🌊 Electromagnetic Wave & Polarization 3D

Maxwell's equations predict self-sustaining waves in which a changing E field makes B and vice versa. In vacuum E ⟂ B ⟂ direction of travel, |B| = |E|/c, and they travel at c = 299,792,458 m/s. Here the wave travels along z with Eₓ = E₀ₓ cos(kz − ωt) and E_y = E₀ᵧ cos(kz − ωt + δ).

• Polarization: δ = 0° or 180° → linear; equal amplitudes with δ = ±90° → circular; anything else → elliptical. The tilt ψ and ellipticity χ come from the Stokes parameters: S₀ = Eₓ² + E_y², S₁ = Eₓ² − E_y², S₂ = 2EₓE_y cos δ, S₃ = 2EₓE_y sin δ, tan 2ψ = S₂/S₁, sin 2χ = S₃/S₀. Handedness is labelled from S₃ (positive = left-handed seen from the receiver, IEEE convention differs — the sign is shown so you can map it).
• Polarizer: an ideal linear polarizer at angle θ passes the component of E along its axis. For linear light this gives Malus's law I = I₀ cos²(θ − ψ); circular light always passes 50 %. The general result used here is I/I₀ = ½(1 + (S₁ cos 2θ + S₂ sin 2θ)/S₀).
• Field strength: for intensity I, E₀ = √(2I / (c ε₀)) and B₀ = E₀ / c. Sunlight at ~1000 W/m² has E₀ ≈ 868 V/m.
• Photons: E = h f = h c / λ, h = 6.62607015×10⁻³⁴ J·s; flux = I / E_photon; radiation pressure on an absorber = I / c.