Optical Fiber Birefringence High-pass Filter

How to use it

cd src/
go mod tidy
CGO_ENABLED=0 go build -o ../gnmic_plugins/event-birefringence-tracker main.go
chmod +x ../gnmic_plugins/event-birefringence-tracker

Copy /gnmic_plugins/event-birefringence-tracker into gnmic custom plugins directory as defined in your gnmic.yaml configuration file.

plugins:
  path: /app/plugins/ # this is the custom plugins directory
  glob: "*"
  start-timeout: 5s


processors:
  birefringence-tracker:
    # This key MUST match the `processorType` string constant in the Go code.
    event-birefringence-tracker:
      tap-rate-hz: 100.0 # nominal frequency of SOP-data sampling
      cutoff-hz: 0.01 # frequency above which changes are considered 'fast' 

# the rest of the gnmic.yaml configuration file

# in the outputs you should include the processor in the list of event-processors:
outputs:
  your-output:
    event-processors:
      - birefringence-tracker

Processor's pseudo-code

Initialize:
    cutoff_hz = High-pass filter cutoff (e.g., 0.01 Hz)
    U_ref = None
    last_timestamp = None

For each incoming 2x2 Jones Matrix A(t) at time t:
    
    // --- 1. Polar Decomposition & SU(2) Projection ---
    // Separate the matrix A into a purely rotational part (U) and a loss/gain part
    Compute U = A * (A^H * A)^(-1/2) 
    
    // Force determinant to 1 to project perfectly onto SU(2) group
    detU = det(U)
    U_now = U / sqrt(detU)
    
    // --- 2. State Initialization ---
    If U_ref is None:
        U_ref = U_now
        last_timestamp = t
        Continue

    // --- 3. Branch-Cut Resolution (The 180-degree flip) ---
    // In SU(2), U and -U represent the EXACT SAME physical rotation in SO(3).
    // To prevent the math from taking the "long way around" the sphere (a 2pi phase jump):
    trace = real( U_now * U_ref^H )
    If trace < 0:
        U_now = -U_now

    // --- 4. Relative Rotation Extraction ---
    // Compute the rotation operator that moves U_ref to U_now
    D = U_now * U_ref^H

    // --- 5. Pauli Vector Projection (The Physics) ---
    // Any SU(2) matrix can be written as cos(θ)I + i*sin(θ)(v_x*σ_x + v_y*σ_y + v_z*σ_z)
    // Extract the physical 3D strain vector (v_x, v_y, v_z) using Pauli matrices
    v_x = imag(D01 + D10)
    v_y = real(D01 - D10)
    v_z = imag(D00 - D11)
    
    norm_v = sqrt(v_x^2 + v_y^2 + v_z^2)
    rotation_angle_rad = 2 * atan2(norm_v, real(D00 + D11))
    
    rotation_axis = (v_x, v_y, v_z) / norm_v

    // --- 6. Time-Aware NLERP (Non-Linear Exponential Rolling Prediction) ---
    dt = t - last_timestamp
    alpha = 1 - exp(-2 * pi * cutoff_hz * dt)
    beta = 1 - alpha

    // Linearly interpolate the reference, then re-normalize to stay on the SU(2) manifold
    U_ref_raw = (beta * U_ref) + (alpha * U_now)
    mag = sqrt(|U_ref_raw_00|^2 + |U_ref_raw_01|^2)
    U_ref = [ U_ref_raw_00 / mag, U_ref_raw_01 / mag ]
            [ -conj(U_ref_raw_01)/mag, conj(U_ref_raw_00)/mag ]
    
    last_timestamp = t

    Return rotation_angle_rad, rotation_axis

How to interpret the outputs

The rotation_axis and rotation_angle_rad quantify the high-frequency differential perturbation (the "fast transient") applied on top of the fiber's baseline birefringence. They do not represent the total birefringence of the optical link. Because this processor acts as a high-pass filter, the outputs isolate sudden mechanical or acoustic impacts (e.g., trains, vibrations, aerial cable wind-whip) while ignoring slow thermal drifts.

If the receiver is currently tracking a stable, low-pass-filtered polarization state $\vec{S}_{ref}$, a transient event will cause the incoming light to suddenly whip away from this baseline into a new polarization state $\vec{S}_{last}$. The rotation_axis and rotation_angle_rad tell you around what axis and by how many radians to rotate $\vec{S}_{ref}$ on the Poincaré sphere to obtain $\vec{S}_{last}$.

rotation_axis: The two polarizations found by intersecting this axis with the Poincaré sphere are the eigenvectors of the transient perturbation. If the light arriving at the perturbation point happens to be polarized with one of these two polarizations, the transient will not induce a change in the polarization.

rotation_angle_rad: This is the clockwise magnitude of the sudden rotation around the rotation_axis. Physically, it is the retardance induced by the transient perturbation of one eigen-polarization with respect to the other. For example, suppose the sudden rotation is around the S1-axis by $\theta$. The input field can be written as a linear combination of H and V polarizations (eigenvectors). Then, after the rotation, the phase difference of H and V components is changed by $\theta$.

Mathematically, the sudden rotation matrix $D$ around S1-axis is:

$$ D = \begin{pmatrix} e^{i\theta/2} & 0 \\ 0 & e^{-i\theta/2} \end{pmatrix} $$

Let the input electric field be an arbitrary mix of H and V:

$$ \vec{E}_{in} = \begin{pmatrix} |E_H| e^{i\phi_H} \\ |E_V| e^{i\phi_V} \end{pmatrix} $$

Applying the birefringence operator $D$:

$$ \vec{E}_{out} = D \vec{E}_{in} = \begin{pmatrix} |E_H| e^{i(\phi_H + \theta/2)} \\ |E_V| e^{i(\phi_V - \theta/2)} \end{pmatrix} $$

The final phase difference between the H and V fields is:

$$ \Delta\phi' = \phi_H' - \phi_V' = \left(\phi_H + \frac{\theta}{2}\right) - \left(\phi_V - \frac{\theta}{2}\right) = (\phi_H - \phi_V) + \theta $$