854 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 10, MAY 15, 2008 Reflectometric Characterization of Hinges in Optical Fiber Links Andrea Galtarossa, Senior Member, IEEE, Daniele Grosso, Luca Palmieri, Member, IEEE, and Luca Schenato, Member, IEEE Abstract—A method for the temporal characterization of hinges in optical fiber links, based on polarization-sensitive reflectometric measurement is presented. Experimental results show the potential effectiveness of the proposed method. Index Terms—Hinge model, polarization-mode dispersion (PMD), reflectometric measurement. T HE experience about polarization-mode dispersion (PMD) accrued in the years has pointed out that the classical model, for which the PMD follows an asymptotic statistical description, is not adequate to effectively describe the PMD of a real link. Actually, real fiber links are more accurately described by the “hinge model” (see [1], [2] and therein references) which assumes that the link is a cascade of fiber sections with almost constant PMD, connected through “hinges” with negligible PMD acting as fast polarization scramblers. The adoption of the hinge model allows the defining of statistics for the PMD temporal evolution of a link. However, this opportunity has not been investigated in great detail, so far, likely because of the lack of knowledge about the time evolution of typical hinges. To fill this gap, new measurement techniques for the location and characterization of the hinges are needed. The technique recently proposed in [3] consists of measuring the state of polarization (SOP) of the backscattered field as a function of both time and distance by means of a reflectometric technique. Actually, a hinge causes an abrupt variation in the time domain of the backscattered SOP. This measurement tech- nique, however, “sees” each hinge through the preceding ones and as a consequence the ability to discern the contribution of a hinge from the contribution of the preceding ones is seriously compromised. In this letter, we tackle this issue by introducing a new measurement technique that can clearly isolate the con- tribution of each hinge. The method employs a polarization-sensitive optical time-domain reflectometer (P-OTDR) to repeatedly mea- sure the Mueller matrix representing the round trip propagation along the link; the experimental setup is a common P-OTDR as already described elsewhere [4]. Let be the Mueller matrix representing the for- ward propagation along the link (see Fig. 1) and let Manuscript received December 14, 2007; revised February 18, 2008. This work was supported by the European IST Nobel Phase 2 Project, by the Italian Ministry of Foreign Affairs (Italy-South Africa project of particular relevance), and by ISCOM, Rome, Italy. The authors are with the Department of Information Engineering, University of Padova, Padova 35131, Italy (e-mail: luca.schenato@dei.unipd.it). Digital Object Identifier 10.1109/LPT.2008.921845 Fig. 1. Matrices and represent the Mueller matrices of the forward propagation along the link up to the point and the transfer matrix from to , respectively. Analogously, and represent the corresponding round-trip propagation. and represent the propagation from the P-OTDR laser source to the fiber input and the propaga- tion from the fiber input to the P-OTDR polarization ana- lyzer, respectively. The measured round-trip matrix reads , where [4]. Note that and are generally unknown and may possibly evolve in time, if the setup is not properly implemented. The Mueller matrix rep- resenting the forward propagation up to a point can be expressed as , where provides the transfer matrix from to and it may possibly correspond to a link section comprising a hinge (see Fig. 1). Similarly, the matrix describes the round-trip propa- gation in the link section between and . According to the above definitions, we introduce the matrix as (1) We remark that is a measured quantity [4]; therefore, can be straightforwardly calculated from the exper- imental data. The matrix can be more conveniently represented as , where represents a -rotation around the axis of the Stokes space, and , , and are the Euler angles. Then, results to be equal to [5], the simplification being possible since the matrices and commute. Using these definitions, (1) yields (2) where and is a function of , , and . Note that Mueller matrices are orthogonal, so is orthogonal as 1041-1135/$25.00 © 2008 IEEE