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We propose a new method to measure polarization mode dispersion (PMD) in optical fibers based on optical frequency domain reflectometry technique. In this method the PMD is directly determined from the beat frequency generated by interference between lights from the Fresnel reflection at the end of the device under test, which makes the measurement at single end of the device possible. An automated PMD measurement system is demonstrated on polarization maintaining fibers with a frequency-shifted feedback fiber laser as a light source.
©2001 Optical Society of America
1. Introduction
Polarization mode dispersion (PMD) in optical fibers and optical devices have become one of major factors limiting the data rate of transmission systems [1]. So far, several methods to measure the PMD have been developed, such as the fixed-analyser method [2], the interferometric method [3], the Poincare sphere method [4], and the Jones matrix eigenanalysis method [5]. To increase the data rate with an installed fiber (such as dark fiber) link, however, PMD testing at single end of the fiber cable are becoming necessary due to its convenience for practical application. In this letter, a new method of PMD measurement based on optical frequency domain reflectometry (OFDR) technique is presented, and an automated PMD measurement system of polarization maintaining fiber (PMF) is demonstrated using a frequency-shifted feedback (FSF) fiber laser as a light source [6].
2. Principle
As light transverses a fiber with birefringence, a time delay arises between the two orthogonal polarization modes along the fast and slow axes of the fiber. Interference between the two polarization modes of frequency-chirped light generates a beat signal with a beat frequency given by
where γ is a chirp rate of the light and Δτ is a differential group delay (DGD) of the fiber. Detection of the back-reflected signal (due to the Fresnel reflection at the far end of the fiber) allows simple determination of the PMD using OFDR technique.
Fig. 1 shows a block diagram of the OFDR based PMD measurement system. When DGD is very small, the measurement becomes difficult because the beat frequency is so low that it overlaps with DC noise level. To solve this problem, a polarization-dependent delay line (PDDL) is added and an offset time τos is fed between the two orthogonal polarization modes. The polarization direction α of the injection light into a fiber under test (FUT) is controlled by a λ/2 plate. The signal reflected back from the far-end of the FUT is detection by a photo-detector (PD), here an analyzer is placed in front of PD to generate a beat between the two orthogonal polarization modes. The intensity I(t) of the detected beat signal is described in matrix form as follows
where β is an angle between the polarizing axis of the analyzer and slow axis of the FUT, U(τos) and U(Δτ) are time delay function, e(t), E 0 and ν 0 are an electrical field of the frequency-chirped light, the field amplitude and the center frequency of the light, respectively. The four matrices correspond to the effects of the analyzer, DGD of FUT, λ/2 plate, and PDDL. According to Eq. (2), three beat signals appear with beat frequencies fB0, fB1, and fB2, where fB0=γτos, fB1=γ (τos+Δτ), and fB2=γ (τos- Δτ), respectively. The intensities of the three beat signals are given as
DGD can be determined by the difference of beat frequencies between fB1 and fB2, and it is given by
When the DGD is very small, however, above three beat signals are overlapped each other so that it is difficult to determine their beat frequencies. So it is necessary to make a condition that only one beat signal is generated. According to Eq. (3), under the condition of β=45° and α=0° (90°), a beat signal with beat frequency fB1 (fB2) is obtained. While under the condition of β=0° and α=0° (90°), no beat signal is obtained, and this relation can help to determine above conditions accurately.
In this method the DGD is measured in frequency domain, and high sensitivity is obtained. So it is possible to measure the PMD in the optical fibers at single terminal. However, a light source in this system must have a high chirp rate, chirp linearity and a wide frequency chirp range. A frequency-shifted feedback (FSF) fiber laser developed by our group satisfies these requirements and it is used for a demonstration of this PMD measurement method.
3. Experimental setup and results
Fig.2 shows an experimental setup. A FSF laser containing an erbium-doped fiber (EDF) as the gain medium was used as a light source. The FSF laser cavity was closed via the first order diffracted light of an inter-cavity acoustooptic modulator (AOM). The laser output consisted of a chirped frequency comb [7,8] that can be expressed as
where νi is instantaneous frequency of the laser output, τRT is the cavity round trip time, νFS is the intracavity frequency shift (the AOM driving frequency) and q is an integer. In this setup, 1/τRT, νFS, and γ were 9.38 MHz, 120 MHz, and 1125.6 THz/s, respectively. The frequency chirp range νBW of each comb component was found to be 120 GHz (FWHM), as limited by the cavity parameters [9]. A PDDL consisted of two polarization beam splitters (PBS) and two mirrors. The delay time τos was 405 ps, which corresponded to a beat signal frequency shift fB0 of 455.8 kHz. The spectrum broadening ΔfB (=γ/νBW) of the beat signal fallen DC level in heterodyne detection of the laser output was 9.4 kHz, so the frequency shift with PDDL was large enough to observe the beat signal without effect of DC level noise. RF spectrum of the beat signal was observed with an electronic spectrum analyzer (ESA) and beat frequency was determined from the center frequency of the spectrum. By controlling λ/2 plate, analyzer and ESA with a personal computer, an automated PMD measurement system was demonstrated. An algorism of the system is as follows:
a) Adjustment of angleα and β to 0°; To make a search of condition in which an intensity of the beat signal is zero with rotatingλ/2 plate and analyzer.
b) Measurement of beat frequency f B1 (fB2); To rotate the angle of analyzer by 45° and measure a relation between the center frequency of the beat signal and the angle of λ/2 plate.
c) Calculation of DGD of the FUT; To calculate DGD value according to Eq. (4).
Fig. 2. Experimental setup for PMD measurement. WDM: wavelength-division multiplexer. OI: Optical Isolator. PC: Polarization controller.
As a demonstration of the system, PMD measurement of several length (0.45, 0.31, 0.21 m) polarization maintaining fibers (PMF) were performed repeatedly for both single-pass (at the two ends of FUT) and double-pass (at single end of FUT) system shown in Fig. 2. Fig. 3 shows a measurement result (0.45 m-PMF, double-pass system) of a relation between the center frequency of the beat signal and the rotation angle of λ/2 plate. In this figure the maximum and minimum value of the beat frequency corresponded to f B1 and f B2, respectively. The measured value of the beat frequency difference f B1–f B2 was 3.03±0.03 kHz, corresponding to Δτ=1.346±0.013 ps. The measurement error of the beat frequency was caused by instability of the laser cavity and a limitation in the frequency chirp range of the light source.
Fig. 3. Beat frequency versus rotation angle of λ/2 plate measured by the round-trip system with a 0.45 m-PMF as a FUT. The broken lines indicate the parabolic fitting curves.
Fig. 4 shows a relation between the fiber length and measured DGD value. The measured values were proportional to the length of the FUT and DGD measured in double-pass was about twice that measured in single-pass. These results show that the OFDR based PMD measurement method is effectively. The comparison with other method will be reported in our next paper.
In case of PMD measurement of PMF, the accuracy of this method is limited primarily by the measurement error of the beat frequency caused by laser performance characteristics such as the frequency chirp range and the stability of the laser cavity. By using an FSF fiber laser as a light source, an accuracy of 0.01 ps can be obtained. In case of PMD measurement of the fiber with polarization mode coupling, however, more devices are necessary to improve the accuracy. A polarization of the detected light is frequently changed in time, and it causes large error of the measurement. Controlling polarization state of probe light corresponding to that of the detected light solve the problem, and such a system will be investigated in next step work.
Fig. 4. Measured DGD value versus fiber length. The solid and broken lines indicate results measured by the double-pass and single-pass systems, respectively.
4. Summary
A new OFDR based PMD measurement method was proposed and demonstrated using an FSF fiber laser. This round-trip measurement technique is of interest to both telecom operators and fiber manufacturers. Further research should improve the accuracy of the PMD measurements of fibers or optical devices.
Acknowledgments
The authors wish to express their thanks to Dr Y. Namihira (KDD R&D Laboratories) and Visiting Professor M. Nakazawa (NTT Network Innovation Laboratories) of our Institute for useful and stimulating discussions. M. Yoshida would like to acknowledge the Foundation for the Promotion of Electrical Communication Engineering for granting a fellowship, and Nianyu Zou thanks the Ministry of Education, Science and Culture of Japan for granting the scholarship.
References and links
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