4138 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 11, NOVEMBER 2006 Polarimetric Characterization of RF Spectra at the Output of Linear Optical Systems Avi Zadok and Avishay Eyal, SeniorMember,IEEE InvitedPaper Abstract—The polarization properties of the optical RF spec- trum at the output of linear systems are studied both theoret- ically and experimentally. An analytical expression for the RF spectra of the Stokes parameters for sources of general statistics is derived. Specific formulas are calculated for broadband sources of Gaussian statistics and laser sources with predominant phase noise. In addition, a novel technique for characterizing the polari- metric dependence of the RF spectra is introduced. The technique is especially suitable for use in deployed links since it can use the communication signal, no prior knowledge of the signal statistics is necessary, and no access to the transmitting end is required. Using the formalism, estimation of the output principal states of polarization from RF measurements is demonstrated. Index Terms—Optical noise, phase noise, polarization mea- surements, polarization mode dispersion (PMD), RF spectrum, statistical optics. I. I NTRODUCTION T HE SPECTRAL properties of the instantaneous intensity of light and how they are affected by propagation have been the subject of many studies [1]–[5]. Typically, the spec- tral range of interest extends up to several tens of gigahertz. Accordingly, the power spectral density (PSD) of instantaneous optical intensity is often referred to as the “RF spectrum” of light. The characteristics of the RF spectrum depend mainly on the type of the optical source, the optical modulation being used, and the transfer properties of the medium. The motivation for characterizing the optical RF spectrum depends on the specific application. In many applications, the random fluctuations in the source amplitude and phase are translated into significant noise in the detected signal. Using optical RF spectrum analysis, it is possible to characterize this source- induced noise, to estimate SNRs, and to investigate propagation effects. Another important application of optical RF spectrum analysis is in optical communications, where the spectrum depends predominantly on the modulation format. The analysis allows comparing the spectral efficiencies of different formats, aiding the design of the electrical part of the receiver, and studying and monitoring propagation effects, among others. Manuscript received April 30, 2006; revised July 31, 2006. This work was supported in part by the Israeli Science Foundation. The work of A. Zadok was supported by the Israeli Clore Foundation. The authors are with the Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: avinoamz@post.tau.ac.il). Digital Object Identifier 10.1109/JLT.2006.883123 Most previous studies of the spectral properties of optical intensity were based on a scalar approximation. Recently, there has been a growing interest in the spectral properties of de- tected signals in polarimetric measurements [6]–[13]. In many of these applications, the measured quantities are the Stokes parameters, and the RF spectrum of such parameters represents measurement noise. It is therefore useful to characterize the RF spectrum of the entire Stokes vectors rather than the intensity alone. In our previous studies, we derived formulations for the RF spectrum of the Stokes parameters at the output of a linear time-invariant optical medium for sources of Gaussian statistics [14] and general known statistics [15]. The two formalisms were expressed in different terms. Here, we show how the results obtained for the Gaussian sources can be derived from the more general case. For completeness, we present again experimental demonstrations of these formalisms [15], [16]. In optical communications, the effects of polarization mode dispersion (PMD) on the RF spectrum have drawn significant attention due to the potential of using them for providing a feedback signal to PMD mitigation systems [17]–[23]. Many mitigation schemes rely on the knowledge of the principal states of polarization (PSPs) at the medium output. Hence, a method for extracting the PSPs from RF spectra measurements can be very useful. Here, we develop and demonstrate such a method. The method has several advantages, which make it especially suitable for deployed operating links: It can be performed at the receiver end of the medium with no need to access the transmitter end, and it can use the communication signal itself. No restrictions are imposed on the signal format. This paper is organized in two main parts. In Section II, the analytical formulation that expresses the RF spectra of the Stokes parameters at the output of an optical medium is presented. The formalism accounts for the statistical properties of the source, as well as the transfer matrix of the optical medium. The derivation is provided for a source of general statistics, with specific results for Gaussian sources and phase- noise-dominated laser sources. Section II is concluded with experimental demonstrations. In Section III, the experimental procedure for PSP estimation using RF spectrum measurements is described. The procedure is based on placing a variable ellip- tical polarizer (analyzer) at the output of the optical medium. Following a set of required calibration measurements, the RF spectrum of the detected intensity can be predicted for an arbitrary state of the analyzer. This prediction does not require 0733-8724/$20.00 © 2006 IEEE