BIFROST: A First-Principles Model of Polarization Mode Dispersion in Optical Fiber

TL;DR

BIFROST addresses the challenge of polarization mode dispersion (PMD) by delivering a first-principles model that ties PMD to physical fiber parameters such as temperature, stress, and geometry. It computes the full polarization transfer using Jones matrices for a cylindrical-waveguide fiber with long segments, hinges, and spun segments, enabling numerical evaluation of the differential group delay $\tau_{\text{DGD}} = L \frac{d\,\Delta\beta}{d\omega}$. The authors validate the framework against commercial fiber data and paddle measurements, demonstrate PMD-aware compensation scenarios in quantum networks, and present operating limits and ensemble-based usage to accommodate real-world uncertainties. By situating PMD within a physically grounded, open-source toolkit, BIFROST provides a versatile platform for PMD analysis across telecom, sensing, and quantum-network applications, helping to design mitigation strategies and explore novel uses of birefringence. The work thus bridges traditional PMD theory with emerging fiber technologies, offering a predictive, extensible framework for PMD investigations.

Abstract

We present BIFROST, a first-principles model of polarization mode dispersion (PMD) in optical fibers. Unlike conventional models, BIFROST employs physically motivated representations of the PMD properties of fibers, allowing users to computationally investigate real-world fibers in ways that are connected to physical parameters such as environmental temperature and external stresses. Our model, implemented in an open-source Python module, incorporates birefringence from core geometry, material properties, environmental stress, and fiber spinning. We validate our model by examining commercial fiber specifications, fiber-paddle measurements, and published PMD statistics for deployed fiber links, and we showcase BIFROST's predictive power by considering wavelength-division-multiplexed PMD compensation schemes for polarization-encoded quantum networks. BIFROST's physical grounding enables investigations into such questions as the sensitivity of fiber sensors, the evaluation of PMD mitigation strategies in quantum networks, and many more applications across fiber technologies.

Figures (8)

• Figure 1: Illustration of the effect of PMD on light pulses whose polarization is not aligned with the birefringence axes of a fiber. As the pulse travels through the fiber, a relative delay accumulates between different polarizations, resulting in pulse broadening. The upper panels show this broadening by comparing the output intensity profile (black solid line) to the input one (red dashed line).
• Figure 2: A comparison between conventional hinge models and BIFROST. Both models rely on splitting the fiber into segments juxtaposed with hinges, but the specifications and simulated behaviors of these elements are fundamentally different.
• Figure 3: Chromatic dispersion of fused silica. Top: the index of refraction of fused silica, using the measurements of Ref. FusedSilica_ThreePole_Temp2 at 20${}^\circ$C. Bottom: calculated $D_\text{CD}$ (thick blue line) using Eqns. \ref{['eqn:BetaFiberFinal']} and \ref{['eqn:Sellmeier']} with the data from the top panel. The orange dashed line indicates the best fit to the heuristic Eqn. \ref{['eqn:Heuristic_D_CD']}, showing a visually good fit to the calculated values. The gray dashed lines indicate the zero-dispersion wavelength. For this figure, we used a core radius $4.1\,\mu$m, a temperature of $20^\circ$C, a pure fused silica core, and a cladding doped with 3.6% germania. (We discuss the numerical implementation of the doping in later sections.)
• Figure 4: The group velocity dispersion $D_{\text{CD}}$ of the simulated Corning SMF-28e+ fiber. The blue curve shows calculated results, and the orange dashed line is a fit to the data using the heuristic Eqn. \ref{['eqn:Heuristic_D_CD']}. The red vertical band indicates the Corning specification for the zero-dispersion wavelength. The good fit to this heuristic indicates that BIFROST produces realistic behavior, but the fitted zero-dispersion wavelength is not an especially good match for the Corning SMF-28e+ specifications, as indicated in Table \ref{['tab:CorningAttemptTable']}.
• Figure 5: Result of a simulation of a single fiber paddle with BIFROST. The input light at 1400 nm is $+45^\circ$ linearly polarized, and the fiber paddle is specified to have diameter 56 mm; six turns of fiber with cladding diameter $125~\mu$m is used to match the ThorLabs fiber paddle set manual ThorLabsPaddles. The output polarization is shown here on the Poincaré sphere, with the color indicating the paddle angle. As the paddle is rotated, the polarization rotation is about the $S_3$ axis, corresponding to a rotation by a half-wave plate whose angle is being varied. This confirms that BIFROST reproduces the behavior specified in the ThorLabs fiber paddle manual. Figure partially made with PyPol PyPol.