Mach-Zehnder Modulator: Phasor & Transfer-Function Diagram

Electro-Optic Drive

Bias V_bias / V_π 0.50

Drive swing V_pp / V_π 0.60

Drive frequency (visual) 0.30 Hz

Drive Topology

Live Readout

Output power (bar)

Cross-port power

Phase diff. Δφ/π

0.00

Extinction ratio

0 dB

How it works

This is a 2D phasor-diagram counterpart to the 3D waveguide-chip modulator. Instead of watching light packets fly down two 3D tubes, each arm's optical field is drawn directly as a unit-length phasor rotating in the complex (Argand) plane — the plane itself is the physics, not a camera angle on it.

E_A = e^(iφ_A),  E_B = e^(iφ_B)        (unit-amplitude arm fields)
E_bar   = (E_A + E_B) / 2   → P_bar   = |E_bar|²   = cos²(Δφ/2)
E_cross = (E_A − E_B) / 2   → P_cross = |E_cross|² = sin²(Δφ/2)
Δφ = φ_A − φ_B = π · V(t) / Vπ,   P_bar + P_cross = 1

Vector-adding the two arm phasors and squaring the resultant's length reproduces the textbook cos² coupler transfer function exactly — the parallelogram construction shown live in the diagram is the interference, not an illustration of it.

Bias sets the DC operating (quadrature) point on the transfer curve.
Drive swing is the peak-to-peak RF voltage riding on top of the bias, in units of Vπ.
Push-pull drives the two arms with equal and opposite voltage (±V/2), reaching the same Δφ as a single-arm drive of V but with half the voltage swing per arm — the standard silicon-photonics topology because it also cancels residual optical-frequency chirp. Watch the two arm phasors: push-pull rotates them symmetrically toward and away from each other, single-arm holds one still and rotates only the other — yet the sum/difference vectors, and therefore the output powers, land on identical values for the same drive.
Extinction ratio is 10·log₁₀(P_max/P_min) of the bar port sampled over one drive cycle — how dark the "off" state gets relative to the "on" state.

Real-world relevance: this exact cos² transfer function governs the silicon-photonic and lithium-niobate MZMs used to encode data onto laser light in every fiber-optic transceiver and data-center interconnect.

Arm A phasor Arm B phasor Bar (sum) output Cross (diff.) output