Mie Scattering Polar Pattern (2D)

Real Mie theory, computed live and drawn flat: a dielectric nanosphere's electric and magnetic dipole scattering coefficients (a₁, b₁) are calculated from exact Riccati-Bessel functions on every parameter change, then combined into the true angular scattering-intensity formula and traced as a 2D polar curve I(θ) around the particle. Because the pattern is symmetric about the incident-beam axis, this single polar slice is exactly as complete as the full 3D lobe — nothing is approximated away. Drag the radius, wavelength and refractive-index sliders and watch the lobe reshape in real time: pushed forward when the electric and magnetic dipoles interfere constructively (the first Kerker condition), or pushed backward when they interfere destructively (anti-Kerker). This directional, loss-free scattering from a single sub-wavelength dielectric particle is the foundation of modern all-dielectric nanophotonics: Huygens' metasurfaces, high-index antireflection coatings and directional nanoantennas all exploit exactly this a₁/b₁ interplay.