fast polarization-dependent loss measurement based on continuous polarization modulation

Fast polarization-dependent loss measurementbased on continuous polarization modulation

Bogdan Szafraniec,1,* Rüdiger Mästle,2 Bernd Nebendahl,2

Evan Thrush,1 and Douglas M. Baney1

1Agilent Laboratories, 5301 Stevens Creek Boulevard, MS 54U-SC, Santa Clara, California 95051, USA2Agilent Technologies, Photonic Test and Measurement, Herrenberger Strasse 130, 71034 Böblingen, Germany

*[email protected]

Received 23 January 2008; revised 8 May 2008; accepted 17 May 2008;posted 20 May 2008 (Doc. ID 92014); published 16 January 2009

A new technique for measuring the insertion loss and the polarization-dependent loss (PDL) of opticalcomponents is proposed. The technique is based on continuous polarization modulation of the stimulusoptical field as opposed to sequential polarization state switching as in the traditional Jones matrix ana-lysis or Mueller matrix methods. This new method relies on the simultaneous observation of multipleharmonics of the transmitted optical signal in the frequency domain. The physical theory of this methodis presented along with PDL measurements performed on a polarization modulator, a polarizer, a PDLstandard, and on an acetylene absorption cell exhibiting spectrally sharp insertion loss features. © 2009Optical Society of America

OCIS codes: 120.4640, 060.2330, 060.2340, 130.1750, 260.5430, 060.4080.

1. Introduction

One of the essential measurements for fiber opticcommunication networks and their constituent com-ponents is the measurement of the polarization-dependent loss (PDL). An optical component havingPDL attenuates optical waves differently, dependingon their respective polarization states. In an opticalnetwork consisting of many concatenated opticalcomponents, the effects of PDL accumulate. So evenfor components with relatively low PDL, the com-bined effect in a large photonic network can besevere, causing fading and transmission errors.The system penalty becomes especially severe whenthe network contains PDL and birefringence that re-sults in polarization mode dispersion. This phenom-enon is known as the combined PDL and polarizationmode dispersion effect [1].The key metrics for PDL measurement techniques

are speed and accuracy. The two most frequentlyused methods for measuring PDL are based on the

Jones matrix analysis [2] and Mueller matrices [3].Both methods require multiple input polarizationstates to determine PDL. The conceptual illustrationof the Mueller matrix technique is shown in Fig. 1(a).Typically, a laser is used to provide light to a polar-ization synthesizer that generates sequentially atleast four states of polarization that are routed tothe device under test (DUT). The transmitted lightfrom the DUT is detected and recorded for each stateof input polarization. From the resulting data theinsertion loss and PDL are calculated.

The Mueller method of Fig. 1(a) relies on sequen-tial power measurements corresponding to at leastfour different input polarization states [3]. The inputpolarization states cannot be coplanar on the Poin-caré sphere; minimum noise for the Mueller methodis obtained when the four polarization states form atetrahedron. Theoretically, the power at the output ofthe DUT is expressed by a dot product of theStokes vector that describes the input opticalwave and a vector that represents the first row ofthe Mueller matrix. For a normalized Stokes vectorð1; q; u; vÞ, which is typically represented by acolumn vector, the fraction of the transmitted power,

0003-6935/09/030573-06$15.00/0© 2009 Optical Society of America

20 January 2009 / Vol. 48, No. 3 / APPLIED OPTICS 573

f p, is described by the following equation:

f p ¼ m11 þm12qþm13uþm14v; ð1Þ

where m1i are the elements of the first row of theMueller matrix. It is important to note that the frac-tion of transmitted power is unitless just like the ele-ments of the Mueller matrix or the elements of thenormalized Stokes vector. The fraction of the trans-mitted power, f p, could also be understood as normal-ized transmitted power or a transmission function hwhose values range between 0 and 1. Thus, fulltransmission corresponds to h ¼ 1, while completeabsorption (zero transmission) corresponds toh ¼ 0. For a known input power, the transmissionfunction allows for recovery of the output power, p.Thus, the concepts of power, normalized power, ortransmission can be used interchangeably. In de-scribing the mathematical model we chose a conceptof transmission. However, as shown in Fig. 1(b), theconcept of transmitted power is just as useful. Bymeasuring transmission for four different input po-larization states, the set of four equations based onEq. (1) can be solved for the Mueller matrix elementsm1i. Then, the maximum and minimum of the polar-ization-dependent transmission can be found fromthe following equation [3]:

hmax;min ¼ m11 �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim2

12 þm213 þm2

14

q: ð2Þ

The polarization-independent insertion loss in deci-bels is found as 10 logððhmax þ hminÞ=2Þ. The PDL indecibels is found as 10 logðhmax=hminÞ.The process of polarization state switching, often

implemented by rotating optical wave plates, is in-

herently slow. Additionally, the sequential natureof the test can introduce errors if the measuredcomponent is subjected to ambient changes suchas temperature variations or vibrations, or if thetransmitted optical power varies. To measure PDLover wavelength, the tunable laser source is sweptwhile the polarization state is stationary. The processis repeated for four different polarization states. Inthis procedure polarization state switching can leadto measurement errors due to conversion of DUT in-sertion loss features into PDL errors. This conversiontakes place when wavelength sweeps are not pre-cisely reproduced between multiple measurements;this leads to an apparent DUT transmission depen-dence on polarization state. These errors can be verylarge for devices with spectral edges or notcheswhose steepness is comparable to the wavelength re-solution or reproducibility of the tunable laser.

Here we propose a modification of the Mueller ma-trix method that eliminates the sequential nature ofcurrent PDL test methods by introducing continu-ous, periodic modulation of the Stokes vector compo-nents and harmonic analysis. This method isconceptually illustrated in Fig. 1(b), where the dis-crete polarization states of Fig. 1(a) are replacedby a continuous trajectory on the Poincaré sphere.The PDL is determined from the transmitted opticalsignal by Fourier analysis as described inSection 2. Thus, multiplexing polarization states inthe time domain of the conventional Mueller ap-proach is replaced by simultaneous observation ofmultiple harmonics of the transmitted optical signalin the frequency domain. As illustrated in Section 2,this changes the nature of the PDL measurement.

2. Polarization State Modulation

Each of the periodically modulated componentsof the input Stokes vector ½1; qðtÞ; uðtÞ; vðtÞ� canbe decomposed into a Fourier series. Symbolically,

0BBB@

1qðtÞuðtÞvðtÞ

1CCCA ¼

0BBB@

1q0 þ q1 þ q2 þ q3 þ � � �u0 þ u1 þ u2 þ u3 þ � � �v0 þ v1 þ v2 þ v3 þ � � �

1CCCA: ð3Þ

In Eq. (3) the subscripts identify the individualharmonics. For example, q1 represents the first har-monic of qðtÞ. The element q1 is described by an am-plitude and a phase. Similarly, all the otherharmonics in Eq. (3) are described by an amplitudeand a phase. This leads to a typical complex notationof the Fourier series. It is important to realize thatthe real periodic function can be expressed in termsof complex harmonics. This does not imply that thefunction is no longer real. Similarly, the Stokes vectorthat contains real time varying elements, as shownin Eq. (3), can be expressed in terms of complex har-monics but it still remains real. For simplicity, we as-sume that all Stokes components are modulated atthe same fundamental frequency. We also assume

Fig. 1. (Color online) Conceptual illustration of PDL test meth-ods. (a) Sequential polarization state switching. (b) Continuous po-larization modulation with simultaneous observation of multipleharmonics.

574 APPLIED OPTICS / Vol. 48, No. 3 / 20 January 2009

that the laser light source used as a stimulus in thetest is instantaneously polarized and highly mono-chromatic and that its intensity remains constant.The last assumption introduces an additional con-straint, qðtÞ2 þ uðtÞ2 þ vðtÞ2 ¼ 1, that simply impliesthat only the polarization state of the optical stimu-lus is modulated.Based on Eq. (1), for a periodically modulated po-

larization state described by Eq. (3), power at theoutput of the DUT (and DUT transmission) is alsoa periodic function. The harmonics of the transmis-sion function hðtÞ depend on the Mueller elementsm1i and on the polarizationmodulation. For example,the first three harmonics of the transmission func-tion hðtÞ can be expressed by the following equation:

0@

h1

h2

h3

1A ¼

0@

q1 u1 v1q2 u2 v2q3 u3 v3

1A0@

m12

m13

m14

1A; ð4Þ

where hi represent harmonics of the transmissionfunction hðtÞ. The matrix that contains harmonicsof qðtÞ, uðtÞ, and vðtÞ represents polarization modula-tion. Therefore, if the polarization modulationmatrix is known and the harmonics of the transmis-sion function hðtÞ are measured, the elements of theMueller matrixm12,m13, andm14 are determined. Asopposed to the traditional method that requires mul-tiple power measurements for multiple input polar-ization states, all harmonics of the output powersignal are measured at the same time. The measure-ment is no longer associated with discrete polariza-tion states but with the continuous motion of thepolarization state. The sequential switching/multiplexing in time is substituted by continuousmonitoring of the spectral components of the trans-mission function, hðtÞ.Equation (4) provides solutions for m12, m13, and

m14; the remaining Mueller element that needs tobe found is m11. The simplest way of finding m11 isby choosing q0 ¼ u0 ¼ v0 ¼ 0. This type of polariza-tion state modulation corresponds to pseudo-depolarized light, i.e., light that does not have, onaverage, a preferred polarization state. This choiceremoves the dependence of the measurement onthe orientation of the PDL. For the pseudo-depolarized light:

h0 ¼ m11: ð5Þ

Thus, the DC component of transmission functionhðtÞ is a measure of the insertion loss of the DUT.The PDL can be determined from Eq. (2).There are many schemes possible for choosing the

polarization modulation trajectory on the Poincarésphere. In general, one should strive to maximizethe determinant of the modulation matrix ofEq. (4), i.e., maximize measurement sensitivity.Qualitatively, the large determinant correspondsto a trajectory that “captures” a large volume ofthe Poincaré sphere. The trajectory must be three

dimensional for the modulation matrix to be nonsin-gular. Below we present an interesting polarizationmodulation scheme that is optimal in several re-spects: it is very simple, it produces only three har-monics, it is highly symmetrical on the Poincarésphere, and it is pseudo-depolarized. To introducethe modulation we start from a Stokes vector,

S ¼

0BBB@

1cosð2αÞ

sinð2αÞ cosðφÞsinð2αÞ sinðφÞ

1CCCA; ð6Þ

which represents an arbitrary polarization state de-scribed by the parameters α and φ. The polarizationstate represented by Eq. (6) can be located on thePoincaré sphere, as illustrated in Fig. 2, by measur-ing the angle 2α from the 0° linear polarization stateH around the vertical axis R − L and by measuringthe angle φ from the equatorial plane around the axisH − V. Now, assume that the angles α and φ increaselinearly with time at the angular rate ω, i.e.,α ¼ φ ¼ ωt. On the Poincaré sphere, this correspondsto a superposition of rotations around the R − L axisand H − V axis at the rates 2ω and ω, respectively.For these rotations, Eq. (6) can be rewritten asfollows:

S ¼

0BBB@

1cosð2ωtÞ

12 sinðωtÞ þ 1

2 sinð3ωtÞ−

12 cosðωtÞ þ 1

2 cosð3ωtÞ

1CCCA: ð7Þ

As illustrated in the preceding equation the Stokesvector components are modulated only at three

Fig. 2. (Color online) Three-tone polarization modulationtrajectory.


frequencies. For the described modulation, the 3 × 3modulation matrix of Eq. (4) is

M ¼0@

0 1 0−j=2 0 −j=2−1=2 0 1=2

1A; ð8Þ

where j ¼ ffiffiffiffiffiffi−1

pis an imaginary number. It is worth

noting that the complex notation of the harmonic ma-trix captures amplitude and phase of the individualharmonics. The trajectory of the described polariza-tion modulation is illustrated in Fig. 2. The modula-tion of the individual components of the Stokesvector, described by Eq. (7), is shown in Fig. 3. Topo-logically, the trajectory on the Poincaré sphere is afigure eight that divides the surface of the sphereinto four equal segments. The symmetry of thetrajectory places the center of gravity at the centerof the sphere, ensuring that the stimulus light ispseudo-depolarized.

3. Experimental Setup

The experimental setup that allows measurementsof insertion loss and PDL according to the methodof this paper is shown in Fig. 4. The experimental set-up comprises a tunable laser source (Agilent 81640B)operating over a wavelength range from 1490 to1640nm, an x-cut, z-propagating lithium niobate po-larization controller (EOSpace), a low PDL coupler, aDUT, and two low PDL receivers. The data from thereceivers are digitized and then processed by a com-puter. The drive signals to the polarization controllerare provided by two locked arbitrary waveformgenerators (Agilent 33250A) after sufficient voltageamplification.A coupler placed after the polarization controller/

modulator enables monitoring of the optical powergoing into the DUT and removal of power fluctua-tions from the insertion loss measurement (m11).The power transmitted through the DUT is moni-tored by the low PDL receiver. If the DUT does nothave any PDL, then the intensity at the receiver isconstant. However, if PDL is present, then the evolu-tion of the polarization state results in intensity fluc-tuations that contain harmonics of the polarizationmodulation frequency. The amplitude and phase of

the harmonics are measured using synchronous de-modulation implemented in software. The detectedharmonics and the measured polarization modula-tion matrix, based on Eq. (4), provide a solutionfor Mueller matrix elements m12, m13, and m14. Itis important to note that, since the measured harmo-nics are complex and the modulation matrix containscomplex elements, the solution for m12, m13, and m14can also be complex. This would imply complex PDL.This problem is resolved by adjusting the referencephase of the synchronous detection to make PDLreal. This procedure is in its nature the same as ad-justment of the reference phase of the lock-in ampli-fier. Since the digitized data are processed by acomputer the easiest way to adjust the referencephase is in software.

The description of the x-cut, z-propagating polari-zation controller that was used in the experiment isbeyond the scope of this paper. Interested readers arereferred to papers on the physics of x-cut modulators[4,5] and their characterization [6]. The trajectoryused in our experiments differed from the idealthree-tone trajectory of Fig. 2; however, its figureeight topology offered similar properties. The pro-duced light was pseudo-depolarized. Some high orderharmonics were present; however, they were not uti-lized in the experiment. The trajectory was traced ata frequency of 100kHz. The polarization modulationmatrix of Eq. (4) was measured experimentally to ac-count for any differences from the ideal three-tonetrajectory.

4. Experimental Results

A very simple and effective way of verifying the setupis the measurement of the polarizer. As a polarizerwe used an Agilent 8169A polarization controllerthat consists of a polarizer, a quarter-wave plate,and a half-wave plate. The wave plates in combina-tion with the polarizer allow construction of an arbi-trary polarizer. The wave plates can be eitherstationary or they can be spun, forming a modulatedpolarizer. We measured the PDL of the stationaryand modulated polarizer over the wavelength rangebetween 1530 and 1610nm. Since the measurementtime in our setup is substantially shorter than themechanical rotation of the wave plates a PDL exceed-ing 15dB was measured in all cases. The typical testresults are shown in Fig. 5. In the case of the modu-lated polarizer we could also observe the time vary-ing position of the polarizer on the Poincaré sphere.This initial test confirms that the matrix describingpolarization modulation was properly measured.

Fig. 3. (Color online) Modulation of the Stokes components in thethree-tone technique.

Fig. 4. (Color online) Simplified diagram of the experimentalsetup.


The simplest and very essential test is the charac-terization of the PDL of the experimental setup itself.The dominant PDL source in our setup is the polar-ization modulator, however, some PDL is also pre-sent in the coupler (10mdB) and the receivers(10mdB). As shown below, the PDL of the polariza-tion modulator can be calibrated out from the mea-surement. The PDL of the power monitor receiver isnot critical since light emerging from the polariza-tion modulator is pseudo-depolarized, substantiallyreducing the polarization dependence of the monitor.Therefore, it is important to mention that only thePDL of the receiver that follows the DUT resultsin an error that cannot be calibrated out.The residual PDL of the system before and after

calibration is shown in Fig. 6. As shown in the figure,the uncorrected residual PDL ranges between 20 and90mdB and exhibits an oscillatory character overwavelength. Since the power transmitted throughthe modulator depends on the controlled outputpolarization, the output power levels arepredictable. Therefore, power variation can be ac-counted for in the calibration process that coversthe full wavelength range of interest. This allows

suppression of the residual PDL to below 10mdBas shown in Fig. 6. Thus, after this calibration stepthe only remaining error source is due to thereceiver PDL.

To validate our PDL accuracy we measured a PDLstandard; the exemplary results are shown in Fig. 7.We used a commercially available PDL standard(manufactured by Taliescent) with a specified PDLequal to 0:468dB. The standard was aged in our me-trology labs. After aging, the PDL increased by about10mdB to 0:478dB. The PDL standard was mea-sured multiple times at different test conditions.As shown in Fig. 7, the PDL measured in our setupvaries between 0.47 and 0:5dB over the wavelengthrange from 1530 to 1610nm. The results are consis-tent with our predictions.

It is essential to mention that a low PDL receiver isrequired to achieve the demonstrated high accuracy.In our experiments we observed drifts of 10 to20mdB due to the receiver PDL. The measurementsgiven in Figs. 5–7(a) were performed using a tunablelaser sweeping wavelength at a rate of 20nm=s. Thecalibration data were averaged over the wavelengthspan of 10pm. After calibration, the system was op-erated for averaging windows of 2:5pm. Thus, thePDL noise level of <10mdB corresponds to the

Fig. 5. (Color online) PDL of the 8169A polarization controller.

Fig. 6. (Color online) Residual system PDL before and aftercalibration.

Fig. 7. (Color online) PDL of Taliescent PDL standard:(a) 20nm=s sweep rate, 2:5nm resolution; (b) 5nm=s sweep rate,0:625nm resolution.


PDL measurement time of 125 μs. For 100kHz polar-ization modulation, the shortest measurement timecorresponds to a single polarization evolutionof 10 μs.The advantage of this new technique over existing

polarization switching methods is clearly evidentfrom measurements performed on an optical absorp-tion cell. The test results of the absorption cell areprovided in Figs. 8(a) and 8(b). In traditional multi-state techniques, it is very difficult to perform a fastswept measurement of a DUT that has spectrallysharp absorption features. If the wavelength is keptconstant but polarization states are switched, the re-sults are accurate; however, the test becomes veryslow as the laser wavelength has to be steppedthrough the wavelength range of interest. Alterna-tively, if the wavelength is swept and the polarizationstates are switched between the sweeps, the mea-surement time is substantially shortened, however,any wavelength reproducibility errors between thewavelength sweeps lead to a conversion of the inser-tion loss features into a perceived PDL. The sameeffect may take place in a dynamically changingenvironment when optical loss of the systemfluctuates.The data in Fig. 8 were taken for a laser sweep rate

of 20nm=s and an averaging window (resolution) of2:5pm. As illustrated in Fig. 8(a) the insertion loss ofthe absorption cell varies between 1 and 15dB overthe wavelength range from 1510 to 1520nm. How-ever, the measured PDL, illustrated in Fig. 8(b), withan exception for an isolated 110mdB noise spike atthe highest absorption peak, is in the range between30 and 60mdB. In the wavelength region free of theabsorption peaks, the PDL measurement noise isabout 10mdB. Some increase in noise, as expected,is observed when the power level drops down dueto absorption. The experiment clearly demonstratesthat the proposed PDL measurement is highly inde-pendent of DUT attenuation spectra.

5. Conclusions

A new optical technique has been proposed for mea-suring insertion loss and PDL using a swept lasersource and continuous polarization modulation ofthe stimulus light. The new theoretical frameworkwas created through modification of the Mueller ma-trix method. This technique overcomes limitations ofearlier techniques based on polarization switching.The approach offers a substantial reduction in mea-surement time, minimizing the dependence of thePDL measurement on the power level. The PDLnoise was shown to be lower than 10mdB in a125 μs measurement time (2:5pm resolution;20nm=s laser sweep rate). The 20mdB accuracy islimited by the PDL of the receiver. Measurementsperformed on an acetylene absorption cell demon-strated high immunity of themethod to optical powerfluctuations. The PDL was measured with accuracyof about 20mdB in the presence of 14dB spectrally

sharp intensity fluctuations. The validity of the pre-sented data was confirmed by measuring a polarizerand a commercial PDL standard. This new techniqueis expected to be used in applications requiring rapidand accurate measurement of the polarization-dependent loss properties of optical components.

References

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2. B. L. Heffner, “Deterministic, analytically complete measure-ment of polarization-dependent transmission through opticaldevices,” IEEE Photon. Technol. Lett. 4, 451–454 (1992).

3. C. Hentschel and D. Derickson, “Insertion loss measure-ments,” in Fiber Optic Test and Measurement, D. Derickson,ed. (Prentice-Hall, 1998), pp. 356–358.

4. F. Heismann, “Compact electro-optic polarization scramblersfor optically amplified lightwave systems,” J. LightwaveTechnol. 14, 1801–1813 (1996).

5. S. Thaniyavarn, “Wavelength-independent, optical-damage-immune LiNbO3 TE-TM mode converter,” Opt. Lett. 11,39–41 (1986).

6. A. J. P. van Haasteren, J. J. G. M. van der Tol, M. O. vanDeventer, and H. J. Frankena, “Modeling and characterizationof an electrooptic polarization controller on LiNb03,” J. Light-wave Technol. 11, 1151–1157 (1993).

Fig. 8. (Color online) Acetylene absorption cell. (a) Insertion loss.(b) PDL.


fast polarization-dependent loss measurement based on continuous polarization modulation

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