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Abstract
Artificial neural networks (ANN) are a groundbreaking technology massively employed in a plethora of fields. Currently, ANNs are mostly implemented through electronic digital computers, but analog photonic implementations are very interesting mainly because of low power consumption and high bandwidth. We recently demonstrated a photonic neuromorphic computing system based on frequency multiplexing that executes ANNs algorithms as reservoir computing and Extreme Learning Machines. Neuron signals are encoded in the amplitude of the lines of a frequency comb, and neuron interconnections are realized through frequency-domain interference. Here we present an integrated programmable spectral filter designed to manipulate the optical frequency comb in our frequency multiplexing neuromorphic computing platform. The programmable filter controls the attenuation of 16 independent wavelength channels with a 20 GHz spacing. We discuss the design and the results of the chip characterization, and we preliminary demonstrate, through a numerical simulation, that the produced chip is suitable for the envisioned neuromorphic computing application.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
We present an integrated programmable spectral filter designed to manipulate an optical frequency comb in the C-band. The foreseen application for the filter is a neuromorphic computing platform based on wavelength multiplexing. Such a platform has been demonstrated in fiber optics, implementing both an Extreme Learning Machine (i.e., a feed-forward neural network) [1] and a reservoir computer (i.e., a recurrent neural network) [2]. Neuron signals are encoded in the lines of an optical frequency comb, and the neuron interconnections are realized through frequency-domain interference, achieved, e.g., via phase modulation. The spacing of comb lines in the above-mentioned experimental implementation is approximately $20$ GHz. The data processing speed is currently bounded by the presence of bench-top elements, such as an LCD-based programmable spectral filter and a meters-long fiber loop. These limitations could be lifted by photonic integration. In this scenario, the integrated programmable spectral filter could be applied both to encode input information and to apply output weights. We remark that, in addition to our platform, other wavelength-multiplexing schemes for computation have been proposed (see, e.g., [3–7]).
Standard filtering architectures, such as the ones based on echelle gratings [8], arrayed waveguide gratings [9,10], and ring resonators [11,12], are not suitable for applications requiring a channel density as high as our wavelength multiplexing platform. Therefore, we adopted an approach based on cascaded interleaved lattice filters [13].
This paper is organized as follows. In Sec. 2 we describe the overall design and its building blocks; in Sec. 3 we discuss essential fabrication features; in Sec. 4 we present and discuss the characterization of the programmable filter, with references to the effect of the fabrication imperfections on the performance of the neuromorphic application; in Sec. 5 we describe the outlook of our work and report our conclusions.
2. Design and functionalities
We present an integrated programmable spectral filter designed to manipulate information in a neuromorphic computing system based on wavelength-multiplexing [1,2]. The channels of this computing platform are generated by phase modulating a continuous wave laser radiation, thus generating a frequency comb whose lines encode the neuronal information. The designed filter does not require active spectral alignment because the spectral position of the comb can be matched with the filter by tuning the laser wavelength. The demonstrator that we realized provides an output layer with programmable attenuation on $16$ independent channels, with a spacing of $20$ GHz. These characteristics are sufficient for a proof-of-concept application on our wavelength-multiplexing neuromorphic computing platform. Scalability is discussed in Sec. 5.
The principle of operation of the programmable spectral filter is schematized in Fig. 1(a). The design is composed of three stages. First, a wavelength de-multiplexer stage separates each channel; second, an attenuation stage composed of $16$ individually addressable attenuators that weight each comb line; third, a wavelength multiplexer stage, symmetric to the de-multiplexer, that recombines the signals into a single output channel.
Fig. 1. (a) Conceptual scheme of the programmable spectral filter. From left to right, the device is composed of a 1-to-16 wavelength demultiplexer, an array of 16 attenuators, and a 16-to-1 wavelength multiplexer. (b) Detail of the demultiplexer architecture. The multiplexer is obtained by the same design upon vertical mirroring. The (de)multiplexer is composed of 15 lattice filters organized in a 4-stages binary tree. The transfer functions of the lattice filters are engineered in such a way to obtain (de)multiplexing behaviour.
The quality of the (de)-multiplexer stages is crucial for a correct operation, as it impacts the quality of the output signal. We outlined four specific goals to consider when developing the (de)-multiplexer: (1) minimal and uniform losses across the 16 channels; (2) flat-top transmission function to improve temperature drift tolerance; (3) high extinction ratio for an efficient weighting process; and (4) limited use of active alignment in the (de)multiplexing stages to simplify the design and reduce power consumption. Figure 1(b) reports the layout of the 1-to-16 channels wavelength de-multiplexer. The de-multiplexer consists of 15 lattice filters organized in a 4-stage binary tree. In general, a 1-to-$N$ de-multiplexer would be composed of $N-1$ lattice filters organized in $\log _2(N)$ stages. The 16-to-1 channel multiplexer is obtained by mirroring the design of the de-multiplexer. The (de)multiplexer functionality relies on the proper tuning of the lattice filters, which are required to be correctly coordinated and collectively act as a series of cascaded de-interleaving wavelength splitters. All the filters, excluding the first stage, are constituted by two multimode interference couplers (MMI) and an optical delay line which introduces a difference of optical path, $\Delta L$, among the two arms (see stages ’2nd’, ’3rd’ and ’4th’ in Fig. 1(b)). The lattice filter in the first stage has the biggest influence on the (de)multiplexing performance. Hence, it is realized through a more complex design involving three MMIs and two optical delay lines (see stage ’1st’ in Fig. 1(b)). This more complex design assures a flatter transfer function [14]. The MMI splitting ratios of the first stage lattice filter are $k_1=0.5$, $k_2=0.71$ and $k_3=0.92$, the splitting ratio of the other MMIs are $k_1=0.5$. The optical path difference, $\Delta L$, defines both the lattice filter free spectral ranges and the relative positioning of their transfer functions. In the following, we briefly report a summary of the design procedure, although similar lattice-filter-based systems are described exhaustively in the literature (e.g., in [15,16]).
We define $\Delta L_\text {base}$ as the optical path difference required to achieve a transfer function that separates two consecutive channels:
where $\lambda$ is the intended central frequency, $\Delta \lambda$ is the channel spacing and $n_\text {g}$ is the waveguide group index. Every stage of the binary tree architecture is required to have a channel spacing doubled with respect to the channel spacing of the previous stage, meaning that the optical path difference $\Delta L$ decreases as the stage index increases. In addition, the transfer functions of each lattice filter need to be properly shifted in such a way as to correctly interleave with the other ones. We define $\Delta L_\text {FS}$ as the optical path difference required to achieve a full free-spectral-range shift in the transfer function: where ${n_\text {eff}}$ is the effective index of the optical propagating mode. In summary, the required difference in optical paths for each lattice filter is expressed as the sum of two contributions: a first one, $\Delta L_\text {FSR}$ defining the wavelength separation provided by the filter, and a (smaller) second one, $\Delta L_\text {shift}$ defining the shift in its transfer function: where, for convenience, $\Delta L_\text {FSR}$ is expressed as a fraction of $\Delta L_\text {base}$, while $\Delta L_\text {shift}$ is expressed as a fraction of $\Delta L_\text {FS}$. The values of these parameters are reported in Table 1.
Table 1. Parameters defining the difference in optical path required by each lattice filter. The overall difference in the optical path for each filter is the sum $\Delta _\text {FSR} + \Delta _\text {shift}$. $\Delta _\text {FSR}$ defines the free spectral range of the transmission function, while $\Delta _\text {shift}$ is a smaller quantity necessary to shift the transmission function in order to obtain the required interleaving among lattice filters.
The MMI couplers in the first stage lattice filter, $k_2$ (71:29) and $k_3$ (92:08) are not common and require an ad-hoc design. Similarly to what was proposed in [17,18], we adopted a technique consisting in optimizing the tapering, up or down, of a canonical MMI body in order to achieve the desired splitting ratio. Exhaustive experimental research based on submicron silicon waveguides was recently reported by Doménech et al. [19], while the notion of tapering a MMI to vary its splitting ratio was first proposed by Besse et al. [20]. Figure 2 reports the experimental characterization of the non-canonical MMIs obtained through this technique. The 71:29 MMI exhibits excess losses of approximately 0.31 dB, with an absolute maximum deviation of 0.28 dB for the cross-state and 0.12 dB for the bar state. The 92:08 MMI, exhibits excess losses of approximately 0.28 dB, with an absolute maximum deviation of 0.51 dB for the cross-state and 0.05 dB for the bar state. We remark that adiabatic couplers [21] can exceed MMIs in terms of broadband operation and tolerance to manufacturing changes, but have been discarded for considerations based on footprint occupations.
Fig. 2. Experimentally measured splitting ratio of the tapered MMIs over the C-band. The horizontal lines in magenta indicate the expected transmissions for each channel.
The attenuation stage is composed of 16 Mach-Zehnder interferometers. Each interferometer contains a thermo-optical phase shifter on one arm allowing to modulate the transmission. The design for the thermo-optical phase shifter is the one offered in the AMF passive project design kit [22] (see also the review of thermo-optic phase shifters based on silicon-on-insulator [23]). The concentration of so many thermal actuators could induce undesirable thermal crosstalk, meaning that the attenuation setting of a channel could influence the other ones. To reduce this risk, the thermo-optic elements are positioned in a "zig-zag" fashion (see Fig. 3(a)). The design is such that the distance between an actuator and the neighboring one is always greater than 200 $\mu$m. In the envisioned application, the desired attenuations (e.g., the weights to apply to neuronal signals) will be set by acting on the electrical currents flowing in the thermo-optical phase shifters. This requires each Mach-Zehnder modulator to be characterized to establish correspondences between electrical currents and attenuations. More information about the characterization is reported in Sec. 4.
Fig. 3. (a) Top view of the programmable spectral filter. The green boxes indicate the (de)multiplexer stages; the red box indicates the attenuator stage. (b) Detail of a lattice filter. (c) and (d) detail of the non-canonical MMIs having 92:08 and 71:29 splitting ratios respectively.
3. Chip fabrication
We identified Silicon Photonics as the most suited platform to implement our design, due to the availability of reliable components, CMOS compatibility, and small footprint. In particular, concerning footprints, we note that the high bending radius of InP would severely hinder the realization of the long delay lines required to achieve the (de)-multiplexing functionality we need. The chip has been fabricated by Advanced Micro Foundry [24] (AMF) in Singapore, in a multi-project wafer run on a silicon-on-insulator platform. The standard process offers $193$ nm deep UV lithography for waveguides, enabling features down to approximately $140$ nm. Every waveguide on the chip has a nominal width of $500$ nm and a nominal thickness of $220$ nm.
Figure 3 reports multiple pictures of the chip. Figure 3(a) is an overall view, comprehending both the (de)multiplexers and the attenuation stages. The top-right of these pictures contains the optical I/O, which are the AMF suspended couplers. Couplers 1 and 2 are ancillary couplers, connected to each other with the sole purpose of facilitating the alignment with a fiber array. The unnumbered coupler (on the right) does not belong to this design. Figure 3(b) is a detail of the 1st stage of the demultiplexer filter. Figure 3(c) and Fig. 3(d) are details of the two non-canonical MMIs, with splitting ratios of 91:08 and 71:29, respectively. The total footprint of the circuit is $5.8x2.8 \text {mm}^2$.
4. Experimental verification
The characterization of the chip consists of the measurement, for each channel, of the insertion loss (i.e., the minimum attenuation), and of the extinction ratio (i.e., the maximum attenuation), while individually scanning, one by one, the currents driving the attenuators. The experimental setup for the characterization of the chip is reported in Fig. 4. The setup is composed of a C + L Band ASE Broadband light source (Connet model VASS-CL-B-100-SM), the device under test, an optical spectrum analyzer (YOKOGAWA AQ6370D), a multi-contact probe and a breakout board to ease the mapping from the probe towards the current source. The heaters that control the attenuators have been driven by a programmable current source (KEITHLEY model 2400). The driving current of each attenuator has been swept in the range [$0\text { mA, }5\text { mA}]$ with a step size of $100\text { }\mu \text {A}$. The output spectrum has been measured with a resolution of $20\text { }\text {pm}$.
Fig. 4. Scheme of the experimental characterization setup. broadband light source; DUT: device under test; OSA: optical spectrum analyzer; breakout board; DC current source.
Figure 5 reports a map of the attenuators crosstalk, i.e., a map summarizing the effects of every attenuator on every channel. Off-diagonal elements represent undesired crosstalks among channels. The average of the crosstalk is $0.57$ dB, which is negligible for our application. The crosstalk is mainly generated by thermal diffusion on chip, meaning that the heat generated to activate a certain attenuator may influence a neighboring attenuator.
Fig. 5. Crosstalk map of the programmable spectral filter. The map reports the extinction ratio evaluated on the ’measured channel’ while sweeping the attenuation of the ’modulated channel’. The average off-diagonal extinction ratio is $0.57$ dB.
Figure 6(a) reports the modulated transmission spectra over the full programmable spectral filter free spectral range, containing 16 channels. In particular, the plot is the result of the union of the individually modulated single channel cropped around the channel bandwidth. Table 2 summarizes insertion losses and extinction ratio for each channel. The average insertion loss is $12.5$ dB; the average extinction ratio is $14.9$ dB. For comparison, we note that the LCD-based programmable spectral filter currently employed in our neuromorphic computer experimental setup is a Coherent II-VI Waveshaper, whose insertion loss can nominally reach $7$ dB.
Fig. 6. (a) Measured transmission function of the spectral filter. The 16 channels $(\lambda _1,\,\lambda _2,\,\ldots,\,\lambda _{16})$ are marked on the top of the figure. The transmission spectrum of each channel has been measured multiple times sweeping the attenuation in 24 steps. (b) Channel transmission as a function of the attenuator driving current. The shown data refers to the first channel. (c) Two simulations of the transmission function of the spectral filter. The first simulation (black line) accounts only for the attenuation introduced by the waveguides and all the other components. The second simulation (red line) also accounts for the losses caused by transfer functions misalignment, which are caused by fluctuations of the modal effective index due to fabrication deviations.
Table 2. Experimentally measured insertion losses and extinction ratios for the 16 channels of the integrated programmable spectral filter.
We identify two contributions to the insertion losses, which also explain the relatively high variability among channels. The first contribution comes from the attenuation introduced by the long waveguides and by the many MMIs. We estimate this contribution to be around $\sim$5 dB, and almost constant for each channel. The second contribution comes from misalignment in the transmission functions of the 30 lattice filters. We argue that this last contribution is due to fabrication errors. Indeed, fluctuations in the fabrication process can cause local deviations of the cross-section from the nominal value, which results in the perturbation of optical modes during the propagation. This effect influences the effective index of refraction and consequently changes the optical paths, making the lattice filter transfer function deviate from the ideal designs. As reported in [25], the fluctuations in the fabrication process can be modeled as zero-mean Gaussian distributions. Experimentally measured fluctuations in waveguide characteristics due to the fabrication were reported in [24,25] for the same fabrication process as in our work (AMF 193 nm lithography), namely waveguide widths have a standard deviation of $\sigma _w=6.4$ nm, while waveguide thicknesses have a standard deviation of $\sigma _t=2.4$ nm. We employed a mode-solver tool (Synopsys OptoDesigner) to estimate the distributions of indexes $n_\text {g}$ and $n_\text {eff}$ resulting from these fluctuations, and we performed a system-level simulation (Synopsys OptSim) of the filter to evaluate the effect of fabrication errors on the overall transfer function. A simulated transfer function is reported in Fig. 6(c). We remark that the losses in the simulation are consistent with the experimental measures.
Figure 6(b) shows the modulation performance of one of the attenuators. The modulation is performed by a thermo-optic Mach-Zehnder interferometer, giving a typical sinusoidal response. The minimum attenuation state corresponds to a driving current of 2 mA; the maximum attenuation state corresponds to a current of 4.5 mA. The average power consumption of a single micro-heater, having a resistance of 1.5 k$\Omega$, is $\sim$15 mW, hence the total power consumption of 16 micro-heaters is 240 mW. Other, low-power-consumption, technologies for attenuators are discussed in Sec. 5.
Although we are determined to improve the performance of the filter in terms of filter homogeneity and overall power consumption in next-generation designs, we note that the current characterization measurements are encouraging and already compatible with the foreseen application of our frequency-multiplexed neuromorphic computing platform. In order to prove this point, here we discuss both the effects of the insertion losses and the extinction ratios on computing applications. The detrimental effect of high insertion losses is the decrease in the output signal-to-noise ratio. We do not expect this to raise problems in our demonstrator application. Indeed, the fabrication platform can safely handle input powers as high as $10$ dBm, hence, the losses introduced by the filter will not hinder the measurement of filtered output signals. The detrimental effect of a low extinction ratio is the impossibility of assigning arbitrarily low attenuations. Our neuromorphic computing application relies on the filter attenuations for the application of output weights. Thus, a limited extinction ratio would reduce the fidelity of the output signal generated by the system. We estimated the potential impact of the limited extinction ratio on the computing performance through a numerical simulation. The simulation is based on the Extreme Learning Machine presented in [1], which is a feedforward neural network employed for classification. The performance of the network is expressed in terms of accuracy, which is the ratio of correct classifications over the total. In the numerical simulation, we swept the extinction ratio in the range $[0\text { dB},\text { }30\text {dB}]$ while measuring the performance for two benchmark classification tasks: Wine classification and Iris classification [26]. The simulation also accounts for the effect of the quantization of the current driving the attenuators. Results are reported in Fig. 7. According to the simulation, the filter would not hinder performances as long as the quantization of the driving current is $\geq 4$ bits. This means current steps $\geq 125\text { }\mu \text {A}$, and is well within experimentally accessible values. The dependence of neuromorphic computing performance on imperfections in the output layer, which could be due to quantization or other kinds of noise, has been studied extensively in [27].
Fig. 7. Numerical simulation of the influence of the limited extinction ratio on the performance of neuromorphic computing. The simulated system is an Extreme Learning Machine similar to what is presented in [1]. Two well-known benchmark classification tasks have been simulated: Iris classification (a) and Wine classification (b). The red vertical line indicates the measured extinction ratio.
5. Conclusion
We have presented the design for a 16-channel integrated programmable spectral filter. The design is composed of a 1-to-16 multiplexer, an array of 16 attenuators and a 16-to-1 multiplexer. The (de)multiplexer stages are based on lattice filters; the attenuators are thermally activated Mach-Zehnder interferometers. The filter does not require active tuning, as in the envisioned neuromorphic computing application it is possible to shift the information-encoding light spectrum to match the filter channels.
We presented the preliminary tested performance of one chip selected among the fabricated ones. We measured an average insertion loss of 12.5 dB and an average extinction ratio of 14.9 dB. The extinction ratio average is affected by the presence of a faulty channel showing an abnormally low ratio of $7.6$ dB. The exclusion of this channel gives an extinction ratio average of $16.5$ dB. We preliminary proved, through numerical simulations, that these characteristics are compatible with the envisioned neuromorphic computing application.
We proved, through a numerical simulation, that the measured insertion losses are compatible with fabrication variability in the (de)multiplexing stage. Although the losses are already compatible with our application, they could be lowered, if necessary, by including active elements for the alignment of the lattice filter transfer functions. We estimated the average power consumption of the presented filter to be $240$ mW. An eventual active alignment mechanism, employing the same micro-heater of the attenuator stage, would require additional $480$ mW.
The current switching speed is $\sim 10\text { }\mu$s, enabling $\sim 100$ kHz operations. Nevertheless, in many of the envisioned neuromorphic applications the filter is required to apply output weights that are mostly fixed and do not require fast switching. Hence, low power micro-heaters could be employed, which are slower but would diminish the power consumption up to a factor of 10 [23], with no influence over the computing performance. Going beyond the current design, many novel technologies are being considered as candidates to substitute micro-heater attenuators, allowing the integration of faster, more scalable, and more efficient neuromorphic architectures for next-generation optical signal processing. These technologies include optical micro-electro-mechanical systems (MEMS) [28], phase change materials [29], and graphene modulators [30].
Funding
H2020 Marie Skłodowska-Curie Actions (Project POST-DIGITAL Grant number 860830).
Disclosures
The authors declare no conflicts of interest.
Data availability
The benchmark datasets employed in this work are already in the public domain and have been obtained from the UCI Machine Learning Repository [26]. All other data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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