Traditional and new simulation techniques for plasmon nanoparticles and photonic crystals

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.