spill out and bulk
atomic-plane corrugation. Additionally, we examine the role of vertical transitions among quantum well states,
severely affected by their in-plane effective mass.
A gap plasmon is an electromagnetic wave propagating in a gap between two noble metal surfaces. Such gap plasmons have previously been studied using only a classical description of the noble metals, but this model fails and shows unphysical behavior for sub-nanometer gaps. To overcome this problem quantum spill-out is included in this paper by applying Density-Functional Theory (DFT), such that the electron density is smooth across the interfaces between metal and air. The mode index of a gap plasmon propagating in the gap between the two metal surfaces is calculated from the smooth electron density, and in the limit of vanishing gap width the mode index is found to converge properly to the refractive index of bulk metal. When neglecting quantum spill out in this limit the mode index shows unphysical behavior and diverges instead.
The mode index is applied to calculate the reflectance of an ultrasharp groove array in silver, as gaps of a few nm are found in the bottom of such grooves. At these positions the gap plasmon field is highly delocalized implying that it mostly exists in the bulk silver region where absorption takes place. Surprisingly, when the bottom width
is a few nm and the effect of spill out at a first glance seems to be negligible, strong absorption is found to take place 1-2 Å from the groove walls as a consequence of the dielectric function being almost zero at these positions. Hence quantum spill out is found to significantly lower the reflectance of such groove arrays in silver.
This paper theoretically studies how the optics of multiple grooves in a metal change as the number of grooves gradually increased from a single groove to infinitely many arranged in a periodic array. In the case of a single groove, the out-of-plane scattering (OUP) cross section at resonance can significantly exceed the groove width. On the other hand, a periodic array of identical grooves behaves radically different and is a near-perfect absorber at the same wavelength. When illuminating multiple grooves with a plane wave, the OUP cross section is found to scale roughly linearly with the number of grooves and is comparable with the physical array width even for widths of many wavelengths. The normalized OUP cross section per groove even exceeds that of a single groove, which is explained as a consequence of surface plasmon polaritons generated at one groove being scattered out of the plane by other grooves. In the case of illuminating instead with a Gaussian beam and observing the limit as the incident beam narrows and is confined within the multiple-groove array, it is found that the total reflectance becomes very low and that there is practically no OUP. The well-known result for periodic arrays is thus recovered. All calculations were carried out using Green’s function surface integral equation methods taking advantage of the periodic nature of the structures. Both rectangular and tapered grooves are considered.
This paper studies theoretically how the optics of multiple grooves in a metal change as the number of grooves is increased gradually from a single groove to infinitely many arranged in a periodic array. In the case of a single groove the out-of-plane scattering (OUP) cross section at resonance can significantly exceed the groove width. On the other hand a periodic array of identical grooves behaves radically different and is a near-perfect absorber at the same wavelength. When illuminating multiple grooves with a plane wave the OUP cross section is found to scale roughly linearly with the number of grooves and is comparable to the physical array width even for widths of many wavelengths. The normalized OUP cross section per groove even exceeds that of a single groove, which is explained as a consequence of surface plasmon polaritons generated at one groove being scattered out-of-the-plane by other grooves. In the case of illuminating instead with a Gaussian beam, and observing the limit as the incident beam narrows and is confined within the multiple-groove array, it is found that the total reflectance becomes very low and that there is practically no out-of-plane scattering. The well-known result for periodic arrays is thus recovered. All calculations were carried out using Greens function surface integral equation methods taking advantage of the periodic nature of the structures. Both rectangular and tapered grooves are considered.
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