Discrete dipole approximation with surface interaction

Abstract

In this chapter, we discuss a methodology to determine absorption and scattering cross sections of particles of different size and shape placed on substrates. This approach is based on the principles of discrete dipole approximation (DDA); however, the interaction matrix between the dipoles is modified to include the effect of the semiinfinite surface by including dipole reflections represented by Sommerfeld integrals. Depending on the direction of an incident plane wave, the particle will be illuminated by the combination of the incident wave with the reflected, transmitted, or evanescent wave. In order to explore problems involving nanomanufacturing or sensing, a new DDA-SI algorithm is constructed as an open-source computational toolbox in a MATLAB environment. Later, two other algorithms (DDA-SI-v and zDDA-SI) were developed to increase the speed of calculations. All three algorithms were considered for atomic force microscopy-based manufacturing applications using dielectric and metallic nanoparticles. Examples of different cases are provided at the end of the chapter.