Sagnac (Ring) Interferometer
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.
More from Optics & Light
Other simulators in this category — or see all 44.
Brewster Angle
tan θ_B = n₂/n₁; R_p→0; θᵢ+θₜ=90°; Fresnel R_s, R_p vs θᵢ.
Fermat's Principle
OPL = n₁AP+n₂PB vs hit point; minimum = Snell path.
Chromatic Aberration
Cauchy n(λ); thin-lens f(λ); paraxial rays R/G/B.
Diffraction
Single and double slit with interference patterns.
Color Mixing
Additive (RGB) and subtractive (CMY) interactive color mixing.
Polarization (Malus)
Two polarizers. Rotate θ, see I = I₁ cos²θ and extinction.