Unified picture of modal loss rates from microwave to optical frequencies in deep-subwavelength metallic structures: A case study with slot waveguides

Abstract

The behavior of the modal loss rate in deep-subwavelength metallic structures depends strongly on frequency: as the mode size decreases, at optical frequencies, the modal loss rate always increases to the theoretical upper bound Γ/2, whereas at microwave frequencies, it remains far lower than Γ/2, where Γ is the electron collision frequency of the metal. By analyzing the metallic slot waveguide as a model system, we show that these significantly different behaviors of the modal loss rate at optical and microwave frequencies are actually two extreme cases of a single universal behavior. Specifically, we show that as the mode size decreases, the loss rate always plateaus first and then increases to Γ/2, regardless of frequency. The only difference between frequencies is the properties of the plateau: at optical frequencies, the plateau is narrow, allowing the loss rate to reach Γ/2 at a relatively large mode size, whereas at microwave frequencies, the plateau is wide and formed at 13ω, defining a practically attainable maximum loss rate that is far lower than Γ/2.