mzi

The Mach-Zehnder Interferometer (MZI) is an optical instrument that splits a light beam into two separate paths, allows phase shifts to occur in one or both paths, and then recombines the beams to produce interference at the outputs. It can be built in free space using beam splitters and mirrors or realized in integrated or fiber-optic form using directional couplers or splitters. The basic operating principle is that the relative phase between the two arms determines the distribution of light at the output ports.

In operation, an input beam is divided by the first beam splitter into two arms. Along these arms, the light may accumulate a relative phase difference due to differences in optical path length, refractive index, or applied modulation. The beams are then recombined at a second beam splitter, yielding two outputs whose intensities depend on the phase difference Δφ. For an ideal 50/50 coupler, the outputs satisfy I1 ∝ 1 + cos(Δφ) and I2 ∝ 1 − cos(Δφ). The phase difference is typically Δφ = (2π/λ) Δn L plus any externally introduced phase φ.

Variants of the MZI include free-space, fiber-optic, and integrated photonic implementations. Applications span precision metrology and sensing (refractive-index, temperature, strain changes), optical communications (modulation and switching), and fundamental experiments in quantum optics where single photons are used to study interference. The Mach-Zehnder interferometer is distinguished from the Michelson interferometer by its two separate beam splitters and the ability to route light through two distinct arms without relying on a single moving mirror.

Historically, the device is named for Ludwig Mach and Ludwig Zehnder, who developed early forms of the interferometer in the late 19th century.