1 June 1999Ž.Optics Communications 164 1999 107–120www.elsevier.comrlocateroptcomFull length articleHigh-speed fiber-optic polarization analyzer: measurements of thepolarization dynamics of an erbium-doped fiber ring laserGregory D. Van Wiggeren, Rajarshi Roy)School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332-0430, USAReceived 15 February 1999; accepted 24 March 1999AbstractŽ.Accurate measurements of fluctuating states of polarization SOP require determinations of the Stokes parameters onshorter time-scales than those of the fluctuations. For light sources that generate very rapid polarization and intensityŽ.fluctuations, such as erbium-doped fiber ring lasers EDFRLs , conventional polarization analyzers are not sufficient. Wedescribe a technique for measuring rapidly fluctuating states of polarization using a fiber-optic polarization analyzer. SOPŽfluctuations at rates up to 125 MHz can be accurately measured, a rate limited by the detection equipment photodiodes and.oscilloscope . Using the polarization analyzer, experimental measurements are made which provide new insights into therapid polarization dynamics of an EDFRL. q 1999 Published by Elsevier Science B.V. All rights reserved.PACS: 07.60.Fs; 42.65.Sf; 42.55.Wd; 42.25.JaKeywords: Polarimetry; Erbium-doped fiber lasers; Laser polarization dynamics; Optical chaos; Instabilities1. IntroductionŽ.Devices to specify the state of polarization SOPof light have been commercially available for manyyears, but these devices are not designed to measurelight with rapid fluctuations of its SOP. Indeed, thesedevices typically require stable SOPs for time-scalesfrom milliseconds to seconds. Accurate measure-ments of some optical phenomena, however, requiretracking a fluctuating SOP on much faster time-scales. The polarization analyzer described here is)Corresponding author. Tel.: q1-404-894-6819; Fax: q1-404-894-9958; E-mail: [email protected] of measuring fluctuating SOPs with time-scales as short as several nanoseconds. Even fastermeasurements are conceptually possible; the band-Ž.width of the photodiodes 3-dB roll-off at 125 MHzultimately limits the speed of the SOP fluctuationsthat can be accurately measured.In Section 2, we present an overview of thetheory of optical polarization that will assist thereader in understanding the description of the appara-tus and the interpretation of the experimental results.Section 3 briefly describes the experimental appara-tus and technique while focusing on experimentalresults and measurements. Specifically, the polariza-tion dynamics of chaotic and self-pulsing light fromŽ.an erbium-doped fiber ring laser EDFRL are mea-0030-4018r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.Ž.PII: S0030-4018 99 00163-7()G.D. Van Wiggeren, R. RoyrOptics Communications 164 1999 107–120108Ž.Fig. 1. Diagram of experimental apparatus. During the calibration process, light from the tunable diode laser TDL is transmitted to theapparatus. Once calibrated, light from an EDFRL is sent to the apparatus for measurement of the Stokes parameters. The variable attenuatorsŽ. Ž.VATs placed before the photodiodes are intended to prevent saturation of the photodiodes. The polarization controllers PCs consist of aŽ.sequence of three waveplates and allow light from any input polarization to be adjusted to any output polarization. The polarizers Pol.ensure that the photodiodes measure only one component of the light. All of these free-space optical elements are placed between coupledŽ. Ž.graded-index GRIN lenses, which allow the light to be coupled out of and back into fiber. The digital sampling oscilloscope DSOrecords the intensities measured by the photodiodes.sured. Section 4, the conclusion, discusses the advan-tages and features of this technique. A more thor-ough description of the apparatus and the calibrationprocedures is provided in Appendix A.2. Theoretical foundationFor a quasi-monochromatic lightwave, the electricfield, E, can be described as the sum of two orthogo-Ž. Ž. Ž.nal components, Ets EtqEt, wherexyˆEts iE t cos kzyvtq´t 1Ž. Ž. Ž. Ž.x 0 xxandˆEts jE t cos kzyvtq´t .2Ž. Ž. Ž. Ž.y 0 yyIn these equation E and E are both real0 x 0 ynumbers. The phase of each component is given by´.x,yFig. 2. This figure is intended to illustrate the accuracy of our measurement of the SOP. The light analyzed is produced by the EDFRL andpossesses rapid intensity and polarization fluctuations. A polarizer at 458 has been placed in the calibration area. Thus, the ideal™Ž. Ž .measurement of the SOP should, in spite of the intensity fluctuations evident in c , give ss 1,0,1,0 . The experimental measurement, asŽ. Ž.indicated by d–f , is very close to this ideal. The DOP shown in b is close to 100%, as one would expect for light that passes through apolarizer.()G.D. Van Wiggeren, R. RoyrOptics Communications 164 1999 107–120 109()G.D. Van Wiggeren, R. RoyrOptics Communications 164 1999 107–120110A common way of specifying the SOP of alightwave is to determine its Stokes parameters. Aswxdescribed in Refs. 1,2 , the four Stokes parametersfor such a lightwave can be defined as²2:²2:S s E q E00x 0 y²2:²2:S s E y E10x 0 y²:S s 2 EEcos´3Ž. Ž.20x 0 y²:S s 2 EEsin´,Ž.30x 0 ywhere´is just the relative phase,´y´, betweenyxthe two electric field components. Clearly, S repre-0sents just the total intensity of the light. S reflects a1tendency for the light to have its energy concentratedalong either the x or y axes. S and S depend on23the relative phase between these two components.²:The expectation-value brackets must be in-Ž.cluded in Eq. 3 because it is possible that thearguments within them can fluctuate on time scalesthat are shorter than the time during which themeasurement is made. To fully measure the time-evolution of a lightwave’s SOP, it is necessary to usea polarization analyzer that operates on time-scalesas fast or faster than the SOP fluctuations. ForŽexample, sunlight is called unpolarized S sS sS123.s0 because any real polarization analyzer averagesover sunlight’s very rapid and statistically randompolarization fluctuations. Yet, the electric field of aray of sunlight at any point in space and time mustpossess an amplitude, orientation, and phase. Whilethe time-scales for the SOP fluctuation of sunlightare much too fast to be measured with the techniquepresented here, some