Integral equations applied to wave propagation in two dimensions: modeling the tip of a near-field scanning optical microscope

Abstract

We present a Green's-function/Green's-theorem integral equation approach to numerically modeling two-dimensional, s-polarized, wave propagation problems effectively for a variety of geometries. The model accurately calculates both near fields and far fields because of the minimal assumptions made on the behavior of the scattered radiation. The method was applied to modeling light emission from a near-field scanning optical microscope fiber tip. Several convergence and energy tests were used to give confidence in the results. The behavior of intensity and power near the tip was investigated. The effects of changing the dielectric constant of a sample material located below the tip were also examined.

Degree of polarization in light transmission through a near-field probe

“…None of the regions in the fibre-tip model is closed. However, to employ the boundary-integral method, the domains must to be closed and for this we adopt the following procedures [6]: the boundaries separating regions 1 and 2, and regions 2 and 4, are extended from x = −R to −∞. Similarly, the boundaries separating regions 1 and 3, and 3 and 4, are extended from x = +R to +∞.…”

“…In this paper we analyse the changes in the partial polarization of light fields in transmission through a near-field probe. We apply the boundary-integral method to rigorously propagate the electromagnetic field through a two-dimensional metal-coated fibre tip used as a model for the near-field probe [6]. In particular, we investigate the influence of the tip's opening angle and the size of the output aperture on the polarization state of the transmitted light using the recently introduced three-dimensional degree of polarization.…”

Quasi-linearly polarized hybrid modes in tapered and metal-coated tips with circular apertures: understanding the functionality of aperture tips

“…Figure 1 illustrates the schematics of the aperture tip that is a tapered and metal-coated fiber where a small aperture is made at the end for light transmission or collection. Many studies have been carried out to explain the light transmission or detection processes with aperture SNOM tips [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For example, dipole and multipole models has been widely used for describing the diffracted fields through the sub-wavelength circular aperture of SNOM tips [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…One can also assume the aperture tip as a point like source and thus represent it by a simple electric dipole [17][18][19][20]. By using numerical methods such as multiple multipole [21,22] and finite difference time domain (FDTD) [23,24], one can accurately calculate electromagnetic fields not only at the aperture plane of the tip but also outside the tip including the influence of the sample surface and particles. However, numerical methods and dipole approximations do not offer detailed understanding of the evolution of modes in the aperture tip and the change of field components during the propagation toward the aperture.…”

Intermode conversion in a near-field optical fiber probe

“…Novotny, Pohl, and Regli have used a multiple-multipole method to simulate the near-field region of a two-dimensional tip, 11 which was then extended to three-dimensional calculations. 18 Analytical consideration of the problem was restricted mainly by the idealized model of a tip coated with a perfect conductor (see, e.g., Ref. 14-16 A system of two coupled differential equations for incident and reflected HE 11 modes in the tapered tip has been numerically solved in Ref.…”