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2 GHz the system is operated in free-run mode with thermal tuning of the laser beat .... response or slow settling-time of high-bandwidth receivers. .... This photocurrent was measured by use of a digital volt meter (DVM) to monitor the voltage.
High-accuracy photoreceiver frequency response measurements at 1.55 µm by use of a heterodyne phase-locked loop Tasshi Dennis* and Paul D. Hale National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA *[email protected]

Abstract: We demonstrate a high-accuracy heterodyne measurement system for characterizing the magnitude of the frequency response of highspeed 1.55 µm photoreceivers from 2 MHz to greater than 50 GHz. At measurement frequencies below 2 GHz, we employ a phase-locked loop with a double-heterodyne detection scheme, which enables precise tuning of the heterodyne beat frequency with an RF synthesizer. At frequencies above 2 GHz the system is operated in free-run mode with thermal tuning of the laser beat frequency. We estimate the measurement uncertainties for the low frequency range and compare the measured high-frequency response of a photoreceiver to a measurement using electro-optic sampling. 2011 Optical Society of America OCIS codes: (060.2330) Fiber optic communications; (040.5160) Photodetectors; (120.3940) Metrology; (060.2380) Fiber optics sources and detectors; (060.2840) Heterodyne

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T. S. Clement, P. D. Hale, D. F. Williams, J. C. M. Wang, A. Dienstfrey, and D. A. Keenan, “Calibration of sampling oscilloscopes with high-speed photodiodes,” IEEE Trans. Microw. Theory Tech. 54(8), 3173–3181 (2006). A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, “Minimum-phase calibration of sampling-oscilloscopes,” IEEE Trans. Microw. Theory Tech. 54(8), 3197–3208 (2006). P. D. Hale, A. Dienstfrey, J. C. M. Wang, D. F. Williams, A. Lewandowski, D. A. Keenan, and T. S. Clement, “Traceable waveform calibration with a covariance-based uncertainty analysis,” IEEE Trans. Instrum. Meas. 58(10), 3554–3568 (2009). P. D. Hale, C. M. Wang, R. Park, and W. Y. Lau, “A transfer standard for measuring photoreceiver frequency response,” J. Lightwave Technol. 14(11), 2457–2466 (1996). P. D. Hale and C. M. Wang, “Calibration service of optoelectronic frequency response at 1319 nm for combined photodiode/RF power sensor transfer standards,” NIST Special Publication 250–51 (1999). J. E. Bowers and C. A. Burrus, “Ultrawide-band long-wavelength p-i-n photodetectors,” J. Lightwave Technol. 5(10), 1339–1350 (1987). R. T. Hawkins, M. D. Jones, S. H. Pepper, J. H. Goll, and M. K. Ravel, “Vector characterization of photodetectors, photoreceivers, and optical pulse sources by time-domain pulse response measurements,” IEEE Trans. Instrum. Meas. 41(4), 467–475 (1992). D. F. Williams, P. D. Hale, T. S. Clement, and J. M. Morgan, “Calibrating electro-optic sampling systems,” in IEEE MTT-S Int. Microw. Symp. Dig., vol. 3 (2001), pp. 1527–1530. D. F. Williams, A. Lewandowski, T. S. Clement, J. C. M. Wang, P. D. Hale, J. M. Morgan, D. A. Keenan, and A. Dienstfrey, “Covariance-based uncertainty analysis of the NIST electrooptic sampling system,” IEEE Trans. Microw. Theory Tech. 54(1), 481–491 (2006). F. Z. Xie, D. Kuhl, E. H. Böttcher, S. Y. Ren, and D. Bimberg, “Wide-band frequency response measurements of photodetectors using low-level photocurrent noise detection,” J. Appl. Phys. 73(12), 8641–8646 (1993). D. M. Baney, W. V. Sorin, and S. A. Newton, “High-frequency photodiode characterization using a filtered intensity noise technique,” IEEE Photon. Technol. Lett. 6(10), 1258–1260 (1994). S. Uehara, “Calibration of optical modulator frequency response with application to signal level control,” Appl. Opt. 17(1), 68–71 (1978). D. A. Humphreys, M. R. Harper, A. J. A. Smith, and I. M. Smith, “Vector calibration of optical reference receivers using a frequency-domain method,” IEEE Trans. Instrum. Meas. 54(2), 894–897 (2005). B. H. Zhang, N. H. Zhu, W. Han, J. H. Ke, H. G. Zhang, M. Ren, W. Li, and L. Xie, “Development of swept frequency method for measuring frequency response of photodetectors based on harmonic analysis,” IEEE Photon. Technol. Lett. 21(7), 459–461 (2009).

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15. J. Wang, U. Krüger, B. Schwarz, and K. Petermann, “Measurement of frequency response of photoreceivers using self-homodyne method,” Electron. Lett. 25(11), 722–723 (1989). 16. N. H. Zhu, J. M. Wen, H. S. San, H. P. Huang, L. J. Zhao, and W. Wang, “Improved optical heterodyne methods for measuring frequency response of photodetectors,” IEEE J. Quantum Electron. 42(3), 241–248 (2006). 17. L. Piccari and P. Spano, “New method for measuring ultrawide frequency response of optical detectors,” Electron. Lett. 18(3), 116–118 (1982). 18. S. Kawanishi and M. Saruwatari, “A very wide-band frequency response measurement system using optical heterodyne detection,” IEEE Trans. Instrum. Meas. 38(2), 569–573 (1989). 19. O. Ishida, H. Toba, and F. Kano, “Optical sweeper with double-heterodyne frequency-locked loop,” Electron. Lett. 25(22), 1495–1496 (1989). 20. A. Beling, H.-G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “High-speed miniaturized photodiode and parallel-fed traveling-wave photodetectors based on InP,” IEEE J. Sel. Top. Quantum Electron. 13(1), 15–21 (2007). 21. T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Tech. 37(8), 1217–1222 (1989). 22. D. A. Humphreys, “Measurement of high-speed photodiodes using DFB heterodyne system with microwave reflectometer,” in High-Speed Electronics and Optoelectronics, Proc. SPIE 1680–15, 138—152 (1992). 23. K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6-34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989). 24. M. Weidman, “Direct comparison transfer of microwave power sensor calibration,” NIST Technical Note 1379 (1996). 25. L. D’Evelyn, L. Hollberg, and Z. B. Popovic, “A CPW phase-locked loop for diode-laser stabilization,” in Microwave Symposium Digest 1994, IEEE MTT-S International (1994), pp. 65–68. 26. B. W. Silverman, Density estimation for statistics and data analysis (Chapman and Hill, London, England, 1986). 27. B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Technical Note 1297 (1994). 28. P. D. Hale, T. S. Clement, and D. F. Williams, “Frequency response metrology for high-speed optical receivers, in Optical Fiber Communication Conference and Exhibit, OFC Technical Digest Series (Optical Society of America, 2001), paper WQ1.

1. Introduction Future optical networks for 100 Gb/s and beyond will continue to demand higher-accuracy characterization of signals to achieve optimum performance as signal margins become tighter. For example, eye-mask testing of transceivers relies critically on accurate time and amplitude calibration of sampling oscilloscopes in order to achieve and maintain economic production yields. NIST has supported the high-accuracy characterization of photodiode-based receivers as calibrated electrical sources to provide time- and frequency-domain transfer standards [1– 5]. A consistent goal of this effort has been to reduce measurement uncertainties for frequency response calibrations while providing them at ever-higher bandwidths to support the everincreasing bit rate of optical networks. However, as networks have moved toward complex modulation formats to achieve higher throughput at the same symbol rates, the signal margins have had to become even tighter. Network testing is also being done with longer data sequences that better resemble real data traffic. Doing so increasingly tests the low-frequency response or slow settling-time of high-bandwidth receivers. In addition, the cable TV (CATV) industry depends critically on being able to accurately characterize the optical response of transceivers from only a few megahertz to about 3 GHz. And finally, testing of microprocessors and interconnects depends critically on quantitative waveform metrology using high-bandwidth sampling oscilloscopes that have been characterized over long durations. Likewise, high-bandwidth photoreceivers used as transfer standards for the calibration of waveform and frequency response measurement equipment should also be calibrated at high as well as low frequencies. With the response calibration of photoreceivers extending into the low-megahertz regime, quantitative measurements of optical and electrical waveforms approaching 1 µs in duration may become technically feasible. In this work we describe a technique for accurately achieving this calibration. A number of techniques have been developed to characterize the frequency response of photoreceivers [6]. The pulse excitation method usin g a sampling oscilloscope [7] is capable

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of providing the magnitude as well as the phase response, but depends on time-domain deconvolutions and some systems modeling. Electro-optic sampling (EOS) is another pulse excitation method that can provide the magnitude and phase response of a photoreceiver [8, 9]. Calibrations using EOS can be related to fundamental quantities; however, the method is not well-suited to measurements below about 600 MHz. The broadband noise excitation method [10, 11] is very simple to implement. However, like a number of techniques, it relies fundamentally on knowing the frequency response of another device, such as a transmittermodulator, reference photoreceiver, or instrumentation such as a network analyzer. In effect, these techniques serve as a method of transferring a known response calibration to a photoreceiver under test. In the harmonic swept-frequency modulation methods [12–14], the frequency response of the modulator does not need to be known, but an assumption that the modulator follows a well-known or ideal process must be made, which may introduce measurement errors. The self-heterodyne methods [15, 16] offer the simplicity of a single laser source, but do not provide a way to control or compensate for linewidth noise on the resulting heterodyne signal. A stimulus with a broadened linewidth will make it difficult to operate at low frequencies or resolve sharp resonant features. Other methods for measuring response may not scale easily to high frequencies or may suffer from temporal instabilities. However, the heterodyne method involving two lasers [4, 5, 17–22] has proven to be of value to photoreceiver metrology for nearly 30 years, for a multitude of reasons. The heterodyne method using two lasers is capable of generating an optical stimulus of very high accuracy, and also at very high frequencies without further difficulty. In fact, the uncertainties for a heterodyne response measurement are typically dominated by the uncertainty of the RF power sensor calibration [4, 5] required by the technique. As we will review, this technique has the advantage that the excitation of the photoreceiver can be calculated from first principles. In addition, the calibration of the measurement system is wellunderstood and well-behaved, remaining largely invariant during operation as the measurement frequency is swept. The first swept heterodyne demonstration using laser diodes to measure the response of an optical detector was performed with temperature tuning at 870 nm [17]. Since that time, the heterodyne technique has expanded to include more wavelengths (1.3 and 1.5 µm), diode and solid state lasers, controlled frequency sweeping [18], frequency locking [19], and very high frequencies on wafer [20]. Phase-locked-loop operation of a heterodyne system has been demonstrated by use of very low-noise Nd:YAG lasers at 1.3 µm, enabling Hertz-level frequency control with a sub-kilohertz heterodyne stimulus for high-accuracy and highresolution response calibrations [5, 23]. However, at the 1.55 µm wavelength commonly used in telecommunications optical networks, a corresponding calibration system has not been realized, to our knowledge. The primary challenge has been the lack of low-noise tunable lasers at 1.55 µm. Most diode lasers, whether tuned by temperature or external gratings, are simply too noisy, with 1-second linewidths of 10 MHz or more. As a result, typical phaselocked-loop systems don’t have enough bandwidth to lock systems based on diode lasers,

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Fig. 1. The heterodyne measurement system is shown with a representative receiver to be measured. A photodiode-based receiver is illustrated within the dotted circle, and a combined receiver and power sensor is illustrated within the dotted rectangle. PLL: phase-locked loop, DVM: digital voltmeter, Vb: bias voltage, Rb: bias resistor, PD: photodiode, RL: load resistor, M: mismatch correction, Kb: calibration factor.

either because of limits to the electronic phase detection or the optical feedback element that corrects the phase. In the phase-locked-loop system we will describe, we avoid the linewidth problem of diode lasers by using 1.5 µm tunable fiber lasers having a linewidth specification of less than 1 kHz. In addition, we use an acousto-optic frequency modulator to externally provide high-bandwidth phase-locking. The heterodyne technique combines the output of two narrow-linewidth lasers having a difference in frequency equal to the desired excitation frequency of the photoreceiver. If the two lasers are equal in power and have the same state of polarization, the desired condition of nearly 100% modulation depth will be achieved. The total optical power incident on the photoreceiver is then described by

Ptotal (t ) = ( P01 + P02 ) + 2 P01 P02 cos(2π ft ),

(1)

where PO1 and PO2 are the incident optical powers of the two lasers, f is their frequency difference, and t is time. We consider here the response of a photoreceiver module, as illustrated within the dashed circle of Fig. 1. Besides the photodiode, a typical module contains a load resistance RL and provides access to the bias current, which can be monitored by the external resistor Rb. The normalized frequency response of the photoreceiver, ℜ2 , is defined as the ratio R2(f)/R2(0), where R(f) is the responsivity (in A/W) of the photoreceiver at frequency f, and R(0) is the DC responsivity. As shown in Ref. 4 and 5, the normalized frequency response can be accurately approximated as the ratio of the RF power delivered to the load RL and designated as PRF, to the DC electrical power that would be delivered to load RL as related to the current idc by

R 2 ( f ) 2 PRF ( f ) (2) ≅ 2 . R 2 (0) 〈idc 〉 RL The convenience of the normalized response, by needing only to measure idc, is that the individual optical powers delivered to the photoreceiver from each laser do not need to be known. Knowing these optical powers throughout a measurement with low uncertainty can be challenging, because the output powers of the lasers can vary with time or wavelength tuning and optical components such as splitters can have wavelength-dependent loss or create etalon effects. Because most high-speed photoreceiver modules are fiber-pigtailed and terminated with a connector, the normalized response includes the optical loss from this packaging. To report the absolute response, additional uncertainty contributions would need to be included to account for the optical power measurement and the optical fiber connector repeatability, both of which would dominate the total uncertainty and raise it to 1 dB or more. By contrast, the ℜ2 ( f ) ≡

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typical uncertainty for a normalized response measurement is 0.051 dB, as will be detailed later in Table 1. 2. Heterodyne measurement system Figure 1 illustrates the system we constructed to measure the magnitude of the frequency response of photoreceivers using the heterodyne technique. The block containing the heterodyne optics and phase-locked loop is described in detail later, and was used to produce a sinusoidally modulated optical stimulus at a frequency determined by the computer controlling the measurement system. The modulated signal was delivered to the photoreceiver under test by use of a singlemode optical fiber. In response to the optical stimulus, the photodiode generated an RF power across the load RL, which was then delivered to a diodebased power sensor by a coaxial waveguide. The coaxial waveguide contained an adaptor to match the connector on the photodiode (1.0 mm) to the connector on the power sensor (1.85 mm). In addition to the RF power, the computer simultaneously recorded the DC current idc. This photocurrent was measured by use of a digital volt meter (DVM) to monitor the voltage drop across the precision 1 kΩ resistor Rb. The computer also recorded the frequency of the heterodyne signal measured by either an electrical counter or a tracking electrical spectrum analyzer (ESA). At high heterodyne frequencies the system was operated without the phaselocked loop, in free-run mode, with thermal tuning of the difference frequency between the lasers. To obtain the frequency response of just the receiver module, illustrated within the dotted circle of Fig. 1, the measurements by the power sensor must be corrected for the response of the coaxial connections to the power sensor, and the sensor itself. While such corrections may be negligible in some cases, they can become sizeable at low frequencies due to AC-coupling of the sensor, or at tens of gigahertz due to resonant features. Power sensors are characterized by a frequency-dependent calibration factor Kb, which accounts for both the effective efficiency and the refection coefficient of the sensor. The calibration factor of our highfrequency power sensor was measured at NIST by use of a direct power comparison technique relying upon transfer standards that have been calibrated against a calorimeter [24]. To account for the coaxial connections, we used a vector network analyzer to measure the scattering parameters of the photodetector, coaxial adaptor, and the power sensor. The scattering information was used to calculate a frequency-dependent impedance-mismatch correction M. An alternative to characterizing the isolated response of a module, when intended to be used as a modulation reference, is to characterize the module in conjunction with a particular power sensor [4, 5]. This combined device requires no corrections and can have uncertainties for the measured response that are more than two times lower than those of the isolated module. This combined reference receiver is illustrated within the dotted rectangle in Fig. 1. If the power sensor inside a combined receiver cannot be made available externally, it will not be possible to calibrate the sensor to an external power source, and the measured frequency response curve will be relative rather than absolute. 3. Heterodyne optics and phase-locked loop Our heterodyne system can operate in closed-loop mode at measurement frequencies up to 1.9 GHz, and in open-loop mode at higher frequencies extending beyond 50 GHz. Figure 2 illustrates in detail the heterodyne optics and phase-locked loop system we constructed. The upper portion of the figure is composed mainly of optical paths (red dotted lines) that alone

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Fig. 2. The complete heterodyne phase-locked-loop system is shown, with red dotted lines in the upper portion representing optical paths. The green inset box details the free-space coupling optics. The solid blue lines in the lower portion designate electrical paths. L1 and L2: fiber lasers, PZT: piezo-transducer, AOM: acousto-optic modulator, PC: polarization controller, DUT: device under test, LF PD and HF PD: low- and high-frequency photodiode receivers, ESA: electrical spectrum analyzer, G: gain, BPF: band-pass filter, 1/8: frequency divider, PLL: phase-locked loop circuit, VCO: voltage-controlled oscillator, LPF: low-pass filter, HV: high voltage, C: collimator, M: mirror, A: attenuator, BS: beamsplitter, ISO: optical isolator.

constitute the open-loop system, while the lower portion adds electrical paths (blue solid lines) that enable phase-locked operation. The single-mode lasers we used were commercial 10 mW fiber lasers having up to 1 nm of continuously single-mode wavelength tuning and a linewidth specification of