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
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 .
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  (2000) and in Walden’s review  (1999).
Both timing and amplitude errors reduce the performance of ADCs. The most important timing errors are random jitter and broadening of the sampling time. Random noise (thermal, shot noise) and nonlinearities are the major sources of amplitude error. All error sources decrease the effective resolution from N, the number of read-out bits, to ENOB, the effective number of bits. Figure 2 illustrates this concept for a signal plus random amplitude noise. The input voltage in green is now shown with and without noise; the red signal illustrates quantization with N = 3, 4, 5 bits, respectively. Without noise the resolution increases with the number of read-out bits; but with the addition of noise, the effective resolution is unchanged from N = 4 to N = 5 and ENOB is limited to about 4. When the only source of noise is quantization error, the signal-to-noise ratio, SNRQ, can be related to the number of bits N through  (Walden, 1999)
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)
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, 144]:
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.
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 , Walden 1999 , Valley et al. 2004 ),
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  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, 6] (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 . 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.
4. Brief review of analog optical links
Aside from the photonic assisted ADCs that use a mode-locked laser as a clock for an electronic ADC, all other photonic ADCs contain an analog optical link between their RF input and their digital output. Thus it is useful to review some basic concepts of analog optical links (Cox, 2004) . As shown in Fig. 4, a generic analog optical link requires an optical source, a modulator and a photodiode. In some cases the optical source is directly modulated by the RF signal, but in most of the work reviewed below a mode-locked fiber or semiconductor laser is used for the optical source and an external modulator, usually a Mach-Zehnder interferometer fabricated from LiNbO3, impresses the RF signal on the optical intensity. A wide range of other modulators can be used as reviewed in . In a more general RF photonic link, there is a long fiber or an optical processing stage between the electro-optic modulator and the photodiode. Like ADCs, the performance of analog optical links is limited by noise and nonlinearities. Similar figures of merit, such as the carrier-to-noise ratio (CNR) and the spur-free dynamic range (SFDR), are used to characterize an analog link. CNR is used in place of SNR in analog links because usually the optical signal following the EO modulator consists of three components, the optical carrier at the optical frequency f O and the upper and lower sidebands at frequencies f O+f RF and f O-f RF. Since the power in the optical carrier is not directly relevant to the link SNR, the CNR is defined in terms of the rms power in the RF signal divided by the rms noise power (Agrawal [8, p. 338]). SFDR is defined as the dynamic range (ratio of signal power in a wavelength band to noise power in a wavelength band) at which the nonlinear distortion just reaches the noise floor [127, p. 18],[144,p. 49].
The standard expression for the carrier-to-noise ratio, CNR, of an analog optical link  is
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 
where q is the charge on the electron, Id is the detector dark current, Δf is the system bandwidth, kb is Boltzmann’s constant, T is the temperature, Fn is the noise figure of an amplifier (if necessary) following the photodiode, RL is the equivalent load resistance of the photodiode, and RIN is the effective relative intensity noise of the optical source. In the absence of nonlinear distortion, the system CNR can be related to the effective number of bits, ENOB, by rewriting Eq. (3) as
Eq. (10) determines the upper bound on the resolution of a photonic ADC in terms of optical properties of the link. Fig. 5 shows ENOB based on eq. (10) as a function of bandwidth for various power at the photodiode under optimistic conditions (RIN = 0, R = 1A/W, RL = 50 ohm, Fn = 1, T = 300, Id = 0, m = 0.5). This is a lossless link with thermal and shot noise. Path losses between the source and photodiode are very dependent on the specific implementation of the photonic ADC. The best modulators now have insertion loss of 2-3 dB, but other components such as dispersive fiber can have much larger loss depending on the required length. Free-space systems usually incur large loss when the beam spills over the photodiode. To illustrate use of Fig. 5, consider path losses between the optical source and photodiode of 10 and 20 dB; then the required source power is a factor of 10 or 100 higher than indicated on the lines in Fig. 5 unless an erbium-doped fiber amplifier (EDFA) is inserted in the link. The EDFA increases the required detector power by roughly the noise figure of the EDFA, but reduces the required source power. One sometimes sees discussion about very high sampling rate, high resolution photonic ADCs. For example, to obtain ENOB = 10 at 2 GHz would require 10 mW at the detector or with 20 dB of path loss and no EDFA, 1 W from an optical source with RIN noise much less than thermal and shot noise. Even with 10 dB of path loss, 100 mW of source power are needed without an EDFA. Alternatively, obtaining ENOB = 6 at 25 GHz requires about 1 mW at the detector or about 100 mW for a 20-dB path loss and 10 mW for a 10-dB path loss. Since the RIN = 0 and no nonlinearity assumptions are optimistic for optical powers above 100 mW and since electronic ADCs are now offered at ENOB ∼ 8 and 2 GHz, this analysis suggests that the moderate resolution 10s of GHz bandwidth ADC may be a better target for photonic ADCs than a high resolution (>10 ENOB) ADC with bandwidth of a few GHz.
Nonlinearities in an analog optical link are characterized by the spur-free dynamic range SFDR. In general, the SFDR depends on both the optical devices causing the nonlinearity and the RF spectrum of the input signal. The simplest case is an input signal that is a pure sine wave [144, p. 49]. In this case nonlinearities cause harmonic distortion (second, third harmonics, etc.). If these harmonics are in the ADC band, one can determine the SFDR by increasing the signal power until the largest harmonic (often, but not always the second harmonic) reaches the noise floor. Since input signals to ADCs (and analog optical links) are rarely pure sine waves, intermodulation products are often the major contributor to the spurious signals. Unfortunately, there is no general formulation for the intermodulation products of arbitrary input spectra, but there is a methodology for an input signal that considers 2 equal intensity sine waves separated by a small frequency such that the third-order intermodulation products are in the band of the ADC or analog link [7, 127, 148]. In the simple link shown in Fig. 4 there are two nonlinear optical devices, the modulator and the photodiode. If the modulator is a Mach-Zehnder modulator, numerous papers and sections of books are devoted to calculating SFDR and related figures of merit and to investigating configurations that minimize nonlinear distortion ([7, pp. 222-224, 240-249], [127, pp. 18-19] and ). Suffice it to say that for the modulation depth of m = 0.5 used in the link calculation in the previous paragraph, nonlinear distortion will reduce the SINAD well below the CNR needed for high resolution unless linearization methods are used. Likewise, high saturation current density photodiodes have been extensively studied for analog optical links and other applications. The trade offs involved in getting higher photodiode saturation current (e.g. lower reponsivity, lower 3-dB frequency) are beyond the scope of this review.
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.
The origins of photonic ADCs date from the paper of Siegman and Kuizenga  (1970) on optical sampling of RF signals although the purpose of that work was to determine the pulsewidths of picosecond lasers. Another early step was the work of Auston  (1975) in which the absorption of a picosecond pulse in a silicon transmision line was used to switch an electrical circuit faster than possible with electronics alone. In his conclusion Auston noted prophetically that “the techniques and devices discussed here provide a capability for generating and measuring electrical signals with a time resolution of a few picoseconds.” Wright et al.  (1974) reported the first optical quantization scheme; in this work the RF voltage modulates the strength of a refractive index grating and this is used to change the relative strength of the optical power diffracted by the grating into side orders and thus to obtain a digital code. Taylor [3,12] described the first photonic sampled and quantized ADC in which he proposed optical sampling as in the work of Siegman and Kuizenga combined with direct digital code generation similar to the ideas of Wright et al. but with the key difference that the RF voltage is applied to a bank of Mach-Zehnder modulators of variable length instead of a diffraction grating. The first optically-strobed sampling oscilloscope was demonstrated by Lawton and Andrews  (1976). Tsunoda and Goodman  (1977) described work using beam deflection to perform optical quantization of an RF signal. In the next 10 years, most work on photonic ADCs focused on implementation and improvement of Taylor’s scheme [3, 15–24] (Taylor et al. 1978, Taylor 1979, Leonberger et al. 1979, Takizawa and Okada 1979, Becker and Leonberger 1982, Leonberger et al. 1982, Dokhikyan et al. 1982, King and Cebulski 1982, Chang and Tsai 1983, Becker et al. 1984 and Walker et al. 1989). The best ADCs reported from this work were 4 bits at 828 MS/s  (Leonberger et al. 1982) and 4 bits at 1.5 GS/s  (Walker et al. 1989). From 1990 to the present, activity in photonic ADCs has grown rapidly.
6. Photonic assisted ADCs
6.1 Optically clocked track-and-hold circuits
It has been recognized since the 1970s [10, 13, 25–28] (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  (1979) who used an optically-addressed InP switch to sample a 68.9 MHz sine wave and Leonberger and Diadiuk  (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] (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 . 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.  used downconversion to demonstrate that the track and circuitry maintained 11.8 SFDR bits and 9.6 SNR bits.
Another approach, developed by workers at Stanford University [33–37] (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.  (2004) targeted high resolution at 1 GHz, Ma et al.  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.
Pease et al.  (2003) and Ioakeimidi et al.  (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.
6.2 Optical replication preprocessor for electronic ADC
Two groups, Johnstone et al. [40, 41] (1998, 1999) and Zmuda et al. [42, 43] (2004, 2005) have investigated a system in which fiber optic replicating loops are used to generate multiple samples of a short duration RF signal. Generating multiple copies of the same RF pulse allows a low-rate ADC to be stepped through the pulse [42, 43] or the number of samples within the pulse to be increased by shifting the sampling times by a small fraction of the sample period, analogous to a vernier scale [40, 41]. These papers discuss a number of sources of error associated with the use of an analog optical link in replication systems as discussed in Section 4, and imperfect replication also introduces distortion. The main difficulty with these approaches, however, is that the low rate electronic ADC, which these approaches effectively convert to a higher rate ADC, has a temporal jitter and sampling time consistent with its ENOB and sampling rate. Since these properties are unchanged by the optical system, the increase in sampling rate comes at the expense of ENOB. For instance, a factor of ten increase in sampling rate costs ln210 ∼ 3.3 bits. Also as shown by Walden [2, 6] (1999, 2006), there are pure electronic means to make this bandwidth-ENOB trade that do not introduce the distortions of an analog optical link and optical replication.
6.3 Optical time stretch preprocessor for electronic ADC
Jalali and co-workers [44, 45, 47–57, 136, 137] have developed the time-stretch ADC (TS-ADC), a completely different approach using photonics to enhance the performance of available electronic ADCs. A related technology called the “time lens” was developed in 1989 by Kolner and Nazarathy , but this technology appears more applicable to stretching ultrafast optical waveforms than to stretching segments of RF waveforms and to my knowledge it has not been used in a photonic ADC. As shown in Fig. 11, the TS-ADC requires the following steps: (1) a wideband optical pulse propagates through a dispersive medium DM1 such as dispersion-compensating fiber, which spreads the pulse to a few ns and introduces an optical chirp, (2) the ns pulse propagates through an optical modulator, which impresses a short segment of an RF signal on the ns pulse, (3) the modulated optical pulse propagates through a second medium with larger dispersion, such as a longer fiber, which spreads the pulse and stretches the RF signal in time, and (4) the stretched optical pulse illuminates a photodiode whose output is directed to an electronic ADC. The stretch ratio of this system is given by (D 2+D 1)/D 1 where D 1 and D 2 are the total dispersion of DM1 and DM2; this equals (L 2+L 1)/L 1 if the same fiber is used for DM1 and DM2 (L 1 and L 2 are the lengths of the fibers). The highest effective sampling rate obtained with the time stretch ADC is 10 tera-samples/second . In this system dispersion compensation modules were used for the stretching fiber and they were pumped so that they also acted as Raman amplifiers to compensate for the distributed loss in the fiber. In other realizations of the TS-ADC, erbium-doped fiber amplifiers (EDFA) have been added at various points in the system to compensate for the loss of the dispersive media.
Achieving continuous time operation with the TS-ADC, as demonstrated in  requires several modifications to the transient digitizer shown in Fig. 11. As shown schematically in Fig. 12 by the grey bars, the broadband pulse from the optical source, which may be either a supercontinuum source or a femtosecond-pulsed laser, is dispersed to a continuous time chirped optical signal, which is shown by the rainbow pattern below and following the first dispersive medium (DM 1). The dispersion of DM 1 necessary to stretch the broadband pulses to the interpulse time is larger than usually used in the transient digitizer system. Next the continuous time RF signal is impressed on the optical intensity by the electro-optic modulator (the modulated rainbow pattern below EO Mod. and DM 2 in Fig. 12). The second dispersive medium DM 2 then stretches the optical signal by the ratio (D 2+D 1)/D 1. This also stretches the RF signal as in the transient digitizer and because the signal incident on DM 2 is already continuous in time, DM 2 mixes RF signals in time. But DM 2 does not mix optical wavelengths in time (see the detailed discussion in ) so a wavelength division multiplexer can be used to separate the channels as shown in Fig. 12. The wavelength bands of the WDM are chosen so that the optical signals at the photodiodes are continuous in time and consist of interleaved time blocks of the RF signal. The number of channels M can be chosen to be slightly larger than the stretch ratio so that the same RF signal is digitized during an overlap period by adjacent channel ADCs and this overlap may be used for calibration of mismatches in the M channels . This is in contrast to the optically sampled and demultiplexed and electronically quantized systems, discussed below, where modulated optical pulses of duration on the order of picoseconds are individually demultiplexed and interleaved at a bank of electronic ADCs. In the limit where the interpulse period of the TS-ADC approaches the sampling period of the electronic ADCs, the continuous time TS-ADC is nearly identical to the optical sampling and demultiplexing ADC—the remaining difference being that short optical pulses sample in one case whereas the wavelength demultiplexing and the electronic ADC perform the sampling in the TS-ADC case.
Realization of a high resolution, continuous time, TS-ADC will require solution of several technical issues. The calibration and channel matching issues common to all interleaved systems must be solved, but block time or time-segment interleaving lowers the maximum frequency of these errors to the pulse-repetition rate of the optical source, which should be in the 10-100 MHz band for continuous time operation, and the flexibility to overlap time segments gives additional information for calibration. Noise on the optical source can map directly into apparent RF noise after the photodiode, but some sources of noise (pulse-to-pulse amplitude, pulse width and timing jitter) again are limited in frequency to the repetition rate. Much more serious is high frequency noise within the femtosecond or supercontinuum pulse that overlaps the RF band of interest after dispersion. Likewise, distortions in the dispersive media, such as chirp ripple in a chirped fiber Bragg grating, or fluctuations in the modulator response with wavelength can give noise in the RF band but these are constant from pulse to pulse and have the potential for calibration. As in all analog optical links the nonlinearity of the optical modulator is an issue. Also, common to analog optical links is the dispersion penalty resulting from the destructive interference between the upper and lower sidebands in the second dispersive medium [55, 151].
6.4 Spatial-spectral holographic preprocessor for electornic ADC
Recently, Babbitt et al. (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
The use of a mode-locked laser to sample an RF signal was discussed first by Taylor et al.  (1978) as part of their all-optical ADC. Later, Bell et al. [58–60] (1989) recognized that optical sampling and temporal demultiplexing would be useful for making a time-interleaved ADC. More recently, many researchers [61–73] have concentrated on the optical sampling process alone without demultiplexing to take advantage of the short pulse widths and low pulse-to-pulse jitter of a mode-locked laser. The basic components of an optically sampled system consist of a stable pulsed laser, an optical modulator, and a detector/integrator as shown in Fig. 13. In optically sampled ADCs, the optical pulse generator is typically a mode-locked fiber or semiconductor laser, the optical modulator is typically a LiNbO3 Mach-Zehnder modulator, and the detector is a high-speed photodiode. Usually, the detector current is amplified and directed to an electronic ADC for quantization. This system contains an analog optical link and thus its performance is characterized by the link SNR, SFDR, modulator bandwidth and modulation index, photodiode saturation current and bandwidth as discussed above and in many texts and references [7, 8, 127]. But it does offer the potential for a sampling time equal to the optical pulse width and a sampling jitter equal to the mode-locked laser jitter.
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, 63, 65, 74].
Another issue for the photonic sampled photonic ADC is photodiode response [64, 74, 75]. The photodiode must turn on rapidly, it must be linear over the whole range of operating power, it cannot exhibit spill-over from one pulse to the next and it should have low noise. A final issue for the photonic sampled system is that the electronic ADC must be clocked at the sampling rate even though the sampling time and jitter are controlled by the optics. Development of the demultiplexed photonic sampling ADCs discussed in the next paragraphs relieved some of the electronic ADC issues.
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] (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] (Twichell et al. 2001, Juodawlkis et al. 2001, 2002, Williamson et al. 2001) investigated many features of optically sampled and demultiplexed ADCs  and demonstrated ENOB = 9.8 at 505 MS/s .
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, 67, 72, 73, 129–131], 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.  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 .
In the late 1990s researchers recognized that one can construct a source with interleaved pulses of different wavelengths [44, 46, 50, 78, 79] (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 ) 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. ). Results reported that use wavelength-interleaved pulses include 2 GS/s with 4 bits [73, 81–82] (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 . 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.
In addition to the issues associated with the built-in analog optical link, which the demultiplexing systems share with all photonic sampling systems, these systems introduce a wide range of path-matching, crosstalk and calibration issues, many of which are common to electronic interleaved systems. For example, achieving N bits in a time-interleaved system without calibration requires matching loss on each path to less than the quantization error, 1/(2N 121/2). At N = 8, this means matching splice losses, photodiode responsivity, electronics gains, etc. to 1 part in 103! Clearly calibration is required and the frequency of calibration depends on the time-dependence of any path losses. In the photonic ADC context, the MIT Lincoln Laboratory group performed the most comprehensive work on path matching and calibration [74, 77] (Juodawlkis et al. 2001). As discussed above, the time-stretch ADC also has calibration and path matching issues, but the TS-ADC introduces two additional degrees of freedom to help calibration and path matching, the number of samples in an interleaved time segment and the fraction of overlap of one time segment with the next segment.
A somewhat different variation on the photonic sampled and demultiplexed theme was reported by Frankel et al.  (1997), Kang et al.  (1998) and Bhushan et al.  (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. (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, 133] (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.
A similar optical quantization scheme has been reported by Johansson et al. (2000) and Pala et al.  (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  (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  (1975) proposed the photonic quantization scheme shown in Fig. 16(a) and subsequently [3, 15] 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.
Many variations of Taylor’s scheme have been reported [17–20, 22–23, 94–96] (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.  (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.  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.  (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  (1994) and Jalali and Xie  (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, 142] (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
The Taylor scheme produced many interesting results through the 1980s, but the inability to obtain more than 4 bits prompted researchers to investigate more direct intensity quantization schemes. The attraction of direct quantization is simplicity and potentially lower insertion loss. The disadvantage is that 2N comparators are needed for N bits. In the most general sense, a comparator is a device that compares two input signals and switches its output to on or off (or to 0 or 1) to indicate which input value is larger. A signal may be digitized to N bits with 2N comparators set at 2N levels, each one Q or the LSB larger than the previous level. There are a wide range of optical processes and devices whose physical response resembles that of a comparator, but many of these processes do not have sharp transitions, cannot be tuned to a large number of equally spaced levels, or operate slowly compared to electronic signals of interest. Referring again to Walden’s chart, Fig. 3, one sees that to make an ADC that is competitive with electronics, the comparator must be capable of at least 256 levels (8 bits) if its response time is longer than about 100 ps, or it must be capable of 16 levels (4 bits) with a response time less than 100 ps.
Loh and LoCicero  (1996) investigated using symmetric self electro-optic devices  (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] (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  (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  (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.  (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.
Konishi et al.  (2002) present a technique closely related to the work of Ho et al . Instead of cross-phase modulation they use self-phase modulation that leads to a frequency shift of a soliton or “dispersive” wave that depends on the intensity of a modulated femtosecond pulse train. Konishi et al. note that the maximum number of levels that can be obtained this way is given by the wavelength shift plus the full-width-half-maximum (FWHM) divided by the FWHM. This criterion appears to limit resolution to less than 4 or 5 bits.
Oda et al.  (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  (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  (2003) add several interesting ideas to the work of Konishi et al.  (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.  (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.  (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
The first photonic ADC demonstrated by Wright et al.  (1974) used an electrically controlled diffraction grating to vary the far-field profile of a beam on an array of photodiodes. Properly setting the threshold on electronic comparators that follow the photodiode allows production of a Gray scale code. Wright et al. actually demonstrated their system with electronic sampling following the optical quantization but one could obviously start with a short pulse laser source and perform optical sampling first, as in most of the work discussed in the previous sections.
Tsunoda and Goodman  (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  (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.  (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 [111,112] (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 .
9.4 Optical delta-sigma modulators
Delta-sigma modulators are a type of ADC that operate on a very different principle than the conventional sample, hold and quantize ADC that has been discussed in the previous sections. Fig. 18 shows the basic components of a first-order delta-sigma modulator (the order of a delta-sigma modulator is given by the number of feedback loops). The input signal at the left is summed with the feedback of the previous bit, integrated, quantized and processed by a digital filter. The quantizer is triggered by an external clock and the sample rate is typically much greater than the bandwidth of the input signal, hence the delta-sigma modulator is often referred to as an oversampling analog-to-digital converter. In a sense it trades a larger number of samples per bandwidth for smaller numbers of quantization levels. Without any feedback, it can be shown that oversampling by a factor of 2 increases the ENOB by 1/2 (Shoop 2000). If the quantizer were a 1-bit quantizer, as is common in Δ–Σ designs, then oversampling by 218 = 2.6 × 105, would be necessary to obtain 10 bits-not a very useful trade. For an mth order Δ–Σ modulator, it can be shown that the number of effective bits increases by m+1/2 for each doupbling of the sampling rate (Shoop 2000). This increase in effective bits is made at the expense of ADC bandwidth a trade-off that is often advantageous for signals with bandwidth, much less than the sampling rate.
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 , 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.
The first proposals for an optical Δ–Σ modulator were made by Shoop and Goodman [113, 114] (1992). They identified two classes of optical Δ–Σ modulators, interferometric and non-interferometric. In the interferometric A-S modulator all optical links are coherent, and all path lengths must be specified and held to a tolerance less than a wavelength. In the non-interferometric Δ–Σ modulator, incoherent optical and electronic links are mixed. Conventional electronic Δ–Σ modulators operate on voltages and currents, which are bipolar, while the non-interferometric optical Δ–Σ uses unipolar signals. This issue has been investigated in detail by Willis et al.  (1998). Shoop and Goodman identified multiple quantum well self electro-optic devices  (SEED) for use as the optical quantizer and most investigators of optical Δ–Σ modulators have continued to use SEEDs. Shoop and Goodman  (1993) reported operation of a first-order, non-interferometric, optical Δ–Σ modulator at sampling rate of 1 kHz. In this device a reflective mode electro-absorption modulator is used to perform both the subtraction and the 1-bit quantization functions.
Marwood et al.  (1999) and Al-Sarawi et al. [118, 140, 141] (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.  (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.  (2003) identified another issue, critical slowing down, that limits use of bistable symmetric SEEDs for comparators. Al-Sarawi et al.  (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, 139, 143] (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, 138] (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.  (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  (2000) and Shoop and Das [123, 124] (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  (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.
This review has attempted to find, reference and discuss all published work on photonic ADCs. This work is fascinating for the breadth of optical processes that researchers have investigated for possible application to analog-to-digital conversion, but it is also frustrating because so few publications report full operation of an ADC, which makes it very hard to compare different schemes on an equal basis similar to the evaluation the Walden has performed for electronic ADCs [2, 6]. In this conclusion, it is useful to highlight some of the most interesting results obtained to date. In the 1980s, the 4 bit realization of Taylor’s scheme at 1 GS/s  and the integrated version with a reported 4 bits and input bandwidth of 1.2 GHz  stand out. The most impressive result of the photonic sampled and electronically quantized work is the ENOB = 9.8 at 505 MS/s obtained with time demultiplexing [74, 146]. More recently, the report of almost 10 ENOB at 1 GS/s for the optical track and hold portion of a photonic assisted ADC  is interesting if it can be integrated with a full ADC. The 4.5 ENOB, 10-TS/s transient digitizer, fabricated with the time-stretch technology, is to my knowledge the fastest sampling rate obtained to date . A number of other technologies offer promise of sampling rates in the 10-100 GS/s range and beyond [39, 73, 74, 84, 85, 112, 135, 142]. Despite all this potential, it is strongly recommended that researchers working on novel photonic ADCs at rates and/or resolutions beyond those offered by present-day electronics continue to monitor developments in commercial ADCs and digital oscilloscopes since progress in these areas can quickly erase the prospective advantage of a photonic ADC.
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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