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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 5 — Mar. 5, 2007
  • pp: 1955–1982
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Photonic analog-to-digital converters

George C. Valley  »View Author Affiliations


Optics Express, Vol. 15, Issue 5, pp. 1955-1982 (2007)
http://dx.doi.org/10.1364/OE.15.001955


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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

1. Introduction

The use of photonic components to make or improve an analog-to-digital converter (ADC) has attracted interest since the early 1970s, and today one can easily assemble more than 100 references on “photonic ADCs”. During this period, lasers and optical components have improved and matured remarkably, but photonics is still not used in any commercial or special purpose ADC to the best of my knowledge. One reason for this may be the rapid advance in electronics since the early 1970s, but as discussed by Walden (1999, 2006), electronic ADCs improve somewhat slower than digital electronics. The purpose of this review is to describe all known ways in which photonics has been used or proposed for use in ADCs that digitize radio-frequency signals, to put these technologies in well-defined classes, and to identify those technologies that offer promise for dramatic improvement over electronics.

Scope. This review covers photonic ADCs for which the input is an analog electronic signal and the output is an electronic digital approximation to that signal. The review excludes work in which the input is an analog optical signal (e.g. images, or optical communications signals) and work in which the output is a digital optical signal.

Sources. I have used the following sources for this review paper: IEEE Xplore, SPIE online journals and proceedings, OSA online journals, Optics Communications online, other references found in journal articles and several books.

2. Brief Review of Electronic ADCs

An electronic analog-to-digital converter must perform two functions on a time-varying voltage: (1) sample and hold it for a specified time and (2) quantize the held voltage into a number of levels. The sampling rate and the number of levels are the most basic properties of an ADC. The time during which the voltage is sampled is usually much less than the inverse of the sampling rate while the time it is held is usually about equal to this. The logarithm to base 2 of the number of levels of the ADC is given in bits so that a 1024-level ADC is a 10-bit ADC. Usually the number of levels is given by 2 raised to an integer power but for some ADCs the number of bits may not be an integer [144

144. IEEE standard for terminology and test methods for analog-to-digital converters, IEEE Std 1241–2000 (2001).

].

Figure 1 shows an example of an input time-varying voltage in green, the sampled and quantized version in red and the difference between the input and the quantized signal, called the quantization error, in blue. In this picture the sampling rate is 2 Samples/sec (S/s), the number of bits is N = 4, the full scale voltage Vfs = 1 V, the voltage quantization is Q = Vfs/(2N -1) = 0.067 V, least significant bit corresponds to a voltage of Vfs/(2N -1), and the root-mean-square (rms) quantization error ΔQ = Q/121/2 = 0.019 V. More detail on these subjects can be found in many textbooks including Shoop [1

1. B. L. Shoop, Photonic Analog-to-Digital Conversion, Springer, New York, 2000.

] (2000) and in Walden’s review [2

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

] (1999).

SNRQ(dB)=20log10(Vfs,rms/ΔQ)
(1)

where the rms full-scale voltage, V fs,rms , equals V fs/23/2 for a sine wave. Substitution for V fs,rms and ΔQ and solution for N yield (for 2N ≫1)

N=[SNRQ(dB)1.76]/6.02.
(2)

For arbitrary sources of noise and nonlinear distortion characterized by the signal-to-noise and distortion ratio, SINAD, Eq. (2) can be generalized to define the effective number of bits (ENOB) of an ADC [6

6. R. H. Walden, “Analog-to-digital conversion in the early 21st century,” submitted for publication 2006.

, 144

144. IEEE standard for terminology and test methods for analog-to-digital converters, IEEE Std 1241–2000 (2001).

]:

ENOB=[SINAD(dB)1.76]/6.02.
(3)

Eq. (3) shows that a 6-dB improvement in SINAD is required to increase the ENOB by 1 bit. This is intuitively sensible since it is clear that doubling V fs or halving the rms noise voltage (either increases the power SNR by 6 dB) gives the equivalent of one additional bit.

Fig. 1. Voltage as a function of time (green), the sampled and quantized voltage (red) and the quantization error (blue).
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.

When timing jitter is the only source of ADC performance degradation, there is a simple relation between the effective number of bits and the sampling rate fs times the rms timing jitter σj, which has been derived by many workers (Taylor 1979 [3

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

], Walden 1999 [2

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

], Valley et al. 2004 [4

4. 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). [CrossRef]

]),

ENOB=log2[1/(31/2πfsσj)].
(4)

Minor variations in the numerical factor in front of fsσj are caused by the choice of Q, Q/2 or Q/121/2 in the calculation for the noise level (Q/121/2 is used here). This equation is applicable to all ADCs including audio. It is amusing to note that the 96 kS/s, 24 bit audio DVD would require a timing jitter of ∼100 fs (the state of the art in 2006 [6

6. R. H. Walden, “Analog-to-digital conversion in the early 21st century,” submitted for publication 2006.

] for electronic ADCs) to achieve ENOB = 24 and of course, the SINAD for other sources of noise and distortion would have to be greater than 146 dB!

3. State of the art in electronic ADCs

Walden [2

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

, 6

6. R. H. Walden, “Analog-to-digital conversion in the early 21st century,” submitted for publication 2006.

] (1999, 2006) has reviewed the performance of electronic ADCs. It is useful to review this work to evaluate what performance is required from photonic ADCs to achieve a significant enhancement over electronic ADC performance. Fig. 3 shows effective number of bits of a wide range of electronic ADCs as a function of ADC bandwidth [6

6. R. H. Walden, “Analog-to-digital conversion in the early 21st century,” submitted for publication 2006.

]. Typically, optics must obtain at least a factor-of-10 improvement (increase in signal bandwidth or decrease in voltage noise) compared to electronics or break through a fundamental limit to make the development effort worth the time and cost. From this standpoint at 1 GHz a photonic system would have to achieve ENOB > 11(3.3 more bits) while at 20 GHz, ENOB = 4 would be sufficient since this exceeds the comparator ambiguity limit for semiconductor circuits with transition frequency f T = 150 GHz by more than a factor of 2.

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].

4. Brief review of analog optical links

Fig. 4. Generic analog optical link.

CNR=(mRP)2/2(σs2+σth2+σRIN2)
(6)

where m is the modulation depth of the EO modulator, R is the responsivity of the photodiode, P is the average optical power on the photodiode, and σs, σth, and σRIN are standard deviations of the photodiode noise currents associated with shot, thermal and RIN noise. Standard expressions for σs, σth, and σRIN are given by [8

8. G. P. Agrawal, Fiber-Optic Communication Systems, Wiley, New York, 336–343, (1997).

]

σs2=2q(RP+Id)Δf
(7)
σth2=4kbTFnΔf/RL
(8)
σRIN2=(RIN)(RP)2Δf
(9)

ENOB=[CNR(dB)1.76]/6.02.
(10)

Fig. 5. ENOB as a function of link bandwidth for an analog optical link with power incident on the photodiode as a parameter.

5. Classes of photonic ADCs and history

Logically, the term photonic ADC should apply to a device in which an analog optical signal (photons) is input and a digital optical signal is output and one could imagine systems that could use such a device—e.g., a movie camera that digitized light from a scene for direct transmission over optical fiber. However, there is almost no work on such devices and the term photonic ADC is generally used to refer to device with an analog RF electronic input and a digital electronic output that uses photonics in the digitization process. Such photonic ADCs can be subdivided into 4 broad classes as shown in Fig. 6: photonic assisted, photonic sampled, photonic quantized and photonic sampled and quantized. Photonic assisted ADCs are electronic ADCs that use photonics to improve one or more limiting properties but perform both sampling and quantization in the electronic domain. Photonic sampled ADCs are those in which sampling is performed in the optical domain while quantization is performed in the electrical domain while in photonic quantized ADCs the domains of quantization and sampling are reversed. Naturally, photonic sampled and quantized ADCs are those in which both sampling and quantization are performed optically. It should be noted, however, that when photons are converted back to electrons in the photonic sampled and/or quantized ADCs some degree of comparator or sampling circuitry is often required. In this sense, one could classify all photonic ADCs as photonic assisted ADCs, but this is not how the term photonic assisted ADC seems to be used and most people working on photonic sampled/quantized ADCs do not think of their work as a photonic assisted ADC.

Fig. 6. Four major classes of photonic ADCs.

6. Photonic assisted ADCs

6.1 Optically clocked track-and-hold circuits

It has been recognized since the 1970s [10

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

, 13

13. R. A. Lawton and J. R. Andrews, “Optically strobed sampling oscilloscope,” IEEE Trans. Instrum. Meas. 25, 56–60 (1976).

, 25–28

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

] (Auston 1975, Lawton and Andrews 1976, Low and Carroll 1978, Leonberger and Moulton 1979, Cox et al. 1983, Leonberger and Diadiuk 1983) that optical pulses shorter than about 100 ps could be used to make fast optoelectronic switches for electronic sampling, as shown generically in Fig. 7. The advantages of optoelectronic switches are faster rise times and lower pulse-to-pulse jitter than electronics as well as the opportunity with fibers to remove the clock from the ADC circuit and to address multiple points in the same circuit from one optical source. At present, however, these advantages apparently have not overcome the disadvantages of integrating an ultra-stable mode-locked laser into a commercial product. Some of the best results obtained before 1990 were those of Leonberger and Moulton [26

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

] (1979) who used an optically-addressed InP switch to sample a 68.9 MHz sine wave and Leonberger and Diadiuk [28

28. F. J. Leonberger and V. Diadiuk, “High-speed InP-based photodetectors,” 1983 International Electron Devices Meeting 29, 460–463 (1983).

] (1983) who reported a 100 MS/s sample and hold circuit again using an InP switch.

More recently, there have been several advances in optically clocked track and hold circuits. One group [29–32

29. 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]

] (Sun et al.1991, 1993, 1998 and Jacobs et al. 2004) recognized the limitations of direct illumination of a single optoelectronic switch for track and hold: (1) in the on state, the hold capacitor is charged by the weak input signal and (2) the turn-off time depends on semiconductor lifetimes, which are generally not sufficiently short for high frequency applications. They demonstrated the use of an optically clocked diode-bridge circuit, as shown in Fig. 8, to overcome these limitations [32

32. E. W. Jacobs, J.B. Sobti, V.F. Vella, R. Nguyen, D.J. Albares, R.B. Olsen, C.T. Chang, C.K. Sun, M.J. Choe, S. Beccue, R. Yu, and J.P.A. van der Wagt , “Optically clocked track-and-hold for high-speed high-resolution analog-to-digital conversion,” Technical Digest, 2004 IEEE International Topical Meeting on Microwave Photonics, 190–192 (2004).

]. The diode bridge circuit is biased in track mode. Simultaneous illumination of the two photodiodes by a 5-ps pulse from a stable mode-locked laser turns the diode bridge off causing a fast transition from track mode to hold mode. The optically clocked diode bridge is followed by an electronic clocked bridge that extends the hold time of the circuit. The major advantages of the optical clock circuit are reduced aperture time, which decreases the nonlinear response of the bridge; high clock isolation, which practically eliminates clock/signal interference; and low clock jitter, which is 1-2 orders of magnitude smaller in mode-locked lasers compared to the best electronics. For an input frequency of 1.0073 GHz and a sampling rate of 1.003 GS/s, Jacobs et al. [32

32. E. W. Jacobs, J.B. Sobti, V.F. Vella, R. Nguyen, D.J. Albares, R.B. Olsen, C.T. Chang, C.K. Sun, M.J. Choe, S. Beccue, R. Yu, and J.P.A. van der Wagt , “Optically clocked track-and-hold for high-speed high-resolution analog-to-digital conversion,” Technical Digest, 2004 IEEE International Topical Meeting on Microwave Photonics, 190–192 (2004).

] used downconversion to demonstrate that the track and circuitry maintained 11.8 SFDR bits and 9.6 SNR bits.

Fig. 7. General schematic of a photonics-assisted ADC in which a stable mode-locked laser is used as a clock.
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).

Another approach, developed by workers at Stanford University [33–37

33. 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). [CrossRef]

] (Urata et al., 2001, 2003a, 2003b, Nathawad et al. 2003, Ma et al. 2004) uses GaAs photoconductive switches integrated with CMOS ADCs to form a time-interleaved ADC. They exploit the low jitter of a mode-locked laser, use a differential device to avoid capacitive feedthrough from the input, and use low-temperature-grown GaAs metal-semiconductor-metal switches to obtain short carrier lifetimes. Fig. 9(a) shows a schematic of the optical interleaving system and Fig. 9(b) shows the differential circuit for feedthrough cancellation. While Jacobs et al. [32

32. E. W. Jacobs, J.B. Sobti, V.F. Vella, R. Nguyen, D.J. Albares, R.B. Olsen, C.T. Chang, C.K. Sun, M.J. Choe, S. Beccue, R. Yu, and J.P.A. van der Wagt , “Optically clocked track-and-hold for high-speed high-resolution analog-to-digital conversion,” Technical Digest, 2004 IEEE International Topical Meeting on Microwave Photonics, 190–192 (2004).

] (2004) targeted high resolution at 1 GHz, Ma et al. [37

37. 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). [CrossRef]

] report their system could obtain 4 ENOB for input bandwidths up to 40 GHz, which would be approximately 6 times the bandwidth of current electronic ADCs.

Fig. 9. (a) Photonics-assisted interleaved ADC architecture. (b) Optically triggered differential sample-and-hold circuit (adapted from [36]).

Pease et al. [38

38. 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]

] (2003) and Ioakeimidi et al. [39

39. 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]

] (2005) reported work with an optically triggered electron beam ADC that also takes advantage of the short pulse width, low jitter and high pulse repetition rate of a mode-locked laser. The use of e-beams for ADCs dates from the 1940s and the optically triggered version, which is based on a streak camera, is shown in Fig. 10. Ioakeimidi et al. target sampling rates of 100 GS/s and suggest that ENOB ∼ 4 should be possible at this rate, which is consistent with the jitter and pulse width of their optical source. They also present detailed analysis of the requirements on the e-beam apparatus to obtain this performance, which is beyond the scope of this review. A potential disadvantage of this approach is that it requires the development of an electronic ADC instead of piggy-backing on the technology of existing electronic ADCs.

Fig. 10. Optically triggered e-beam ADC (adapted from [38, 39]).

6.2 Optical replication preprocessor for electronic ADC

6.3 Optical time stretch preprocessor for electronic ADC

Fig. 11. Single shot version of the time-stretch ADC.
Fig. 12. Continuous time version of the time-stretch ADC.

6.4 Spatial-spectral holographic preprocessor for electornic ADC

Recently, Babbitt et al. (2006) [135

135. W. R. Babbitt, M. A. Neifeld, and K. D. Merkel, “Broadband analog to digital conversion with spatial-spectral holography,” submitted to Journal of Luminescence (2006).

] have developed a different approach to a time-stretch preprocessor designed to precede a low rate electronic ADC. In this approach, the first step is to mix the RF signal of interest with a reference RF signal. The second step is to write a spectral hologram of the Fourier transform of the mixed RF signal in a rare-earth-doped crystal at a temperature around 4K. Such crystals, Er3+:LiNbO3 for example, have huge inhomogeneosly broadened linewidths (250 GHz) and very small homogenous linewidths (∼kHz), which enables capture of broadband signals with high resolution. The third step is to read the hologram out with a slowly chirped optical source, effectively compressing the frequency content of the RF signal or stretching it in time. After a photodetector converts the signal back into the electrical domain, it can be digitized by a low rate, high resolution electronic ADC.

7. Photonic sampled and electronically quantized ADCs

Fig. 13. Photonic sampled and electronically quantized ADC.

Photonic sampled ADCs have several other issues besides jitter and pulse width. Like all analog optical links they require linear modulator response. One way to obtain linear modulator response is to use a low modulation index but this often increases the optical power requirements beyond what is practical. A better technique involves digitizing both outputs of the Mach-Zehnder optical modulator and inverting the nonlinear transfer function of the modulator with post-processing [62

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

, 63

63. J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photonic Technol. Lett. 12, 1237–1239 (2000). [CrossRef]

, 65

65. T. R. Clark, M. Currie, and P. J. Matthews, “Digitally linearized wide-band photonic link,” J. Lightwave Technol. 19, 172–179 (2001). [CrossRef]

, 74

74. 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]

].

Although photonic sampling improves the sampling time and jitter of the system shown in Fig. 13, it does not reduce the rate at which the electronic ADC must quantize the input signal and for high sampling rates (>10 GS/s) the interpulse time may be shorter than the photodiode recovery time. Demultiplexing the data stream after the modulator to an array of photodiodes and ADCs, as shown in Fig. 14, reduces the operating frequency of the electronic ADC and increases the interpulse time at the photodiode by the number of channels. Bell et al. [58–60

58. J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Moran, H. F. Taylor, and Y.-H. Lee, “Extension of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” 23rd Asilomar Conf. on Signals, Systems and Computers, ed. R. R. Chen, 1, 289–293 (1989).

] (1989, 1991) first performed time demultiplexing to obtain ENOB = 2.8 with a sampling rate of 2 GS/s. Later, a group at MIT Lincoln Laboratory [74–77

74. 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]

] (Twichell et al. 2001, Juodawlkis et al. 2001, 2002, Williamson et al. 2001) investigated many features of optically sampled and demultiplexed ADCs [74

74. 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]

] and demonstrated ENOB = 9.8 at 505 MS/s [146

146. R. C. Williamson, R. D. Younger, P. W. Juodawlkis, J. J. Hargreaves, and J. C. Twichell, “Precision calibration of an optically sampled analog-to-digital converter,” Digest of IEEE LEOS Summer Topical Meeting on Photonic Time/Frequency Measurement and Control, 22–23 (2003).

].

Two major sources of error in photonic sampled ADCs are pulse-to-pulse amplitude fluctuations and timing jitter. The requirements on jitter are the same as for timing jitter in an electronic ADC given by eq. (4). Many groups have measured timing jitter on ultra-stable mode-locked lasers [5

5. 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]

, 67

67. 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]

, 72

72. 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). [CrossRef]

, 73

73. 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). [CrossRef]

, 129–131

129. D. J. Jones, K. W. Holman, M. Notcutt, J. Ye, J. K. Chandalia, L. A. Jiang, E. P. Ippen, and H. Yokoyama, “Precise timing stabilization of a mode-locked semiconductor laser at 1550 nm to an optical frequency standard,” Conference on Lasers and Electro-Optics CLEO 2003, paper JtuB4 (2003).

], but many of these measurements have been made over an incomplete frequency band and extrapolated via physical arguments to the whole band. For an ADC, the jitter should be measured from the inverse of the sample time to the Nyquist frequency (1/2 the sampling rate). DePriest et al. [67

67. 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]

] did this and obtained σj = 121 fs over 10 Hz to 5 GHz for a laser with a pulse repetition rate of 10 GHz. If this optical pulse-to-pulse jitter were the only source of error in a 10 GS/s ADC, the effective number of bits would be 7.25. DePriest et al. also obtained rms amplitude fluctuations of σA = 0.21% over the same frequency band. If the amplidute fluctuations are not compensated, one can equate σA to the quantization error at the ENOB, 1/[(2ENOB-1)121/2to obtain 7.11 effective bits if amplitude fluctuations were the only source of error. Note that two independent sources of error that yield the same ENOB decrease the ADC ENOB by another 0.5 bits if one assumes that the variances of the two noise sources add so the best possible ENOB that could be obtained at 10 GS/s with this laser source is about 6.7. There are additional sources of jitter in the photonic sampled ADC that occur if the electronic ADC or ADCs are not synchronized with the pulse repetition rate of the laser or if the response time of the photodiode and associated electronics are not fast enough [74

74. 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]

].

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.

In the late 1990s researchers recognized that one can construct a source with interleaved pulses of different wavelengths [44

44. 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]

, 46

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

, 50

50. 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]

, 78

78. A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34, 2012–1023 (1998). [CrossRef]

, 79

79. 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]

] (Bhushan et al. 1998, 1999, Yariv and Koumans 1998, Kang and Esman 1999, Coppinger et al. 2000). This permits replacement of optical switches (insertion loss of 6.8 to 8.4 dB for 8 channels [74

74. 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]

]) used in time demultiplexing by dense wavelength demultiplexing devices, which offer loss less than 4 dB for 16 channels (AOC Technologies, APA Optics Inc., BaySpec Inc. [149]). Results reported that use wavelength-interleaved pulses include 2 GS/s with 4 bits [73

73. 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). [CrossRef]

, 81–82

81. 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]

] (Clark et al. 1999a, 1999b), 10 GS/s (Fok et al. 2004) and 4 GS/s (Ng et al. 2004). More recently, progress towards a silicon electronic photonic integrated version of the wavelength demultiplexed photonic sampling ADC has been reported [150

150. F. X. Kartner, R. Amataya, G. Barbastathis, H. Byun, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, O. O. Olubuyide, J. S. Orcutta, M. Par, M. Perrotta, M. A. Popovic, P. T. Rakich, R. J. Ram, H. I. Smith, M. Geis, M. Grein, T. Lyszczarz, S. Spector, and J. U. Yoon, “Silicon electronic photonic integrated circuits for high speed analog to digital conversion,” 3rd OEEE International Conference on Group IV Photonics, 203–205 (2006).

]. In all of these systems, generation of low-noise pulses interleaved in wavelength, as shown in Fig. 14, may be more difficult than generating the narrower band, identical wavelength pulses needed for the time-division demultiplexing system and some of the photonic assisted systems.

A somewhat different variation on the photonic sampled and demultiplexed theme was reported by Frankel et al. [83

83. M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33, 2096–2097, (1997). [CrossRef]

] (1997), Kang et al. [84

84. 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]

] (1998) and Bhushan et al. [46

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

] (1999). Frankel et al. started with a 1-ps, 50-nm bandwidth pulse and used dispersion to stretch it to a chirped 2.6-ns pulse. They modulated the RF signal on this pulse just as in the time-stretch photonic ADC discussed above, but then they demultiplexed this pulse with 4 wavelength filters whose bandwidths were much less than 50 nm. Thus the WDM device performs the sampling. After demultiplexing the 4 short-pulse signals are routed to electronic ADCs as in the time sampled, time or wavelength demultiplexed systems. Jiang et al. [85

85. P. Jiang, Y. Chai, I. White, R. Penty, J. Heaton, A. Kuver, S. Clements, C. G. Leburn, A. McWilliam, A. A. Lagatsky, C T. A. Brown, and W. Sibbett, “80 GSPS Photonic analogue to digital conversion system using broadband continuous wave source,” Conference on Lasers and Electro-Optics (CLEO) 2005, Digest 874–876 (2005).

](2005) report demultiplexing a 30-nm bandwidth optical source with a 32 channel array waveguide grating (AWG) to obtain an effective sampling rate of 80.64 GS/s with a bank of 32, 2.5-GS/s ADCs.

8. Photonic quantized and electronically sampled ADCs

In this class of photonic ADC, an electronic sample and hold circuit produces a staircase voltage waveform that is used to vary the wavelength of a semiconductor laser [86–91

86. H. Zmuda, “Analog-to-digital conversion using high-speed photonic processing,” Proc. SPIE 4490, 84–95 (2001). [CrossRef]

, 133

133. J. Stigwall and S. Galt, “Analysis of the resolution-bandwidth-noise trade-off in wavelength-based photonic analog-to-digital converters,” Appl. Opt. 45, 4310–4318 (2006). [CrossRef] [PubMed]

] (Zmuda 2001, Zmuda et al. 2001, 2002 and Toughlian et al. 2000, Pala et al. 2001, Johansson et al. 2000, Stigwall and Galt 2006) as shown in Fig. 15. Splitting into N channels and N filters of variable length then produces a digital output called a “Gray code”. The quantized output in the optical domain can be used directly or converted back to electronics with photodiodes. Obviously, this system gives up the advantages of photonic sampling, and furthermore, it is limited by the response time and nonlinearities of wavelength-tunable lasers.

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])

A similar optical quantization scheme has been reported by Johansson et al. [90

90. 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]

](2000) and Pala et al. [91] (2001). Although not discussed in these references, an electronic sample and hold circuit apparently precedes the photonic quantizer. Similar to the work of Zmuda et al., these researchers modulate the wavelength of a laser diode with the sampled and held electrical signal. Then they propose to quantize the optical signal with a diffractive optical element in a method similar to that proposed by Tsunoda and Goodman [14

14. Y. Tsunoda and J. W. Goodman, “Combined optical AD conversion and page composition for holographic memory applications,” Appl. Opt. 16, 2607–2609 (1977). [CrossRef] [PubMed]

] (1977). Johansson et al. suggest that the number of bits is limited by the number of resolvable wavelength bands to about 100 levels (6-7 bits), but no consideration of the nonlinearity of the transfer function (voltage to optical wavelength) or the effect of laser diode noise is given.

9. Photonic sampled and quantized ADCs

9.1 Intensity modulation and conversion to Gray code

Taylor [12

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

] (1975) proposed the photonic quantization scheme shown in Fig. 16(a) and subsequently [3

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

, 15

15. 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]

] suggested using this scheme with a stable short-pulse laser to make a photonic sampled and quantized ADC. The basic idea of this scheme is that the 4 modulators shown in Fig. 16(a) differ in length by a factor of 2 such that the output of each channel is one bit. With appropriate bias voltage, the output intensity as a function of the drive voltage for each of the four modulators is shown in Fig. 16(b). Use of an electronic comparator set at the threshold intensity It, yields the Gray code indicated by the grey and white bars below the intensity curves in Fig. 16(b). For V = -Vm, one obtains 0000, for V = 0, 0100 and for V = Vm, 1000. The longest modulator is used for the least significant bit and its length is chosen so that V pi = 2 V LSB. In LiNbO3 waveguide modulators V pi ∼ 5 V, making the least significant bit = 2.5 V. Since the full scale voltage is N times V LSB for the Gray code shown in Fig. 16(b), full scale for 4 bits requires 10 V.

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.

Many variations of Taylor’s scheme have been reported [17–20

17. 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]

, 22–23

22. 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]

, 94–96

94. B. Jalali and Y. M. Xie, “Optical folding-flash analog-to-digital converter with analog encoding,” Opt. Lett. 20, 1901–1903 (1995). [CrossRef] [PubMed]

] (Dokhikyan et al. 1982, Takizawa and Okata 1979, Leonberger et al. 1982, Becker and Leonberger 1982, Chang and Tsai 1983, Becker et al. 1984, Walker et al. 1989, Pace and Styer 1994, Jalali and Xie 1995, Currie et al. 2000, Ikeda et al. 2005). Becker et al. [23

23. 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]

] (1984) reported resolution of 4 bits at 1 GS/s and carried out a detailed analysis of the limits on speed and resolution in this device. Their conclusions about what they called “electrooptic” ADCs (ref. [23

23. 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]

] p. 816) are relevant to our thinking more than 20 years later. Referring to “the Taylor multi-interferometer electrooptic A/D converter” they wrote “The electrooptic apparatus—the sampling laser, multiple modulators, and sensing photodiodes-is not of itself an A/D converter because its output is not digital. Instead, it is a completely analog device that may more properly be termed an ‘amplitude analyzer’.” They go on to point out that the utility of the device then depends on whether or not it resolves more issues for the electronic ADC than the conversion back and forth to the optical domain creates. From this point of view, Taylor’s scheme would be more correctly called a “photonics-assisted ADC”.

Walker et al. [24

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

] (1989) fabricated an integrated version of Taylor’s scheme using GaAs/AlGaAs technology. They used a single interferometer tapped along its length at 1, 2, 4 units of length with a full length of 8 units. Pace and Styer [93

93. 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]

] (1994) and Jalali and Xie [94

94. B. Jalali and Y. M. Xie, “Optical folding-flash analog-to-digital converter with analog encoding,” Opt. Lett. 20, 1901–1903 (1995). [CrossRef] [PubMed]

] (1995) discuss methods to circumvent the need to double the length of the least significant bit interferometer for an additional bit of resolution. Both methods use Taylor’s scheme as an optical folding system for an electronic flash ADC. No comparison of photonic to conventional electronic folding flash ADCs has been presented. Another variant on Taylor’s scheme uses nonlinear optical switches based on the Sagnac interferometer to achieve the Gray code [96

96. 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). [CrossRef] [PubMed]

, 142

142. K. Ikeda, J. M. Abdul, H. Tobioka, T. Inoue, S. Namiki, and K. Kitayama, “Design considerations of all-optical A/D conversion: nonlinear fiber-optic sagnac-loop interferometer-based optical quantizing and coding,” J. Lightwave Technol. 24, 2618–2628 (2006). [CrossRef]

] (Ikeda et al. 2005, 2006). Additional nonlinear optical loop mirrors are used to perform thresholding in the optical domain, and this would reduce the burden on the comparators necessary to convert back to the electronic domain. Besides the usual issues associated with photonic sampling (jitter, pulse width, SNR, SFDR) the scheme of Ikeda et al. suffers from a walk-off problem in the interferometers and is power consuming and complex. Producing an 8-bit device with this technology to compare with contemporary electronic ADCs operating at a few GS/s is expected to be a challenge.

Reviewing 30 years of work on Taylor’s 1975 interferometric photonic ADC shows that the maximum number of bits obtained with this method has always been less than 4. Until there is a breakthrough in ultra-low V π modulators, this is not likely to change.

9.2 Intensity modulation-optical comparator

Loh and LoCicero [97

97. 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]

] (1996) investigated using symmetric self electro-optic devices [132

132. 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]

] (S-SEEDs) as comparators for an ADC. They detail many difficulties that they encountered and report a response time a little less than 100 ps. There is no indication how to obtain as many as 256 levels, however, so at present this technology does not seem to be competitive with electronics.

Hayduk et al. [98–100

98. 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). [CrossRef]

] (2000a, 2000b, 2002) investigated use of a semiconductor saturable absorber as an optical comparator. The saturable absorber alone does not behave like an ideal comparator so Hayduk et al. investigated putting the saturable absorber in a Fabry-Perot resonator to improve contrast ratio, but this decreased the absolute transmission of the device to less than 7%. Sakata [101

101. H. Sakata, “Photonic analog-to-digital conversion by use of nonlinear Fabry-Perot resonators,” Appl. Opt. 40, 240–248 (2001). [CrossRef]

] (2001) also investigated nonlinear Fabry-Perot resonators for use as quantizers in a photonic ADC. He reports an upper limit of 6 bits achievable at 500 MS/s.

Jeong and Marhic [102

102. 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]

] (1992) suggest converting optical intensity to phase through the n 2 nonlinearity in a fiber and then using an interferometer as a comparator. This proposal is similar to the Taylor scheme except that the nonlinear phase of an intensity modulated signal replaces the electro-optic phase in the Mach-Zehnder interferometer. At the maximum signal level, the least significant bit channel must have a nonlinear phase of 2N-1π and this severely limits the maximum number of bits possible with this scheme. As Jeong and Marhic point out, other nonlinearities become important before the n 2 nonlinearity can reach many factors of π.

Ho et al. [103

103. P. P. Ho, Q. Z. Wang, J. Chen, Q. D. Liu, and R. R. Alfano, “Ultrafast optical pulse digitization with unary spectrally encoded cross-phase modulation,” Appl. Opt. 36, 3425–3429 (1997). [CrossRef] [PubMed]

] (1997) investigated using cross-phase modulation caused by the n 2 nonlinearity to digitize an intensity-modulated signal. In this work, n 2 I (I is the signal intensity) causes a change in the refractive index of the medium that modulates the phase and hence broadens the spectrum of a weak probe pulse co-propagating with the signal. A grating is used to demultiplex the broadened probe pulse to a linear array of photodiodes. They reported obtaining 4 bits of resolution at 5 GS/s. This system is also limited by the maximum achievable nonlinearity.

Oda et al. [105

105. S. Oda, A. Maruta, and K. Kitayama, “All-optical quantization scheme based on fiber nonlinearity,” IEEE Photonic Technol. Lett. 16, 587–589 (2004). [CrossRef]

] (2004) investigated a system in which an analog optical signal is sampled by four-wave mixing with a pulsed optical signal. This produces an intensity-modulated pulse stream similar to the pulse stream produced by other researchers by directly modulating a pulsed optical source. This technique may be useful for sampling an analog optical signal but appears to be more complicated than necessary when the analog input is electronic. After sampling Oda et al. propose a unique quantization device using solitons in optical fiber. They note that the number of solitons produced is a step function of the optical intensity, which provides a natural quantization method. The resolution that can be obtained with this method is probably limited to a few bits.

Oda and Murata [106

106. 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). [CrossRef]

] (2005) later suggested another nonlinear optical method for quantizing an intensity-modulated pulse train. First, the pulse train is amplified and then it is injected into dispersion-flattened fiber to generate a supercontinuum. Finally, the supercontinuum spectrum is split into wavelength bands by an arrayed waveguide grating (AWG) and directed to individual photodiodes. The width of the supercontinuum is proportional to the intensity of the optical pulses so the number of wavelength channels that contain optical power provides a quantization method.

Xu and Liu [107

107. 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). [CrossRef] [PubMed]

] (2003) add several interesting ideas to the work of Konishi et al. [104

104. T. Konishi, K. Tanimura, K. Asano, Y. Oshita, and 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). [CrossRef]

] (2002) on soliton self-frequency shifting (SSFS). In particular they propose decreasing the pulse width prior to the nonlinear medium to increase the soliton self-frequency shift and then using dispersion increasing fiber to restore the original pulse shape. They also propose using a 1×N splitter to N “interleaving filters” that output the digital code. Issues for this system include the nonlinearity of the intensity-wavelength curve for SSFS and its very small dynamic range. There are other nonlinearities in the fiber, and the frequency content of the pulse itself blurs the resolution.

Kitayama et al. [108

108. K. Kitayama, K. Ikeda, H. Tobioka, T. Inoue, and S. Namiki, “Photonic analog-to-digital conversion,” Digest of the LEOS Summer Topical Meetings, 209–210 (2005).

] (2005) propose a scheme to obtain a Gray code in which optical pulses sample an RF signal as usual, and these pulses are split into a bank of N encoders, each of which is a nonlinear optical loop mirror in which the transmission depends on the intensity of the sample pulses. Thresholders (or comparators) complete the process of Gray coding in a manner similar to Taylor’s scheme. No analysis is presented on the number of bits possible with this scheme but it seems likely to be small; 3 bits were demonstrated.

More recently, Goncharenko et al. [109

109. I. A. Goncharenko, A. K. Esman, V. K. Kuleshov, and V. A. Pilipovich, “Optical broadband analog-digital conversion on the base of microring resonator,” Opt. Commun. 257, 54–61 (2006). [CrossRef]

] (2006) proposed using an intensity-modulated signal to address the center of a micro-ring resonator and hence change the resonant wavelength of the resonator. Optical radiation in the form of pulses of wavelengths λ1 to λn is input into the resonator and the intensity of the modulated signal controls which of the wavelengths passes through the resonator. This process would transform analog intensity variations into a digital pulse-code modulation. The authors suggest that this technique may be limited to less than 1 GS/s and moderate resolution.

9.3 Voltage controlled optical beam diffraction/deflection

Tsunoda and Goodman [14

14. Y. Tsunoda and J. W. Goodman, “Combined optical AD conversion and page composition for holographic memory applications,” Appl. Opt. 16, 2607–2609 (1977). [CrossRef] [PubMed]

] (1977) took a somewhat different approach by using voltage-controlled beam deflection to 2N positions to quantize the optical signal. They also devised an optical means for conversion to a Gray code. The sampling in this system is apparently produced by the rate at which optical spots traverse detectors, but again the input optical beam could be derived from a repetitively pulsed short-pulse laser. Tsunoda and Goodman suggest that the beam deflector could be mechanical, acoustical or electro-optical and discuss the relation between the speed of the deflector and the speed of the ADC.

Along the same lines as Tsunoda and Goodman’s work, Li and Zhang [92

92. 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]

] (1991) reported obtaining 6 bits of resolution by using an acousto-optic modulator to deflect a beam by an angle proportional to RF voltage. The sampling in time must be either done with an optical pulse train or with an electronic sample and hold before the AO modulator. The response time of the AO modulator seems to limit application of this idea to bandwidths that are no longer competitive with electronics.

Galt et al. [110

110. S. Galt, A. Magnusson, and S. Hard, “Dynamic demonstration of diffractive optic analog-to-digital converter scheme,” Appl. Opt. 42, 264–270 (2003). [CrossRef] [PubMed]

] (2003) also report use of an AO modulator to deflect a beam to an array of diffractive optical elements. These authors fully recognize the bandwidth limitations of AO modulators and use this system to illustrate the potential of a system using a fast tunable diode laser and fixed grating to replace the AO deflection system. The fast tunable laser diode system is discussed above in Section 7.3, the half-photonic/optical quantization section, since no optical sampling mechanism appears to be consistent with the wavelength tuning process.

Stigwall and Galt [111

111. J. Stigwall and S. Galt, “Interferometric analog-to-digital conversion scheme,” IEEE Photonic. Technol. Lett. 17, 468–470 (2005). [CrossRef]

,112

112. J. Stigwall and S. Galt, “Demonstration and analysis of a 40-Gigasample/s interferometric analog-to-digital converter,” J. Lightwave Technol. 24, 1247–1256(2006). [CrossRef]

] (2005, 2006) propose another variation on the voltage-to-angle theme. They use a short pulse optical source followed by an interferometer with phase modulation in one leg and a detector array at the interference plane. As shown in Fig. 17, introducing a phase shift in one leg translates the interference pattern on a photodiode array and the currents from this array are converted to a digital signal by comparators. A major advantage of this scheme compared to Taylor’s scheme is the use of only one phase modulator. Another advantage is that electro-optic phase modulation is extremely linear compared the intensity modulation, which is used in many of the photonic ADCs described above. More recently, an implementation of this scheme has been developed that avoids the free-space propagation [152

152. W. Li, H. Zhang, M. Yao, and M. Yan, “All-optical analog-to-digital conversion using a single phase modulator in a multi-channel polarization-differential interferometer,” submitted to OFC (2007).

].

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].

9.4 Optical delta-sigma modulators

At first glance, it would appear that an optical Δ–Σ modulator would be an attractive technology. While sampling rates for electronic Δ–Σ modulators peak at about 20 GS/s [125

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

], the pulse-repetition rate for mode-locked lasers can be as high as ∼50 GHz or higher with optical interleaving. Furthermore, one of the major advantages of Δ–Σ modulators compared to Nyquist rate ADCs is a reduced requirement on component matching and calibration. This again suggests compatibility with optical circuits in which immature components are imprecise compared to electronic counterparts. On the other hand, none of the key components of a Δ–Σ modulator, the adder, integrator, quantizer and DAC, are very well developed in the optical domain.

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.

Marwood et al. [117

117. W. Marwood, P. Atanackovic, J. Munch, N. Burgess, and S. Al-Sarawi, “A MMIC compatible photonic A/D converter,” Third International Conference on Advanced A/D and D/A Conversion Techniques and their Applications, (Conf. Publ. No. 466), 27–28 July 1999, 17–20 (1999).

] (1999) and Al-Sarawi et al. [118

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

, 140

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

, 141

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

] (2000, 2001, 2002) made further progress towards an optical Δ–Σ modulator. They recognized that an ultrastable high PRF, mode-locked semiconductor laser would be needed for a clock and that the optical components that perform the optical subtraction and quantization ultimately must be integrated in a very small area. The reason integration is required is that the feedback delay must be on the order of the inter-pulse time or clock period. For a PRF = 50 GHz, the inter-pulse time is 20 ps, which corresponds to a delay of 2 mm in a medium with a refractive index of 3. Marwood et al. note that the SEEDs are expected to have dimensions of the order of microns, which would facilitate integration. Al-Sarawi et al. [118

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

] (2001) noted an issue with the use of SEED devices for the optical quantizer, hysteresis in their I-V characteristics. In addition, the switching time appears to depend on optical intensity. Typically, the switching time in a Δ–Σ modulator must be substantially smaller than the clock period, for example the 20-ps interpulse time in the 50-GHz system. Clare et al. [119

119. 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]

] (2003) identified another issue, critical slowing down, that limits use of bistable symmetric SEEDs for comparators. Al-Sarawi et al. [118

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

] (2001) also proposed encoding the RF input signal as the difference between two optical signals instead of developing a unipolar Δ–Σ modulator. Sarros et al. [121

121. 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]

, 139

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

, 143

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

] (2002, 2004, 2005) investigated use of 2 S-SEEDs for the differential subtractor in an optical Δ–Σ and identified mismatch between the two S-SEEDs as one of the critical issues. Clare et al. [120

120. B. A. Clare, K. A. Corbett, and K. J. Grant, “Performance of a photonic oversampled sigma-delta quantizer,” Proc. SPIE 5814, 248–261 (2005). [CrossRef]

, 138

138. B. A. Clare, K. A. Corbett, K. J. Grant, A. Massie, J. Munch, and W. Marwood, “Photonic A/Ds employing S-SEED Comparators,” Proc. SPIE 5277, 42–53 (2004). [CrossRef]

] (2004, 2005) simulated an end-to-end model of the optical Δ–Σ modulator and obtained a peak of 54 dB for signal-to-quantum-noise ratio with an oversampling ratio of 100.

Pace et al. [122

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

] (2000) proposed a somewhat different approach to an optical Δ–Σ modulator. Their system uses a high-PRF laser as proposed above, but maintains a coherent system. The feedback loop is electrical and the subtraction is performed in a Mach-Zehnder modulator. The integration function shown in Fig. 18 is performed by a fiber-optic delay-line processor that Pace et al. call a “fiber-lattice accumulator”. Finally, the quantizer function is performed in the electrical domain after a photodetector. Shoop [1

1. B. L. Shoop, Photonic Analog-to-Digital Conversion, Springer, New York, 2000.

] (2000) and Shoop and Das [123

123. 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]

, 124

124. 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). [CrossRef]

] (2001, 2002) proposed a version of the optical Δ–Σ modulator that would convert the input optical signal to a 2-dimensional array and use a neural network processor.

In summary, several realizations of a photonic or mixed photonic-electronic Δ–Σ modulator ADC have been investigated over the past 15 years. At present, the maximum sampling rate of electronic Δ–Σ technology is 18 GHz [125] (Jaganathan et al. 2001) and optical sampling rates substantially greater than this would seem to be required to justify the investment in developing an optical Δ–Σ modulator, perhaps a 100 to 200 GHz sampling rate. At present semiconductor mode-locked lasers have a maximum PRF of about 50 GHz so new, smaller MLLs or interleaved sources would need to be developed for this application. The clock period at 100 GS/s is 10 ps, and a feedback loop with a delay of less than a clock period means that the feedback path must be less than 1 mm (2 mm) in length in a medium with a refractive index of 3 (1.5). Finally, the response time of the comparator in a Δ–Σ modulator must be much smaller than the 10-ps clock period, which appears to be inconsistent with existing choices for photonic comparators. Integrating multiple fast optical components for addition, integration, and quantization in such a small size is expected to be challenging.

10. Conclusions

Acknowledgements

This work was supported under The Aerospace Corporation’s Independent Research and Development Program. I am grateful to Drs. Bill Jacobs, Bahram Jalali, Steven Moss, Johan Stigwall, Robert Walden and the referees for helpful criticisms of earlier versions of this paper.

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139.

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

140.

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143.

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146.

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149.

http://www.bayspec.com/default.htm, http://www.apacn.com/, http://www.aoctech.com/.

150.

F. X. Kartner, R. Amataya, G. Barbastathis, H. Byun, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, O. O. Olubuyide, J. S. Orcutta, M. Par, M. Perrotta, M. A. Popovic, P. T. Rakich, R. J. Ram, H. I. Smith, M. Geis, M. Grein, T. Lyszczarz, S. Spector, and J. U. Yoon, “Silicon electronic photonic integrated circuits for high speed analog to digital conversion,” 3rd OEEE International Conference on Group IV Photonics, 203–205 (2006).

151.

J. Stigwall and S. Galt, “Signal reconstruction by phase retrieval and optical back-propagation in phase-diverse photonic time-stretch systems,” submitted to J. Lightwave Technol. (2006).

152.

W. Li, H. Zhang, M. Yao, and M. Yan, “All-optical analog-to-digital conversion using a single phase modulator in a multi-channel polarization-differential interferometer,” submitted to OFC (2007).

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(230.0250) Optical devices : Optoelectronics

ToC Category:
Optical Processing

History
Original Manuscript: September 25, 2006
Revised Manuscript: February 16, 2007
Manuscript Accepted: February 21, 2007
Published: March 5, 2007

Citation
George C. Valley, "Photonic analog-to-digital converters," Opt. Express 15, 1955-1982 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-1955


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