Silicon Photonic Modulator Neuron

There has been recent interest in neuromorphic photonics, a field with the promise to access pivotal and unexplored regimes of machine intelligence. Progress has been made on isolated neurons and analog interconnects; nevertheless, this renewal of interest has yet to produce a demonstration of a silicon photonic neuron capable of interacting with other like neurons. We report a modulator-class photonic neuron fabricated in a conventional silicon photonic process line. We demonstrate the behaviors of transfer-function configurability, fan-in, inhibition, time-resolved pulse processing, and, crucially, autaptic cascadability—a sufficient set of behaviors for a device to act as a neuron participating in a network of like neurons. The silicon photonic modulator neuron constitutes the final piece needed to make photonic neural networks fully integrated on currently available silicon photonic platforms.

Figure 1

A broadcast-and-weight network [55] using MRR modulator neurons and MRR weight banks (WEI) [56]. The entire network is integrated with the exception of the pump-laser diodes (LD), which lie outside of the high-bandwidth signal pathway. The red (blue) arcs are $n$-doped ($p$-doped) regions. The green lines are the wires connecting balanced photodiodes (BPD) to modulators (MOD) within each neuron. Each MRR interacts with only one wavelength, ${\lambda }_i$.

Figure 2

(a) A simplified equivalent circuit diagram of the MRR modulator neuron. (b) A false-color confocal micrograph of the fabricated device. (c) A cross section of the MRR modulator with embedded $p$-$n$ modulator and $n$-doped heater. (d) A cross section of the $\mathrm{Si}$-$\mathrm{Ge}$ photodetector, showing the cathode ($V_{+}$) and the anode($V_{-}$).

Figure 3

Spectrum vs heat and forward-current bias under different permutations of illumination. Columns distinguish heating; rows distinguish the modulator bias current. Traces distinguish optical input conditions: blue, no light, just electrical bias; orange, green, only one optical input at a time; red, both inputs creating complementary effects. Ideally, the red traces should overlap with the blue.

Figure 4

The experimental setup. A Mach-Zehnder modulator (MZM), followed by a DEMUX and $\mathrm{\Delta }T$ delay, is used to create two distinct signals. An arbitrary-wave-form generator (AWG) or a PPG is used to drive the modulator. A fiber switch directs the second (${\lambda }_2$) input either to the same IN+ port as the first input (${\lambda }_1$) or to the complementary $\mathrm{IN}-$ port. Light going into IN($+/-$) waveguides impinges on the photodetectors, resulting in complementary photocurrents $i^{(+/-)}$. Current injected to the MRR modulator (“mod.”) is the sum of the photocurrents and the bias current ($I_b$): $I_b+i^{+}-i^{-}$. The MRR resonance wavelength is also affected by a heater biased at $I_h$. The transmission of the modulator is probed by a cw pump (“PUMP”) at ${\lambda }_n$. Its optical output is monitored by an oscilloscope (“Scope”). The dashed box indicates the on-chip/off-chip boundary.

Figure 5

(a)–(f) A variety of relevant O-E-O transfer functions seen from the PD-modulator pair, taken at different bias conditions: (a),(b) sigmoids; (c),(d) rectified linear units (“ReLU”); (e) a radial basis function (RBF); and (f) a quadratic function. (g)–(i) Time resolved pictures of these transfer functions: (g) the input is a 40-ns burst of a 100-MHz carrier; (h) both ReLUs; (i) the quadratic function. All plots display experimental data.

Figure 6

Reproduction, rectification, and pulse compression. (a) The input is a 25.0-ns burst of a 1.0-GHz rf carrier modulated on a ${\lambda }_1$ optical carrier. (b) In a linear regime, the modulating signal is faithfully reproduced on a different carrier wavelength, ${\lambda }_n$. (c) In the nonlinear ReLU regime, the output wave form is a rectified version of the input. (d)–(f) Enlarged windows interpreting the signals as pulsed signals: (d) input, (e) reproduction, and (f) rectification resulting in pulse-width compression.

Figure 7

Burst addition and two-channel rectification. The solid lines are experimentally measured; their colors correspond to the wavelengths in Fig. 4. (a),(b) Inputs. (c)–(f) Outputs under different biasing configurations performing the two-variable functions on the right. The dashed black curves are ideal outputs calculated from the measured inputs. The functions shown demonstrate linear and/or nonlinear capabilities as well as excitatory and/or inhibitory capabilities. Input $B$ is slightly stronger than input $A$.

Figure 8

Pulse-coincidence experimental results. (a),(b) The input is a 2-ns pulse doublet, which is delayed between two input wavelengths to create a pulse coincidence at $t=0$. (c) Neuron outputs under different biasing conditions, compared to the linear solution (sum of inputs, black). The first pulse is used as a normalization to 0.5, meaning that the linear sum should peak at 1.0 (i.e., 100%): blue, biased for nonlinear enhancement, where coincidence is 157% of the linear solution; orange, biased for nonlinear saturation, where coincidence is 56% of the linear solution; green, inhibition; the fiber connections are switched such that IN 2 is directed to the $\mathrm{IN}-$ photodetector, and the neuron is biased in a linear region. The coincident pulses result in approximately zero output, and the noncoincident pulses cause complementary perturbations. The leading pulse from IN 1 results in a positive perturbation, while the lagging pulse from IN2 results in a negative perturbation.

Figure 9

The autapse concept and experiment. (a) An autapse is a neuron fed back to itself with a unitless round-trip gain of $g$. (b) The experimental setup. The output of the neuron on ${\lambda }_n$ is wavelength multiplexed with a sawtooth-modulated external input $u(t)$ on ${\lambda }_1$. Both are then fed into the positive-input photodetector. An oscilloscope records the output and the external input. (c) The response to a triangle-wave input (black), showing monostability. The feedback attenuator is blocking so that $W_F=0$. (d)–(g) The response with feedback $W_F=1$ and $g>1$, showing bistability. This is apparent from the difference in falling (d) and (e) and rising (f) and (g) edge responses. Changing the input from 100 kHz (d),(f) to 50 kHz (e),(g) makes little appreciable difference. (h) The output plotted against the input, illustrating the opening of a bistable regime. The colors correspond to the output traces in (c)–(g).

Figure 10

A photonic autapse implemented by a microring modulator neuron. The modulator junction is reverse biased by a voltage source with impedance $R_b$.