In contrast with aperture-<i>limited</i> Scanning Near-field Optical Microscopy, where the focusing of light is achieved only with very high attenuation, in aperture<i>less</i> near-field optics light is both focused <i>and strongly amplified</i> by the surface plasmons of the probe. Although the general feasibility of this idea and the unprecedented in optics lateral resolution of ~ 15-30 nm have already been demonstrated, the actual field enhancement has so far been well below theoretical expectations, and the useful optical signals have been weak. To bridge the gap between the "proof-of-concept" experiments and reliable optical microscopy with molecular-scale resolution, one needs to unify accurate simulation with effective measurements of the optical properties of the tips and with fabrication. We use dark-field microscopy with side collecting optics for measurements of the optical properties of the tip. The side view allows us to observe the radiation of the tip and hence to analyze its optical properties at the apex. In addition, the measured Raman signal provides an estimate of the electric field enhancement by the tip. Our simulation protocol consists of two parts: electrostatics and wave analysis. Electrostatic simulations give good qualitative predictions, are very fast and therefore conducive to multiparametric optimization. Full wave analysis is needed to evaluate the dephasing effects and far-field signals. The Finite Element Method is used for
all simulations. Various tip designs with the field enhancement ranging from ~ 50 to over 250 (depending on various parameters),
with the commensurate enhancement of the Raman signal by ~ 45<sup>4</sup> (for gold coating) and ~ 270<sup>4</sup> (for silver coating), are presented and analyzed.
The paper briefly reviews existing computational techniques for electromagnetic wave propagation at optical frequencies (Discrete Dipole Approximation, the T-matrix - Extended Boundary Condition methods, the Multiple Multipole Method, Finite Difference (FD) and Finite Element (FE) Methods), and contributes to the development of FD
methods. The overall objective is to put together a set of complementary tools for simulations in nanoscale photonics. One powerful tool - FE analysis - is applied to optimization of plasmon-enhanced AFM tips in apertureless near-field optical microscopy. Another tool is a new FD calculus of "Flexible Local Approximation MEthods" (FLAME). In this calculus, any desirable local approximations (e.g. scalar and vector spherical harmonics, Bessel functions, plane waves, etc.) are seamlessly incorporated into FD schemes. FLAME achieves a remarkable accuracy improvement, as compared
to FEM, for problems with cylindrical and spherical plasmon nanoparticles and for a photonic crystal with an array of cylindrical rods and a waveguide bend.
The local electric field enhancement in the vicinity of a metal-coated or metal tip is a significant factor in the performance of apertureless near-field optical microscopy and spectroscopy techniques. Enhancement, which is related to the generation of localized surface plasmons in the metal tip, can be maximized when the plasmons resonate at the probing wavelength. Thus the resonance frequencies of the tip apex are crucial to near-field optics. However, it remains a challenge to measure the optical properties of the apex of a tip with a radius much smaller than the wavelength of light. A dark-field scattering spectroscopy method is presented in combination with a side-illumination nano-Raman spectrometer to experimentally determine the optical properties of the tip. The dependence of the optical resonance on the metal deposited is shown for silver- and gold-coated tungsten tips as well as gold-coated silicon nitride tips. The enhancement for Si using gold-coated silicon nitride tips is somewhat larger for a wavelength of 647 nm than for a wavelength of 514.5 nm. The former is closer to the plasmon resonance observed for this tip at ~680 nm.
Several classes of computational methods are available for computer simulation of electromagnetic wave propagation and scattering at optical frequencies: Discrete Dipole Approximation, the T-matrix - Extended Boundary Condition methods, the Multiple Multipole Method, Finite Difference (FD) and Finite Element (FE) methods in the time and frequency domain, and others. The paper briefly reviews the relative advantages and disadvantages of these simulation tools and contributes to the development of FD methods. One powerful tool - FE analysis - is applied to optimization of plasmon-enhanced AFM tips in apertureless near-field optical microscopy. Another tool is a new FD calculus of "Flexible Local Approximation MEthods" (FLAME). In this calculus, any desirable local approximations (e.g. scalar and vector spherical harmonics, Bessel functions, plane waves, etc.) are seamlessly incorporated into FD schemes. The notorious 'staircase' effect for slanted and curved boundaries on a Cartesian grid is in many cases eliminated - not because the boundary is approximated geometrically on a fine grid but because the solution is approximated algebraically by suitable basis functions. Illustrative examples include problems with plasmon nanoparticles and a photonic crystal with a waveguide bend; FLAME achieves orders of magnitude higher accuracy than the standard FD methods, and even than FEM.