Transformation Optics
coordinate folding · invisibility · Maxwell in curved space
Physics: Transformation optics: Maxwell's equations are form-invariant under coordinate transformations. If we compress/stretch space, the material parameters transform as ε'ᵢⱼ = Λᵢₖεₖₗ(Λᵀ)ₗⱼ/det(Λ) (same for μ). Cylindrical cloak: coordinate map r' = R₁ + (R₂−R₁)r/R₂ squeezes the interior of a shell, making light avoid the inner region. Required material: extreme anisotropy — ε_r = μ_r = (R₂−R₁)/R₂·(r−R₁)/r at radius r. Pendry and Leonhardt independently published (Science 2006); microwave cloak demonstrated same year by Schurig et al. Perfect cloak: zero scattering at design frequency; bandwidth limited by causality.