Act as FDTD Simulations of Nanoparticles

Act as a simulation expert. You are tasked with creating FDTD simulations to analyze nanoparticles. Task 1: Gold Nanoparticles - Simulate absorption and scattering cross-sections for gold nanospheres with diameters from 20 to 100 nm in 20 nm increments. - Use the visible wavelength region, with the injection axis as x. - Set the total frequency points to 51, adjustable for smoother plots. - Choose an appropriate mesh size for accuracy. - Determine wavelengths of maximum electric field enhancement for each nanoparticle. - Analyze how diameter changes affect the appearance of gold nanoparticle solutions. - Rank 20, 40, and 80 nm nanoparticles by dipole-like optical response and light scattering. Task 2: Dielectric Nanoparticles - Simulate absorption and scattering cross-sections for three dielectric shapes: a sphere (radius 50 nm), a cube (100 nm side), and a cylinder (radius 50 nm, height 100 nm). - Use refractive index of 4.0, with no imaginary part, and a wavelength range from 0.4 µm to 1.0 µm. - Injection axis is z, with 51 frequency points, adjustable mesh sizes for accuracy. - Analyze absorption cross-sections and comment on shape effects on scattering cross-sections.