# 法拉第旋转 — 磁光效应

线偏振光沿磁场方向传播时偏振面旋转 β = V·B·L。调节 B、L 和介质，观察偏振螺旋的缠绕、β-B 直线，以及支撑光学隔离器的非互易双程旋转。

> 标准页面: https://elysiatools.com/zh/visualizations/faraday-rotation

- **分类:** Physics

## 概述

Interactive Faraday rotation (magneto-optic effect) visualization. When linearly polarized light propagates along a magnetic field B through a medium of length L, its polarization plane rotates by β = V·B·L, where V is the material's Verdet constant (rad/(T·m)). Microscopically B makes the medium circularly birefringent (left/right circular eigenwaves travel at different speeds n₊/n₋), so β = π L (n₋−n₊)/λ. The defining NONRECIPROCAL property: the rotation sense is fixed by B, not by the propagation direction, so a round trip adds another +β (total 2β) instead of canceling — this is what powers optical isolators and distinguishes Faraday rotation from reciprocal optical activity (sugar solution, which cancels to 0 on return). Three visualization panels: (1) Main animated scene showing the magnetized medium block (cyan) with the E-field vector (green) rotating steadily along the optical axis, its tip tracing a 3D-projected polarization helix whose total twist is β = VBL; B-field arrows (purple) along the beam; input E-vector (vertical, 0°) and output E-vector (rotated by β) drawn before and after the block with a live rotation arc annotation. (2) Rotation β vs Field B plot showing the strictly linear law (slope V·L), with ghost curves for all five materials (water/crown/flint/TGG/terbium), the 45° isolator reference line, and the live operating point. (3) Nonreciprocal Double-Pass dial comparison showing single-pass (β), Faraday round-trip (2β, nonreciprocal — does not cancel), and reciprocal optical-activity round-trip (0, cancels) as three polarization needles, illustrating the optical-diode principle. Adjustable parameters: magnetic field B (0–5 T), path length L (0–10 cm), wavelength λ (400–700 nm with V ∝ 1/λ² Becquerel scaling so blue rotates more than red), and medium selection from a library of real Verdet constants — Water (V≈1.6), Crown Glass (V≈3.5), Flint Glass (V≈8), TGG Crystal (V≈40, isolator grade), Terbium Glass (V≈75). Five scenario presets: 45° Isolator (TGG tuned to exactly 45°), Glass Block (weak crown-glass rotation), Water Cell (water needs large B·L), Strong TGG, B=0 (no rotation reference). Real-time statistics: rotation β (°), Verdet constant V, round-trip 2β (°), and the B required to reach 45° isolator angle. Educational content covers the Faraday law β=VBL and circular-birefringence mechanism (Faraday 1845), the nonreciprocal optical-diode principle and Faraday isolator design, and applications (interstellar plasma magnetometry via Δβ∝∫nₑB∥dl/λ² mapping Galactic magnetic fields, TGG+NdFeB laser isolators, fiber-optic current/field sensors and gyroscopes, magneto-optical recording, fusion-plasma electron-density diagnostics). Multi-language support (zh, en, es, fr, de, ru, pt).

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