Electromagnetic transmission of nanometric circular aperture on top of a metal coated optical fiber tip: Theory

Abstract

Within the framework of the direct moment method, a theory for calculating the optical transmission of nanometric circular aperture on top of a metal coated optical fiber tip is developed. The primary purpose of the study is to estimate transmission efficiency of near field probes widely used in near field scanning optical microscopy. Field distributions immediately after the aperture in the core and cladding of the fiber tip can be accurately calculated in three dimensions. It turns out that the transmission is a function of many variables, such as the radii of the aperture and fiber core, the thickness of the metallic coat, the material responses in the core and cladding area of the fiber, and finally the light frequency.

On the coupling efficiency of metal‐coated near‐field probes

“…A theory has been developed analogous to that of Roberts, that even though it retains some of the usual assumptions of the models of transmission through circular apertures, it also includes the geometry of the fibre tip, making it possible to calculate both aperture and guided transmission coefficients. This theory was described in a previous article (Alvarez & Xiao, 2000). Figure 2 shows the geometry in which the theory is based.…”

“…The parameters Y k Λ ( α,β ), Y j Π , Y k Ω ( ξ ), and Y k Γ , are the transversal admittances of the mode in the case when the mode can be described as TE or TM polarized (all modes of zone 1 and zone 2, and some of zone 3). The actual form of the three sets of modes can be found in a previous publication (Alvarez & Xiao, 2000).…”

Theoretical and Experimental Study on Optical Near and Far Field Transmission of Thin Metallic Films With Randomly Distributed Subwavelength Holes

“…12 we presented the details of the modes. Two boundary conditions can be matched at the exit and entrance of the aperture respectively.…”

“…(1), (2) and (3) be solved from the two infinite matrix equations obtained from the two boundary conditions. 12 In computation, the dimension of the matrix is truncated when further including elements does not bring out significant changes in the final results. For example, in the calculations we present in this paper, we included about 250 to 300 guided modes and found that including more modes would bring about only insignificant changes (δ < 0.1%).…”

“…12,13 The theory is established within the framework of the direct moment method (DMM). 14 In the theory, all the field components are included properly, especially the evanescent modes.…”