A Sagnac interferometer sends two light beams around the same closed path in opposite directions. When the platform rotates, the effective path lengths differ slightly, producing a phase shift proportional to the enclosed area A, the angular velocity Ω, the refractive index n of the medium, and inversely to wavelength λ (Δφ = 8π Ω A n / (λ c) for the textbook planar-loop scalar form used on this page). Fiber-optic gyroscopes wrap many turns to multiply the effective area. The visualization is schematic: an ellipse stands in for the loop and a slow rotation hints at the phase bias. The model is non-relativistic and does not treat general relativity or detailed shot-noise limits; it is meant to connect rotation, area, and fringe shift qualitatively and in order of magnitude.
Who it's for: Students in optics, inertial navigation, and rotational sensing who need a clear link between geometry, rotation rate, and interferometric phase.
Key terms
Sagnac effect
Ring interferometer
Optical gyro
Enclosed area
Angular velocity
Phase shift
Fiber gyro
Counter-propagating beams
How it works
A ring interferometer compares counter-propagating beams; rotation breaks symmetry and produces a phase shift proportional to angular velocity — the optical gyro principle.
Frequently asked questions
Why does rotation break the symmetry between the two directions?
In a rotating frame the effective transit times for clockwise vs counter-clockwise beams around the loop differ slightly: one beam travels a bit farther in space-time than the other before they recombine. That tiny time difference becomes a measurable phase shift at the detector.
How do fiber gyros get large sensitivity from a small coil?
Many fiber turns multiply the effective optical area: N loops contribute roughly N times the single-loop phase shift, so a compact coil can rival a large free-space loop for the same Ω.
Is the formula on the page exact for any shape?
The compact scalar form quoted assumes a planar loop and the usual textbook approximations. Real devices account for non-planar paths, source spectrum, and noise; the simulator emphasizes scaling (Δφ ∝ Ω A / λ) rather than engineering-grade calibration.
Does the Sagnac effect depend on the medium’s refractive index?
In the standard derivation for light guided in a medium, n enters the phase shift because the optical path length changes with the slowing of the wave. The page exposes n as a slider to remind that fiber cores are not vacuum.