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Sagnac Interferometer

Rotation-induced phase shift in optical loops

Ring Interferometer

Clockwise beam
Counter-clockwise beam
Interference pattern

Interference Fringes

Sensitivity Curve

Phase shift Δφ: -
Fringe shift: -
Time difference Δt: -
Path difference ΔL: -
Earth rotation (≈Ω): 7.3×10⁻⁵ rad/s

The Sagnac Effect

First demonstrated by Georges Sagnac in 1913, this effect shows that two light beams traveling in opposite directions around a rotating loop accumulate different phases. When the interferometer rotates, one beam travels a slightly longer path (co-rotating) while the other travels shorter (counter-rotating), producing a measurable phase difference.

Δφ = (8πAΩ) / (λc) = (4πNRLΩ) / (λc)   where A = loop area, N = number of loops

This principle is used in ring laser gyroscopes (RLGs) and fiber optic gyroscopes (FOGs) for precision navigation in aircraft, submarines, and spacecraft. The sensitivity scales with the enclosed area (A = πR²N), making fiber optic coils with many loops extremely sensitive.