Light, EM Waves, and Beam Transport

Stub. Full prose lives in STUDY_PLAN.md §Week 1. Will be filled in following the Week 0 pattern.

Goals

• Know Maxwell's four equations and what each one physically says.
• Derive the EM wave equation in vacuum.
• Understand polarization, reflection, refraction — the physics behind every NIF mirror and the Pockels cell.

Master equations

Maxwell's equations (vacuum, SI):

$\nabla \cdot \mathbf{E} = \rho/\varepsilon_0 \qquad \nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{E} = -\partial_t \mathbf{B} \qquad \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0\,\partial_t \mathbf{E}$

EM wave equation (vacuum, no sources):

$\nabla^2 \mathbf{E} - \tfrac{1}{c^2}\,\partial_t^2 \mathbf{E} = 0$

Brewster's angle (no reflection for p-polarization):

$\theta_B = \arctan(n_2/n_1)$

NIF tie-in

Every mirror in NIF's transport system is polarization-dependent. The Pockels cell (PEPC) works by rotating polarization under an electric field — when off, the cell is transparent to one polarization and the beam passes; when on, it rotates 90° and a downstream polarizer reflects the beam into the main amplifier for another pass. This is how multi-pass amplification is achieved without moving any mirror. The entire gating system is pure Fresnel and Maxwell.

Self-check