Variable Bit-Width All-Optical Content-Addressable Memory Enabled by Sb2Se3 for Similarity Search

1. Introduction

In the artificial intelligence era, the explosive growth of big data has established similarity search as a fundamental task across machine learning, recommendation systems, and data mining. This imposes increasingly stringent demands not only on processing speed and energy efficiency, but also on adaptability to diverse application scenarios [1,2]. The core operation of similarity search involves calculating the distance (or similarity) between a search vector and all vectors stored in memory. Conventional memory systems rely on address-based access, necessitating sequential data retrieval and subsequent computation. In contrast, CAMs offer a parallel search mechanism by comparing the input search vector against all stored entries simultaneously and returning the address of any matching content, thereby significantly accelerating search operations and improving energy efficiency [3,4,5,6,7]. The underlying matching operation in CAMs is typically based on calculating the Hamming distance between binary vectors, and numerous studies have implemented similarity search using electronic CAMs [8,9,10,11,12,13,14,15,16,17]. However, electronic CAMs face an inevitable bottleneck: resistance-capacitance (RC) delay severely constrains their operating speed [18].

Optical computing has emerged as a promising alternative to electronic computing due to its inherent high speed, low power consumption, and parallel processing capabilities [19,20,21]. Several optical CAMs (OCAMs) utilizing photonic matching structures have been proposed to overcome the limitations of electronic CAMs. For instance, OCAMs employing InP-based flip-flops for data loading and SOA-MZI-based XOR gates for bitwise comparison have been demonstrated [22,23,24]. Another common approach exploits the resonant states of microring resonators for matching [25,26,27]: transmission is suppressed when the input wavelength aligns with the ring’s resonance, whereas a detuned state allows light to pass through. By performing the matching operation directly in the optical domain, such OCAMs can achieve search rates up to 10 Gb/s. A critical limitation, however, is that they still rely on electronic memory, imposing an additional energy overhead to maintain the stored data state on optical devices during queries.

Non-volatile phase-change materials (PCMs) offer a promising solution to this problem. PCMs exhibit reversible phase transitions between amorphous and crystalline states, accompanied by a significant contrast in both the refractive indices (n) and extinction coefficients (k). This property has enabled their use in optical memories and photonic in-memory computing [28,29,30,31]. Recently, all-optical CAMs with non-volatile optical storage have been realized using Ge₂Sb₂Te₅ (GST), a representative PCM, -based microring resonators [32] and MZIs [33], respectively. Notably, all existing OCAMs perform bit-wise matching, which ensures matching precision but lacks the flexibility required for diverse tasks. For example, routing lookups [34] demands exact matching, whereas recommendation systems [35] can tolerate approximate results. Bioinformatics applications like DNA classification [14] rely on Hamming distance calculation for binary data, while other tasks (e.g., iris recognition) involve continuous data and may require various distance metrics, including Hamming, Manhattan, and Euclidean distances. Furthermore, most existing OCAMs typically output only the Hamming distance, offering limited functional versatility.

In this work, we propose and demonstrate a variable bit-width all-optical CAM architecture based on MZIs and the low-loss Sb₂Se₃. Sb₂Se₃ exhibits an ultra-low extinction coefficient (k<10^-5) across the telecommunications transmission band, making it highly suitable for low-loss photonic device [36]. By integrating multiple independently programmable Sb₂Se₃ segments and phase shifters on the arms of an MZI, the system can adaptively trade off matching precision against storage capacity, while also supporting enhanced functional flexibility. The similarity between the search and stored data is encoded in the output optical power of the MZI. We designed and fabricated a 6-element, 3-bit OCAM on a SiN-SOI platform, experimentally validating its matching functionality and further demonstrating through simulations its applicability to kNN classification across multiple datasets.

2. Principle

The design philosophy of this study is to compress the data that would otherwise occupy multiple binary memory units into a single analog unit. Meanwhile, the direct writing and loading of binary data are realized via multi-segment memory and modulation technology, without the need for any additional configuration of digital-to-analog converter (DAC) hardware. As shown in Figure 1(a), the multi-segment memory unit (MSMU) is based on an MZI, consisting of a beam splitter, a directional coupler, and two optical waveguides (arms) between them. Each arm is integrated with Sb₂Se₃ cells and phase shifters, divided into N segments. In the i-th segment ($0\le i\le N-1$ ), there are $2^i$ Sb₂Se₃ cells dedicated to storing the i-th bit of the N-bit data $x:x^{\left[0\right]}{x}^{\left[1\right]}\dots x^{[N-2]}{x}^{[N-1]}$. Correspondingly, the phase shifter length is $2^i{L}_0$ for loading the i-th bit of the N-bit search data, where $L_0$ is the minimum length of the phase shifter. Moreover, the phase shift generated by the phase shifter with length $L_0$ is equal to that generated by a single Sb₂Se₃ cell, denoted as $\Delta {\phi }_0$.

The output optical power of the MZI is determined by the phase difference between the two arms, following the interference formula:

$$P_{out}={\displaystyle \frac{P_{in}}{2}}[1\pm cos\left(\sum _{i=0}^{N-1}(x^{\left[i\right]}-s^{\left[i\right]})2^i\Delta {\phi }_0\right)]$$

(1)

where $P_{in}$ is the input optical power. When the stored data x matches the search data s, the output optical power reaches maximum/minimum; the lower the similarity, the larger the deviation from matching extremum. To ensure an accurate mapping relationship, the total phase shift must not exceed $\pi$ (i.e., $\Delta \Phi \in [-\pi ,\pi ]$). By adjusting the number of Sb₂Se₃ cells and phase shifter length in each segment, binary numbers are weight-mapped to phase shifts according to bit significance, enabling analog subtraction. Note that the mapping of binary data (0 and 1) depends on the implementation of the phase shifter in the search arm: for example, the refractive index increases with temperature in thermo-optic effects but decreases with voltage in electro-optic effects, resulting in inverted data mapping. Combining the output ports of M MSMUs enables searching match and similarity calculation for M-element N-bit vectors as shown in Figure 1(b).

Notably, while previous studies used GST for non-volatile OCAMs, it is unsuitable for this device. As mentioned earlier, GST exhibits a non-negligible, state-dependent extinction coefficient, meaning the MZI output power is simultaneously affected by phase difference and loss variations. This complicates establishing an accurate mapping between output power and data similarity for multi-segment configurations. Although storing and searching data via GST is a potential solution, the search speed is limited by GST’s switching speed ( 100 ns), and significant loss restricts the number of segments. In contrast, Sb₂Se₃’s ultra-low extinction coefficient makes it an excellent choice for non-volatile reconfigurable phase tuning, and it has been widely used in various reconfigurable photonic devices [37,38,39,40,41,42].

Obviously, the greater the number of segments, the smaller the step sizes between output power levels, the lower the noise immunity, and the higher the memory capacity. Thus, for precision-sensitive matching or similarity calculation tasks, data can be distributed across multiple MSMUs to reduce the bit-width per MSMU, thereby improving precision, as shown in Figure 2(a). Prioritizing high-bit segments when reducing the bit-width increases the step size between levels. In the extreme case, 1-bit operation can be achieved, which is consistent with previous studies. Alternatively, it is also feasible to employ more segments when operating at a low bit-width. For instance, all segments can be utilized at the 1-bit-width mode to fully exploit the extinction ratio of the Mach-Zehnder Interferometer (MZI). The advantage of this approach is that higher noise immunity can be achieved; however, driving N phase shifters simultaneously will lead to a significant increase in power consumption. This involves a trade-off between performance and power consumption when catering to different environmental and application requirements, and the subsequent work of this paper still adopts the configuration illustrated in Figure 2(a).

A more detailed illustration, taking the 3-bit-width and 1-bit-width as examples, is presented in Figure 2(b). For scalar search, the 3-bit-width mode can directly yield an analog nonlinear distance (NL-distance) via the MSMU, and is also capable of performing match search with a comparator to output a digital match state; in contrast, the 1-bit-width mode directly outputs the Hamming distance, while match search can be equally realized using a comparator. In addition, for vector search, the 3-bit-width mode enables separate aggregation of the two types of outputs derived from scalar search, thus yielding both the NL-distance and Hamming distance of the vector, whereas the 1-bit-width mode can only obtain the vector Hamming distance by summing the scalar match results.

3. Results and Discussion

3.1. Fabrication

A 6-MSMU optical CAM was designed and fabricated on a SiN-SOI platform [Figure 3(a)]. The silicon nitride single-mode waveguide has a width of 1000 nm and a thickness of 400 nm. After being split by a Y-junction waveguide, the input light undergoes interference in a 2×2 multimode interferometer (MMI). One of the output ports is connected to a 6×1 MMI for combining the output signals of other MSMUs, corresponding to Port A in Figure 2(b); the other port is routed directly to a grating coupler, which can be connected to a comparator following photoelectric conversion, corresponding to Port D in Figure 2(b). For the Sb₂Se₃ cells, the silica cladding above the waveguide was etched (oxide window opening), followed by deposition of a 30-nm-thick Sb₂Se₃ layer and a 10-nm-thick silica capping layer. Figure 3(b) shows a scanning electron microscope (SEM) image of the 6×1 MMI and oxide windows. Each cell has an oxide window size of 5 µm × 10 µm, in which Sb₂Se₃ is fully deposited. A total of 34 Sb₂Se₃ cells are integrated on each arm, with some used for data storage and others for initial state calibration and standby. Due to experimental constraints, optoelectronic phase shifters were not integrated; instead, Sb₂Se₃ cells were used as substitutes. The feasibility for high-speed multi-segment phase shifting has been validated in previous optical digital-to-analog converter (ODAC) studies [43,44,45].

3.2. Results

The experimental setup [Figure 3(c)] includes a multi-channel laser, an optical power meter and a spatial light focusing system (for controlling Sb₂Se₃ cells). The spatial light focusing system irradiates Sb₂Se₃ cells with 532-nm laser pulses (500 ms , ∼ 7mW) via an objective lens to switch their phase states [36]. Each irradiation is performed with only a single pulse.

To characterize the phase tuning capability of Sb₂Se₃ cells, a single arm of the MZI was tested [Figure 4(a)]. Sb₂Se₃ cells were irradiated sequentially; the sweep results show that 11 Sb₂Se₃ cells produce a phase shift exceeding $\pi$, limiting the maximum 3 bit width for subsequent experiments. We tested the Sb₂Se₃ cells on 6 MSMUs, and estimated the phase shift generated by each Sb₂Se₃ cell via curve fitting. Statistical results demonstrate that the Sb₂Se₃ cells exhibit favorable consistency, as shown in Figure 4(b). Next, the bit precision of MSMU was tested for 1-bit, 2-bit, and 3-bit configurations [Figure 4(c)]. Each level was measured 10 times with different devices, and the results confirm that stored data can be reliably identified even at 3 bits, although higher bit-widths exhibit reduced noise immunity and interference resistance.

We irradiated 1, 4, and 7 Sb₂Se₃ cells on one arm of each of the three MSMUs, corresponding to the stored data values of 1, 4, and 7 respectively. On the other arm, we sequentially irradiated 7 Sb₂Se₃ cells, scanned to obtain the NL-distances for different search values, and determined the matching status via threshold judgment. Figure 4(d) shows search results; although the output power for matching queries is close to that of adjacent values, reliable discrimination is still achievable.

As noted previously, the switching speed of Sb₂Se₃ cells is very slow (500 ms-width switching laser pulse), and the limited number of fabricated devices fails to meet the required dataset size. To validate the architecture’s performance in similarity search, kNN simulations were conducted based on statistical phase shift data of Sb₂Se₃ cells. In the simulations, the extinction ratio of the MZI was set to 20 dB, with random noise added when loading search data into the phase shifters. We implemented classification tasks via the kNN algorithm based on the iris, wine, and breast cancer datasets, respectively. As shown in Figure 5(a), to adapt to the work presented in this paper, the feature values of all data were quantized to 3 bits. Then, all datasets are randomly divided into a training set and a test set in a ratio of 7:3.

Based on the vector search depicted in Figure 2(b), we simulated three search results under the 1-bit-width and 3-bit-width modes, denoted as 1-bw HD, 3-bw HD and 3-bw NL respectively. To obtain more objective results, we scanned the k from 1 to 15, conducted 100 random tests for each configuration to derive the average accuracy, and then selected the optimal results from those corresponding to all k values. The relationship between the simulation results of the three datasets, the signal-to-noise ratio (SNR) applied to the phase shifters, as well as three theoretically calculated benchmarks are presented in Figure 5(b–d). It is evident that the Manhattan distance and Euclidean distance are more suitable for kNN than the Hamming distance. At relatively high SNR levels, 1-bw HD yields results consistent with the Hamming distance, and the same applies to 3-bw HD, while the latter imposes a higher requirement on SNR. In contrast, 3-bw NL is closer to the Manhattan distance and Euclidean distance, which achieve higher accuracy—or more precisely, closer to the Euclidean distance (pronounced in the wine dataset). This may be attributed to the fact that both the NL-distance and Euclidean distance exhibit concave curves in the near-zero interval. At relatively low SNR levels, 1-bw HD outperforms 3-bw HD by a significant margin, which is consistent with the noise immunity characteristics analyzed earlier. However, 3-bw NL, which also has poor noise resistance, exhibits mixed performance relative to 1-bw HD across different datasets, a phenomenon that may benefit from its adoption of a more suitable distance function.

The above experimental results indicate that storing multi-bit information in a single MSMU improves memory capacity, or equivalently memory density, at the cost of certain noise immunity and computational accuracy. However, in scenarios with high SNR or in applications with error tolerance such as kNN, the obtained results can be comparable to those of the theoretical distance algorithm. Therefore, we can perform flexible configuration according to different operating environments and application scenarios to achieve a trade-off between noise immunity and memory capacity, as well as the selection of different distance functions.

3.3. Energy estimation

Considering the trade-off between search speed and energy consumption, and with reference to the general performance of existing OCAMs, the phase shifter speed is set to 10 Gb/s, which is much lower than the limit speed of the optical digital-to-analog converter (ODAC) [45]. The system energy consumption is evaluated under the above conditions. The total power consumption is given by:

$$P_{total}={\displaystyle \frac{M·P_{in}}{WPE}}+M·P_{PS}+P_{PD}$$

(2)

where $P_{in}$ is the input optical power, WPE is the wall-plug efficiency of laser source, and $P_{PS}$ and $P_{PD}$, are the power consumptions of the phase shifter and photodetector, respectively. Assuming an MZI extinction ratio of 20 dB and a photodetector sensitivity of -25 dBm [46], the minimum $P_{in}$ is 0.32 mW with a WPE of 16% [47]. Ref. [48] demonstrated a PN silicon-based MZI with a $V_{\pi }L$ of 0.07 V·cm. To avoid crosstalk between the phase shifters and Sb₂Se₃ cells, it is assumed that each MSMU employs a single-arm phase shifter with a total length of 1 mm, yielding a $V_{\pi }$ of 1.4 V. The operating voltage of the i-th phase shifter segment is thus given by $V_i=V_{\pi }·2^i/(2^N-1)$ V. Under the conditions of uniform data distribution (equal numbers of 0 and 1) and a resistance of 50 $\Omega$, the power consumption is calculated as $P_i=V_i^2/100$ W. The $P_{PD}$ is set to 3 mW [46]. For the structure fabricated in this work where $M=6$ and $N=3$, the power consumption values are 364 fJ/bit and 890 fJ/bit for the 3-bit-width and 1-bit-width modes, respectively. In comparison, a recently demonstrated O-TCAM based on a heterogeneous III-V/Si microrings exhibits an energy consumption of 703 fJ/bit [49]. It is evident that the impact of M on the energy consumption per bit is only reflected in the PD, and the $P_{PD}$ is relatively low. Therefore, we only evaluate the impact of the bit-width N on power consumption, as illustrated in Figure 6, where the deep color blocks represent the N-bit-width mode and the light blocks represent the 1-bit-width mode. Notably, the power consumption of the phase shifters, which accounts for the largest proportion, decreases with the increase of N, since the multi-segment electrodes share the $V_{\pi }$.

3.4. Discussion

Despite discrepancies between the fabricated device and the target design, the experiments validate the feasibility of the proposed architecture. However, it also has to address other challenges. Currently, phase shifters generally have relatively long lengths, and the multi-segment structure requires additional consideration of crosstalk effects, resulting in low integration density. As the bit-width increases, the number of required Sb₂Se₃ cells grows exponentially, and errors caused by the randomness of state switching accumulate accordingly. Furthermore, the nonlinearity of MZIs makes precise matching more challenging due to noise and randomness, which is more pronounced at high bit-widths. Three feasible optimization directions are identified:

1.

Reducing footprint and energy consumption. Indium Tin Oxide (ITO) is a promising active material that enables high refractive index modulation. Ref. [50] demonstrated a heterogeneously integrated ITO plasmonic MZI modulator on an SOI platform, whose experimental characterization revealed that a $\pi$ phase shift is achievable with a device length on the micrometer scale, alongside an ultra-low $V_{\pi }L$ of 95 V·µm. Furthermore, Ref. [51] demonstrated the 100 GHz modulation capability of an ITO-based MZI.

2.

Improving noise immunity. Due to the presence of noise, MZI nonlinearity poses challenges for high bit-width operations, particularly near matching conditions where adjacent levels are closely spaced. Previous work [52] demonstrated that optimizing phase shifter lengths and control vectors can eliminate nonlinearity and improve ODAC bit-width, which is applicable to this architecture.

3.

Reducing randomness. For the study reported in this paper, the 5-µm-wide Sb₂Se₃ cells utilized in experiments are of overly large dimensions. A phase shift close to $\pi /2$ would be induced by the complete crystallization of the whole cell. As a result, only a small localized area within the cell was subjected to partial crystallization via a single pulse, which introduced non-negligible randomness to the experimental data. The adoption of Sb₂Se₃ cells with reduced dimensions is anticipated to diminish randomness through full crystallization, while simultaneously facilitating higher-precision phase tuning and enabling support for larger bit-widths.

4. Conclusions

This work proposes and demonstrates a variable bit-width all-optical CAM based on MZIs and Sb₂Se₃, addressing the limitations of conventional optical and electronic CAMs such as fixed bit-widths and limited functionality. The core multi-segment memory unit (MSMU) compresses multi-bit binary data into a single analog unit, enabling direct data writing/loading without digital-to-analog converters, flexible bit-width adjustment, and support for both Hamming distance and NL-distance calculations. Experimental validation of a 6-element 3-bit OCAM fabricated on a SiN-SOI platform confirms reliable matching performance, while kNN simulations on iris, wine, and breast cancer datasets demonstrate that the 3-bit-width mode achieves accuracy comparable to Manhattan and Euclidean distances under high SNR, and the 1-bit-width mode offers robust noise immunity. Energy estimation shows superior efficiency (364 fJ/bit for 3-bit-width) compared to state-of-the-art OCAMs. Despite challenges including low integration density, Sb₂Se₃ state switching randomness, and MZI nonlinearity, future optimizations using ITO phase shifters, phase parameter tuning, and miniaturized Sb₂Se₃ cells are promising. This work provides a flexible, high-density, and energy-efficient solution for all-optical similarity search, with broad potential in big data analytics and artificial intelligence applications.