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Propagation Delay of Waveguide Photodetector Yifei Li, Member, IEEE, Renyuan Wang, Member, IEEE, Jonathan Klamkin, Member, IEEE, Shannon M. Madison, Paul W. Juodawlkis, Senior Member, IEEE, Peter Herczfeld, and John E. Bowers, Fellow, IEEE

Abstract—Optical phase locked loop (OPLL) photonic integrated circuits (PIC) are critical for the high dynamic range phase modulated RF/photonic links. They provide for linear phase demodulation. A challenge for implementing the OPLL PICs is how to reduce the loop propagation delay. In this paper we analyze the delay of a waveguide photodetector, which is a critical component of an OPLL. We also introduce and experimentally validate a counter propagating photodetector device concept. This enables the elimination of the propagation delay due to the finite length of a waveguide photodetector.

Fig. 1. PM fiber-optic link with ACP-OPLL phase demodulator/detector.

Index Terms—Coherent optical link, optical phased locked loop, propagation delay.

I. INTRODUCTION F/PHOTONIC links are attractive for replacing the coaxial cables in radar frontend applications. A major obstacle for deploying the RF/photonic links is their small spurious free dynamic range (SFDR) [1]–[8]. A phase modulated RF/photonic link employing an optical phase locked loop (OPLL) linear phase demodulator [9], [10] has been proposed as shown in Fig. 1. The OPLL contains a pair of local phase modulators, a balanced photodetector pair, and a 3-dB optical coupler. The OPLL performs linear phase demodulation by tight phase tracking, which requires the OPLL to have a large open loop gain and a wide bandwidth. For feedback stability, it is imperative that the OPLL have an extremely short loop propagation delay. To reduce the loop delay, we have proposed the concept of an attenuation-counter-propagating (ACP) optical phase modulator [11]. We have shown that by allowing the RF electric field to counter-propagate with respect to the optical field, and simultaneously introducing strong RF attenuation, the propagation delay of the phase modulator is eliminated. In this paper, we perform the first analysis of the propagation delay of the waveguide photodetector inside the OPLL PIC.

R

Manuscript received March 16, 2010; revised May 12, 2010; accepted May 14, 2010. Date of publication June 28, 2010; date of current version July 20, 2010. This work was based upon work supported by DARPA under AFRL Contract No. FA8750-05-C-0265. The views, opinions, and/or findings contained in this article are those of the authors and should not be interpreted as representing the official views or policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the Department of Defense. Y. Li and R. Wang is with Department of Electrical and Computer Engineering, University of Massachusetts at Dartmouth, Dartmouth, MA 02748 USA (e-mail: [email protected]). J. Klamkin, S. M. Madison, and P. W. Juodawlkis are with Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 02420 USA (e-mail: [email protected]). P. R. Herczfeld, was with Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). J. Bowers is with Department of Electrical and Computer Engineering, the University of California Santa Barbara, Santa Barbara, CA 93116 USA. Digital Object Identifier 10.1109/JLT.2010.2052349

Fig. 2. Waveguide photodetector.

We will show that the concept of the Attenuation and Counter Propagating can be extended to the waveguide photodetector by allowing the optical field and the photo-generated RF field to counter-propagate. Thereby, the photodetector length does not contribute to the propagation delay. This allows for optimization of the length of the photodetector to maximize its saturation optical power without adding to the loop propagation delay. Thus, this enables an OPLL phase demodulator with a larger stable open loop gain, and consequently a better phase demodulation linearity. II. THEORETIC MODEL In order to clarify the discussion, in this paper we define the propagation delay as the delay that has the following frequency , where is the delay time. This redomain response: sponse contains an unbounded phase lag when increasing It is responsible for instabilities in the OPLL. An arbitrary waveguide photodetector is depicted in Fig. 2. We are interested in and the end determining the voltage signals at the start of the detector optical waveguide. They represent the photodetector outputs when it is configured as a forward and backward propagating photodetector, respectively. In Fig. 2, the photodetector termination impedances at the optical input and output are and , respectively. given by The waveguide photodetector can be conveniently analyzed using a transmission line model as shown in Fig. 3. The voltage and current on the waveguide photodetector must satisfy:

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(1a) (1b)

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(5b) In addition, the voltage and current signals also satisfy the following boundary conditions: (6a) (6b)

Fig. 3. Circuit model of waveguide photodetector.

where , and are resistance, inductance, capacitance, and admittance per unit length of the transmission line, respec(x) is the photocurrent per unit length of tively. In addition, the photodetector and is given by

where and are the normalized loading impedances at the photodetector optical input and output, respectively. Upon substituting (5b) and (2) into (5a) we obtain: (7)

(2) The general solution for (7) is: is the complex propagation constant of the optical where field envelope in the PD optical waveguide, is the input is the photo-reoptical power in frequency domain, and is detersponsivity per unit length of the waveguide PD. mined by the carrier transport process inside the photodetector. For the uni-traveling carrier (UTC) photodetector [12] used in is given by (3), shown at the bottom the OPLL design, and are the lengths of the abof the page, [13] where , R is sorber and the collector, respectively, the hole relaxation time in the absorber, is the electron is the electron drifting time in the collection layer, current, is the diffusion constant, is the electron mobility, is is the the recombination life-time, is the generation rate, optical absorption as defined earlier, is a quantum efficiency, h is Planck’s constant, is the optical frequency, is a function , and is the hole reof frequency: laxation in the absorber. Equations (1a) and (1b) can be rewritten as: (4a) (4b) where and are the complex propagation constant and the characteristic impedance of the transmission line, respectively. (5a)

(8) and are constants that are determined by the where boundary conditions (6). (See equation at the bottom of the page.)Therefore, the voltages ( and ) are given, respectively, by:

(10a)

(10b) Next, we use (10) to determine the frequency responses of a co-propagating photodetector and a counter-propagating photodetector. A. Co-Propagating Waveguide Photodetector , When the output of a photodetector is extracted at the photodetector is in the co-operating configuration where the optical field and the output RF voltage signal propagate in the

(3)

(9a)

(9b)

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same direction. As given by (10a), the transfer function of a co-propagating waveguide photodetector is given by:

and are the absorption to the optical and RF where and are the velocities of the fields, respectively and optical and RF fields, respectively. Thus, (15) can be re-written as:

(11)

(17)

In an ideal situation where both load impedances ( and ) are matched to the waveguide characteristic impedance, the transfer function is reduced to:

Except for the term, (17) shows a lumped low-pass response, containing no propagation delay. The bandwidth of the counter-propagating photodetector is given by:

(12)

(18)

In addition, if we further assume that the optical power is completely absorbed by the waveguide photodetector, which is genshould approach zero. Thus, erally the case, the term (12) can be further simplified to: (13) where is the RF attenuation and is the propagation speed are related to the complex propagaof the RF field. and . As shown in (13), the photion constant by: todetector response contains a phaser term , which . corresponds to the propagation delay of the RF field: Thus, in the conventional co-propagating traveling waveguide photodetector, the length of the photodetector will contribute to the delay. B. Counter-Operating Waveguide Photodetector The photodetector output can also be extracted at . If we ignore the reflection of the RF and the optical fields, this is equivalent to having the optical and RF field counter-propagate with respect to each other. In this situation, the frequency response of the photodetector is given by:

(14) Next, we will show that a counter-propagating photodetector can achieve a similar operation as that of an ACP-phase modulator. For this, we take the following two assumptions: a) The optical field is almost entirely absorbed, i.e., . is matched to the characteristic b) The impedance . impedance of the photodetector electrode, i.e., Thus, the frequency response is simplified to: (15) Note that the complex propagation constants are also given by (16a) (16b)

In addition, the term in (17) describes the carrier transport process in an infinitely short waveguide photodetector section. For the UTC waveguide photodetector used in the optical phase locked loop photonic integrated circuits, the time delay due to the carrier transport is determined by the time duration for the electron to drift through the detector collector region. This time delay is very short and it is less than 1 ps. The operation of a counter-propagating photodetector can also be interpreted through its impulse response through the thought experiment as depicted in Fig. 4. Here we ignore the carrier transport process in the photodetector. Let’s first assume that an optical impulse enters the photodetector waveguide at . Then at a time instance , the optical pulse propagates to the location . The forward and the backward photocurrents and - will be generated. Both currents should be proportional to the magnitude of the optical impulse at the time instance . When the backward propagating photocurrent, -, arrives at , it produces an output voltage, which is proportional to the magnitude of the optical impulse at the time instant . Since the optical impulse is gradually absorbed and experiences exponential decay as it propagates inside the optical waveguide, the photodetector output voltage should be an exponential decay as a function of time. In other words, the impulse response of the counter propagating photodetector is an exponential delay. As we know, only a lumped element low pass filter has such an exponential delay impulse response. This indicates that its frequency response is a lumped element low pass filter that contains no propagation delay. We hope to emphasize that although the lumped-element low pass response as shown in (17) contains no propagation delay defined in the beginning of this section, it always has group delay. Thus, it preserves causality. III. EXPERIMENTAL VALIDATION The concept of counter-propagating photodetector was verified using a 6 mm long slab-coupled optical waveguide photodiode (SCOWPD) [14] as shown in Fig. 5. The SCOWPD has a conventional PIN photodetector structure. We choose to use the SCOWPD to validate the theoretical derivations as it is easier to measure its frequency response than that of the short ( microns) UTC waveguide photodetectors that are employed in the OPLL PICs. The SCOWPD can be configured either as a counter-propagating photodetector or a more conventional co-propagating

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Fig. 4. Physical interpretation of the latency free operation.

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Fig. 6. Measured characteristic impedance of traveling wave SCOWPD.

Fig. 7. Measured RF loss of traveling wave SCOWPD.

Fig. 5. Traveling wave SCOWPD. Fig. 8. Experimental setup.

photodetector by selecting proper pads for signal extraction and termination as depicted in Fig. 5. The optical absorption length of the photodetector is 2.2 mm. Figs. 6 and 7 show the measured characteristic impedance and RF loss of the photodetector traveling wave electrode, respectively. The measured characteristic impedance contains both the real and the imaginary parts. At lower frequencies the real part of the impedance is close to GHz) it is approaching 50 ohms and at higher frequencies ( 38 ohms. Thus, when terminated by a standard 50 ohm termination, we anticipate a small but finite reflection of RF signals. In addition, the measured RF loss of the electrode increases with the RF frequency. The RF loss is attributed to the electrode series resistance and also to the finite shunt conductance of the photodetector. The RF loss helps to attenuate the unwanted RF reflection from the load. We employed the experimental setup as shown in Fig. 8 to determine the response of the photodetector. The output from a single mode fiber laser (Orbits Ethernal) was amplified (to 100 mW) and fed into a high speed MZ modulator. The output of the MZM was coupled to the SCOWPD by a tapered fiber. The transfer function from the MZM input to the photodetector

output was measured with a microwave vector network analyzer (HP 8510B). From the phase response of the transfer function, the propagation group delay from the MZM modulator to the photodetector output can be determined. We first set the SCOWPD to operate in the co-propagating configuration (Fig. 5(a)). We measured the transfer function from the MZ modulator RF input to the SCOWPD output. The measured transfer function was used as the baseline for comparison. Then, we re-measured the transfer function after the SCOWPD was configured to the counter-propagating configuration (Fig. 5(b)). Fig. 9 shows the relative magnitude response of the counter-propagating photodetector configuration over the co-propagating photodetector configuration. As expected, for high frequencies the magnitude response of the counter-propagating photodetector is smaller than that of the co-propagating photodetector. But at lower frequencies, the magnitude response of the counter-propagating photodetector is a little larger. This is attributed to the RF loss. Due to optical absorption, more photocurrent was generated in the first few

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propagation delay at the frequencies far beyond its passband, we verify that in the counter propagating photodetector the length does not contribute to the propagation delay. Except for the carrier transport process inside the photodetector, the counter-propagating photodetector can be modeled as a lumped element device. IV. CONCLUSION

Fig. 9. Relative magnitude response between the CP and COP configuration.

Fig. 10. Relative phase response between COP and CP configurations.

millimeters of the optical waveguide. In the counter-propagating photodetector case, it takes a shorter distance for the photocurrent to propagate to the photodetector output. Thus, this photocurrent experiences less RF attenuation, resulting in a higher magnitude response. The measured relative phase response between the co-propagating and counter-propagating photodetectors is depicted in Fig. 10, together with the theoretical curve. Except for the noise in the phase response measurement, the measurement agrees well with the theoretical prediction. Relative to the co-propagating photodetector, the counter-propagating photodetector contains a negative phase lag (or phase forward), the magnitude of which increases with the RF frequency. The phase lag curve is not a linear function with frequency. This is expected as suggested by the frequency response of the counter-propagating photodetector (see (17)). The group delay difference between the counter-propagating and the co-propagating photodetector is determined by the derivative of the phase lag with respect to the frequency. At high frequencies the group delay of the counter-propagating photodetector is found to be 65 ps shorter than that of the co-propagating photodetector. Since the velocities of the optical and the RF m/s and fields inside the photodetector are m/s, respectively. The measured 65 ps group delay difference at high frequencies closely approximates to the 68 ps propagation delay of the co-propagating photodetector as calculated by (13). The 3 ps difference is within the measurement error. Since the group delay of a lowpass system should approach to its

A waveguide photodetector is critical for the optical phase locked loop photonic integrated circuit where the delay of each loop component must be minimized. We derived the closedform frequency response of an arbitrary waveguide photodetector. Using the frequency response, we analyzed the propagation delay of the waveguide photodetector. In particular, we found that if the photodetector operates in the counter-propagating mode, it will behave like a lumped element low pass filter. Thus, the photodetector length will not contribute to propagation delay. This is highly desirable for the optical phase locked loop photonic integrated circuit, which requires both a large photocurrent and a short propagation delay. A longer photodetector design can have a larger detector surface area and thereby a larger total photocurrent. The penalty is the bandwidth. However, this is not a major problem for the optical phase locked loop photonic integrated circuits where the bandwidth is in the GHz range. At present, the optical phase locked loop photonic integrated circuits that employ the counter-propagating photodetector concept are under development. ACKNOWLEDGMENT The authors would like thank Dr. Rosen (Drexel University), B. Krantz (Boos Allan Hamilton), and Dr. R. Esman (DARPA) for useful discussions. REFERENCES [1] J. H. Schaffner and W. B. Bridges, “Inter-modulation distortion in high dynamic range microwave fiber-optic links with linearized modulators,” J. Lightw. Technol., vol. 11, no. 1, pp. 3–6, Jan. 1993. [2] Y. Chiu, B. Jalali, S. Garner, and W. Steier, “Broad-band electronic linearizer for externally modulated analog fiber-optic links,” IEEE Photon. Technol. Lett., vol. 11, pp. 48–50, Jan. 1999. [3] E. Ackerman and C. H. Cox, “Effect of pilot tone-based modulator bias control on external modulation link performance,” in Int. Topical Meeting on Microwave Photonics Tech. Dig., Sep. 2000, pp. 121–124. [4] G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech., vol. 42, pp. 2642–2649, Dec. 1994. [5] E. I. Ackerman, “Broad-band linearization of a Mach–Zehnder electrooptic modulators,” IEEE Trans. Microw. Theory Tech., vol. 47, pp. 2271–2279, Dec. 1999. [6] L. D. Westbrook, D. G. Moodie, I. F. Lealman, and S. D. Perrin, “Method for linearization analogue DFB lasers using an integrated MQW electroabsorption modulator,” Electron. Lett., vol. 32, pp. 134–135, Jan. 1996. [7] S. A. Pappert, C. K. Sun, R. J. Orazi, and T. E. Weiner, “Microwave fiber-optic links for shipboard antenna applications,” in Proc. IEEE Int. Conf. Phased Array Syst. Tech., May 2000, pp. 345–348. [8] R. Sadhwani and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightw. Technol., vol. 21, pp. 3180–3193, Dec. 2003. [9] J. E. Bowers, A. Ramaswamy, L. A. Johansson, J. Klamkin, M. N. Sysak, D. Zibar, L. A. Coldren, M. J. Rodwell, L. Lembo, R. Yoshimitsu, D. Scott, R. Davis, and P. Ly, “Linear coherent receiver based on a broadband and sampling optical phase-locked loop (Invited),” in Proc. Microwave Photonics’07 , Victoria, Canada, Oct. 2007, pp. 225–228. [10] Y. Li and P. Herczfeld, “Coherent PM optical link employing ACPPPLL,” J. Lightw. Technol., vol. 27, no. 9, pp. 1086–1094, May 2009.

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[11] Y. Li and P. R. Herczfeld, “Novel attenuation counter-propagating phase modulator for highly fiber-optic links,” J. Lightw. Technol., vol. 24, no. 10, pp. 3709–3718, Oct. 2006. [12] J. Klamkin, Y.-C. Chang, A. Ramaswamy, L. A. Johansson, J. E. Bowers, S. P. DenBaars, and L. A. Coldren, “Output saturation and linearity of waveguide uni-traveling-carrier photodiodes,” IEEE J. Quantum Electron., vol. 44, no. 4, pp. 354–359, Apr. 2008. [13] T. Ishibashi, N. Shimizu, S. Kodama, H. Ito, T. Nagatsuma, and T. Furuta, “Uni-Traveling-Carrier photodiodes,” Proc. Tech. Dig. Ultrafast Electronics and Optoelectronics, pp. 166–168, 1997. [14] S. M. Madison, J. J. Plant, D. C. Oakley, D. C. Chapman, A. Napoleone, and P. W. Juodawlkis, “Slab-coupled optical waveguide photodiode,” in Proc. Conf. Lasers Electro-Optics (CLEO), 2008, paper CWF4..

Yifei Li (M’03) received the B.Eng. degree in optoelectronics from Huazhong University of Science and Technology, China, in 1996. He received the M.S. and Ph.D. degrees in electrical engineering, in July 2001 and September 2003, respectively, both from Drexel University, Philadelphia, PA. From 2003 to 2007, he was a research faculty member with the Center for Microwave/Lightwave Engineering, Drexel University. Currently, he is with the University of Massachusetts at Dartmouth. His research interests include: high dynamic range RF/photonic links, tunable microchip lasers, hybrid lidar/ radar, fiber radio systems, coherent optical communications, and laser nonlinear dynamics.

Renyuan Wang (M’08) received the B.Eng in electronic science and technology from Harbin Institute of Technology, China, in 2007. He is currently working toward the M.S. degree in electrical and computer engineering at University of Massachusetts Dartmouth. In 2007, he joined the RF/Photonics groups at University of Massachusetts Dartmouth, where he was involved with development of high dynamic photonic RF radar front-ends. His research interests include quantum electronics, optoelectronic, photonic and high speed electronic devices.

Jonathan Klamkin (M’00) received the B.S. degree in electrical and computer engineering from Cornell University, Ithaca, NY, in 2002 and the M.S. degree in electrical and computer engineering and Ph.D. degree in electronic materials from the University of California, Santa Barbara, CA (UCSB) in 2004 and 2008 respectively. At UCSB he worked on design, growth, fabrication, and characterization of widely-tunable semiconductor lasers, photodetectors, optical intensity and phase modulators, and semiconductor optical amplifiers for InP-based photonic integrated circuits with emphasis on high power photodiodes and novel coherent integrated receivers for highly linear microwave photonic links. In 2008 he joined the Electrooptical Materials and Devices Group at MIT Lincoln Laboratory where he is a member of the Technical Staff. His current research interests include directly modulated frequency stabilized slab-coupled optical waveguide lasers, GaN-based optical modulators, microwave photonic subsystems, high power photodiode arrays, and quantum well intermixing techniques for novel photonic integrated circuits and devices.

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Shannon M. Madison received the B.S. degree in physics from Fort Hays State University, Hays, KS, in 2003 and the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, GA, in 2004. Her graduate work was focused on the development, fabrication, and characterization of a monolithically integrated AlGaN/GaN-based FET device and a Ti-diffused LiNbO waveguide. She also contributed to projects involving GaN-based acoustic devices, e-beam lithography for the fabrication of FET devices having T-gates, and SOI photonic crystal slab waveguides. Since 2006, she has been a member of the Electro-Optical Materials and Devices Group at Lincoln Laboratory, Massachusetts Institute of Technology (MIT), Lexington, MA. She is involved in the development, fabrication, and characterization of advanced optoelectronic devices, including InP-based high-power waveguide photodiodes and GaAs-based vertical cavity surface emitting laser (VCSEL) arrays.

Paul W. Juodawlkis (S’86-M’86-SM’06) received the B.S. degree from Michigan Technological University, Houghton, the M.S. degree from Purdue University, West Lafayette, IN, and the Ph.D. degree from the Georgia Institute of Technology, Atlanta, all in electrical engineering. From 1988 to 1993, he was a Technical Staff Member at Lincoln Laboratory, Massachusetts Institute of Technology (MIT), Lexington, where he was a Hardware Systems Engineer on a multi-sensor airborne testbed program. He then joined the Ultrafast Optical Communications Laboratory (UFOCL), Georgia Institute of Technology. In 1999, he rejoined the Lincoln Laboratory, MIT, as a member of the Electro-Optic Materials and Devices Group. He is currently Assistant Group Leader of the Electro-Optic Materials and Devices Group at the Lincoln Laboratory, MIT, where he is leading research on semiconductor optoelectronic devices and microwave photonics. His research efforts have focused on the development of optical sampling techniques for photonic analog-to-digital converters (ADCs), quantum-well electrorefractive modulators, high-power waveguide photodiodes, and high-power semiconductor optical amplifiers (SOAs) and their application in mode-locked lasers and narrow-linewidth external-cavity lasers. Dr. Juodawlkis is the Program Co-Chair of the 2010 Conference on Lasers and Electro-Optics (CLEO). He has served as Chair of the IEEE Photonics Society Technical Committee on Microwave Photonics (2003–2006), Program Co-Chair of the 2003 Photonics Society Summer Topical Meeting on Photonic Time/Frequency Measurement and Control, and committee member of the International Topical Meeting on Microwave Photonics (2004, 2008). He is also a member of the Optical Society of America (OSA) and the American Association for the Advancement of Science (AAAS).

Peter Herczfeld, photograph and biography unavailable at time of publication.

John E. Bowers (F’04) received the M.S. and Ph.D. degrees from Stanford University, Stanford, CA. He is a Professor in the Department of Electrical Engineering, and in the Technology Management Program at the University of California, Santa Barbara. He is also CTO and cofounder of Calient Networks. His research interests are primarily concerned with silicon photonics, optoelectronic devices, optical switching, and transparent optical networks. He is cofounder of the Center for Entrepreneurship and Engineering Management, and founder of Terabit Technology. Previously, he had worked for AT&T Bell Laboratories and Honeywell before joining UCSB. He has published eight book chapters, 400 journal papers, 600 conference papers, and has received 49 patents. Dr. Bowers is a Fellow of the Optical Society of America (OSA) and the American Physical Society, and a recipient of the IEEE LEOS William Streifer Award and the South Coast Business and Technology Entrepreneur of the Year Award. He was an elected member of the IEEE LEOS Board of Governors, a LEOS Distinguished Lecturer, and Vice President for Conferences for LEOS. He is a member of the National Academy of Engineering. He received the ACE Award for Most Promising Technology for the hybrid silicon laser in 2007.