Proposal of Compact Photonic Quantization Based on Dual-Output Mach-Zehnder Modulators

Abstract

In this paper, to reduce system complexity and improve performance, we propose a novel compact photonic quantization scheme based on dual-output Mach–Zehnder modulators (DOMZMs). By exploiting the complementary outputs of DOMZMs and introducing a cross-channel differential combination strategy, multiple effective quantization channels are generated without increasing the number of modulators. Furthermore, an adaptive thresholding mechanism based on intrinsic signal intersections enables direct Gray code output with improved noise tolerance. Proof-of-concept experimental results fully confirm the correctness of the principle, and 4-bit quantization is successfully demonstrated. Experimental and numerical results both demonstrate good linearity over the full-scale input range, and confirm the feasibility of the proposed scheme. More performance evaluations are provided through simulations. We also discuss challenges relating to practical deployment of the proposed approach. The presented approach provides a promising solution for compact photonic analog-to-digital conversion systems.

1. Introduction

Currently, signal bandwidths in fields such as wireless communications, radar, optical communications, and precision measurement are continuously increasing. This trend poses significant challenges to the sampling rates of conventional analog-to-digital converters (ADCs) [1,2]. Electronic ADCs encounter performance bottlenecks primarily due to the limited bandwidth of sample-and-hold circuits and to sampling clock jitter, making it difficult to simultaneously achieve high sampling rates and high bit resolution [3]. In the past decade, microwave photonic signal processing has received widespread attention due to the inherent bandwidth advantages of photonics [4,5,6,7,8,9,10]. Photonics-assisted ADCs (PADCs) have emerged as a promising alternative, leveraging the unique advantages of photonics to overcome the speed and precision barriers of electronic systems. Generally, PADC technologies are classified into three main categories: optical sampling, photonic time stretch (as a preprocessing stage), and photonic quantization. Optical sampling typically utilizes mode-locked lasers as the sampling source to achieve high-speed, low-jitter sampling [11,12,13,14]. Photonic time stretch slows down high-frequency signals in the optical domain to match the bandwidth of electronic ADCs [15,16,17,18]. Photonic quantization refers to the process of mapping the analog amplitudes of an input signal into digital codes in the optical domain [19,20,21,22].

Research on photonic quantization can be traced back to the work of Taylor in the 1970s. In 1979, Taylor first proposed a photonic ADC scheme based on a Mach–Zehnder modulator (MZM) array [19]. This scheme incorporates an array of MZMs whose electrode lengths increase in a geometric progression, so as to achieve a geometrically decreasing half-wave voltage across the MZMs. The requirement for a geometrically progressive half-wave voltage is still challenging to satisfy with today’s modulator fabrication processes, particularly for quantization precision beyond three bits. To overcome this limitation, Jalali proposed the optical folding-flash scheme. By cascading multiple identical MZMs to increase the effective electrode length, this scheme circumvents the stringent requirement for ultra-low half-wave voltage in a single modulator [21]. However, the cascaded structure significantly increases system complexity, and issues such as waveguide delay and electro-optic synchronization in distributed structures reduce the practicality of the system. In 2006, Stigwal et al. proposed an optical quantization scheme based on a spatial MZI structure [23]. The core of this scheme lies in its use of a phase shift among the modulation curves, rather than folding (i.e., the successive halving of the half-wave voltage), thereby avoiding the difficulties inherent in Taylor’s scheme. Subsequently, several equivalent photonic quantization schemes based on modulation-curve phase shift were proposed, including a scheme utilizing an MZM array with identical half-wave voltages and a scheme based on all-fiber optical polarization interference [24,25,26]. Compared to Taylor’s scheme, the phase-shifting photonic quantization scheme eliminates the need for MZMs with extremely low half-wave voltages. However, it suffers from a major drawback: lower bit precision. Specifically, with N channels, it achieves a resolution of only log₂(2N) bits, whereas Taylor’s scheme achieves N bits. However, several improved versions of the phase-shifting photonic quantization scheme have been reported in recent years, including a scheme with improved bit resolution using multi-threshold comparators and symmetrical number system [27], a scheme that incorporates an additional MZM to achieve a larger quantization range [28], and a scheme that utilizes logic circuits to combine signals and thus obtain more transfer curves [29]. In [30], a scheme using an unbalanced MZM was shown to improve the phase-shifting method; this scheme utilizes arm-length differences coupled with multi-wavelength sources to achieve phase shifting of the modulation transfer curves [30]. Some schemes have employed differential encoding or balanced detection techniques to further enhance system performance [31,32].

In this paper, we propose and demonstrate a novel, compact, and hardware-efficient photonic quantization scheme leveraging dual-output Mach–Zehnder modulators (DOMZMs) with identical half-wave voltages. By utilizing the complementary outputs of DOMZMs and employing a linear combination module, our architecture significantly increases the bit resolution without requiring additional modulators. Furthermore, due to the differential nature of the combination module, the output signals are inherently zero-mean, allowing the decision thresholds of the subsequent comparators to be fixed at zero. Compared to the scheme utilizing an MZM array with identical half-wave voltages [24], which requires $2^{n-1}$ modulators to achieve $n$-bit resolution, the proposed architecture accomplishes the same resolution using only $2^{n-3}$ modulators. In the present work, proof-of-concept experiments are performed, and the experimental results of a 4-bit quantization clearly verify the correctness and feasibility of the proposed scheme. Comprehensive simulation analyses are further provided to thoroughly investigate noise tolerance, modulator bias drift, and the challenges posed by limited receiver bandwidth. We believe the present approach offers a promising, scalable solution for high-performance, compact photonic quantization.

2. Principle

The proposed photonic quantization scheme with a 4-bit resolution is schematically illustrated in Figure 1. A pulsed laser is employed as the sampling source. Two DOMZMs with identical half-wave voltages generate complementary outputs. An array of photodetectors (PDs) following the DOMZMs perform optical-to-electrical (O/E) conversion. A linear combination module is then used to perform weighted summation and subtraction of the electrical signals from the PDs. The repetitive pulse train emitted by the pulsed laser is split into two channels, each of which is modulated by the input analog signal via the DOMZMs. To ensure correct coding, the two DOMZMs must be properly biased. The eight-channel outputs are then directed to a comparator array, where they are transformed into binary “0” or “1” via thresholding.

The proposed scheme is an improvement of the phase-shifting-based photonic quantization. Consequently, the output follows a Gray code—in which adjacent codewords differ by only one bit—thereby enhancing the system’s noise tolerance. Specifically, the proposed scheme incorporates DOMZMs in conjunction with a linear combination module, significantly reducing the required number of modulators. In the following sections, the theoretical analysis is carried out using 4-bit quantization as a representative case. The half-wave voltages of the two modulators are assumed to be identical, denoted by $V_{\pi }$. We assume the incident optical power to each DOMZM is the same, denoted by $P_0$. The responsivity of each PD is denoted by $\Re$, and the voltage signal to be quantized is denoted by $V_s(t)$. The electrical signals from the two PDs after the upper-path DOMZM can be expressed as:

$$I_1={\displaystyle \frac{1}{2}}{I}_0[1+\cos ({\phi }_s+{\varphi }_{b1})]$$

(1)

and

$$I_2={\displaystyle \frac{1}{2}}{I}_0[1-\cos ({\phi }_s+{\varphi }_{b1})]$$

(2)

where $I_0=\Re P_0$, ${\phi }_s=\pi V_s(t)/V_{\pi }$ is the time-varying phase function induced by the input voltage signal $V(t)$, and ${\varphi }_{b1}=\pi V_{b1}/V_{\pi }$ is the bias phase induced by the bias voltage $V_{b1}$ on the upper DOMZM. Due to the complementary property of the two output ports from the DOMZM, we have $I_0=I_1+I_2$. The electrical signals after the lower-path DOMZM are expressed as

$$I_3={\displaystyle \frac{1}{2}}{I}_0[1+\cos ({\phi }_s+{\varphi }_{b2})]$$

(3)

and

$$I_4={\displaystyle \frac{1}{2}}{I}_0[1-\cos ({\phi }_s+{\varphi }_{b2})]$$

(4)

where ${\varphi }_{b2}=\pi V_{b2}/V_{\pi }$ is the bias phase induced by the bias voltage $V_{b2}$ on the lower DOMZM. To achieve correct coding, the bias phases applied to the two DOMZMs should satisfy ${\varphi }_{b1}=0$ and ${\varphi }_{b2}=\pi /2$.

In order to achieve more outputs with different equivalent phase shifts in the modulation transfer functions, we introduce an intermediate signal $I_5$, which is the weighted summation of $I_1$ and $I_3$, expressed as

$$I_5=A(I_1+I_3)-I_{bias}=I_{0}A[1+\cos ({\displaystyle \frac{{\varphi }_{b1}-{\varphi }_{b2}}{2}})\cos ({\phi }_s+{\displaystyle \frac{{\varphi }_{b1}+{\varphi }_{b2}}{2}})]-I_{bias},$$

(5)

where $A=1/\sqrt{2}$ and $I_{bias}=A(I_1+I_2)-0.5I_0=(1/\sqrt{2}-0.5)I_0\approx 0.207I_0$ are the normalization coefficient and the bias value, respectively. Substituting the aforementioned parameters, $I_5$ can be expressed as $I_5={\displaystyle \frac{1}{2}}{I}_0[1+\cos ({\phi }_s+\pi /4)]$. The linear combination module is utilized to perform differential operations among the signals from $I_1$ to $I_5$. The eight outputs from the module are expressed as

$$\left\{\begin{array}{c}{L}_1=I_1-I_2=I_0\cos ({\phi }_s)\\ L_2=I_1-I_3={\displaystyle \frac{\sqrt{2}}{2}}{I}_0\cos ({\phi }_s-\pi /4)\\ L_3=I_1-I_4={\displaystyle \frac{\sqrt{2}}{2}}{I}_0\cos ({\phi }_s+\pi /4)\\ L_4=I_3-I_4=I_0\cos ({\phi }_s+\pi /2)\\ L_5=I_5-I_1={\displaystyle \frac{\sqrt{2-\sqrt{2}}}{2}}{I}_0\cos ({\phi }_s+5\pi /8)\\ L_6=I_5-I_2={\displaystyle \frac{\sqrt{2+\sqrt{2}}}{2}}{I}_0\cos ({\phi }_s+\pi /8)\\ L_7=I_5-I_3={\displaystyle \frac{\sqrt{2-\sqrt{2}}}{2}}{I}_0\cos ({\phi }_s-\pi /8)\\ L_8=I_5-I_4={\displaystyle \frac{\sqrt{2+\sqrt{2}}}{2}}{I}_0\cos ({\phi }_s+3\pi /8)\end{array}\right.$$

(6)

It can be seen from the above equation that the minimum phase-shift interval between the output channels is $\pi /8$. Since all output channel signals are zero-mean, the comparator thresholds can be fixed at zero. The transfer functions for the eight output ports are illustrated in Figure 2a. In the quantization stage, a comparator array employs a zero-threshold decision rule to convert these analog signals into 8-channel digital outputs: an input signal exceeding the threshold is mapped to ‘1’, while those below are assigned ‘0’. The coding mechanism, depicted in Figure 2b, naturally yields a Gray code output. By ensuring that adjacent codewords differ by only a single bit, this scheme effectively minimizes readout errors at decision boundaries and enhances the robustness of high-speed conversion. The dependence of the quantized value on the phase shift induced by the input signal is shown in Figure 2c, where a linear relationship may be observed.

Generally, to achieve a bit resolution of $N$ ($N\ge 5$), only $2^{N-3}$ DOMZMs are required. Compared with conventional parallel phase-shifting schemes requiring $2^{N-1}$ modulators [24], this architecture achieves significant hardware simplification. For an $N$-bit system, the number of required DOMZMs is denoted as$M=2^{N-3}$. The bias phases applied to each modulator should have uniform spacing, with a phase increment defined as:

$$\Delta {\varphi }_b={\displaystyle \frac{\pi }{2^{N-3}}}$$

(7)

The bias phase ${\varphi }_{bk}$ of the k-th DOMZM ($1\le k\le M$) can be expressed as ${\varphi }_{bk}=(k-1)\cdot \Delta {\varphi }_b$. The photocurrent signals generated by the two complementary output ports of the k-th DOMZM can be represented as follows:

$$I_{k,1}=I_0[1+\cos ({\varphi }_s+{\varphi }_{bk})]$$

(8)

$$I_{k,2}=I_0[1-\cos ({\varphi }_s+{\varphi }_{bk})]$$

(9)

The linear combination module needs to generate $2^{N-1}$ output ports to achieve quantization. To refine the quantization intervals, in addition to directly utilizing the differential outputs of each DOMZM, an intermediate signal $S_{\mathrm{int}}$ must be introduced. For instance, in a 5-bit system, the intermediate signal can be generated by combining the positive output signals of the first and second modulators, which is

$$S_{\mathrm{int}}=\alpha \cdot (I_{1,1}+I_{2,1})+\beta$$

(10)

where the coefficients $\alpha$ and $\beta$ are used to normalize the amplitude and align the dc components. By performing cross-differential operations between the intermediate signal $S_{\mathrm{int}}$ and the primary signals from each DOMZM, the module eventually generates $2^{N-1}$ parallel signals. Since all differential output signals possess a zero-mean property, the decision thresholds for the subsequent comparator array can be uniformly fixed at zero.

3. Results and Discussion

3.1. Proof-of-Concept Experiment

We implemented proof-of-concept experiments to verify the principle of the proposed photonic quantization scheme. The experimental setup is shown in Figure 3. In the experiment, a continuous-wave light generated by a tunable laser source (IDPhotonics) operating at 1550 nm was utilized as the optical carrier. This was modulated by an analog signal via an MZM (Avanex 792000450) with a half-wave voltage of 1.8 V. A polarization controller was employed to minimize the polarization-dependent loss of the modulator. The analog signal to be quantized was generated by a signal generator (R&S SMB100A). The signal from the signal generator was injected into a microwave amplifier (Ceyear 3871FS). After amplification, it was then fed into the MZM. After optical-to-electrical conversion performed by a PD (KG-PD-10G), the output time-domain waveforms were captured by a digital sampling oscilloscope (Keysight 86100D). To emulate the multi-channel parallel sampling architecture, a sequential bias-tuning and offline synthesis approach was adopted. Specifically, the dc bias of the MZM was adjusted to meet the required phase shifts for each channel, with the corresponding waveforms being recorded individually. To ensure temporal alignment across different measurements, the sampling oscilloscope was triggered by a reference signal from the signal generator. The linear combination and encoding processes were carried out through offline data processing in a computer program.

In the experiment, the analog signal to be quantized was a 2 GHz sinusoidal signal. In order to demonstrate a 4-bit photonic quantization, the dc bias of the MZM was sequentially adjusted to four specific points, corresponding to phase shifts of 0, π/2, π, and 3π/2, and the corresponding output waveforms were each recorded. Considering that harmonics may occur under different bias conditions, the 10 GHz bandwidth of the PD still meets the requirements. The experimental results of the proposed 4-bit quantization are given in Figure 4. By performing offline linear combination operations on the captured waveforms, eight parallel channel signals ($L_1$ to $L_8$) were successfully generated; these are shown in Figure 4a,b. After the thresholding decision of the comparators, 8-bit Gray code outputs corresponding to their amplitude levels could be obtained.

By implementing a look-up table mapping process, a quantized waveform could be obtained. This is shown in Figure 5a, where it may be seen that the quantized waveform shows good agreement with the fitted sinusoidal signal, successfully achieving a quantization level of 16 for the 2 GHz signal input. Figure 5b provides the quantization error along the time axis. The results demonstrate that the majority of error fluctuations are strictly confined within the theoretical limits of $\pm 0.5$ least significant bit (LSB). The minor performance degradation compared to the ideal 4-bit quantization, as well as occasional error spikes, are primarily attributed to bias phase errors in the modulators and noise in the detection process. The signal-to-noise ratio (SNR) of the quantized waveform was estimated to be approximately 22.97 dB, which corresponds to an effective number of bits (ENOB) of 3.52. The experimental results demonstrate the correctness and feasibility of the proposed photonic quantization principle.

3.2. Error Tolerance Analysis and Impact of Receiver Bandwidth

The experimental results indicate that both bias phase error and system noise affect quantization performance. Accordingly, we conducted a systematic simulation to study the influence of these two factors. First, we investigated the impact of system noise. In the simulation, a 2 GHz signal was employed as the analog signal to quantized, 4-bit quantization was considered, and the bandwidth of the receiver was set to 10 GHz, all of which were similar to the experimental conditions. We added additive white Gaussian noise to electrical signals after the PDs and obtained ENOB values under different SNR conditions. The result of ENOB vs. SNR is shown in Figure 6. It may be seen that in the low-SNR region (e.g., SNR < 15 dB), system performance is severely limited, with the ENOB far below the ideal bit resolution. As the SNR increases, the simulated ENOB grows monotonically and gradually approaches the ideal limit of 4 bits. When the SNR is 20 dB, the ENOB decreases by approximately 0.7 bits compared to the ideal bit resolution.

Next, we investigated the bias phase error induced by the MZM bias voltage error on quantization performance. The simulation conditions were set to be the same as those in the previous simulation. In the simulation, the bias phase of one DOMZM is set to deviate from the ideal value, whereas the other DOMZM is maintained with no deviation. The bias phase error is defined as $\delta \varphi =\pi \times \delta V/V_{\pi }$, where $\delta V$ is the bias voltage error (the value deviated from the ideal voltage). The result of ENOB vs. bias phase error is shown in Figure 7. It may be seen that a phase deviation of $0.05\pi$ in a single MZM causes the ENOB to drop to around 3.57 bits. These findings underscore the necessity of precisely locking the bias voltage of each MZM to an optimal operating point, to mitigate the detrimental impact of phase errors on system performance.

In the MZM-based quantization, after the signal is modulated via the MZM, multiple orders of harmonics are generated, imposing high bandwidth requirements on the receiver (including the PD and processing circuits). Figure 8a shows the generation of harmonics when the input signal is a 10 GHz sinusoidal signal and the MZM is biased at $\pi /4$. To investigate the impact of the receiver bandwidth on the quantization performance, we conducted further simulations. In the simulation, the receiver bandwidth is set to 40 GHz, while the input analog signals to be quantized ranged from 1 GHz to 25 GHz. Noise was excluded in the simulation. As illustrated in Figure 8b, the ENOB undergoes a sharp decline for input signals exceeding 10 GHz. The underlying cause is the generation of high-order harmonics stemming from the MZM’s inherent nonlinearity, which significantly increases the requirement on the receiver bandwidth. This issue is also a common challenge for phase-shifting photonic quantization based on MZMs.

3.3. Performance Comparison

We compare the scheme proposed in this paper with typical phase-shifting photonic quantization and its improved solutions, as shown in

Table 1. Comparison of the complexity index N among five typical photonic quantization schemes based on phase-shifting quantization.

Bit	4	5	6	n
N
Scheme
Scheme using spatial interference scheme [23]	9	17	33	$2^{n-1}+1$
Scheme using MZM array [24]	16	32	64	$2^n$
Improved scheme using additional MZM [28]	7	11	19	$2^{n-2}+3$
Improved scheme with post processing [29]	6	10	18	$2^{n-2}+2$
This work	6	12	24	$2^{n-2}+2^{n-3}$

. To facilitate comparison, we first define an optical system complexity index N, which is the sum of the electro-optic modulators and PDs used in the scheme. The typical schemes compared include a phase-shifting quantization approach with spatial optical interference scheme [23], an approach using identical half-wave voltages [24], an improved scheme using additional MZM [28] and an improved scheme with post processing [29]. It can be seen from the table that the optical complexity index of the proposed scheme is roughly comparable to that of the two improved schemes, but much smaller than that of the conventional phase-shifting photonic quantization schemes [23,24]. It should be pointed out that the scheme in [28] includes an optical phase-shifting module, which is relatively complex and is not reflected in the aforementioned optical complexity index N. In addition, the threshold of the comparators in the scheme of [29] is related to the input optical power. Compared to schemes that do not require an optical phase shifting module, our proposed architecture utilizes fewer modulators. For example, the scheme using MZM array require $2^{n-1}$ modulators to achieve n-bit quantization [24], while the improved scheme with post processing requires $2^{n-3}+1$ modulators [29]. In contrast, our scheme only needs $2^{n-3}$ modulators. Moreover, with fewer modulators employed, our scheme utilizes differential encoding to effectively counteract optical power fluctuations. Therefore, considering both system performance and complexity, the proposed scheme in this work is competitive.

3.4. Challenges to Practical Deployment

The key to the linear combination module lies in achieving precise mathematical operations. In practical circuits, this typically necessitates an analog signal processing chain composed of broadband amplifiers, analog adders, and programmable gain amplifiers used to implement operations such as addition, subtraction and coefficient scaling. The entire circuit must exhibit high linearity and low noise characteristics to ensure quantization precision. In addition, ensuring a sufficient and flat bandwidth across the entire signal chain from the PDs to the combination circuit is critical; otherwise, signal distortion and quantization performance degradation will result.

Regarding the practical transition toward a photonic integrated circuit platform, most discrete components in this architecture, including the DOMZMs, PDs, linear combination module, and comparator arrays, are highly compatible with silicon photonic integration technology. However, achieving a fully integrated system remains challenging, primarily due to the pulsed laser source which is currently difficult to implement on-chip with high performance. Despite the hurdle of integrating the pulse generation system, the feasibility of migrating the core processing components to a silicon photonic chip underscores the potential of this architecture for future scalable and compact implementations.

4. Conclusions

In summary, we propose here a compact and hardware-efficient photonic quantization scheme utilizing DOMZMs and a linear combination module. By leveraging the complementary nature of DOMZM output ports and implementing a novel cross-channel differential linear combination operation, the presented approach can improve the number of bits while using the same number of modulators. At the same time, the scheme also avoids complex optical phase-shifting components and enables adaptive decision threshold setting, meaning that the threshold level is independent of the input optical power. Proof-of-concept experiments with 4-bit quantization were successfully demonstrated. The experimental results fully confirmed the correctness of the principle and the feasibility of the scheme. Further performance evaluation, including the impact on performance of noise, bias point drift of a single DOMZM, and receiver bandwidth in terms of ENOB, was carried out through simulations. We also discussed the challenges to practical deployment of the proposed approach. We believe that the proposed scheme provides a competitive solution for photonic quantization.