Glossary entry

Mach–Zehnder modulator (MZM)

An optical intensity modulator based on a Mach–Zehnder interferometer with electro-optic phase shifters in one or both arms. The dominant external modulator in telecom and PIC applications.

A Mach–Zehnder modulator splits incoming light into two waveguide arms, applies an electric field to phase-modulate at least one arm, and recombines the arms. The transmitted intensity depends on the relative phase difference $\Delta\phi$ between the arms:

T \;=\; \cos^2\!\left(\frac{\Delta\phi}{2}\right) \;=\; \frac{1}{2}\left[1 + \cos(\Delta\phi)\right].

For a balanced MZM (equal-length arms), $\Delta\phi = 0$ at zero drive voltage produces full transmission. A drive voltage producing $\Delta\phi = \pi$ produces full extinction. The voltage required for full switching is the half-wave voltage:

V_\pi \;=\; \frac{\lambda \, d}{n_e^3 \, r \, L \, \Gamma},

where $d$ is the electrode gap, $n_e$ is the relevant refractive index, $r$ is the electro-optic coefficient, $L$ is the electrode length, and $\Gamma$ is the field-mode overlap.

Material platforms:

Platform	Mechanism	Typical $V_\pi \cdot L$
Lithium niobate (LiNbO $_3$ )	Linear electro-optic	5 – 15 V·cm
Thin-film LNOI	Linear electro-optic	1 – 3 V·cm
Silicon (free-carrier dispersion)	Plasma effect, nonlinear	1 – 3 V·cm
InP (QCSE in MQW)	Quantum-confined Stark effect	1 – 5 V·cm
Polymer EO	Linear electro-optic	0.5 – 2 V·cm

Standard MZM design choices:

Single-arm drive vs push-pull: push-pull (differential drive on both arms) halves $V_\pi$ and cancels chirp from refractive-index nonlinearity
Bias point: typically quadrature ( $\Delta\phi = \pi/2$ ) for analog modulation; null ( $\Delta\phi = \pi$ ) for OOK transmitters using duobinary
Bandwidth: 30 GHz (telecom), $>$ 100 GHz (coherent transceivers)
Insertion loss: 3 – 7 dB (LNOI), 4 – 8 dB (silicon)
Extinction ratio: 20 – 30 dB

The MZM is the workhorse modulator for digital coherent optical communication. Its linear electro-optic response (in LiNbO $_3$ or LNOI) produces minimal chirp, which is critical for long-haul transmission where any imposed chirp interacts with chromatic dispersion to degrade the signal. Silicon MZMs are nonlinear and intrinsically chirped but compensate with much higher integration density.