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1、1422IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003 Calibrated Measurement of Optoelectronic Frequency Response Paul D. Hale, Senior Member, IEEE, and Dylan F. Williams, Fellow, IEEE AbstractWe describe the most straightforward method for accurately measuring the fre
2、quency response of optoelectronic devices. The method uses a calibrated optical reference receiver, a modulated optical source, and a calibrated electrical vector network analyzer. Index TermsCalibration, frequency response, measurement, optoelectronic devices, scattering matrices. I. INTRODUCTION W
3、 E DESCRIBE how a calibrated electrical vector net- work analyzer (VNA), modulated optical source, and calibrated optical reference receiver are used to accurately mea- surethefrequencyresponseofalargeclassofoptoelectronicde- vices including MachZehnder modulators, electroabsorption modulators,direc
4、tlymodulatedsemiconductorlasers,andlinear optical receivers. Although this type of measurement system is commonly used in the optoelectronics community, the theory behind the measurements and the procedures and restrictions necessary for accurate calibration are not generally well known. Indeed, the
5、re are several competing approaches to optical and optoelectronic network analysis in the literature, some of which may not be justified given the physics of the optoelectronic in- teractions and the limited information that the simple measure- ment system can provide. Toclarifytheoperationofthesesy
6、stemsandtheirlimitations, we develop a simple optoelectronic scattering matrix formalism that is consistent with standard microwave theory and practice. The formalism relates the optical modulation envelope at one port of the device to the electrical wave at the other port and describes the performa
7、nce of optical receivers and modulated optical sources. We then apply the formalism to calibration of the optoelectronic measurement system and demonstrate with some simple examples. Our formalism requires that no optical signals propagate in the reverse direction between the modulated optical sourc
8、e and receivertoeliminateinterferenceoftheopticalcarrierwithitself that cannot be accounted for by the test equipment or the scat- tering matrix formalism. To the best of our knowledge, this re- strictionhasneverbeendiscussedintheliterature.InSectionIX, wediscussthereasonsforthisrestrictionandcompar
9、eourtreat- mentwithotheroptoelectronicscatteringmatrixformalismsand measurement methods in the literature. Manuscript received January 29, 2002. The authors are with the National Institute of Standards and Technology, Boulder, CO 80305 USA (e-mail: haleboulder.nist.gov). Digital Object Identifier 10
10、.1109/TMTT.2003.809186 Fig. 1.Schematic showing waves flowing in and out of component. Ports 1 and 2 are represented by dotted lines. The calibration and measurement procedure we describe in this paper is easier to perform than the one we previously describedin1:thecalibratedVNAperformsalloftheelect
11、rical mismatch corrections automatically and it does not require a calibratedpowermeter.Lightwavecomponentanalyzers(LCAs) suchasthosedescribedin2canalsoperformthemeasurements described here, and must also be calibrated. In Appendix V, we describe how to apply the method to calibration or verificatio
12、n of LCAs. Some of the theory and procedures we describe in this paper have been outlined in 3 and 4, and are similar to those recommended by LCA manufacturers 2. Finally, AppendixesIIII discuss relations between the quan- titiesmeasuredbytheVNAsystemdescribedhereandThvenin and Norton equivalent sou
13、rces, normalized receiver response, and the input drive voltage, input drive current, and-voltages of modulated sources. II. ELECTRICALSCATTERINGMATRICES We start by briefly reviewing standard microwave circuit theory 5, 6. We explicitly define the electrical quantities we will use since their defin
14、itions effect our measured optoelec- tronic quantities. Standard microwave circuit theory defines all electrical pa- rameters in single-mode electrical waveguides connecting all devices. As illustrated in Fig. 1, we begin by defining a single- frequency sinusoidal voltageand current at each port, wh
15、eregives the real part of its argument, is the complex amplitude of the voltage, is the complex ampli- tudeofthecurrent,is thefrequency inradians persecond,and is the time. We also define an incident-wave amplitudeand a reflected-wave amplitudeat each port in terms of the voltage amplitudeand curren
16、t amplitudevia (1) 0018-9480/03$17.00 2003 IEEE HALE AND WILLIAMS: CALIBRATED MEASUREMENT OF OPTOELECTRONIC FREQUENCY RESPONSE1423 Fig. 2.Schematic showing electrical waves and optical power flowing in and out of an optoelectronic system. The electrical and optical ports are represented by dashed li
17、nes. Here,isarealreferenceimpedance,whichisusuallysetto 50. These waves are the “pseudo-waves” of 6. These waves correspondtothetravelingwavesinthewaveguide6 whenthe characteristic impedance of the waveguide is real and equal to . The incident and reflected waves in (1) are scaled by the factorso th
18、at the powerdelivered to each port is (2) That is, the power crossing the reference plane at each port is the incident powerless the reflected powerleaving the port. We call a one-port device with an impedance equal toa matched load. For a matched load, the reflected wave amplitude(i.e., the reflect
19、ion coefficientof a one-portmatchedloadiszero),andthematchedloadcompletely absorbs the incident wave. Fig.1illustratestheincidentandreflectedwavesatatwo-port device, where subscripts “1” and “2” indicate the port number. Theincidentandreflectedwavesofatwo-portdevicearerelated via the scattering or-m
20、atrix (3) An electrical VNA calibrated in the conventional fashion mea- sures the scattering parametersof the device with a refer- ence impedance6. The elements of the-matrix are dimensionless because they are ratios of theandwaves. We calla reflection coefficient andthe forward trans- mission coeff
21、icient of the device. III. SCATTERINGMATRICES OFOPTOELECTRONICSYSTEMS Let us determine the scattering parameters of the optoelec- tronic system shown in Fig. 2. It consists of two separate com- ponents connected by an optical fiber: an optical modulator (or directlymodulatedlaser)ontheleft-handside,
22、andanopticalre- ceiver on the right-hand side. The system has a single electrical input port and a single electrical output port. The optical modu- lator uses electrical signals at its input port (port 1 in this figure) to linearly modulate the intensity (power) of the optical signal at the optical
23、port. The receiver responds linearly to the optical power, not the carrier, and is sometimes called a square-law de- tector. Hence, the receiver linearly converts the intensity-modu- lated optical signal back into an electrical signal at its electrical output port (port 2 in this figure). We require
24、 that the optical powerpropagating in the for- ward direction at the optical port between the modulator and re- ceiver, due to a single-frequency electrical excitation, be of the form 79 (4) In (4),is a (real) modulation index andis the phase of the modulation envelope. We do not restrict the freque
25、ncy or phase modulation of the optical carrier because the optical receiver does not respond to the optical carrier: it only responds to the modulation envelope. The linear modulation described by (4) is generally available from directly modulated semiconductor lasers and integrated modulators that
26、are suitably biased and driven by a small signal. We can reasonably neglect harmonics of the drive electrical signal generated by the modulator 10 because the VNA has a tuned receiver that effectively blocks the weak harmonics generated by real modulated sources. As we stated earlier, we also requir
27、e that there be no optical power propagating in the reverse direction (i.e., coming from or reflected by the receiver or other optical component). This con- straint avoids optical interference that would further complicate (4). We discuss this further in Section IX. The modulator reflects some of th
28、e electricalwave inci- dent on the circuit from the left-hand side, generating an out- goingwave. However, since no optical power travels from right-hand side to the left across the optical port, a wavein- cidentfromtheright-handsidecannotcontributetotheoutgoing wave. Thus, we have, whereis the elec
29、trical reflection coefficient of the modulator. We have already required that the modulator linearly modu- late the power in the optical beam so the instantaneous optical power coming out of the modulator can be written as (5) whereis the complex response of the modulator. Since we have required tha
30、t there be no optical interference at the optical port, we can equate the modulated signal generated by the mod- ulator with the modulated signal entering the receiver: (6) Sincerelates an electrical amplitude to an optical power, it has the rather peculiar units of (optical power)/(square root of e
31、lectrical power), i.e., the square root of power. The electrical waveemanating from the receiver has two sources: the modulated optical power incident on the receiver and the electricalwave incident from the right-hand side and reflected back by the receivers imperfect match. We define the receivers
32、 complex responseby (7) describes the amplitude of the forward electrical wave cre- ated by an intensity modulated optical signal with modulation indexwhen, i.e., when the receiver is connected to a matched load. Sincelinearly relates an optical power to an 1424IEEE TRANSACTIONS ON MICROWAVE THEORY
33、AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003 electrical amplitude, it has the units of one over the square root of power. Since the electrical system is linear, we can add the signal generated by the optical wave incident on the receiver to the electrical wave it reflects from its electrical port to o
34、btain , whereis the electrical reflection coeffi- cient of the receiver. Combining (6) with the above relation, we obtain the fol- lowing equations relating the electrical waves with frequency at ports 1 and 2: (8) These equations can be written in matrix form as (9) giving the electrical scattering
35、 matrix for the total system com- prised of the laser, modulator, and receiver. IV. MEASUREMENT OFANDIN ACOAXIALSYSTEM Now that we have built a framework for our optoelectronic measurements, measurement oforwith a calibrated elec- trical VNA is straightforward. First, we calibrate the VNA with a ful
36、l two-port calibration with a 50-reference impedance and use it to measure the scattering parameters of a modulated optical source connected to our calibrated reference receiver with known response(see Fig. 2). Using (9), we determine the responseof the optical modulator fromand its reflection coeff
37、icientfrom, completing characteri- zation of the modulator. If we replace our calibrated reference receiverwithanuncharacterizedreceiver,wecanrepeatthepro- cedure and determine the uncharacterized receivers response from, and its reflection coefficientfrom, where the primed quantities refer to the m
38、easurements of the second receiver. Our calibration approach uses a complex responsethat ac- counts for both the magnitude and phase response of the refer- encereceiver.Inthepast,calibrationofthephaseresponseofthe reference receiver has relied on methods that are not traceable to fundamental physica
39、l principles. In 11, a VNA and a model of the modulator was used to estimate the phase response of the referencereceiver.Anoscilloscopewhoseresponsewasderived from a model was used in 12 to estimate the phase response of a receiver. Also, oscilloscopes that were calibrated with the nose-to-nose meth
40、od (described in 13 and 14) were used to characterize the phase response of receivers in 15. A recently developed method for measuring both the magnitude and phase response of an optical receiver, which can be made traceable to fundamental physical principles, is described in 16 and 17. Traceable me
41、asurement of the response phase of a reference re- ceiver is currently an area of intense research and is outside the scope of this tutorial. Fig. 3.Comparison of measured normalized response (?, described in Appendix I) of a commercial optical receiver. The data has also been normalized to 0 dB at
42、the lowest frequency. The expanded uncertainty?in the heterodyne measurements is approximately 0.12 dB. V. MEASUREMENTEXAMPLE We applied the method described above to determine the magnitude response of a commercial receiver. We used an integrated MachZehnder modulator in the experiment, and we cali
43、brated the response magnitude of our reference receiver with the heterodyne method of 18 and microwave correc- tions of 1. The heterodyne measurement method is used in standards laboratories because it is traceable to fundamental physical principles and can be implemented with a very low uncertainty
44、 19. Fig.3comparesournormalizedVNAmeasurementtoadirect heterodynemeasurementperformedwiththeprocedures of18 and 1, which has a typical combined standard uncertainty of approximately 0.06 dB. The calibrated VNA curve is noisy because of the weak signal from the unamplified receiver, which is operatin
45、g at a low photocurrent to maintain receiver linearity. Nevertheless, this figure demonstrates the accuracy of the procedure based on a calibrated VNA and calibrated reference receiver. To illustrate the importance of the corrections performed by the network analyzer, we turned off the network analy
46、zers cal- ibration and repeated the measurement. The uncalibrated VNA curve of Fig. 3 clearly shows the importance of corrections and the need for calibrating the network analyzer. VI. LINEARITY As mentioned above, the linearity of the receiver is an important consideration. The unmodulated portiono
47、f the optical signal flowing through the modulator can saturate the response of the receiver 20. Reference receivers with a high compression point minimize this effect. Examples of highly linear receives are given in 2123. You can verify linear operation by changingto(where) and verifying thatchange
48、s to, within an acceptable level of accuracy. HALE AND WILLIAMS: CALIBRATED MEASUREMENT OF OPTOELECTRONIC FREQUENCY RESPONSE1425 VII. SCATTERINGMATRICES OFINDIVIDUAL OPTOELECTRONICCOMPONENTS The electrical behavior of any modulatorreceiver pair sat- isfying the basic assumptions we employed in this
49、study can be analyzed with the scattering matrix (9). However, the scat- tering parameters of a modulatorreceiver pair can be formally decomposed into a scattering matrixfor the modulator and a scattering matrixfor the receiver with (10) These matrices have the properties that, when cascaded using the conventional rules for combining electrical circuits outlined in 5 and 6, they give the matrix (9). That is, when andare converted into cascade matrices (as described in Appendix IV), multiplied together, a