Jones Calculus for Fiber Optics

The Jones calculus represents polarization states as 2-component complex vectors and optical elements as 2×2 complex matrices. For fiber optic systems, this formalism is essential because single-mode fibers exhibit birefringence that evolves the polarization state unpredictably.

Key Matrices

A wave plate with retardation and fast axis at angle has Jones matrix:

For a fiber section, the birefringence is characterized by the beat length — the propagation distance over which the two polarization modes accumulate a phase difference.

Application to OCT

In intravascular OCT, the catheter fiber introduces unknown birefringence that must be calibrated out. This connects to the polarization-sensitive extension described in Optical Coherence Tomography Fundamentals.

The round-trip Jones matrix through the catheter is , which can be decomposed to extract the sample’s Jones matrix if the fiber matrix is known or can be calibrated.

Müller Matrix Alternative

For depolarizing samples, the Jones formalism is insufficient — we need the 4×4 Müller matrix formalism that handles partially polarized light. See Müller Matrix Polarimetry for the extension to depolarizing media.

Practical Considerations

In practice, fiber birefringence drifts with temperature, stress, and bending — making real-time calibration essential. The standard approach uses a reference reflector to measure the fiber’s round-trip Jones matrix before each imaging frame.

This is an active area of research in our group — see the Inverse Problems in Optical Imaging note for how we incorporate polarization into the spectroscopic inverse framework.