Continuous Relative-Phase Control of Synthetic Magnetoelectric Coupling in Space-Time Modulated Transmission Media

This technical note records a proposed continuous-relative-temporal-phase extension of the weak-modulation homogenized magnetoelectric-coupling relation for space-time-modulated electromagnetic media. The underlying in-phase mechanism, requirement for simultaneous electric and magnetic modulation, and transmission-line realization are acknowledged prior art. The contribution recorded here introduces a continuously variable relative temporal phase δ between nonzero electric and magnetic modulation channels sharing a common traveling spatial phase progression while modulation depths and modulation velocity remain fixed. The proposed normalized relation is ξ̃(δ) = (mₑmₘ/2)[u/(1-u²)]cosδ. This predicts continuous control through zero and sign reversal of the effective magnetoelectric coupling without turning either constitutive modulation channel off. A falsifiable experimental model ξ̃measured(δ) = A cos(δ−δ₀) + B is proposed using signed forward and reverse propagation constants. First public disclosure: GitHub commit 8d961e851e488aa0b1a4b227d4af532a76f7bd37, 9 September 2026.