The Principle and Development of Optical Analog-to-Digital Converters
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画中画广告结束 Abstract : Analog-to-digital converters (ADCs) are key components of many information processing systems. The slow progress of electronic analog-to-digital converters has made them a bottleneck between analog signals and digital processing systems, which has prompted people to use optical technology to improve the sampling rate and accuracy of analog-to-digital converters. This paper elaborates on the principle and development of optical analog-to-digital converters (OADCs), and discusses their applications and future developments. Keywords : optical analog-to-digital converters; optical waveguides; wavelength division multiplexing; technical indicators摘要CH(结束)←
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I. Introduction
Today's world is a highly digital world. System designers are increasingly inclined to digitize all processing processes due to the many attractive features of digital technology, such as high speed, great flexibility, serialization, and high reliability. As a result, the role of analog-to-digital converters as a bridge connecting the real analog world and the digital world is becoming increasingly important, and the requirements for their performance are becoming increasingly higher. High-performance analog-to-
digital converters are an indispensable link between analog sensors (such as radar, communication equipment, and electronic warfare equipment) and digital signal processing systems. In recent years, on the one hand, with the popularization and application of electronic computers and the continuous improvement of the degree of automation of detection, higher requirements have been put forward for the performance of analog-to-digital converters (bit accuracy, sampling rate, etc.). Signal processing systems such as broadband radar, electronic reconnaissance, electronic countermeasures, nuclear weapon monitoring, and spread spectrum communications all require high conversion rates of more than Gsps. For example, a phased array antenna ideally requires hundreds or even thousands of low-power analog-to-digital converters, typically each of which requires 100 MHz bandwidth and 16-bit accuracy. Although these devices may only account for a small part of the entire system, they may be the bottleneck factor affecting the performance of the entire system [5] . On the other hand, the development of parallel computing structures and technologies has produced digital processors with 100GHz floating-point computing capabilities, but they cannot be fully utilized due to the limitations of ADC performance. If an analog-to-digital converter with a sampling rate , it can not only improve the performance of existing systems, but also have new application prospects. At present, there are three main types of analog-to-digital converters in terms of the technology used: electronic semiconductor analog-to-digital converters, superconducting material analog-to-digital converters, and optical analog-to-digital converters (OADCs). Superconducting materials require low temperature conditions, which greatly limits their application areas. At present, the most widely used is the electronic analog-to-digital converter, which has many advantages such as a wide range of applications, mature manufacturing technology, and low cost. However, in the field of high-performance analog-to-digital converters, it has inherent deficiencies. When the sampling rate is greater than 2 Msps, the sampling time is uncertain due to the influence of aperture jitter. The trend is that when the sampling rate doubles, its bit accuracy decreases by about 1 bit. In the past nearly 10 years, at a given sampling rate, the bit accuracy of electronic analog-to-digital converters has increased by an average of only 1.5 bits. At present, the fastest sampling rate that electronic analog-to-digital converters can achieve is 8 Gsps with an accuracy of 3 bits; at 8-bit accuracy, a sampling rate of 4 Gsps can be achieved. However, this is already close to its theoretical limit. Even if the sampling rate can be further increased, its corresponding bit accuracy will also decrease accordingly [1] . Therefore, in order to meet the requirements of practical applications, that is, sampling rates above 10 Gsps and having appropriate bit accuracy (above 4 bits), new breakthroughs must be sought. The use of optical analog-to-digital converter technology has become the development trend of high conversion rate and high bit accuracy analog-to-digital converters. 2. Main technical indicators of optical analog- to-digital converters Like other analog-to-digital converters, the main technical indicators of optical analog-to-digital converters include: stated resolution (expressed in the number of bits of the encoded binary digits N, usually represented by the number of bits), sampling rate (expressed in samples per second, samples/s or sps), signal-to-noise ratio (SNR), spurious-free dynamic range (SFDR, i.e., spurious-free dynamic range) and power consumption (P diss ), among which calibration accuracy and sampling rate are its main performance indicators. Another commonly used technical indicator of analog-to-digital converters is effective bit accuracy (Neff ) . Effective bit accuracy refers to how many bits of the output calibrated accuracy are actually effective. It can be expressed by the signal-to-noise ratio, and its conversion relationship is: 3. Research progress of optical analog-to-digital converters Optical analog-to-digital conversion technology was first proposed by S. Wright [2] et al. in 1974. Since then, there have been two mainstream research stages in terms of the technology used. The first was from the mid-to-late 1970s to the mid-1980s, mainly using integrated optical technology. Its main device forms were LiNbO3 waveguide Mach-Zehnder interferometer arrays, balanced bridge modulators, and channel optical waveguide Fabry-Perot modulator arrays. The second was from the early 1990s, by drawing on the technical solutions of time-division multiplexing and wavelength-division multiplexing in optical communications, and began to use optoelectronic hybrid time-division or wavelength-division analog-to-digital converters to reduce the required sampling rate through parallel processing. The optical analog-to-digital converter proposed by Wright applies the analog signal voltage V to the interdigital electrodes built on the electro-optical material substrate, and performs spatial periodic phase modulation on the wavefront of the laser beam passing through the substrate, resulting in different diffraction orders in the far field. By adjusting the zero-order and first-order thresholds, a 2-bit Green code output can be obtained, and the sign bit can be included by applying a third comparator. Compared with the subsequent schemes, this scheme is undoubtedly crude, but it has pioneered the optical analog-to-digital converter. The principles of using electro-optical modulators and photodetectors proposed by it are still applicable today. The analog-to-digital converter that really had a wide impact on the development of optical analog-to-digital converters was the analog-to-digital converter using the integrated optical Mach-Zehnder interferometer array proposed by Taylor in 1975 [3] , as shown in Figure 1.
It uses several integrated Mach-Zehnder interferometers to form an array. The analog voltage V to be digitized is applied to the electrodes of each modulator at the same time. The length of the electrode Ln changes according to the binary sequence (2n ) . When the laser with input intensity I0 passes through one of the modulators, the output light intensity In synthesized by the two arms changes due to interference. The change can be expressed as:
where ψn is the additional light phase difference between the two arms caused by the external voltage V; ψn
is the static phase difference between the two arms due to the asymmetry of the two arms. After the output light intensity of each modulator is received by the photodetector, it is compared with the same threshold voltage to quantize the light intensity value into a binary digital "0" or "1". Another way to use is to slightly change the design of the comparator array, including setting a fixed phase for some modulators to produce an output in Gray code format, the output form of which is shown in Figure 2. The reason for choosing Gray code is that it only produces a bit code change at each quantization level, unlike the shift binary code, which has multiple bit changes at some specific quantization levels.
φn in equation (2) can be expressed as
(  1/2) (the length of the electrode of the least significant bit). Thus, when the bit number increases, the half-wave voltage quickly decreases to the extent that can be achieved by the process level, which is also a major aspect that limits the improvement of the bit accuracy of optical analog-to-digital converters.
Tayler's scheme is simple in form and can directly generate Gray code output, and all devices can be integrated on a chip in principle. One of the devices using this scheme achieved a sampling rate of 1 GHz, 4-bit code conversion, and a signal bandwidth of 500 MHz [4] . However, a basic limitation of this scheme is that the length of the modulator electrode of the least significant bit needs to be doubled for each additional bit. Taking LiNbO3 as an example, when its effective bit number is 6 bits, the limitation of the transit time makes its sampling rate about 1 GHz [5] . In addition, as the number of bits increases, the number of Y splitters also increases accordingly, which will lead to an increase in the total insertion loss, which also limits the improvement of bit accuracy.
The balanced bridge optical analog-to-digital converter uses a 3 dB coupler instead of a Y-branch waveguide [6] (see Figure 3) to reduce transmission loss. Moreover, since the two input ends of the comparator after the modulator are subjected to the same action, even if the intensity of the light source fluctuates, it will not cause obvious conversion errors. However, the structure is more demanding in terms of process, and compared with the Mach-Zehnder type analog-to-digital converter, it requires twice as many comparators.
The channel optical waveguide Fabry-Perot modulator [7] (see Figure 4) does not require the production of complex Y-branch waveguides, but only requires the production of straight channel waveguides, avoiding technical complexity and reducing the total length of the device, thereby reducing optical insertion loss. However, each bit requires a laser, which affects its bit improvement. 
上述2种器件都是由Taylor的方案改进、演化而来，从原理上来说，它们都依然摆脱不了半波电压带来的限制，总的说来性能也没有能够超过Mach－Zehnder型的光学模数转换器的性能限制。但Taylor提出的方案具有很深远的影响，进入90年代以后，还有人对其进一步加以改进，以期能提高它的性能。这里值得一提的有2种方法。一种方法提出了一种对称数字系统［8］，其核心思想是通过增加少量比较器，得到多个不同的量化级，从而显著的增加了比特精度，其编码方案如图5所示。该方法采用3个干涉仪，39个比较器，可实现 11 bit的精度。但这种方法提高的是标称精度，对有效比特位提高远不如标称精度那么大。另一种方法通过优化波导的设计，提出了一种光学folding－ flash模数转换器［9］，免除了每增加一个比特位，就需要增加电极长度一倍的限制，其波导设计如图6所示。但是其Y分支波导 图6 光学folding－flash模数转换器示意图的设计无疑将更加复杂。上述2种方法各有其限制，但其思想方法还是很值得我们借鉴的。总的说来，对第一代光学模数转换器的研究，在进入90年代以后，已基本趋于停滞。这里一方面是由于第一代光学模数转换器本身原理上的限制，另一方面也是由于电子模数转换器的进一步发展，其性能已经超过了第一代光学模数转换器所能达到的水平。 
In the 1990s, people were faced with such a situation: on the one hand, the analog-to-digital converter was still the bottleneck factor for further improving the performance of many systems, and on the other hand, the performance of electronic analog-to-digital converters and the first generation of optical analog-to-digital converters could not meet the requirements. This forced people to actively seek new analog-to-digital converter technology. At this time, the gradual maturity of optical communication technology and its rapid development provided people with new ideas for the development of optical analog-to-digital converter technology. People began to learn from time division multiplexing and wavelength division multiplexing methods in optical communication, using the high speed and high time accuracy of lasers for sampling, and using the multiplexing devices of optical communication to parallelize the sampled signals to reduce the high speed required for quantization. Most of these solutions are combined with electronic technology in the device, and electronic analog-to-digital converters are used for post-quantization processing. Two relatively simple solutions were proposed earlier. The first one is to use the technology of time division multiplexing, use the high repetition rate pulses of the mode-locked laser to sample the electrical signal through the modulator, and perform optical time division multiplexing through the optical switch, distribute the signals at different time sequences to different optical paths, and after photoelectric conversion, quantize them through the electronic analog-to-digital converter [10, 11] (as shown in Figure 7). The second method is to use multiple lasers, and by precisely controlling the timing of each different laser pulse, let the laser pulses of each wavelength sample the analog signal in turn, and then after wavelength division multiplexing, distribute the sampling signals of different wavelengths to different optical paths, and the subsequent processing is the same as the multiplexing [12, 13] (as shown in Figure 8). Both of these analog-to-digital converters have higher sampling speed and bit accuracy than the first-generation optical analog-to-digital converters, but both schemes require complex and accurate timing devices, which undoubtedly increases the complexity of the system. In addition, the increase in the sampling rate of the time division multiplexing scheme also depends on the increase in the rate of the optical switch, and the improvement in the bit accuracy of the wavelength division multiplexing scheme is at the expense of increasing the number of lasers. These are the bottleneck factors that limit the performance improvement of these two schemes. 
Based on the above two schemes, people continued to carry out research and proposed an analog-to-digital converter based on optical delay, which absorbs the advantages of the above two schemes and eliminates the complex timing circuit. One of the implementation schemes is shown in Figure 9. It uses a supercontinuum wide-spectrum EDFL fiber laser (spectral width of tens of nanometers, pulse width of sub-picoseconds, and repetition rate of about gigahertz). After being transmitted through a section of optical fiber, it first passes through a polarization beam splitter (PBS), and then passes through a WDM device to split it into several wavelengths. After each wavelength passes through a polarization-maintaining fiber of different lengths, the light of each wavelength is reflected back by a Faraday mirror. After passing through WDM and polarization beam splitter again, a pulse sequence containing different wavelengths of light is synthesized. The RF signal is sampled through a modulator. The sampled pulse sequence passes through another WDM device and is distributed to different optical paths according to wavelength, realizing parallel processing [14] . A device using this scheme has achieved a sampling rate of 18 Gsps and a sampling accuracy of 7 bits [15] . 
相对于国外光学模数转换器的飞速发展，国内在光学模数转换器领域的研究起步较晚，在80年代末期才开始这一方面的研究。上海交通大学应用物理系在90年代初期对Mach－Zehnder型集成光学模数转换器做了研究［16］，沈阳工业学院和中科院长春物理研究所合作在1994年研制了LiNbO3质子交换光波导Fabry－Perot型4位电光模数转换器［17］。目前国内尚未有对第二阶段的光学模数转换器进行研究。
四、光学模数转换器的应用
光学模数转换器在许多方面有着重要应用，目前对光学模数转换器的研究，主要集中在需要高速信息采集处理的系统中的应用上，其中最主要的应用是微波数字雷达。众所周知，现在的微波数字接收器要求将接收到的模拟信号经过几步的混频和滤波，以将信号频率降到电子模数转换器的基带范围内，这一过程不仅昂贵，而且又限制了系统的可靠性和瞬时带宽，同时也增加了系统的尺寸和重量。另外，每一次的混频过程，都会带来信号的失真，增加电磁干扰。如果能研制出一个高速、高动态范围的的模数转换器，使其能够直接对射频信号进行数字化，这样就会极大地改善数字接收器的性能。据《简氏国际防务评论》1998年6月报道：美国国防高级研究计划局计划在今后4年中在“光电模－数转换器技术”上花费约4 000万美元，其目的是提供能处理高达1 000 Gsps采样速率的装置。“光电模－数转换器”计划的目的是通过应用先进的光电部件（例如激光器、调制器、探测器以及微电子和光电子器件）来克服过去采用的电子电路的局限性。这将允许在军事系统感兴趣的整个频谱范围内在信号源处对信号进行直接的模－数转换，从而在以下几方面获得性能改进：改进数字波形成形以抑制干扰；具有较宽的动态范围以便探测杂波中的目标；具有较宽的瞬时带宽以便改进对目标的识别，例如，当采样速率达到1 000 Gsps时，可能会产生对毫米波信号进行直接宽带模－数转换的新能力。
五、结 语
光学模数转换器技术除了上述提到的主流技术外，还有着各种各样的非主流和辅助技术，如采用SEED的光学模数转换器［18］、采用声光热调制的光学模数转换器［19］和利用光学过采样技术（∑Δ技术）［20］以提高模数转换器的有效比特精度等等。这些技术的存在，一方面说明了光学模数转换技术还处于探索阶段，是一种还没有真正成熟的技术，另一方面也说明了光学模数转换器具有广阔的研究前景。从光学模数转换器的发展趋势来看，系统趋于复杂，要实现现采样速率超过100 Gsps的实用模数转换器还要依靠器件及材料上有新的突破。 ［1］ Robert H．Walden．Analog－to－Digital converter surveyand analysis［J］．IEEEJ．on selected areas in communica－tion，1999，Vol．17，No．4，539～550．
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