Theory of Near‐field Optical Imaging with a Single Molecule as Light Source

Abstract

Scanning near-field optical microscopes (SNOM) illuminate a sample in the very near-field using a nanometer sized tip. Ideally, the light source should be point-like and many efforts have been made to optimize tip efficiency (see, for example, the article of Heimel et al in this issue). Very recently, Sandoghdar et al have realized a molecular probe tip in which a terrylene molecule inserted in a paraterphenyl microcrystal is attached at the extremity of the probe tip [1]. The excited molecule behaves as a point-like light source which is raster scanned over an aluminium patterned structure. We propose here an analysis of this experiment based on the field-susceptibility formalism (also called Green's Dyadic Method) [2,3]. In particular, in strong analogy with the Scanning Tunneling Microscope (STM), we will show that the detected signal is proportional to the Local Density of photonic States (LDOS) available at the immediate proximity of the sample. The molecular light source behaves as a dipole p(t), located at rtip and oscillating at the wavelength λ0=2π/ω0=630 nm where u is a unit vector that gives the dipole orientation.The electric field E(r,t) created at the point r below the surface by the dipole p(t) is evaluated thanks to the field-susceptibility S(r,rtip,ω) associated to the experimental geometry Then, the detected signal is the intensity scattered in the solid angle Ω below the surface (see figure 1) Additionally, we demonstrate that for large angle of detection, this signal is directly proportional to the partial LDOS nu(rtip,ω0) [2,3] where the partial LDOS nu(rtip,ω0) depends on the orientation u as following [3] We also propose a simple interpretation of the relationship between the LDOS and the detected signal in strong analogy with the STM [3]. This analogy can be made thanks to the equivalency between the illuminating mode SNOM and a particular collecting mode configuration [3,4]. Finally, the experiment realized by Sandoghdar et al is analysed both numerically and theoretically [1,3]. Moreover, the concept of optical corrals is introduced [5].