Abstract

Analog photonic links require high-fidelity, high-speed optical-to-electrical conversion for applications such as radio-over-fiber, synchronization at kilometer-scale facilities, and low-noise electronic signal generation. Photodetector nonlinearity is a particularly vexing problem, causing signal distortion and excess noise, especially in systems utilizing ultrashort optical pulses. Here we show that photodetectors designed for high power handling and high linearity can perform optical-to-electrical conversion of ultrashort optical pulses with unprecedented linearity over a large photocurrent range. We also corroborate and expand upon the physical understanding of how the broadband, complex impedance of the circuit following the photodiode modifies the linearity - in some cases quite significantly. By externally manipulating the circuit impedance, we extend the detector’s linear range to higher photocurrents, with over 50 dB rejection of amplitude-to-phase conversion for photocurrents up to 40 mA. This represents a 1000-fold improvement over state-of-the-art photodiodes and significantly extends the attainable microwave power by a factor of four. As such, we eliminate the long-standing requirement in ultrashort pulse detection of precise tuning of the photodiode’s operating parameters to coincide with a nonlinearity minimum. These results should also apply more generally to reduce nonlinear distortion in a range of other microwave photonics applications.

Full Article  |  PDF Article
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References

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    [Crossref]
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2017 (5)

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

Y. Hu, C. R. Menyuk, X. Xie, M. N. Hutchinson, V. J. Urick, J. C. Campbell, and K. J. Williams, “Computational Study of Amplitude-to-Phase Conversion in a Modified Unitraveling Carrier Photodetector,” IEEE Photonics J. 9, 1–11 (2017).

X. Xie, J. Zang, A. Beling, and J. Campbell, “Characterization of Amplitude Noise to Phase Noise Conversion in Charge-Compensated Modified Unitravelling Carrier Photodiodes,” J. Light. Technol. 35, 1718–1724 (2017).
[Crossref]

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406 (2017).
[Crossref]

R. Bouchand, D. Nicolodi, X. Xie, C. Alexandre, and Y. Le Coq, “Accurate control of optoelectronic amplitude to phase noise conversion in photodetection of ultra-fast optical pulses,” Opt. Express 25, 12268 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (1)

2014 (8)

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204 (2014).
[Crossref] [PubMed]

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581 (2014).
[Crossref] [PubMed]

M. Y. Peng, A. Kalaydzhyan, and F. X. Kärtner, “Balanced optical-microwave phase detector for sub-femtosecond optical-RF synchronization,” Opt. Express 22, 27102 (2014).
[Crossref] [PubMed]

X. Xie, Q. Zhou, K. Li, Y. Shen, Q. Li, Z. Yang, A. Beling, and J. C. Campbell, “Improved power conversion efficiency in high-performance photodiodes by flip-chip bonding on diamond,” Optica 1, 429 (2014).
[Crossref]

Y. Li, A. Rashidinejad, J.-M. Wun, D. E. Leaird, J.-W. Shi, and A. M. Weiner, “Photonic generation of W-band arbitrary waveforms with high time-bandwidth products enabling 39 mm range resolution,” Optica 1, 446 (2014).
[Crossref]

W. Sun, F. Quinlan, T. Fortier, J.-D. Deschenes, Y. Fu, S. Diddams, and J. Campbell, “Broadband Noise Limit in the Photodetection of Ultralow Jitter Optical Pulses,” Phys. Rev. Lett. 113, 203901 (2014).
[Crossref] [PubMed]

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

V. Torres-Company and A. M. Weiner, “Optical frequency comb technology for ultra-broadband radio-frequency photonics,” Laser & Photonics Rev. 8, 368–393 (2014).
[Crossref]

2013 (6)

T. M. Fortier, F. Quinlan, C. W. Nelson, A. Hati, Y. Fu, J. C. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” 2013 IEEE Photonics Conf. IPC 2013 38, 350–351 (2013).

A. J. Metcalf, V. Torres-Company, D. E. Leaird, and A. M. Weiner, “High-Power Broadly Tunable Electrooptic Frequency Comb Generator,” IEEE J. Sel. Top. Quantum Electron. 19, 231–236 (2013).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[Crossref]

Q. Zhou, A. S. Cross, Yang Fu, A. Beling, B. M. Foley, P. E. Hopkins, and J. C. Campbell, “Balanced InP/InGaAs Photodiodes With 1.5-W Output Power,” IEEE Photonics J. 5, 6800307 (2013).
[Crossref]

A. Ferrero and M. Pirola, “Harmonic Load-Pull Techniques: An Overview of Modern Systems,” IEEE Microw. Mag. 14, 116–123 (2013).
[Crossref]

M. Lessing, H. S. Margolis, C. T. A. Brown, P. Gill, and G. Marra, “Suppression of amplitude-to-phase noise conversion in balanced optical-microwave phase detectors,” Opt. Express 21, 27057 (2013).
[Crossref] [PubMed]

2012 (1)

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

2011 (6)

Haifeng Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise Floor Reduction of an Er:Fiber Laser-Based Photonic Microwave Generator,” IEEE Photonics J. 3, 1004–1012 (2011).
[Crossref]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes,” IEEE Photonics J. 3, 140–151 (2011).
[Crossref]

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-Haul Analog Photonics,” J. Light. Technol. 29, 1182–1205 (2011).
[Crossref]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654 (2011).
[Crossref] [PubMed]

Z. Li, Y. Fu, M. Piels, H. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385 (2011).
[Crossref]

2010 (3)

B. Cabon, “Microwave Photonics Mixing,” Sci. Iran. 17,149 (2010).

Z. Li, H. Pan, H. Chen, A. Beling, and J. C. Campbell, “High-Saturation-Current Modified Uni-Traveling-Carrier Photodiode With Cliff Layer,” IEEE J. Quantum Electron. 46, 626–632 (2010).
[Crossref]

Huapu Pan, Zhi Li, and J. Campbell, “High-Power High-Responsivity Modified Uni-Traveling-Carrier Photodiode Used as V-Band Optoelectronic Mixers,” J. Light. Technol. 28, 1184–1189 (2010).
[Crossref]

2009 (3)

T. Nagatsuma, H. Ito, and T. Ishibashi, “High-power RF photodiodes and their applications,” Laser & Photonics Rev. 3, 123–137 (2009).
[Crossref]

P. Devgan, V. Urick, J. Diehl, and K. Williams, “Improvement in the Phase Noise of a 10 GHz Optoelectronic Oscillator Using All-Photonic Gain,” J. Light. Technol. 27, 3189–3193 (2009).
[Crossref]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331 (2009).
[Crossref] [PubMed]

2008 (2)

D. Eliyahu, D. Seidel, and L. Maleki, “RF Amplitude and Phase-Noise Reduction of an Optical Link and an Opto-Electronic Oscillator,” IEEE Transactions on Microw. Theory Tech. 56, 449–456 (2008).
[Crossref]

A. Joshi, S. Datta, and D. Becker, “GRIN lens coupled top-illuminated highly linear InGaAs photodiodes,” IEEE Photonics Technol. Lett. 20, 1500–1502 (2008).
[Crossref]

2007 (2)

2006 (2)

J. Kim, F. X. Kärtner, and F. Ludwig, “Balanced optical-microwave phase detectors for optoelectronic phase-locked loops,” Opt. Lett. 31, 3659 (2006).
[Crossref] [PubMed]

J. F. Cliche and B. Shillue, “Applications of control Precision timing control for radioastronomy maintaining femtosecond synchronization in the atacama large millimeter array,” IEEE Control. Syst. 26, 19–26 (2006).
[Crossref]

2005 (1)

E. Ivanov, S. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Transactions on Ultrason. Ferroelectr. Freq. Control. 52, 1068–1074 (2005).
[Crossref]

2004 (2)

N. Li, X. Li, S. Demiguel, X. Zheng, J. Campbell, D. Tulchinsky, K. Williams, T. Isshiki, G. Kinsey, and R. Sudharsansan, “High-Saturation-Current Charge-Compensated InGaAs–InP Uni-Traveling-Carrier Photodiode,” IEEE Photonics Technol. Lett. 16, 864–866 (2004).
[Crossref]

H. Fushimi, T. Furuta, T. Ishibashi, and H. Ito, “Photoresponse Nonlinearity of a Uni-Traveling-Carrier Photodiode and Its Application to Optoelectronic Millimeter-Wave Mixing in 60 GHz Band,” Jpn. J. Appl. Phys. 43, L966–L968 (2004).
[Crossref]

2003 (1)

G. Jaro and T. Berceli, “A new high-efficiency optical-microwave mixing approach,” J. Light. Technol. 21, 3078–3084 (2003).
[Crossref]

1997 (1)

M. Frankel, P. Matthews, and R. Esman, “Fiber-optic true time steering of an ultrawide-band receive array,” IEEE Transactions on Microw. Theory Tech. 45, 1522–1526 (1997).
[Crossref]

1996 (2)

K. Williams, R. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Light. Technol. 14, 84–96 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725 (1996).
[Crossref]

1990 (1)

P. Lui, “Passive intermodulation interference in communication systems,” Electron. & Commun. Eng. J. 2, 109 (1990).
[Crossref]

1986 (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[Crossref]

Alexandre, C.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

R. Bouchand, D. Nicolodi, X. Xie, C. Alexandre, and Y. Le Coq, “Accurate control of optoelectronic amplitude to phase noise conversion in photodetection of ultra-fast optical pulses,” Opt. Express 25, 12268 (2017).
[Crossref] [PubMed]

Baynes, F. N.

Becker, D.

A. Joshi, S. Datta, and D. Becker, “GRIN lens coupled top-illuminated highly linear InGaAs photodiodes,” IEEE Photonics Technol. Lett. 20, 1500–1502 (2008).
[Crossref]

Beha, K.

Beling, A.

X. Xie, J. Zang, A. Beling, and J. Campbell, “Characterization of Amplitude Noise to Phase Noise Conversion in Charge-Compensated Modified Unitravelling Carrier Photodiodes,” J. Light. Technol. 35, 1718–1724 (2017).
[Crossref]

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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
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F. N. Baynes, F. Quinlan, T. M. Fortier, Q. Zhou, A. Beling, J. C. Campbell, and S. A. Diddams, “Attosecond timing in optical-to-electrical conversion,” Optica 2, 141 (2015).
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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
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T. M. Fortier, F. Quinlan, C. W. Nelson, A. Hati, Y. Fu, J. C. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” 2013 IEEE Photonics Conf. IPC 2013 38, 350–351 (2013).

Z. Li, Y. Fu, M. Piels, H. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385 (2011).
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Q. Zhou, A. S. Cross, Yang Fu, A. Beling, B. M. Foley, P. E. Hopkins, and J. C. Campbell, “Balanced InP/InGaAs Photodiodes With 1.5-W Output Power,” IEEE Photonics J. 5, 6800307 (2013).
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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[Crossref]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes,” IEEE Photonics J. 3, 140–151 (2011).
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X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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Q. Zhou, A. S. Cross, Yang Fu, A. Beling, B. M. Foley, P. E. Hopkins, and J. C. Campbell, “Balanced InP/InGaAs Photodiodes With 1.5-W Output Power,” IEEE Photonics J. 5, 6800307 (2013).
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Y. Hu, C. R. Menyuk, X. Xie, M. N. Hutchinson, V. J. Urick, J. C. Campbell, and K. J. Williams, “Computational Study of Amplitude-to-Phase Conversion in a Modified Unitraveling Carrier Photodetector,” IEEE Photonics J. 9, 1–11 (2017).

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N. Li, X. Li, S. Demiguel, X. Zheng, J. Campbell, D. Tulchinsky, K. Williams, T. Isshiki, G. Kinsey, and R. Sudharsansan, “High-Saturation-Current Charge-Compensated InGaAs–InP Uni-Traveling-Carrier Photodiode,” IEEE Photonics Technol. Lett. 16, 864–866 (2004).
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A. J. Metcalf, V. Torres-Company, D. E. Leaird, and A. M. Weiner, “High-Power Broadly Tunable Electrooptic Frequency Comb Generator,” IEEE J. Sel. Top. Quantum Electron. 19, 231–236 (2013).
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S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331 (2009).
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P. Devgan, V. Urick, J. Diehl, and K. Williams, “Improvement in the Phase Noise of a 10 GHz Optoelectronic Oscillator Using All-Photonic Gain,” J. Light. Technol. 27, 3189–3193 (2009).
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N. Li, X. Li, S. Demiguel, X. Zheng, J. Campbell, D. Tulchinsky, K. Williams, T. Isshiki, G. Kinsey, and R. Sudharsansan, “High-Saturation-Current Charge-Compensated InGaAs–InP Uni-Traveling-Carrier Photodiode,” IEEE Photonics Technol. Lett. 16, 864–866 (2004).
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Y. Hu, C. R. Menyuk, X. Xie, M. N. Hutchinson, V. J. Urick, J. C. Campbell, and K. J. Williams, “Computational Study of Amplitude-to-Phase Conversion in a Modified Unitraveling Carrier Photodetector,” IEEE Photonics J. 9, 1–11 (2017).

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-Haul Analog Photonics,” J. Light. Technol. 29, 1182–1205 (2011).
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Wun, J.-M.

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R. Bouchand, D. Nicolodi, X. Xie, C. Alexandre, and Y. Le Coq, “Accurate control of optoelectronic amplitude to phase noise conversion in photodetection of ultra-fast optical pulses,” Opt. Express 25, 12268 (2017).
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Y. Hu, C. R. Menyuk, X. Xie, M. N. Hutchinson, V. J. Urick, J. C. Campbell, and K. J. Williams, “Computational Study of Amplitude-to-Phase Conversion in a Modified Unitraveling Carrier Photodetector,” IEEE Photonics J. 9, 1–11 (2017).

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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A. Beling, X. Xie, and J. C. Campbell, “High-power, high-linearity photodiodes,” Optica 3, 328 (2016).
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X. Xie, Q. Zhou, K. Li, Y. Shen, Q. Li, Z. Yang, A. Beling, and J. C. Campbell, “Improved power conversion efficiency in high-performance photodiodes by flip-chip bonding on diamond,” Optica 1, 429 (2014).
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X. Xie, J. Zang, A. Beling, and J. Campbell, “Characterization of Amplitude Noise to Phase Noise Conversion in Charge-Compensated Modified Unitravelling Carrier Photodiodes,” J. Light. Technol. 35, 1718–1724 (2017).
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Zhang, W.

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N. Li, X. Li, S. Demiguel, X. Zheng, J. Campbell, D. Tulchinsky, K. Williams, T. Isshiki, G. Kinsey, and R. Sudharsansan, “High-Saturation-Current Charge-Compensated InGaAs–InP Uni-Traveling-Carrier Photodiode,” IEEE Photonics Technol. Lett. 16, 864–866 (2004).
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Zhou, Q.

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IEEE J. Sel. Top. Quantum Electron. (1)

A. J. Metcalf, V. Torres-Company, D. E. Leaird, and A. M. Weiner, “High-Power Broadly Tunable Electrooptic Frequency Comb Generator,” IEEE J. Sel. Top. Quantum Electron. 19, 231–236 (2013).
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Haifeng Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise Floor Reduction of an Er:Fiber Laser-Based Photonic Microwave Generator,” IEEE Photonics J. 3, 1004–1012 (2011).
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Q. Zhou, A. S. Cross, Yang Fu, A. Beling, B. M. Foley, P. E. Hopkins, and J. C. Campbell, “Balanced InP/InGaAs Photodiodes With 1.5-W Output Power,” IEEE Photonics J. 5, 6800307 (2013).
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J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of Power-to-Phase Conversion in High-Speed P-I-N Photodiodes,” IEEE Photonics J. 3, 140–151 (2011).
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Y. Hu, C. R. Menyuk, X. Xie, M. N. Hutchinson, V. J. Urick, J. C. Campbell, and K. J. Williams, “Computational Study of Amplitude-to-Phase Conversion in a Modified Unitraveling Carrier Photodetector,” IEEE Photonics J. 9, 1–11 (2017).

IEEE Photonics Technol. Lett. (2)

N. Li, X. Li, S. Demiguel, X. Zheng, J. Campbell, D. Tulchinsky, K. Williams, T. Isshiki, G. Kinsey, and R. Sudharsansan, “High-Saturation-Current Charge-Compensated InGaAs–InP Uni-Traveling-Carrier Photodiode,” IEEE Photonics Technol. Lett. 16, 864–866 (2004).
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P. Devgan, V. Urick, J. Diehl, and K. Williams, “Improvement in the Phase Noise of a 10 GHz Optoelectronic Oscillator Using All-Photonic Gain,” J. Light. Technol. 27, 3189–3193 (2009).
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V. Torres-Company and A. M. Weiner, “Optical frequency comb technology for ultra-broadband radio-frequency photonics,” Laser & Photonics Rev. 8, 368–393 (2014).
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Figures (8)

Fig. 1
Fig. 1 The inherent nonlinearity of the photodiode. The carrier dynamics are affected by the electric fields in the device, which change as a function of average photocurrent due to the photocarrier-generated fields. This leads to (a) average photocurrent dependent impulse response which translates into (b) photocurrent dependent microwave phase. (c) Shows the microwave delay as a function of photocurrent, converting (d) amplitude modulation to phase modulation. The width of the impulse response of the photodiode is depicted in (a) to have a minimum at a certain photocurrent, causing the existence of a turn-around point in the phase of the extracted microwave signal and a zero crossing of the AM-to-PM coefficient. This is emphasized by the circles in (c) and (d). (e) Frequency domain picture of the nonlinearity in a diode illuminated by a periodic optical pulse-train. All the tones generated are harmonically related, leading to a myriad of mixing products feeding into the same harmonic of the repetition frequency. The combined nonlinear phase-shifts to the harmonic of interest produce the AM-to-PM conversion shown in (d).
Fig. 2
Fig. 2 Amplitude-to-phase conversion measurement setup. By using a microwave demultiplexer it is possible to have improved control over the reflections of each harmonic present in the circuit. The 3.33 GHz and 6.67 GHz harmonics are reflected using a controllable delay and a short circuit. In the case of the 10 GHz harmonic a fraction of it can also be reflected by using a circulator as shown in the dashed box. The signal is re-amplified in the loop, but the overall gain remains below unity to avoid oscillation. The pulse-train shown in this figure corresponds to the interleaved mode-locked laser pulse-train and is amplitude modulated by an acousto-optic modulator before impinging on the photodiode. Three separate demodulation systems of different type were used in these experiments to verify our results.
Fig. 3
Fig. 3 Measured AM-to-PM coefficient with the mode-locked pulse-train. In this case the 3.33 GHz and 6.67 GHz harmonics are terminated to 50 Ω and a small amount of 10 GHz signal is reflected to the diode with a delay via a microwave circulator as shown in the setup in Fig. 2. Notice the shift of the AM-to-PM null to higher photocurrents for phases > 0 in the reflected signal. Also notice that for phases < 0 the AM-to-PM coefficient may show a minimum without going through zero or no minimum at all. Each of these cases can be qualitatively explained by our simple single diode mixing model in the Appendix.
Fig. 4
Fig. 4 AM-to-PM coefficient obtained by “best effort” termination and by optimizing the reflection phase of the 3.33 GHz and 6.67 GHz harmonics to obtain the lowest AM-to-PM coefficient at 24 mA.
Fig. 5
Fig. 5 AM-to-PM coefficient and microwave power using a 10 GHz pulse-train. When a small amount of 10 GHz reflection is allowed, we can reduce the AM-to-PM coefficient and maintain it below −50 dB out to 40 mA of photocurrent (blue empty squares). The power measurement shown in red (right axis) is calibrated to the connector at the bias tee.
Fig. 6
Fig. 6 Nonlinear performance comparison between leading photodiode structures. The blue range shows values of AM-to-PM typically considered to be acceptable. Notice how in standard photodiodes this range is only reached in a narrow photocurrent range.
Fig. 7
Fig. 7 A simulated AM-to-PM coefficient and its modification by microwave mixing at the diode. The purple solid and dashed curves show the cases when the nonlinearity adds with opposite signs respectively. (a) shows “typical” photodiode AM-to-PM. Notice that in (a), the modification only induces a slight variation in the location of the AM-to-PM null. (b) shows the AM-to-PM in a high linearity photodiode and its modification.
Fig. 8
Fig. 8 Modification of the AM-to-PM coefficient for a few chosen values of the reflected phase.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

s ( t ) = sin ( x ) + A sin ( x + ϕ ) ,
s ( t ) = 1 + 2 A cos ϕ + A 2 sin ( x + θ ) ,
θ = tan 1 [ A sin ϕ 1 + A cos ϕ ] .
d θ d I = d θ d A d A d I .
A ( I ) = β I ,
d θ d I / I = A sin ϕ 1 + 2 A cos ϕ + A 2 .