A novel photonic analog-to-digital conversion scheme implemented using an array of Mach-Zehnder modulators (MZMs) with identical half-wave voltages is proposed and demonstrated. It is different from the scheme proposed by Taylor where the MZMs should have geometrically scaled half-wave voltages; the proposed scheme here uses MZMs with identical half-wave voltages, which eliminates the need for the MZMs to have very low half-wave voltages. By properly biasing the MZMs, the transfer functions of the MZMs are laterally shifted, which leads to the generation of a linear binary code to represent the analog input signal. The use of the MZMs with identical half-wave voltages simplifies greatly the design and implementation, which provides a high potential for integration. A proof-of-concept experiment for analog-to-digital conversion with a quantization level of 16 is demonstrated.
© 2008 Optical Society of America
High speed analog-to-digital converters (ADCs) are vital for many modern applications, such as broadband wireless communications, high-speed medical imaging, high-resolution radar, wideband software-defined radio, advanced instrumentation, and modern electronic warfare. Although there is a remarkable progress in analog-to-digital conversion technologies in the last two decades, the advancement in electronic ADCs lags largely behind the digital electronics. Since 1970s, the use of optical technologies in ADCs has attracted great interest thanks to the inherent broad bandwidth offered by optics. One major breakthrough in photonic ADCs is the use of mode-locked lasers. A state-of-the-art mode-locked laser can produce high-frequency (over 10 GHz) optical sampling pulses with timing jitter significantly below that of electronic circuitry [1, 2]. In addition, optical sampling would make the back-coupling between the optical sampling pulses and the electrical signal being sampled negligible.
By now, different approaches for photonic ADCs have been proposed and demonstrated [3–6]. Taylor first proposed the use of an array of Mach-Zehnder modulators (MZMs) for analog-to-digital conversion . In his scheme, the input analog signal is symmetrically folded by the MZMs with each MZM having an electrode length that is twice that of its nearest more significant bit (MSB), leading to a doubled folding frequency. The folding property in the transfer function imposes a requirement that the half-wave voltage of the MZM at the least significant bit (LSB) should be very low, which is difficult to realize using current waveguide technology. To avoid using MZMs with very low half-wave voltages, Jalali et al. proposed to use cascaded MZMs . The use of cascaded phase modulators  was also proposed. Recently, Stigwall et al. proposed a scheme to use a free-space interferometric structure in which a phase modulator is incorporated in one arm of the interferometer [9, 10]. By placing the photodetectors (PDs) at the specific locations of the diffraction pattern generated at the output of the interferometer, linear binary code digital data are generated. The same concept was recently demonstrated by Li et al., but the interferometric structure was realized based on a fiber-optic platform, which makes the system more compact .
In this paper, we propose a novel scheme to implement a photonic ADC using an array of MZMs with identical half-wave voltages. By properly biasing the MZMs, the required shifts in transfer functions of MZMs can be realized, which is used to generate the linear binary code representation of the analog input signal. The use of the MZMs with identical half-wave voltages simplifies greatly the design and implementation, which provides a high potential for integration. The operation principle is discussed with an emphasis on the encoding concept. A proof-of-concept experiment is then implemented. Analog-to-digital conversion with a quantization level of 16 is demonstrated.
2. Operation principle
A 4-channel ADC using four MZMs with identical half-wave voltages is shown in Fig. 1. The system consists of a mode-locked laser source, four MZMs, four PDs, and four electronic comparators. An optical pulse train from the mode-locked laser is sent to the four MZMs, to sample the RF signal to be digitized, which is applied to the MZMs via the RF ports. The output signals from the MZMs are then sent to the PDs to perform optical to electrical (O/E) conversions. An electronic comparator is connected to the output of each PD. All the MZMs employed have identical electrode lengths, and therefore identical half-wave voltages (Vπ). To quantize the sampled RF signal, the MZMs should be properly biased. In the proposed scheme, the output optical intensity from a specific MZM is determined by the bias voltage applied to the specific MZM and the voltage of the RF signal. Mathematically, the output optical intensity is given by
where Ii is the input optical intensity, φs=πVs(t)Vπ is the phase shift induced by the applied RF signal Vs(t), φb=πVb/Vπ is the phase shift induced by the bias voltage Vb. φb=πVb/Vπ is the phase shift induced by the bias voltage Vb.
To get a uniform quantization, the bias voltages applied to the MZMs should be set to have a uniform phase spacing of Δφb=π/n, where n is the number of modulators in the system. Consider the 4-channel case as shown in Fig. 1, Δφb should be π/4. We set the bias phase shift φb of the 4 modulators as -π/8, π/8, 3π/8 and 5π/8. The corresponding transfer functions of the 4 modulators are shown in Fig. 2(a). The quantization threshold could be set at any value, but for convenience, we assume that an optical signal greater than half of the full scale is a “1”, and smaller than half of the full scale is a “0”. The corresponding outputs from the comparators with a threshold level as half of the full scale are shown in Fig. 2(b). Fig. 2(c) gives the quantized values of the signal at the output of the 4-channel ADC. It is different from previous approaches in [6, 7] where the generated code is a Gray code; the proposed scheme here generates a linear binary code. For an n-channel ADC, the code length of this scheme is 2n, while the code length is 2n for the schemes in [6, 7]. Note that the channel number n in this approach does not equal to the bit resolution NR when n is greater than 2. The bit resolution NR of our approach is given by NR=log2 (2n) (or ). For an ADC with 4 channels (corresponding to NR=3), the code length is 8 which are given by (1110, 1100, 1000, 0000, 0001, 0011, 0111, 1111), corresponding to 8 values form 0 to 7. It is same as the commonly used Gray code, an important advantage of the linear binary code is that there is only a single bit position change at each step. This property would reduce the possible readout error when the input signal level is near the decision point of the comparator. Since the number of valid code words is 2n in the 2n possible code words, there are 2n-2n invalid code words. In the post-procession, the created invalid code words induced by system noise can be replaced by the nearest valid words. Note that the encoding concept in this approach is similar to the phase-modulator-based optical ADC techniques in [9–11]. A more detailed discussion on the coding property can be found in .
3. Experiment results and discussions
A proof-of-concept experiment with the setup shown in Fig. 3 is demonstrated. The lightwave generated by a continuous-wave laser diode (Yokogawa AQ2201) operating at 1550 nm is sent to a 20-GHz JDS-Uniphase intensity modulator through a polarization controller (PC). The PC is carefully adjusted to minimize the polarization-dependent loss in the modulator. A 45-GHz PD (New Focus 1104) is used to implement the O/E conversion. To proof the concept, the modulator is driven with a 4-GHz sinusoidal signal generated by a signal generator (Agilent E8254A). A digital sampling oscilloscope (Agilent 86100C) is used to capture the temporal waveforms, which is triggered by the signal generator. The half-wave voltage Vπ of the modulator is 9.2 V.
In the experiment, we emulate the output characteristics of an 8-channel system by tuning the bias voltage of the modulator at a constant step Vπ/8=1.2 V. Since the channel number n is 8, the bit resolution NR is 4. For each bias voltage, we measure and record the waveform by the oscilloscope. The recorded 8 traces (without averaging) are shown in Fig. 4(a). Based on the recorded waveforms, we use a program to sample the waveforms to get discrete intensity data at a fixed time interval. Then, a digitized signal is obtained by comparing the sampled data with the threshold value. The threshold value is set as half of the maximum output. The quantized value obtained according to the final binary code is shown in Fig. 4(b). As a comparison, the fitted sinusoidal signal is also shown in Fig. 4(b). Note that, the maximum quantized value is 13, which is equivalent to a phase shift of 1.625~1.75 π. The maximum phase shift is decided by the input RF signal power. Fig. 4(c) shows the errors between the quantized signal and the fitted signal. Due to the noise in the detected waveforms, errors in some sampling points are larger than the size of the LSB.
Based on the errors between the quantized value and the fitted signal, the digital signal-to-noise ratio (dSNR) is estimated to be around 219 (23.4 dB), which corresponds to an effective number of bits (ENOB) of 3.6, according to the following formula 
Since the bit resolution NR of the system is 4, the ENOB deviation from the ideal case is 0.4 dB. This ENOB degradation is owing to the noise sources in the system, which include the relative intensity noise (RIN) of the laser source, the shot noise and the thermal noise of the PD, and the instrument noise.
To clarify the relationship between the system noise and the ENOB degradation, we implement computer simulation using the Monte-Carlo method based on the model given in . In the simulation, the overall noise in the system is modeled by a Gaussian distributed random variable, which has the probability density function,
where σ is the standard deviation of the noise. The modulation depth in the simulation is set to be 1.72π, the same value in our experimental. In the simulation, each created invalid word is replaced by the word with the rounded average value among all nearest valid words. The simulation result is shown in Fig. 5, where the detection SNR denotes the SNR of the detected waveform of channel 1 (which is related to σ), and the ENOB is related to dSNR as in Eq. (2). The detection SNR of the obtained waveform (channel 1) shown in Fig. 4(a) is measured to be 23.3 dB. From Fig. 5, we can see that this value corresponds to a dSNR of around 24.5 dB and an ENOB of 3.7 dB, which match well with the measured dSNR of 23.4 dB and ENOB of 3.6. Note also that our simulation result agrees well with the calculated results by Stigwall et al. in .
In an ideal ADC, the limitation on the ADC performance is mainly owing to the steepness of the digitized signals which would lead to errors in the output waveforms. In this case, the ENOB of the system is just the bit resolution NR. The noise-induced ENOB degradation has been found and investigated in our experiment. In practical realization of the proposed ADC, the effects of aperture jitter and clock jitter have to be taken into account in the performance evaluation, since the random sampling time variations due to the aperture and clock jitter would also lead to errors in the output waveform. For more details, readers may refer to . The lithium niobate phase modulators in the MZMs have an almost ideal linear response from input electrical voltage to optical phase shift; spurious free dynamic range (SFDR) over 90 dB has been measured . The major limitation on the system dynamic range is the allowed maximum 2π phase swing due to the 2π periodicity of the transfer function of the MZMs, as can be seen in Fig. 2(a), which indicates that the phase shift variation induced by the input voltage signal should be kept within 2π.
We should note that the proposed scheme has some similarity in principle with the scheme proposed by Stigwall et al. [9, 10]. In [9, 10], the ADC has a structure using a free-space Mach-Zehnder interferometer (MZI), with a phase modulator incorporated in one arm of the MZI. An array of probe detectors is used to perform O/E conversions. The probe detectors are placed at specific positions along the diffraction pattern, which corresponds to the different bias phase shifts in our proposed system. In both cases, the transfer functions are shifted instead of folded, which leads to the generation of a linear binary code with a code length of 2n instead of a Gray code with a code length of 2n. This is the major drawback of the proposed scheme. The major advantage of our scheme is that the MZMs have identical half-wave voltages, which eliminates the requirement for the geometrical scaling of the half-wave voltages. Therefore, our scheme provides a viable solution for photonic ADC, especially for low bit resolution applications. In addition, no free-space optics is involved in the scheme, which makes the system more compact and stable with high potential for integration.
As a comparison to the approaches based on cascaded phase or intensity modulators [7, 8], our approach features a simpler design with a parallel structure, which avoids the problems such as non-uniform loss among different channels. In addition, the parallel design in our scheme avoids the requirement for a precise synchronization between the electrical and the optical signals in the cascaded modulators.
In conclusion, a novel scheme for photonic ADC using an array of MZMs with identical half-wave voltages was proposed and experimentally demonstrated. The quantization and encoding in the proposed system was realized by properly biasing the MZMs to have shifted transfer functions such that a linear binary code was generated at the output of the system. Compared to Taylor’s scheme where the MZMs should have geometrically scaled half-wave voltages realized by increasing the electrode length, the proposed scheme uses MZMs with identical half-wave voltages which eliminate the need for MZMs with very low half-wave voltages thereby simplifying greatly the design and implementation. In addition, the proposed ADC with parallel MZM structure provides a high potential for integration. A proof-of-concept experiment to demonstrate the feasibility of the proposed scheme was implemented in which an analog-to-digital conversion with a quantization level of 16 was realized.
This work was supported by The Natural Sciences and Engineering Research Council of Canada. H. Chi was supported in part by the National Natural Science Foundation of China (No. 60407011) and in part by the Zhejiang Provincial Natural Science Foundation (No. Y104073).
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