IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 12, JUNE 15, 2006 1383 Performance Analysis of Polarimetric PMD Monitoring by Real-Time Optical Fourier Transformers Roberto Llorente, Raquel Clavero, and Javier Marti Abstract—A spectral polarimeter based on the real-time optical Fourier transform of one or some consecutive Gaussian pulses extracted from an optical transmission link is proposed and its operational limits evaluated. Polarization-mode dispersion (PMD) is calculated from the state-of-polarization spectral rotation rate with 0.36-GHz spectral resolution. The experimental results show sucessful PMD measurement inside 1.9-ps Gaussian return-to-zero pulses in good agreement with the theoretical calculations. Index Terms—Optical communication, optical fiber polariza- tion, optical fiber measurements, polarization-mode dispersion (PMD). I. INTRODUCTION T HE STEADY increase of the channel bit rate in dense wavelength-division-multiplexed networks over installed standard single-mode fiber (SSMF), reaching 160 Gb/s in sev- eral transmission experiments [1], reveals polarization-mode dispersion (PMD) as a key transmission impairment to over- come [2]. PMD requires dynamic compensation [3] which in turn requires a fast monitoring signal from the optical transmis- sion link [4]. Polarimetric PMD measurement techniques eval- uate the state-of-polarization (SOP) Stokes vector evolution in frequency over the signal frequency span. This approach allows a high accuracy in the PMD measurement and enables PMD estimation inside picosecond-wide optical pulses as reported in [5]. Several techniques have been proposed to evaluate the SOP evolution in frequency: Sweeping a continuous-wave (CW) laser probe and employing coherent detection [6], sweeping a Fabry–Pérot filter [7], or sweeping an acustooptic filter [8]. These techniques can be further improved employing nonlinear processes like SPM to broaden the spectrum [9] increasing the spectral resolution, which is a key parameter [10]. By using a fiber grating diffracting light and a photodetector array [11], the spectral sweep can be completely avoided and faster operation is achieved. In this case, the spectral resolution depends on the photodetector number of elements and the grating bandwidth, which are technical constrains. In this letter, a PMD monitoring scheme based on polari- metric analysis is reported, where the SOP components are translated from frequency to time domain by the use of real-time optical Fourier transformers (OFTs). The OFT approach has the advantage of providing a high number of spectral samples from optical pulses in the picosecond range. The real-time OFT Manuscript received October 24, 2005; revised March 17, 2006. The authors are with the Fibre-Radio Group, Nanophotonics Technology Centre, Valencia 46022, Spain (e-mail: rllorent@dcom.upv.es). Digital Object Identifier 10.1109/LPT.2006.875522 maps the SOP evolution in frequency to time waveforms, where can be photodetected and sampled by conventional electronics. This process exchanges a fine spectral resolution by fast sam- pling rate in time, feasible by conventional analog-to-digital converters (ADCs). The high number of spectral samples is of special interest for accurate PMD measurements. II. PRINCIPLE OF OPERATION The proposed technique is based on the evaluation of the SOP Stokes vector evolution over frequency inside one or some consecutive optical pulses extracted from a given optical transmission link. The proposed approach evaluates the SOP spectral evolution employing a fiber-based OFT [12]. In this approach, an optical pulse centered at angular frequency , with analytical representation , where is the field complex envelope, travels through an OFT fiber. The pulse will output with a field complex envelope , where , and denotes the Fourier transform operation. This holds if sufficient chromatic dispersion is provided by the OFT fiber, i.e., the first-order dispersion coefficient is sufficiently large to meet [13], where is the pulsewidth. The normalized Stokes vector can be then defined as (1) from [14] by the projection of over the Cartesian coordinates in planes transverse to the light propagation, and , respectively (1) The OFT process can be seen as if the chromatic dispersion in the fiber causes the short-wavelength components of spectrum to travel faster than the long wavelength components, which broadens the pulse in time and, given enough dispersion, establishes a unique relationship between time output and pulse spectrum. Sampling the OFT output it is actually sampled spectrum. The pulse spectrum is presented in a waveform of duration . The possible time overlap of OFT out- puts from different pulses must be avoided properly spacing the pulses at the OFT input. The real-time OFT is the basis of the spectral SOP monitor shown in Fig. 1 embraced by the dotted box. This system eval- uates the PMD in three steps: First, the optical pulses are pro- jected over a reference set of four polarization axis obtaining 1041-1135/$20.00 © 2006 IEEE