summary:

Show description

In the following, we will use the notation EP for the first partial derivative with time, @E/@t, and ER D @2 E/@t 2 for the 11 12 1 Preliminaries second partial derivative. 50) are referred to as the inhomogeneous Maxwell’s equations since they contain the electric charge density and the current density, while the other two are called the homogeneous Maxwell’s equations. E and B are functions of three spatial coordinates (for example, the Cartesian coordinates x, y and z) and the time coordinate t.

In its integral form, one can express the second of Maxwell’s equations as “ Z D da D dV D q . 5. q is the electrical charge contained in the integration volume. For decreasing dimensions of the integration volume (and surface, respectively), q is approximated by the surface charge σ at the interface. One can then argue that at the interface of two dielectric media, the extension of surface charges into the media is so small that for Δz ! 0, the amount of surface charge between two dielectric media σ !

37 after a distance of z1/e D λ/2π. For example, if λ D 633 nm, then z1/e 100 nm. In other words, with conventional imaging optics and macroscopic working distances, it is not possible to resolve such fine structures. Near-field microscopy is a technique to collect the evanescent wave field by a tapered optical fiber used as a nanoscale probe. H. Synge in the 1920s and first demonstrated at visible wavelengths in the 1980s. NSOM (for near-field optical scanning microscopy, also known under the acronym SNOM for scanning near-field microscopy) can improve the classical resolution limit by one to two orders of magnitude.