Abstract

This paper reviews over 30 years of work on photonic analog-to-digital converters. The review is limited to systems in which the input is a radio-frequency (RF) signal in the electronic domain and the output is a digital version of that signal also in the electronic domain, and thus the review excludes photonic systems directed towards digitizing images or optical communication signals. The state of the art in electronic ADCs, basic properties of ADCs and properties of analog optical links, which are found in many photonic ADCs, are reviewed as background information for understanding photonic ADCs. Then four classes of photonic ADCs are reviewed: 1) photonic assisted ADC in which a photonic device is added to an electronic ADC to improve performance, 2) photonic sampling and electronic quantizing ADC, 3) electronic sampling and photonic quantizing ADC, and 4) photonic sampling and quantizing ADC. It is noted, however, that all 4 classes of “photonic ADC” require some electronic sampling and quantization. After reviewing all known photonic ADCs in the four classes, the review concludes with a discussion of the potential for photonic ADCs in the future.

© 2007 Optical Society of America

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2005 (7)

K. Ikeda, J. M. Abdul, S. Namiki, and K. Kitayama, "Optical quantizing and coding for ultrafast A/D conversion using nonlinear fiber-optic switches based on Sagnac interferometer," Opt. Express 13, 4296-4302 (2005).
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J. Stigwall and S. Galt, "Interferometric analog-to-digital conversion scheme," IEEE Photonic. Technol. Lett. 17, 468-470 (2005).
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S. Oda and A. Maruta, "A novel quantization scheme by slicing supercontinuum spectrum for all-optical analog-to-digital conversion," IEEE Photonic Technol. Lett. 17, 465-467 (2005).
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B. A. Clare, K. A. Corbett, and K. J. Grant, "Performance of a photonic oversampled sigma-delta quantizer," Proc. SPIE 5814, 248-261 (2005).
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T. Sarros, S. R. Al-Sarawi, P. Celinski, K. A. Corbett, "Optical threshold logic analog-to-digital converters using self electro-optic effect devices," Proc. SPIE 5649, 227-236 (2005).
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K. Ioakeimidi, R. F. Leheny, S. Gradinaru, P. R. Bolton, R. Aldana, K. Ma, J. E. Clendenin, J. S. Harris, Jr., and R. F. W. Pease, "Photoelectronic analog-to-digital conversion: sampling and quantizing at 100 Gs/s," IEEE Trans. Microwave Theory and Tech. 53, 336-342 (2005).
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H. Zmuda, S. Hanna, R. J. Bussjager, M. L. Fanto, M. J. Hayduk, S. T. Johns, J. E. Malowicki, and P. L. Repak, "Optically assisted high-speed, high resolution analog-to-digital conversion," Proc. SPIE 5814, 51-61 (2005)
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2004 (12)

M. Currie, "Hybrid photonic analog-to-digital conversion using superconducting electronics," IEEE Trans. Applied Superconductivity 14, 2047-2052 (2004).
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W. Ng, and Y. M. So, "Characterizations of absolute phase noise in fibe-laser modelocked by sapphire-loaded cavity resonator oscillator at 10 GHz," Electron. Lett. 40, 672-674 (2004).
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M. P. Fok, K. L. Lee, and C. Shu, "4 x 2.5 GHz repetitive photonic sampler for high-speed analog-to-digital signal conversion," IEEE Photonics Technol. Lett. 16, 876-878 (2004).
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H. Zmuda and S. Hanna, "High-speed, high resolution optically assisted analog-to-digital conversion," Proc. SPIE 5435, 153-163 (2004).
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Y. Han, O. Boyraz, and B. Jalali, "Real-time A/D conversion at 480 GSample/s using the phase diversity photonic time-stretch system," Proc.Microwave Photonics 2004, 186-189 (2004).

G. C. Valley, J. P. Hurrell, and G. A. Sefler, "Photonic analog-to-digital converters: fundamental and practical limits," Proc. SPIE 5618, 96-106 (2004).
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K. Ma, R. Urata, D. A. B. Miller and J. S. Harris, Jr., "Low-temperature growth of GaAs on Si used for ultrafast photoconductive switches," IEEE J. Quantum Electron. 40, 800-804 (2004).
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B. A. Clare, K. A. Corbett, K. J. Grant, A. Massie, J. Munch, W. Marwood, "Photonic A/Ds employing S-SEED Comparators," Proc. SPIE 5277, 42-53 (2004).
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T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
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X. Meng, "Designing high dynamic range microwave photonic links for radio applications," Fiber and Integrated Optics 23, 1-56 (2004).
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S. Oda, A. Maruta, K. Kitayama, "All-optical quantization scheme based on fiber nonlinearity," IEEE Photonic Technol. Lett. 16, 587-589 (2004).
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W. Ng, Y. M. So, R. Stephens, and D. Persechini, "Characterization of the jitter in a mode-locked Er-fiber laser and its application in photonic sampling for analog-to-digital conversion at 10 Gsample/s," J. Lightwave Technol. 22, 1953-1961, (2004).
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2003 (11)

S. Galt, A. Magnusson, and S. Hard, "Dynamic demonstration of diffractive optic analog-to-digital converter scheme," Appl. Opt. 42, 264-270 (2003).
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C. Xu and X. Liu, "Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters," Opt. Lett. 28, 986-988 (2003).
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G. L. Li and P. K. L. Yu, "Optical intensity modulators for digital and analog applications," J. Lightwave Technol. 21, 2010-2030 (2003).
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B. A. Clare, K. A. Corbett, K. J. Grant, P. B. Atanackovic, W. Marwood, and J. Munch, "Investigation of critical slowing down in a bistable S-SEED," J. Lightwave Technol. 21, 2883-2890 (2003).
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Y. Han and B. Jalali, "Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103, (2003).
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R. Urata, L. Y. Nathawad, R. Takahashi, K. Ma, D. A. B. Miller, B. A. Wooley, and J. S. Harris, Jr., "Photonic A/D conversion using low-temperature-grown GaAs MSM switches integrated with Si-CMOS," J. Lightwave Technol. 21, 3104-3114 (2003).
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R. F. Pease, K. Ioakeimidi, R. Aldana, and R. Leheny, "Photoelectronic analog-to-digital conversion using miniature electron optics: Basic design considerations," J. Vac. Sci. Technol. 21, 2826-2829 (2003).
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L. Y. Nathawad, R. Urata, B. A. Wooley, and D. A. B. Miller, "A 40-GHz-bandwidth, 4-bit, time-interleaved A/D converter using photoconductive sampling," IEEE J. Solid-State Circuits 38, 2021-2030 (2003).
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R. Urata, R. Takahashi, V. A. Sabnis, D. A. B. Miller, and J. S. Harris, Jr., "Ultrafast optoelectronic sample and hold using low-temperature-grown GaAs MSM," IEEE Photon. Technol. Lett. 15, 724-726 (2003).
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Y. Han, and B. Jalali, "Time-bandwidth product of the photonic time-stretched analog-to-digital converter," IEEE Trans. Microwave Theory and Tech. 51, 1886-2003, (2003).
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Y. Han, B. Jalali, J. Han, B. Seo, and H. Fetterman, "Demonstration and analysis of single sideband photonic time-stretch system," IEICE Trans. Electron.E 86-C, 1276-1280 (2003).

2002 (8)

A.S. Bhushan, P. V. Kelkar, B. Jalali, O. Boyraz, and M. Islam, "130-GSa/s photonic Analog-to-digital converter with time stretch preprocessor, IEEE Photonic Technol. Lett. 14, 684-686, (2002).
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C. M. DePriest, M. T. Yilmaz, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "High-quality photonic sampling streams from a semiconductor diode ring laser," IEEE J. Quantum Electron. 38, 380-389 (2002).
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H. Zmuda, M. J. Hayduk, R. J. Bussjager, and E. N. Toughlian, "Wavelength-based analog-to-digital conversion," Proc. SPIE 4547, 134-145 (2002).
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T. Konishi, K. Tanimura, K. Asano, Y. Oshita, Y. Ichioka, "All-optical analog-to-digital converter by use of self-frequency shifting in fiber and a pulse-shaping technique," J. Opt. Soc. Am. B 19, 2817-2823 (2002).
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M. J. Hayduk, R. J. Bussjager, S. T. Johns, and C. M. Gerhardstein and G. Wicks, "Contrast ratio enhancement in a saturable absorber based photonic analog to digital converter," Proc. SPIE 4732,46-52 (2002).
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B. L. Shoop and P. K. Das, "Mismatch-tolerant distributed photonic analog-to-digital conversion using spatial oversampling and noise shaping," Opt. Eng. 41, 1674-1687 (2002).
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T. Sarros, S. F. Al-Sarawi, K. A. Corbett, K. J. Grant, B. A. Clare, W. Marwood, "Oversampled optoelectronic analog-digital converters using sigma-delta modulation," Proc. SPIE 4935, 178-187 (2002).
[CrossRef]

S. F. Al-Sarawi, P. B. Atanackovic, W. Marwood, B. A. Claire, K. A. Corbett, K. J. Grant, J. Munch, "Differential oversampling data converters in SEED technology," Microelectronics J. 33, 141-151 (2002).
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2001 (15)

S. Jaganathan, S. Krishnan, D. Mensa, T. Mathew, Y. Betser, Y. Wei, D. Scott, M. Urteaga, and M. Rodwell, "An 18-GHz continuous time Σ−Δ analog-digital converter implemented in InP-transferred substrate HBT technology," IEEE J. Solid-State Circuits 36, 1343-1350 (2001).
[CrossRef]

S. F. Al-Sarawi, W. Marwood, and P. Atanackovic, "An integrated optoelectronics oversampling analog-to-digital converter," Proc. SPIE 4236, 351-360 (2001).
[CrossRef]

B. L. Shoop and P. K. Das, "Wideband photonic A/D conversion using 2-D spatial oversampling and spectral noise shaping," Proc. SPIE 4490, 32-51 (2001).
[CrossRef]

H. Sakata, "Photonic analog-to-digital conversion by use of nonlinear Fabry-Perot resonators," Appl. Opt. 40, 240-248 (2001).
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T. R. Clark, M. Currie, and P. J. Matthews, "Digitally linearized wide-band photonic link," J. Lightwave Technol. 19, 172-179 (2001).
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R. C. Williamson, P. W. Juodawlkis, J. L. Wasserman, G. E. Betts, and J. C. Twichell, "Effects of crosstalk in demultiplexers for photonic analog-to-digital converters," J. Lightwave Technol. 19, 230-236 (2001).
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P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray and R. C. Williamson, "Optically sampled analog-to-digital converters," IEEE Trans. Microwave Theory Tech. 49, 1840-1853, (2001).
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J. C. Twichell, J. L. Wasserman, P. W. Juodawlkis, G. E. Betts, and R. C. Williamson, "High-linearity 208-MS/s photonic analog-to-digital converter using 1-to-4 optical time-division demultiplexers," IEEE Photonic Technol. Lett. 13, 714-716, July 2001.
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H. Zmuda, "Analog-to-digital conversion using high-speed photonic processing," Proc. SPIE 4490, 84-95 (2001).
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T. P. E. Broekaert, W. Ng, J. F. Jensen, D. Yap, D. L. Persechini, S. Bourgholtzer, C. H. Fields, Y. K. Brown-Boegeman, B. Shi and R. H. Walden, "InP-HBT optoelectronic integrated circuits for photonic analog-to-digital conversion," IEEE J. Solid-State Electron. 36, 1335-1342 (2001).
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W. Ng, R. Stephens, D. Persechini and K. V. Reddy, "Ultra-low jitter modelocking of Er-fiber laser at 10 GHz and its application in photonic sampling for analog-to-digital conversion," Electron. Lett. 37, 113-115 (2001).
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C. M. DePriest, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "External-cavity semiconductor diode ring laser for application in hybrid optoelectronic analog-to-digital converter," Proc. SPIE 4386, 37-41 (2001).
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R. Urata, R. Takahashi, V. A. Sabnis, D. A. B. Miller, and J. S. Harris, Jr., "Ultrafast differential sample and hold using low-temperature-grown GaAs MSM for photonic A/D conversion," IEEE Photon. Technol. Lett. 13, 717-719 (2001).
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J. M. Fuster, D. Novak, A. Nirmalathas and J. Marti, "Single-sideband modulation in photonic time-stretch analogue-to-digital conversion," Electron. Lett. 37, 67-68 (2001).
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C. M. DePriest, A. Braun, J. H. Abeles, and P. J. Delfyett, Jr., "10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser," IEEE Photon. Technol. Lett. 13, 1109-1111 (2001).
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2000 (9)

F. Coppinger, A. S. Bhushan and B. Jalali, "12 Gsample/s wavelength division sampling analog-to-digital converter," Electron. Lett. 36, 316-318 (2000).
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J. C. Twichell, and R. Helkey, "Phase-encoded optical sampling for analog-to-digital converters," IEEE Photonic Technol. Lett. 12, 1237-1239 (2000).
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D. Ralston, A. Metzger, Y. Kang, P. Asbeck and P. Yu, "Highly linear photoreceiver design for application to ultrahigh bandwidth photonic A/D converters," Proc. SPIE 4112, 132-140 (2000).
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A.S. Bhushan, P. Kelkar and B. Jalali, "30 Gsample/s time-stretch analogue-to-digital converter," Electron. Lett. 36, 1526-1527, Aug. 2000.
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M. Currie, T. R. Clark, and P. J. Matthews, "Photonic analog-to-digital conversion by distributed phase modulation," IEEE Photonics Technol. Lett. 12, 1689-1691 (2000).
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M. J. Hayduk, R. J. Bussjager, and M. A. Getbehead, "Photonic analog to digital conversion techniques using semiconductor saturable absorbers," Proc. SPIE 4042, 54-60 (2000).
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P. E. Pace, S. A. Bewley, and J. P. Powers, "Fiber-lattice accumulator design considerations for optical ΣΔ analog-to-digital converters," Opt. Eng. 39, 1517-1526 (2000).
[CrossRef]

S. F. Al-Sarawi, N. Burgess, W. Marwood, P. Atanackovic, D. Abbott, "Very high speed differential optoelectronic algorithmic ADC using n-i(MQW)-n SEED technology," Microelectronics J. 31, 593-604 (2000).
[CrossRef]

M. Johansson, B. Lofving, S. Hard, L. Thylen, M. Mokhtari, U. Westergren and C. Pala, "Study of an ultrafast analog-to-digital conversion scheme based on diffractive optics," Appl. Opt. 39, 2881-2887 (2000).
[CrossRef]

1999 (7)

Bhushan, A.S. , F. Coppinger, S. Yegnanarayanan, and B. Jalali, "Non-dispersive wavelength-division sampling," Opt. Lett. 24, 738-740 (1999).
[CrossRef]

T. R. Clark, T. F. Carruthers, P. J. Matthews, I. N. Duling, III, "Phase noise measurements of ultrastable 10 GHz harmonically modelocked fiber laser," Electron. Lett. 35, 720-721 (1999).
[CrossRef]

J. U. Kang and R. D. Esman, "Demonstration of time interweaved photonic four-channel WDM sampler for hybrid analogue-digital converter," Electron. Lett. 35, 60-61 (1999).
[CrossRef]

T. R. Clark, J. U. Kang and R. D. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photonic Technol. Lett. 11,1168-1170 (1999).
[CrossRef]

F. Coppinger, A. S. Bhushan, and B. Jalali, "Photonic time stretch and its application to analog-to-digital conversion," IEEE Trans. Microwave Theory and Tech. 47,1309-1314 (1999).
[CrossRef]

R. Helkey, "Narrow-band optical A/D converter with suppressed second-order distortion," IEEE Photonics Technol. Lett. 11, 599-601 (1999).
[CrossRef]

R. H. Walden, "Analog-to-digital converter survey and analysis," IEEE J. Sel. Areas Comm. 17, 539-550 (1999).
[CrossRef]

1998 (8)

C. K. Sun, D. T. Chang, G. A. Massey, T. Y. Lee, R. Yu, and D. J. Albares, "High energy and low jitter picosecond optical pulser for sample and hold," Proc. SPIE 3463, 212-218 (1998).
[CrossRef]

A. Johnstone, M. F. Lewis, and J. D. Hares "Optical replication technique for wideband transient waveform digitisation," Proc. SPIE 3285, 209-216 (1998).
[CrossRef]

A. S. Bhushan, F. Coppinger, B. Jalali, S. Wang and H. F. Fetterman, "150 Gsample/s wavelength division sampler with time-stretched output," Electron. Lett. 34, 474-475 (1998).
[CrossRef]

A. Yariv, and R. G. M. P. Koumans, "Time interleaved optical sampling for ultra-high speed A/D conversion," Electron. Lett. 34, 2012-2023 (1998).
[CrossRef]

J. U. Kang, M. Y. Frankel, and R. D. Esman, "Highly parallel pulsed optoelectronic analog-digital converter," IEEE Photonic Technol. Lett. 10, 1626-1628 (1998).
[CrossRef]

A. P. Willis, D. Griffiths, and P. B. Atanackovic, "The use of unipolar loop signals in the error diffusion modulator," IEEE Trans. Circuits and Syst. II 45, 1597-1599 (1998).
[CrossRef]

F. Coppinger, A.S. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

B. Jalali, F. Coppinger, and A.S. Bhushan, "Photonic time-stretch offers solution to ultrafast analog-to-digital conversion," Optics in 1998, Optics and Photonics News, 31-32, December (1998).

1997 (2)

1996 (1)

L. M. Loh, and J. L. LoCicero, "Subnanosecond sampling all-optical analog-to-digital converter using symmetric self-electro-optic effect devices," Opt. Eng. 35, 457-466 (1996).
[CrossRef]

1995 (1)

1994 (2)

G. E. Betts, "Linearized modulator for suboctave-bandpass optical analog links," IEEE Trans. Microwave Theory and Tech. 42, 2642-2649 (1994).
[CrossRef]

P. E. Pace and D. D. Styer, "High-resolution encoding process for an integrated optical analog-to-digital converter," Opt. Eng. 33, 2638-2645 (1994).
[CrossRef]

1993 (2)

C. K. Sun, C. T. Chang, and W. H. McKnight, "A high-speed, high precision optically controlled sample and hold circuit for analog to digital conversion," Proc. SPIE 2051, 758-767 (1993).
[CrossRef]

B. L. Shoop and J. W. Goodman, "A first-order error diffusion modulator for optical oversampled A/D conversion," Opt. Commun. 97, 167-172 (1993).
[CrossRef]

1992 (3)

J.-M. Jeong, and M. E. Marhic, "All-optical analog-to-digital and digital-to-analog conversion implemented by a nonlinear fiber interferometer," Opt. Commun. 91, 115-122 (1992).
[CrossRef]

B. L. Shoop and J. W. Goodman, "Optical oversampled analog-to-digital conversion," Appl. Opt. 31, 5654-5660 (1992).
[CrossRef] [PubMed]

T. Shibata and M. Yoneyama, "A novel sample and hold system using an optical modulator," IEEE Photonics Technol. Lett. 4, 588-591 (1992).
[CrossRef]

1991 (4)

C. K. Sun, C.-C. Wu, C. T. Chang, and W. H. McKnight, "A bridge type optoelectronic sample and hold circuit," J. Lightwave Technol. 9, 341-346 (1991).
[CrossRef]

J. A. Bell, M. C. Hamilton, D. A. Leep, H. F. Taylor, and Y.-H. Lee, "A/D Conversion of microwave signals using a hybrid optical/electronic technique," Proc. SPIE 1476, 326-329 (1991).
[CrossRef]

J. A. Bell, M. C. Hamilton, and D. A. Leep, "Optical sampling and demultiplexing applied to A/D conversion," Proc. SPIE 1562, 276-280 (1991).
[CrossRef]

Y. Li and Y. Zhang, "Optical analog-to-digital conversion using acousto-optic theta modulation and table lookup," Appl. Opt. 30, 4368-4371 (1991).
[CrossRef] [PubMed]

1989 (2)

B. H. Kolner and M. Nazarathy, "Temporal imaging with a time lens," Opt. Lett. 14, 630-632 (1989).
[CrossRef] [PubMed]

R. G. Walker, I. Bennion, A. C. Carter, "Novel GaAs/AlGaAs guided-wave analog/digital converter," Electron. Lett. 25, 1443-1444 (1989).
[CrossRef]

1984 (2)

R. A. Becker, C. E. Woodward, F. J. Leonberger, and R. C. Williamson, "Wideband electrooptic guided-wave analog-to-digital converters," Proc. IEEE 72, 802-819 (1984).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood and C. A. Burrus, "Nove hybrid optically bistable switch: the quantum well self electro-optic effect device," Appl Phys. Lett. 45, 13-15 (1984).
[CrossRef]

1983 (2)

C. L. Chang and C. S. Tsai, "Electro-optic analog-to-digital converter using channel waveguide Fabry-Perot modulator array," Appl. Phys. Lett. 43, 22-24 (1983).
[CrossRef]

C. H. CoxIII, V. Diadiuk, I. Yao, F. J. Leonberger and R. C. Williamson, "InP optoelectronic switches and their high-speed signal-processing applications," Proc. SPIE 439, 164-168 (1983).

1982 (4)

R. A. Becker and F. J. Leonberger, "2-bit 1 Gsample/s electrooptic guided-wave analog-to-digital converter," IEEE J. Quantum Electron. 18, 1411-1413 (1982).
[CrossRef]

F. J. Leonberger, C. E. Woodward, and R. A. Becker, "4-bit 828-megasample/s electro-optic guided-wave analog-to-digital converter," Appl. Phys. Lett. 40, 565-568 (1982).
[CrossRef]

R. G. Dokhikyan, E. M. Zolotov, S. S. Karinskii, V. F. Maksimov, V. T. Popkov, A. M. Prokhorov, I. N. Sisakyan, and E. A. Shcherbakov, "Prototype of an integrated-optics four-digit analog-digital converter," Kvantovaya Elektron. (Moscow) 9, 1272-1273 (1982) [Sov. J. Quantum Electron. 12, 806-807 (1982)].
[CrossRef]

G. D. H. King and R. Cebulski, "Analogue-to-digital conversion using integrated electro-optic interferometers," Electron. Lett. 18, 1099-1100 (1982).
[CrossRef]

1979 (4)

F. J. Leonberger and P. Moulton, "High-speed InP optoelectronic switch," Appl. Phys. Lett. 35, 712-714 (1979).
[CrossRef]

H. F. Taylor, "An optical analog-to-digital converter—design and analysis," IEEE J. Quantum Electron. 15, 210-216 (1979).
[CrossRef]

F. J. Leonberger, C. E. Woodward, and D. L. Spears, "Design and development of a high-speed electrooptic A/D converter," IEEE Trans. Circuits and Syst. 26, 1125-1131 (1979).
[CrossRef]

K. Takizawa, and M. Okada, "Analog-to-digital converter: a new type using an electrooptic light modulator," Appl. Opt. 18, 3148-3151 (1979).
[CrossRef] [PubMed]

1978 (2)

H. F. Taylor, H. F., M. J. Taylor, and P. W. Bauer, "Electro-optic analog-to-digital conversion using channel waveguide modulators," Appl. Phys. Lett. 32, 559-561 (1978).
[CrossRef]

A. J. Low and J. E. Carroll, "10ps optoelectronic sampling system," Solid-State and Electron Devices 2, 185-190 (1978).
[CrossRef]

1977 (1)

1976 (1)

R. A. Lawton and J. R. Andrews, "Optically strobed sampling oscilloscope," IEEE Trans. Instrum. Meas. 25, 56-60 (1976).

1975 (2)

H. F. Taylor, "An electro-optic analog-to-digital converter," Proc. IEEE 63, 1524-1525 (1975).
[CrossRef]

D. H. Auston, "Picosecond optoelectronic switching and gating in silicon," Appl. Phys. Lett. 26, 101-103 (1975).
[CrossRef]

1974 (1)

S. Wright, I. M. Mason, M. G. F. Wilson, "High-speed electro-optic analogue-digital conversion," Electron. Lett. 10, 508-509 (1974).
[CrossRef]

1970 (1)

A. E. Siegman, and D. J. Kuizenga, "Proposed method for measuring picosecond pulsewidths and pulse shapes in cw mode-locked lasers," IEEE J. Quantum Electron. 6, 212-215 (1970).
[CrossRef]

Abbott, D.

S. F. Al-Sarawi, N. Burgess, W. Marwood, P. Atanackovic, D. Abbott, "Very high speed differential optoelectronic algorithmic ADC using n-i(MQW)-n SEED technology," Microelectronics J. 31, 593-604 (2000).
[CrossRef]

Abdul, J. M.

Abeles, J.

C. M. DePriest, M. T. Yilmaz, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "High-quality photonic sampling streams from a semiconductor diode ring laser," IEEE J. Quantum Electron. 38, 380-389 (2002).
[CrossRef]

C. M. DePriest, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "External-cavity semiconductor diode ring laser for application in hybrid optoelectronic analog-to-digital converter," Proc. SPIE 4386, 37-41 (2001).
[CrossRef]

Abeles, J. H.

C. M. DePriest, A. Braun, J. H. Abeles, and P. J. Delfyett, Jr., "10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser," IEEE Photon. Technol. Lett. 13, 1109-1111 (2001).
[CrossRef]

Albares, D. J.

C. K. Sun, D. T. Chang, G. A. Massey, T. Y. Lee, R. Yu, and D. J. Albares, "High energy and low jitter picosecond optical pulser for sample and hold," Proc. SPIE 3463, 212-218 (1998).
[CrossRef]

Aldana, R.

K. Ioakeimidi, R. F. Leheny, S. Gradinaru, P. R. Bolton, R. Aldana, K. Ma, J. E. Clendenin, J. S. Harris, Jr., and R. F. W. Pease, "Photoelectronic analog-to-digital conversion: sampling and quantizing at 100 Gs/s," IEEE Trans. Microwave Theory and Tech. 53, 336-342 (2005).
[CrossRef]

R. F. Pease, K. Ioakeimidi, R. Aldana, and R. Leheny, "Photoelectronic analog-to-digital conversion using miniature electron optics: Basic design considerations," J. Vac. Sci. Technol. 21, 2826-2829 (2003).
[CrossRef]

Alfano, R. R.

Al-Sarawi, S. F.

T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
[CrossRef]

T. Sarros, S. F. Al-Sarawi, K. A. Corbett, K. J. Grant, B. A. Clare, W. Marwood, "Oversampled optoelectronic analog-digital converters using sigma-delta modulation," Proc. SPIE 4935, 178-187 (2002).
[CrossRef]

S. F. Al-Sarawi, P. B. Atanackovic, W. Marwood, B. A. Claire, K. A. Corbett, K. J. Grant, J. Munch, "Differential oversampling data converters in SEED technology," Microelectronics J. 33, 141-151 (2002).
[CrossRef]

S. F. Al-Sarawi, W. Marwood, and P. Atanackovic, "An integrated optoelectronics oversampling analog-to-digital converter," Proc. SPIE 4236, 351-360 (2001).
[CrossRef]

S. F. Al-Sarawi, N. Burgess, W. Marwood, P. Atanackovic, D. Abbott, "Very high speed differential optoelectronic algorithmic ADC using n-i(MQW)-n SEED technology," Microelectronics J. 31, 593-604 (2000).
[CrossRef]

Al-Sarawi, S. R.

T. Sarros, S. R. Al-Sarawi, P. Celinski, K. A. Corbett, "Optical threshold logic analog-to-digital converters using self electro-optic effect devices," Proc. SPIE 5649, 227-236 (2005).
[CrossRef]

Andrews, J. R.

R. A. Lawton and J. R. Andrews, "Optically strobed sampling oscilloscope," IEEE Trans. Instrum. Meas. 25, 56-60 (1976).

Asano, K.

Asbeck, P.

D. Ralston, A. Metzger, Y. Kang, P. Asbeck and P. Yu, "Highly linear photoreceiver design for application to ultrahigh bandwidth photonic A/D converters," Proc. SPIE 4112, 132-140 (2000).
[CrossRef]

Atanackovic, P.

S. F. Al-Sarawi, W. Marwood, and P. Atanackovic, "An integrated optoelectronics oversampling analog-to-digital converter," Proc. SPIE 4236, 351-360 (2001).
[CrossRef]

S. F. Al-Sarawi, N. Burgess, W. Marwood, P. Atanackovic, D. Abbott, "Very high speed differential optoelectronic algorithmic ADC using n-i(MQW)-n SEED technology," Microelectronics J. 31, 593-604 (2000).
[CrossRef]

Atanackovic, P. B.

B. A. Clare, K. A. Corbett, K. J. Grant, P. B. Atanackovic, W. Marwood, and J. Munch, "Investigation of critical slowing down in a bistable S-SEED," J. Lightwave Technol. 21, 2883-2890 (2003).
[CrossRef]

S. F. Al-Sarawi, P. B. Atanackovic, W. Marwood, B. A. Claire, K. A. Corbett, K. J. Grant, J. Munch, "Differential oversampling data converters in SEED technology," Microelectronics J. 33, 141-151 (2002).
[CrossRef]

A. P. Willis, D. Griffiths, and P. B. Atanackovic, "The use of unipolar loop signals in the error diffusion modulator," IEEE Trans. Circuits and Syst. II 45, 1597-1599 (1998).
[CrossRef]

Auston, D. H.

D. H. Auston, "Picosecond optoelectronic switching and gating in silicon," Appl. Phys. Lett. 26, 101-103 (1975).
[CrossRef]

Becker, R. A.

R. A. Becker, C. E. Woodward, F. J. Leonberger, and R. C. Williamson, "Wideband electrooptic guided-wave analog-to-digital converters," Proc. IEEE 72, 802-819 (1984).
[CrossRef]

F. J. Leonberger, C. E. Woodward, and R. A. Becker, "4-bit 828-megasample/s electro-optic guided-wave analog-to-digital converter," Appl. Phys. Lett. 40, 565-568 (1982).
[CrossRef]

R. A. Becker and F. J. Leonberger, "2-bit 1 Gsample/s electrooptic guided-wave analog-to-digital converter," IEEE J. Quantum Electron. 18, 1411-1413 (1982).
[CrossRef]

Bell, J. A.

J. A. Bell, M. C. Hamilton, and D. A. Leep, "Optical sampling and demultiplexing applied to A/D conversion," Proc. SPIE 1562, 276-280 (1991).
[CrossRef]

J. A. Bell, M. C. Hamilton, D. A. Leep, H. F. Taylor, and Y.-H. Lee, "A/D Conversion of microwave signals using a hybrid optical/electronic technique," Proc. SPIE 1476, 326-329 (1991).
[CrossRef]

Bennion, I.

R. G. Walker, I. Bennion, A. C. Carter, "Novel GaAs/AlGaAs guided-wave analog/digital converter," Electron. Lett. 25, 1443-1444 (1989).
[CrossRef]

Betser, Y.

S. Jaganathan, S. Krishnan, D. Mensa, T. Mathew, Y. Betser, Y. Wei, D. Scott, M. Urteaga, and M. Rodwell, "An 18-GHz continuous time Σ−Δ analog-digital converter implemented in InP-transferred substrate HBT technology," IEEE J. Solid-State Circuits 36, 1343-1350 (2001).
[CrossRef]

Betts, G. E.

J. C. Twichell, J. L. Wasserman, P. W. Juodawlkis, G. E. Betts, and R. C. Williamson, "High-linearity 208-MS/s photonic analog-to-digital converter using 1-to-4 optical time-division demultiplexers," IEEE Photonic Technol. Lett. 13, 714-716, July 2001.
[CrossRef]

R. C. Williamson, P. W. Juodawlkis, J. L. Wasserman, G. E. Betts, and J. C. Twichell, "Effects of crosstalk in demultiplexers for photonic analog-to-digital converters," J. Lightwave Technol. 19, 230-236 (2001).
[CrossRef]

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray and R. C. Williamson, "Optically sampled analog-to-digital converters," IEEE Trans. Microwave Theory Tech. 49, 1840-1853, (2001).
[CrossRef]

G. E. Betts, "Linearized modulator for suboctave-bandpass optical analog links," IEEE Trans. Microwave Theory and Tech. 42, 2642-2649 (1994).
[CrossRef]

Bewley, S. A.

P. E. Pace, S. A. Bewley, and J. P. Powers, "Fiber-lattice accumulator design considerations for optical ΣΔ analog-to-digital converters," Opt. Eng. 39, 1517-1526 (2000).
[CrossRef]

Bhushan,

Bhushan, A. S.

F. Coppinger, A. S. Bhushan and B. Jalali, "12 Gsample/s wavelength division sampling analog-to-digital converter," Electron. Lett. 36, 316-318 (2000).
[CrossRef]

F. Coppinger, A. S. Bhushan, and B. Jalali, "Photonic time stretch and its application to analog-to-digital conversion," IEEE Trans. Microwave Theory and Tech. 47,1309-1314 (1999).
[CrossRef]

A. S. Bhushan, F. Coppinger, B. Jalali, S. Wang and H. F. Fetterman, "150 Gsample/s wavelength division sampler with time-stretched output," Electron. Lett. 34, 474-475 (1998).
[CrossRef]

Bhushan, A.S.

A.S. Bhushan, P. V. Kelkar, B. Jalali, O. Boyraz, and M. Islam, "130-GSa/s photonic Analog-to-digital converter with time stretch preprocessor, IEEE Photonic Technol. Lett. 14, 684-686, (2002).
[CrossRef]

A.S. Bhushan, P. Kelkar and B. Jalali, "30 Gsample/s time-stretch analogue-to-digital converter," Electron. Lett. 36, 1526-1527, Aug. 2000.
[CrossRef]

F. Coppinger, A.S. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

B. Jalali, F. Coppinger, and A.S. Bhushan, "Photonic time-stretch offers solution to ultrafast analog-to-digital conversion," Optics in 1998, Optics and Photonics News, 31-32, December (1998).

Bolton, P. R.

K. Ioakeimidi, R. F. Leheny, S. Gradinaru, P. R. Bolton, R. Aldana, K. Ma, J. E. Clendenin, J. S. Harris, Jr., and R. F. W. Pease, "Photoelectronic analog-to-digital conversion: sampling and quantizing at 100 Gs/s," IEEE Trans. Microwave Theory and Tech. 53, 336-342 (2005).
[CrossRef]

Bourgholtzer, S.

T. P. E. Broekaert, W. Ng, J. F. Jensen, D. Yap, D. L. Persechini, S. Bourgholtzer, C. H. Fields, Y. K. Brown-Boegeman, B. Shi and R. H. Walden, "InP-HBT optoelectronic integrated circuits for photonic analog-to-digital conversion," IEEE J. Solid-State Electron. 36, 1335-1342 (2001).
[CrossRef]

Boyraz, O.

Y. Han, O. Boyraz, and B. Jalali, "Real-time A/D conversion at 480 GSample/s using the phase diversity photonic time-stretch system," Proc.Microwave Photonics 2004, 186-189 (2004).

A.S. Bhushan, P. V. Kelkar, B. Jalali, O. Boyraz, and M. Islam, "130-GSa/s photonic Analog-to-digital converter with time stretch preprocessor, IEEE Photonic Technol. Lett. 14, 684-686, (2002).
[CrossRef]

Braun, A.

C. M. DePriest, M. T. Yilmaz, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "High-quality photonic sampling streams from a semiconductor diode ring laser," IEEE J. Quantum Electron. 38, 380-389 (2002).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, and P. J. Delfyett, Jr., "10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser," IEEE Photon. Technol. Lett. 13, 1109-1111 (2001).
[CrossRef]

C. M. DePriest, A. Braun, J. Abeles, and P. J. Delfyett, Jr., "External-cavity semiconductor diode ring laser for application in hybrid optoelectronic analog-to-digital converter," Proc. SPIE 4386, 37-41 (2001).
[CrossRef]

Broekaert, T. P. E.

T. P. E. Broekaert, W. Ng, J. F. Jensen, D. Yap, D. L. Persechini, S. Bourgholtzer, C. H. Fields, Y. K. Brown-Boegeman, B. Shi and R. H. Walden, "InP-HBT optoelectronic integrated circuits for photonic analog-to-digital conversion," IEEE J. Solid-State Electron. 36, 1335-1342 (2001).
[CrossRef]

Brown-Boegeman, Y. K.

T. P. E. Broekaert, W. Ng, J. F. Jensen, D. Yap, D. L. Persechini, S. Bourgholtzer, C. H. Fields, Y. K. Brown-Boegeman, B. Shi and R. H. Walden, "InP-HBT optoelectronic integrated circuits for photonic analog-to-digital conversion," IEEE J. Solid-State Electron. 36, 1335-1342 (2001).
[CrossRef]

Burgess, N.

S. F. Al-Sarawi, N. Burgess, W. Marwood, P. Atanackovic, D. Abbott, "Very high speed differential optoelectronic algorithmic ADC using n-i(MQW)-n SEED technology," Microelectronics J. 31, 593-604 (2000).
[CrossRef]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood and C. A. Burrus, "Nove hybrid optically bistable switch: the quantum well self electro-optic effect device," Appl Phys. Lett. 45, 13-15 (1984).
[CrossRef]

Bussjager, R. J.

H. Zmuda, S. Hanna, R. J. Bussjager, M. L. Fanto, M. J. Hayduk, S. T. Johns, J. E. Malowicki, and P. L. Repak, "Optically assisted high-speed, high resolution analog-to-digital conversion," Proc. SPIE 5814, 51-61 (2005)
[CrossRef]

H. Zmuda, M. J. Hayduk, R. J. Bussjager, and E. N. Toughlian, "Wavelength-based analog-to-digital conversion," Proc. SPIE 4547, 134-145 (2002).
[CrossRef]

M. J. Hayduk, R. J. Bussjager, S. T. Johns, and C. M. Gerhardstein and G. Wicks, "Contrast ratio enhancement in a saturable absorber based photonic analog to digital converter," Proc. SPIE 4732,46-52 (2002).
[CrossRef]

M. J. Hayduk, R. J. Bussjager, and M. A. Getbehead, "Photonic analog to digital conversion techniques using semiconductor saturable absorbers," Proc. SPIE 4042, 54-60 (2000).
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K. Ioakeimidi, R. F. Leheny, S. Gradinaru, P. R. Bolton, R. Aldana, K. Ma, J. E. Clendenin, J. S. Harris, Jr., and R. F. W. Pease, "Photoelectronic analog-to-digital conversion: sampling and quantizing at 100 Gs/s," IEEE Trans. Microwave Theory and Tech. 53, 336-342 (2005).
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T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
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T. R. Clark, T. F. Carruthers, P. J. Matthews, I. N. Duling, III, "Phase noise measurements of ultrastable 10 GHz harmonically modelocked fiber laser," Electron. Lett. 35, 720-721 (1999).
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I. A. Goncharenko, A. K. Esman, V. K. Kuleshov, V. A. Pilipovich, "Optical broadband analog-digital conversion on the base of microring resonator," Opt. Commun. 257, 54-61 (2006).
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T. R. Clark, J. U. Kang and R. D. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photonic Technol. Lett. 11,1168-1170 (1999).
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A. S. Bhushan, F. Coppinger, B. Jalali, S. Wang and H. F. Fetterman, "150 Gsample/s wavelength division sampler with time-stretched output," Electron. Lett. 34, 474-475 (1998).
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M. J. Hayduk, R. J. Bussjager, and M. A. Getbehead, "Photonic analog to digital conversion techniques using semiconductor saturable absorbers," Proc. SPIE 4042, 54-60 (2000).
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M. J. Hayduk, R. J. Bussjager, M. A. Getbehead, and J. A. Louthain, "Recent advancements in photonic converters," Proc. SPIE 4112, 28-37.

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I. A. Goncharenko, A. K. Esman, V. K. Kuleshov, V. A. Pilipovich, "Optical broadband analog-digital conversion on the base of microring resonator," Opt. Commun. 257, 54-61 (2006).
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Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood and C. A. Burrus, "Nove hybrid optically bistable switch: the quantum well self electro-optic effect device," Appl Phys. Lett. 45, 13-15 (1984).
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K. Ioakeimidi, R. F. Leheny, S. Gradinaru, P. R. Bolton, R. Aldana, K. Ma, J. E. Clendenin, J. S. Harris, Jr., and R. F. W. Pease, "Photoelectronic analog-to-digital conversion: sampling and quantizing at 100 Gs/s," IEEE Trans. Microwave Theory and Tech. 53, 336-342 (2005).
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B. A. Clare, K. A. Corbett, and K. J. Grant, "Performance of a photonic oversampled sigma-delta quantizer," Proc. SPIE 5814, 248-261 (2005).
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T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
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T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
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Han, Y.

Y. Han, O. Boyraz, and B. Jalali, "Real-time A/D conversion at 480 GSample/s using the phase diversity photonic time-stretch system," Proc.Microwave Photonics 2004, 186-189 (2004).

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H. Zmuda, S. Hanna, R. J. Bussjager, M. L. Fanto, M. J. Hayduk, S. T. Johns, J. E. Malowicki, and P. L. Repak, "Optically assisted high-speed, high resolution analog-to-digital conversion," Proc. SPIE 5814, 51-61 (2005)
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H. Zmuda, S. Hanna, R. J. Bussjager, M. L. Fanto, M. J. Hayduk, S. T. Johns, J. E. Malowicki, and P. L. Repak, "Optically assisted high-speed, high resolution analog-to-digital conversion," Proc. SPIE 5814, 51-61 (2005)
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M. J. Hayduk, R. J. Bussjager, S. T. Johns, and C. M. Gerhardstein and G. Wicks, "Contrast ratio enhancement in a saturable absorber based photonic analog to digital converter," Proc. SPIE 4732,46-52 (2002).
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S. F. Al-Sarawi, W. Marwood, and P. Atanackovic, "An integrated optoelectronics oversampling analog-to-digital converter," Proc. SPIE 4236, 351-360 (2001).
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T. Sarros, K. A. Corbett, S. F. Al-Sarawi, K. J. Grant, B. A. Clare, K. J. Grant and W. Marwood, "Differential optoelectronic subtractor using self electro-optic effect devices for use in sigma-delta modulation," Proc. SPIE 5274, 252-263 (2004).
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Figures (18)

Fig. 1.
Fig. 1.

Voltage as a function of time (green), the sampled and quantized voltage (red) and the quantization error (blue).

Fig. 2.
Fig. 2.

Input voltage as a function of time (green) and the sampled and quantized voltage as a function of time (red). The upper row shows digitization of a noiseless signal with N = 3, 4, and 5. The lower row shows digitization of the same signal plus noise with N = 3, 4, and 5. In the upper row one can clearly see the additional benefit of higher numbers of bits N (for N = 5 look at t = 0-1, 5-7 and 9-10) and of course, the ENOB equals the number of bits N through the definition in eqs. (2) and (3). In the lower row, one sees a benefit in increasing the bits from 3 to 4, but no apparent improvement is obtained by increasing N from 4 to 5 because the ENOB is limited to about 4 by the noise on the signal and not by the quantization noise.

Fig. 3.
Fig. 3.

Effective number of bits, ENOB, of electronic ADCs as a function of analog input frequency. The red points indicate existing ADCs. The dashed lines represent fundamental limits due to jitter for rms aperture jitter of 100 fs and 1 ps (blue) comparator ambiguity for transition frequencies f T = 100, and 500 GHz (green), thermal noise with equivalent load resisitance of 50 and 2000 ohms (brown) and the Heisenberg uncertainty principle (red) as discussed by Walden [2, 6].

Fig. 4.
Fig. 4.

Generic analog optical link.

Fig. 5.
Fig. 5.

ENOB as a function of link bandwidth for an analog optical link with power incident on the photodiode as a parameter.

Fig. 6.
Fig. 6.

Four major classes of photonic ADCs.

Fig. 7.
Fig. 7.

General schematic of a photonics-assisted ADC in which a stable mode-locked laser is used as a clock.

Fig. 8.
Fig. 8.

Schematic of the optically clocked diode bridge circuit used by Jacobs et al. [32] as the track and hold circuit of an electronic ADC (2004) (PD = photodiode).

Fig. 9.
Fig. 9.

(a) Photonics-assisted interleaved ADC architecture. (b) Optically triggered differential sample-and-hold circuit (adapted from [36]).

Fig. 10.
Fig. 10.

Optically triggered e-beam ADC (adapted from [38, 39]).

Fig. 11.
Fig. 11.

Single shot version of the time-stretch ADC.

Fig. 12.
Fig. 12.

Continuous time version of the time-stretch ADC.

Fig. 13.
Fig. 13.

Photonic sampled and electronically quantized ADC.

Fig. 14.
Fig. 14.

Photonic sampled and demultiplexed ADC. The electronic ADCs operate at a rate reduced by the factor M from the sampling rate of the optical system.

Fig. 15.
Fig. 15.

Optically quantized photonic ADC based on tuning the wavelength of an optical source, reflecting that source from a diffraction grating and focusing the output through a diffractive optical element to an array of detectors. (Adapted from [134])

Fig. 16.
Fig. 16.

Taylor’s multi-interferometric electro-optic ADC [3, 12, 15]. (a) block diagram showing 4 interferometers with lengths increasing by a factor of 2, photodiode receivers, electronic amplifiers and comparators. (b) Optical intensity as a function of voltage applied to the modulator with Gray code output produced by comparator below.

Fig. 17.
Fig. 17.

All-optical photonic ADC using a mode-locked laser source for sampling and the voltage-controlled phase shift of a free-space interference pattern to obtain quantization (adapted from [111, 112, 133].

Fig. 18.
Fig. 18.

Delta-sigma modulator. The input signal at the left is summed with the fed back bit from the previous sample, integrated, quantized and processed by a digitial filter.

Equations (9)

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

SNR Q ( dB ) = 20 log 10 ( V fs , rms / Δ Q )
N = [ SNR Q ( dB ) 1.76 ] / 6.02 .
ENOB = [ SINAD ( dB ) 1.76 ] / 6.02 .
ENOB = log 2 [ 1 / ( 3 1 / 2 πf s σ j ) ] .
CNR = ( mRP ) 2 / 2 ( σ s 2 + σ th 2 + σ RIN 2 )
σ s 2 = 2 q ( R P + I d ) Δ f
σ th 2 = 4 k b TF n Δ f / R L
σ RIN 2 = ( RIN ) ( RP ) 2 Δ f
ENOB = [ CNR ( dB ) 1.76 ] / 6.02 .

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