Theory of Attenuated Total Reflection Including Effects of Roughness

Abstract

We have developed a theory of attenuated total reflection applicable to multi-layered samples with roughness at surfaces and/or interfaces. Angle dependence of reflectivity for incident light with any polarization are expressed by a power series of profile functions of roughness, and the terms up to the second order polynomials of the profile functions are presented. Numerical analyses for Au films in the Kretschmann configuration reveal that differences between the predictions taking into account roughness and the ones assuming flat interfaces depend on both lateral and longitudinal sizes of roughness, and that the differences becomes not negligible for roughness greater than a certain level, e.g., roughness whose correlation length a and root-mean-square δ of the amplitude are 20 and 2 nm, respectively.

Efficient Surface Plasmon Polariton Excitation and Control over Outcoupling Mechanisms in Metal–Insulator–Metal Tunneling Junctions

“…To demonstrate how the outcoupling of the MIM‐SPP mode can be affected by surface roughness and changes in t eff , we simulated the mode profile for MIM‐TJ structures with changes in the topography of the electrodes that represent various types of defects (see Section S4.4, Supporting Information for simulation details). Modeling roughness for highly confined plasmonic systems is notoriously complex due to nanoscale mode profiles 50,64. Here, we only aim to show how a variety of local features in the electrode topography can affect the MIM‐SPP outcoupling pathways and improve the outcoupling efficiencies to the bound‐SPP modes.…”

“…Mode overlap is only efficient when the thickness of the electrode t m is on the order of the δ MIM ,48,49 and even then requires a roughened topography to momentum match. Surface roughness enables momentum‐matching of the MIM‐SPP mode and the daughter mode by modifying the local permittivity ε m ′ (as a function of frequency ω) by ε m ′ (ω, σ m ) = ε m (ω) + δε m (ω, σ m ) where δε m is the local perturbation to ε m which modifies the local electromagnetic environment 50–52. Dawson et al22 calculated that, for Al‐AlO x ‐Au MIM‐TJs, the ideal σ m for the most efficient out‐coupling of the MIM‐SPP mode to photons is σ m ≈5 nm 22,26.…”