Fiber Loop Mirror (Sagnac)
Sagnac fiber loop mirror reflectance and transmission versus coupling ratio and loss, and the comb filter made by a polarization-maintaining section.
Reflectance (isotropic loop)
100.00 %
4k(1 − k)·τ
Transmission (isotropic loop)
0.00 %
(1 − 2k)²·τ
Comb Period
6.006 nm
λ²/(B·L)
Comb Extinction
∞
T from 0.0 % to 100.0 %
Formulas
Isotropic loop: R = 4k(1 − k)·τ, T = (1 − 2k)²·τ; k = ½ reflects everything
PM section, axes exchanged between directions: Δφ = 2πBL/λ
T = τ·[(1 − 2k)² + 4k(1 − k)·sin²(Δφ/2)], R = τ − T
Comb period: Δλ = λ²/(B·L)
The comb assumes the polarization controller is set for full contrast, so the counter-propagating waves cross the PM section on opposite axes; any input polarization then sees the same response. Only the period and contrast are meaningful: the fringe positions shift with the controller type and with L on a scale of λ/B. τ lumps the coupler excess loss and the loop loss.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Coupler with wavelength-flat coupling k; losses lumped into τ. PM comb at the full-contrast setting (counter-propagating waves on opposite axes); phase birefringence, no dispersion.
- Mortimore D. B. (1988). Fiber loop reflectors. J. Lightwave Technol. 6, 1217. R = 4k(1 − k), T = (1 − 2k)². doi:10.1109/50.4119
- Fang X., Claus R. O. (1995). Polarization-independent all-fiber wavelength-division multiplexer based on a Sagnac interferometer. Opt. Lett. 20, 2146. T = sin²(πBL/λ). doi:10.1364/OL.20.002146