Photonic matrix multiplication taps two spatial modes: a 185-micrometre engine keeps its weights after power-off

Matrix-vector multiplication is the most frequent operation in neural-network forward and backward passes, and this design moves it onto a silicon-photonic chip where two computing channels share two spatial modes of the same waveguide instead of two wavelengths or two lasers. Earlier mode-division-multiplexed matrix multipliers relied on thermo-optic tuning, which costs power and area, while an ultra-compact photonic-crystal 2×2 design lacked reconfigurable dynamic weight updates. The design uses TM0 and TM1 as independent input channels; the modes are orthogonal with non-overlapping spatial profiles, so the multiplexer sums the weighted powers optically at the output waveguides without any phase analysis.

Weights are stored without continuous power, using the refractive-index difference between the amorphous and crystalline states of a phase-change material to attenuate light. Each weighting path holds five GSST cells in series, twenty cells across the chip, and a path's transmission is set by how many of its cells are crystalline, giving six discrete weight levels per path. At 1550 nm the five-cell array reaches an extinction ratio of 11.29 dB for TM0 and 17.3 dB for TM1, and the four independently programmable paths together support 1296 matrix configurations.

Switching is driven by Joule heat from an indium tin oxide heater beneath each cell, with pulse parameters deciding whether the material crystallizes or amorphizes. Electro-thermal simulation sets the conditions: a 5 V, 33 ns pulse holds the temperature between 523 and 900 K for crystallization, while a 12 V, 5 ns pulse drives melting above 900 K followed by rapid quenching. Simulated currents are 4.76 mA in the amorphous state and 2.00 mA in the crystalline state, giving 285.6 pJ per cell for amorphization and 330 pJ for crystallization, and under 6.6 nJ to rewrite the full 2×2 weight matrix.

All reported performance comes from numerical optical and electro-thermal simulation, covering the 2×2 core in both modes over 1540 to 1580 nm plus fabrication-tolerance sweeps of the power splitter, demultiplexer and weighting section; no experimental measurement is given.

Weights take only six non-negative real levels, and negative or complex weights cannot be represented by an attenuation mechanism; quantization gives a normalized mean-square error of about 0.013 for TM0 and 0.019 for TM1, with the largest level gap at low crystalline counts, reducible by equalizing level spacing or adding cells per path. Device-to-device variability is not experimentally quantified, and the authors suggest per-cell calibration on a fabricated device could reduce it.