Brian L. Heffner

Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis

Polarization mode dispersion (PMD), which can limit the bandwidth of optical transmission links, has been difficult to measure in a manner independent of human judgment, leading to difficulties in automating the measurement. It is shown that PMD in any linear, time-invariant network can be completely characterized by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, even for networks exhibiting polarization-dependent loss. A fast, automated system using a tunable laser and an accurate, real-time polarimeter affords the temporal accuracy of approximately 2% down to a limit of several femtoseconds, as demonstrated by comparison with other techniques and comparison with known samples. Both the principal states of polarization and the group delay difference were measured as a function of optical frequency.<<ETX>>

Deterministic, analytically complete measurement of polarization-dependent transmission through optical devices

Polarization dependence of the loss or gain of an optical device has been difficult to measure in a consistent and reproducible manner because it has been necessary to search for the extrema of transmission over a two-dimensional polarization space. It is shown that the global variation of the transmission through any linear, time-invariant optical device, over all states of polarization, can be found in a strictly deterministic, analytically complete manner by measuring the polarization responses to only three input polarizations. A series of fast, automated measurements of two test devices yielded standard deviations of 0.017 and 0.033 dB and agreement with manual measurements.<<ETX>>

Accurate, automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis

Polarization mode dispersion can be described to first order by principal states of polarization (PSPs) and a differential group delay (DGD), and to second order by wavelength variation of the PSPs and by DGD dispersion (DGDD), the wavelength derivative of DGD. The high accuracy and wavelength resolution of Jones matrix eigenanalysis allows precise measurement of DGDD and PSP variation. A fast, automated system based on a tunable laser and an accurate, real-time polarimeter is used to measure DGD, DGDD, and PSP variation by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, and the system accuracy is demonstrated. Measurements at 2-nm intervals of a device whose DGDD is a known function of wavelength yield values of DGDD which differ from theory by less than 13 fs/nm.<<ETX>>

Single-Mode Propagation of Mutual Temporal Coherence: Equivalence of Time and Frequency Measurements of Polarization Mode Dispersion

A formalism is presented for treatment of the mutual temporal coherence between orthogonal polarization modes in single-mode optical systems, permitting calculation of the effect of propagation through birefringent devices on this coherence. We demonstrate that, allowing for differences similar to the birefringent effects of fiber pigtails, polarization-mode dispersion data measured by use of frequency-scanning techniques are related by the Fourier transform to data measured by use of interferometric techniques.

Attosecond-resolution measurement of polarization mode dispersion in short sections of optical fiber

A new technique is presented for the measurement of the differential group delay (DGD) between principal states of polarization of an optical device, with a demonstrated accuracy and resolution of roughly 50 attoseconds (50 × 10−18 s). Accuracy was directly assessed by measurement of a crystal-quartz DGD Standard. This permits what is to the authors knowledge the first complete measurement of the polarization mode dispersion (PMD) of straight, submeter lengths of optical fiber. PMD can be reliably measured only when the fiber is straight, since spooling of the fiber changes its PMD by introducing additional mode coupling. Measurement of four fiber samples revealed correlation between DGD and fiber core ovality.

43Gb/s Adaptive Polarization Mode Dispersion Compensator Field Trial

We describe long-term field measurements at 43Gb/s over a high-PMD link, using one receiver with adaptive PMD compensation and a second receiver without. The Q at both receivers is monitored and correlated with instantaneous DGD.

Diffraction of light by acoustic waves on a membrane

The diffraction of light by acoustic waves on a membrane is reported. A device can be made to perform acousto-optic signal processing at much lower frequencies than can be handled by the standard Bragg acousto-optic cell. Acoustic waveguiding phenomena are demonstrated. The device can handle simultaneous parallel-array data processing.

Reset-free system for real-time polarization control and synthesis.

A reset-free polarization controllsynthesis system is described. The desired polarization state can be selected by keyboard control with no insertion or rearrangement of optical components.

Simplified Calculation of System Outage Caused by Polarization-Mode Dispersion

Measuring system outage probability using known combinations of first- and second-order polarization-mode dispersion (PMD) is a powerful technique that has been difficult to implement due to the obstacle of approximating the joint probability density function (PDF) of PMD. We describe a closed-form approximation to this joint PDF in terms of elementary functions and assess its accuracy by comparison with a previous numerical integration and by comparing marginalizations of the approximation to known theoretical distributions. We then present a simple calculation of PMD-induced outage probability based upon measured performance.

PMD measurement techniques-a consistent comparison

Several different techniques are now widely used for measurement of polarization-mode dispersion (PMD), which can limit the transmission bandwidth of both analog and digital fiber-optic transmission systems. The wavelength scanning technique relies on measurement of the spectral transmission through a polarizer-fiber-polarizer concatenation. The transmission spectrum is analyzed either by the counting of extrema, or by application of a Fourier transform. The interferometric technique uses a similar polarized optical source, but relies on measurement of the mutual coherence between different polarizations at the fiber output. In the Jones matrix technique the polarization response to three input polarizations is measured as a function of wavelength to allow calculation of the wavelength-dependent polarization dispersion vector. Ideally, all techniques would be rigorously linked by theory, which in turn would be confirmed by measurement. As we progress toward this level of understanding, a skeptical review of the theoretical relations between the physics of the various measurement techniques can help establish foundations upon which to build.