Optical trap detector for calibration of opticalfiber powermeters: coupling efficiency

John H. Lehman and Christopher L. Cromer

The optical trap detector is based on two, 1 cm � 1 cm silicon photodiodes and a spherical mirrorcontained in a package that is highly efficient for measuring light diverging from the end of an opticalfiber. The mathematical derivation of the coupling efficiency relies on the integral directional responseweighted by the angular intensity distribution of an idealized parabolic optical beam. Results ofdirectional-uniformity measurements, acquired with the aid of a six-axis industrial robotic arm, indicatethat the trap has a collection efficiency greater than 99.9% for a fiber numerical aperture of 0.24. Spatialuniformity measurements indicate that the variation of detector response as a function of position is lessthan 0.1%. The detector’s absolute responsivity at 672.3, 851.7, and 986.1 nm is also documented bycomparison with other optical detectors and various input conditions and indicates that the design is wellsuited for laser and optical fiber power measurements.

OCIS codes: 060.2380, 120.3930.

1. Introduction

The demand for laser and optical fiber powermeter�OFPM� calibrations has increased along with theproliferation of optical communications systems. Asthese systems become more sophisticated and themarket for such equipment becomes increasinglycompetitive, the need for measurements having loweruncertainty is urgent. The accurate calibration ofOFPMs is made difficult by the limited field of view ofprimary standards for laser power �devices that com-pare absorbed optical power to dissipated electricalpower� and because of most available transfer stan-dards. The measurement uncertainty associatedwith the coupling of the diverging radiation from theoptical fiber and the OFPM are typically a majorcontribution to the total uncertainty of an OFPMcalibration. This uncertainty often exceeds 1%, andis substantially greater than the uncertainty of theprimary standards used with collimated beams.1

In this paper we describe our efforts to providelower uncertainty for OFPM calibrations through thedevelopment of a transfer standard with a couplingefficiency very near unity for optical fiber with a nu-

The authors are with the National Institute of Standards andTechnology 81501, Sources and Detectors Group, 325 Broadway,Boulder, Colorado 80305. J. H. Lehman’s e-mail address islehman@boulder.nist.gov.

Received 20 February 2002; revised manuscript received 11 July2002.

merical aperture �NA� of as much as 0.26; this accom-modates measurements with most optical fiberpresently used in optical communications. Thetransfer standard can thus be calibrated directlyagainst a primary standard with collimated radiationand used to measure optical power from a fiber accu-rately, without intervening optics.

The detector described here makes use of two de-tecting elements and a spherical mirror to achieve ahigh coupling efficiency over broad angles. We haveimplemented it initially with silicon �Si� photodiodes,which cover the important 800- to 900- and 980-nmspectral regions. They are, however, suitable for usein calibrating instruments over the broader range of450 to 990 nm, which is supported by some commer-cial OFPMs. The same design has been used witheither germanium �Ge� or indium gallium arsenide�InGaAs� photodiodes to extend its range to 1800 nm.

2. Design Description

The trap detector is based on two Si photodiodes 10mm � 10 mm square and a silver-coated concavemirror �40-mm focal length, 15-mm diameter�. Thephotodiodes and mirror are placed in a hardwarefixture having a threaded aperture suitable for anoptical fiber connector. This design is similar to apreviously documented Ge-photodiode and mirror-trap design.2 Unlike in the previous design, the di-odes are mounted on a ceramic carrier, withelectrical-contact pads in the same plane. Thismounting allows the diodes to be placed closer to-

1 November 2002 � Vol. 41, No. 31 � APPLIED OPTICS 6531

gether and closer to the input aperture. A schematicof a single diode mounted on the ceramic carrier isshown in Fig. 1. The relation of the five-sided car-rier and the position of the diodes �with the mirrorremoved� is shown in Fig. 2.

Shown in Fig. 3 are the orientation of the photo-diodes and the mirror, along with a geometric repre-sentation of light diverging from the center of theaperture as from the end of an optical fiber. Eachphotodiode is oriented relative to the aperture so thatthe principal ray intersects each diode once in se-quence at a 45° angle of incidence, and after reflectingfrom the concave mirror, the ray intersects back

again in reverse order. The concave-mirror curva-ture was selected and the mirror surface positionedso that the path of the reflected beam is nearly iden-tical to that of the incoming beam �which has a 28°divergence angle�. A collimated beam, after beingreflected by the concave mirror, has a focal planelocated between the fourth and the fifth reflections�the beam converges before exiting the trap cavity�.

3. Robotic Arm and Measurement Apparatus

The measurements of the field of view and spatialuniformity were accomplished with the aid of a six-axis, industrial �commercially available� robot armhaving six degrees of freedom, with optical encodersproviding position information on each axis. Themanufacturer has specified that the robotic arm iscapable of positioning the robot’s wrist with a preci-sion of 10 �m in terms of orthogonal coordinates x, y,and z and with a rotation precision of 0.01° in termsof angular coordinates �, �, and �. For convenience,we refer to these coordinates �x, y, z, �, �, and �� asrobot coordinates. In principle, robot coordinates re-fer to spherical coordinates relative to some arbitrarypoint in space that is fixed relative to the robot andcoincident with the center of the aperture of the de-tector being evaluated. These coordinates, shown inFig. 4, are useful for mapping the normalized inten-sity profile �discussed later� in coordinates that areconsistent with the measurement results for the de-tector’s directional responsivity.

The robotic arm was used to position atemperature-stabilized, 850-nm wavelength laser di-ode. The laser diode was attached to the robot’swrist so that the beam axis was coaxial with the wristrotation, defined by robot coordinate �. The diodelaser was focused at coordinates x � 0, y � 0, and z �0, with a 100-mm focal-length lens, and to a beam

Fig. 1. Plan view of the diode mounted on a five-sided ceramiccarrier with electrical-contact pads.

Fig. 2. Two Si photodiodes mounted relative to each other �mirrorand aperture-bearing case removed�.

Fig. 3. Relative orientation of the photodiodes, concave mirror,and diverging input beam depicted in three views.

6532 APPLIED OPTICS � Vol. 41, No. 31 � 1 November 2002

diameter of approximately 0.1 mm �that is, 99.9% ofthe total beam power was within a radius of 0.05 mmof the beam’s centroid�. For each measurement, thefocal point and the optical axis of the probe beamwere initially aligned to be centered and normal tothe detector-aperture plane. The absolute position-ing accuracy was approximately three times thevalue of the precision stated by the manufacturer.Using the spatial response of a lithographically pat-terned pyroelectric detector as a resolution target, wehave determined that the positioning uncertainty iswithin the stated accuracy of 30 �m and 0.03°.

During each field-of-view measurement the laserwas incrementally rotated by an angle � away fromnormal incidence. Then the laser was incrementallyrotated by angle �, for each angle �, to define theprobe beam’s orientation relative to the center of thedetector aperture. At each increment, the detector’sresponse was sampled, and the variation relative tothe response at normal incidence was recorded. Theessential data from the measurement were the incre-mental position of ��, �� and the detector’s currentresponse at each increment.

For each spatial uniformity measurement, the la-ser was incrementally positioned in a two-dimensional plane defined by z � 0, � � 0, and � � 0.For each position in the plane, the detector’s currentresponse was sampled and recorded.

4. Beam-Profile Formulation

To evaluate the detector design, we have estimatedthe uncertainty for a given optical fiber using a math-ematical model of the beam’s intensity profile basedon the NA of the optical fiber. The intensity profilewas translated into robot coordinates and mappedonto the directional-uniformity measurements of thedetector to determine the overall coupling efficiency.

The far-field intensity distribution of laser lightemitted from a multimode fiber is principally a func-

tion of the fiber NA, the launching conditions at theinput, and the length of fiber. The far-field diver-gence from multimode telecommunications fibergreatly exceeds that of single-mode fiber. For thatreason we consider the output of a multimode fiber asan example of the largest divergence likely to be en-countered by an OFPM.

Regardless of the wavelength and the fiber chosen,the divergence of light from the exit end of the fiber isless than the angle defined by the NA of the fiber.Multimode, graded-index communication fiber typi-cally has a range of NA between 0.20 and 0.28, whichcorresponds to a maximum full divergence angle 2wof approximately 32°. The NA is related to w by

NA � sin�w�. (1)

We have used an approximation to a strictly para-bolic intensity distribution, which is

P�r� �1 � r�rw�2

1 � r�rw�40 , (2)

where

r � c tan��, (3)

rw � c tan�w�. (4)

The value of r is a distance from the optical axisdefined by incidence angle and a distance c beyondthe aperture plane. The beam’s half-width rw is de-fined for a specified divergence half-angle w fromEq. �1��. This profile matches the generally observedoutput distribution of a multimode fiber with a qua-dratic behavior near the center of the distributionand a small tail near the maximum divergence half-angle. This equation is based on the criterion ofdefining the beam width rw as equal to the beamdiameter where the irradiance is 5% of the irradianceat the center �r � 0�. �The choice of the 5% level isbased on the recommendation of the Telecommuni-cation Industry Association in the United States, andothers, for determining the NA of an optical fiber.3�

To evaluate the detector’s coupling efficiency, wemust incorporate the detector’s measured directionalresponse R��, �� as a function of angle of incidence,relative to the center of the X–Y plane of the detectoraperture. The position ��, �� is related to the angleof incidence by the equation

cos�� � cos���cos���. (5)

An example of the normalized intensity profile for2w � 4° ��2°�, 20° ��10°�, and 32° ��16°� is shownin Fig. 5.

In principle, the collection efficiency, , of the trapdetector is a convolutionlike integral of the calculatedbeam profile P��, �� and the measured, relative di-rectional response R��, �� of the detector for a finite

Fig. 4. Geometric relation of the robot’s coordinates, the detec-tor’s aperture plane, and the orientation of the angle of incidenceof the probe beam at angle .

1 November 2002 � Vol. 41, No. 31 � APPLIED OPTICS 6533

beam divergence �2w� and the entire, field of view ofthe detector:

� ����2

��2

����2

��2 �P��, �� R��, ��

cos���cos2�� �d�d�. (6)

In Eq. �6�, it is assumed that the detector’s responseR��, �� � 1 at ��, �� � �0, 0� and that the beam profileis normalized so that

1 � ����2

��2

����2

��2 � P��, ��

cos���cos2���d�d�. (7)

In practice, evaluation of the coupling efficiency islimited because one has a finite data set that is ac-quired when the detector’s response is sampled atincremental positions of the robotic arm, thus satis-fying a two-dimensional array of positions. For thedetector’s response R��, �� at each robotic arm posi-tion , we calculated a value of the normalized inten-sity profile P��, ��.

5. Directional Uniformity and Coupling Efficiency

We acquired R��, �� and calculated P��, �� for valuesof � and � ranging from 0° to �16° at 2° increments�maximum � 22.5°�. The measurement results ofR��, �� are shown in Fig. 6, with the relative detectorresponse as ordinate values and with the angle ofincidence as abscissa values. Several values ofR��, �� for a single value of are apparent in Fig. 6because the value of is the same for unique pairs of�� and ��, directed in each quadrant of the X–Yplane. Figure 7 shows the relative coupling effi-ciency as a function of NA calculated from Eq. �6�,where the NA is related to w as shown in Eq. �1�.Each data point corresponds to incremental values ofthe normalized intensity profile �three examples ofwhich are shown in Fig. 5�. The coupling efficiencyis a quantitative basis for expressing the uncertaintyof the directional-uniformity measurements shown inFig. 6. The uncertainty can be stated for any NAthat we wish to define as long we assume that the

parabolic intensity profile is a reasonable worst-casesituation for light leaving a fiber and entering thedetector. The results shown in Fig. 7 indicate thatthe coupling efficiency of the trap detector is greaterthan 99.9% for NA values of as much as 0.24 ��14°fiber-exit divergence� and 99.5% for subsequent NAvalues of as much as 0.28 ��16° fiber-exit diver-gence�. The coupling efficiency loss is therefore be-tween 0.1% and 0.5% for an NA between 0.24 and0.28, which may be associated with the extremerange of the expected divergence from multimodecommunication fiber �core diameter of 50 or 62.5 �mand transmitting laser light in the visible and in thenear infrared�. Therefore, for multimode fiber-coupled measurements of absolute responsivity it isreasonable to incorporate a type B uncertainty of0.1% to 0.5% into the overall measurement uncer-tainty of which the detector is capable.4

6. Spatial Uniformity

Evaluation of the detector’s spatial uniformity isparticularly important when we compare differ-ences between fiber-coupled and free-space lasermeasurements. In the case of fiber-coupled mea-

Fig. 5. Sample profiles of the normalized beam irradiance at �2°,�10°, and �16°.

Fig. 6. Directional responsivity measurement results.

Fig. 7. Coupling efficiency of the optical trap detector deter-mined from the normalized beam profile and measurement resultsshown in Fig. 6.

6534 APPLIED OPTICS � Vol. 41, No. 31 � 1 November 2002

surements, the position of an incoming beam is fixedrelative to the fiber connector, which is rigidly at-tached to the detector. The position and size of anincoming free-space laser beam may vary. If thedetector’s response is not uniform as a function of theposition, then all other things being equal betweenthe fiber and the free-space measurement, the uncer-tainty of the measurement depends on the variationof the detector’s response as a function of position.

We measured the detector’s spatial uniformity us-ing a laser mounted on the robotic arm as describedin Section 3. The laser beam was scanned at0.5-mm intervals across a 10 mm � 10 mm planararea and centered on the detector aperture �normal tothe detector aperture and at a 45° angle of incidencerelative to the first photodiode surface� while the de-tector output data were collected. The resultsshown in Fig. 8 indicate that the responsivity variesby less than 0.1% over a 7 mm � 7 mm area centeredon the detector aperture. This variation is signifi-cantly less than that of our existing transfer standardfor OFPM calibrations for the 450- to 1100-nm wave-length range.5 Based on this variation, we must in-corporate a type B uncertainty of 0.1%.

We have addressed the properties of spatial and ofdirectional uniformity, and hence the relative cou-pling efficiency, because they represent an evaluationof the aspects of the detector design that are new andunique. The absolute responsivity is also importantfrom the standpoint of comparing the detector’s per-formance for fiber-coupled versus free-space mea-surements and represents the necessary andintended use of the transfer standard over a range ofwavelengths and optical input conditions. In otherwords, the outcome of the absolute responsivity com-

parisons tells us whether the transfer standard cando the work for which it was designed.

7. Absolute Responsivity

We measured the absolute responsivity using threedifferent comparison methods. The responsivitywas compared with a wedge-trap pyroelectric detec-tor over a range of wavelengths from 450 to 1100 nm,at 10-nm increments by means of a monochromatorand a broadband-lamp source.1 The responsivitywas also compared with that of an electrically cali-brated pyroelectric detector at discrete laser wave-lengths in two different ways. In one case the lightwas transmitted by fiber and connected to the detec-tor aperture with an FC-type connector, and in theother case the light was nearly collimated and trans-mitted through space. In the latter two compari-sons, the calibration traceability and uncertaintyhave been documented and discussed by Vayshenkeret al.6 By finding agreement in the absolute respon-sivity measured three different ways, we have fur-ther evidence that the detector is highly efficient andthat the measurement uncertainty we assess on thebasis of directional and spatial uniformity measure-ments is reasonable.

The results of the absolute responsivity measure-ments are shown in Table 1. Using collimated laserbeams at 672.3, 851.7, and 986.1 nm, we found thatthe absolute spectral responsivity was nearly thesame as that measured with a lamp source and amonochromator. With the same laser sources, butwith the radiation transmitted through fibers termi-nated with FC�PC-type connectors, the absolute re-sponsivity at each wavelength was nearly identical tothat obtained when collimated beams or a lampsource was used. The expanded uncertainty �withan expansion factor of k � 2� of the lamp and themonochromator measurements was less than 1.25%,and less than 0.5% for the laser-based measure-ments.

8. Comparison

The maximum difference in absolute responsivity be-tween open-beam and fiber-coupled measurement re-sults, determined from the calibration of laserpowermeters at our facility, has been as large as10%.7 The 0.1% difference �fifth column, Table 1�measured for the current device demonstrates thatthe large uncertainties of absolute responsivity ob-

Fig. 8. Spatial uniformity of the Si trap detector.

Table 1. Absolute Spectral Responsivity

Wavelength�nm�

LaserCollimated

�A�W�

Laser FC�PCFiber Connector

�A�W�

LampMonochromator

�f�4��A�W� Difference �%�a

672.3 0.5389 0.5370 0.5376 �0.11851.7 0.6804 0.6815 0.6810 �0.07986.1 0.7770 0.7770 0.7766 0.05

aDifferences from laser FC�PC fiber connector and lamp monochromator.

1 November 2002 � Vol. 41, No. 31 � APPLIED OPTICS 6535

tained in the past depend on the test detector and noton the measurement system. This fact does notmean that the laser powermeters we have calibratedin the past are unsuitable for optical fiber power mea-surements. Rather, if fiber-coupled absolute re-sponsivity measurements are to be compared withopen-beam absolute responsivity measurements�that is, without fiber attached to a fiber connector�,some detector designs are better suited than others.

9. Discussion

The trap design has been adapted to Ge as well as toInGaAs photodiodes for measurements at longerwavelengths, such as between 850 and 1750 nm. Inprinciple, Ge or InGaAs photodiodes in the trap con-figuration are as equally well suited at longer wave-lengths as the Si photodiodes are for shorterwavelengths. It may be argued, however, that In-GaAs photodiodes are preferred over Ge photodiodesbecause InGaAs photodiodes have higher quantumefficiency at room temperature and are less sensitiveto ambient temperature variations.8 Unfortunately,spatially uniform InGaAs photodiodes, if available,are nearly ten times more expensive than Ge photo-diodes.9 Also, as with the use of any large-area pho-todiodes �or several small photodiodes electricallyconnected in parallel�, one must know the shunt re-sistance when using large Ge or InGaAs photodiodes.Unacceptably low shunt resistance may prevent ac-curate evaluation of small optical signals that arecommon for optical fiber power measurements.10

The problem of low shunt resistance can be addressedby use of a current-to-voltage converter for each pho-todiode in the trap or by use of an amplifier designedto accommodate the low shunt resistance, but thiscomplicates the design and introduces other trade-offs.8

10. Conclusion

The feature that distinguishes this trap detector fromits predecessors is its uniform directional responsiv-ity over a larger acceptance angle. Our goal in per-forming this evaluation was to state an uncertaintycontribution based on the quantitative evaluation ofthe coupling efficiency rather than on estimates usedin the past. Our measurement results indicate thatthe detector is well suited for input from collimatedlaser sources as well as from multimode fiber having

an NA as large as 0.26. The benefits of high optical-to-electrical conversion efficiency, reasonable cost,and excellent directional and spatial uniformitymake the detector a valuable tool for calibrating laserand OFPMs.

We thank Igor Vayshenker for the optical fiberpower measurements and the Calibration Coordina-tion Group �by direction of the U.S. Navy and the U.S.Army Standards Laboratories� for support of this re-search.

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laser and optical-fiber power meters at wavelengths between0.4 �m and 1.8 �m,” NIST Spec. Publ. 250-53 �National Insti-tute of Standards and Technology, Boulder, Colo., 1999�, pp.1–39.

2. J. H. Lehman and X. Li, “A transfer standard for optical fiberpower metrology,” Eng. Lab. Notes in Opt. & Photon. News,May 1999 Appl. Opt. 38, pp. 7164–7166 �1999��.

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7. R. L. Gallawa and X. Li, “Calibration of optical fiber powermeters: the effect of connectors,” Appl. Opt. 26, 1170–1174�1987�.

8. G. Eppeldauer, “Optical radiation measurement with selecteddetectors and matched electronic circuits between 200 nm and20 �m,” NIST Technical Note 1438 �National Institute of Stan-dards and Technology, Boulder, Colo., 2001�, pp. 63–68.

9. E. Theocharous, N. P. Fox, and T. R. Prior, “A comparison ofthe performance of infrared detectors for radiometric applica-tions,” in Optical Radiation Measurements III, J. M. Palmer,ed., Proc. SPIE 2815, 56–68 �1996�.

10. N. P. Fox, “Improved near-infrared detectors,” Metrologia 30,321–325 �1993�.

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