Self-consistent modelling of all-optical switching and magneto-optic readout in an integrated Si$_3$N$_4$/GdFeCo waveguide

Abstract: What a guided beam carries after passing through an all-optically switched magnetic film has not been computed, although such switching has been demonstrated on a silicon nitride waveguide with electrical readout. We close the chain for an integrated Si$_3$N$_4$/GdFeCo element, an 8 nm film on a 60 $μ$m waveguide, coupling a three-dimensional dispersive finite-difference time-domain solver to absorbed optical work, a four-temperature model, and stochastic two-sublattice Landau-Lifshitz-Bloch dynamics with a fluctuation-dissipation-consistent Langevin field, the magnetization feeding back into the gyrotropic permittivity that a second guided shot reads. Transmission, reflection and absorption are magnetization-blind, closing to 0.974-0.975 and shifting by at most 0.02 between saturated, demagnetized and multidomain films, because magnetization enters the dielectric tensor only through an antisymmetric element on which absorbed power depends at second order; the odd-in-magnetization polarimetry separates them by an order of magnitude in Faraday rotation and two in Kerr. The guided geometry levies a cost free-space measurement does not: a $-11.77<sup>\circ$ geometric pedestal on the reflected channel, exceeding the $8.24<sup>\circ$ rotation it hides. Referencing against a demagnetized film returns it to $0.063<sup>\circ$. The transmitted mode carries a second signature in its lobe balance, needing no polarimetry. Calibrated pulses toggle 0.859 of the film from either saturated state across a $2.4\times$ fluence window, and the shortfall from unity is photonic rather than magnetic: the switched fraction is the complementary cumulative distribution of the guided-mode absorption map at the single-cell threshold, holding to $8\times10<sup>{-4}$ at five full-wave anchors. From exactly zero magnetization, branch selection passes to the Langevin field alone, at occupancy $0.502 \pm 0.004$ over 16 seeds.