The Mach–Zehnder interferometer splits a coherent beam into two arms, delays one relative to the other, and recombines them so interference can be read at an output port. This page uses the standard two-beam intensity law for balanced amplitudes: I/I_max = cos²(πΔ/λ), where Δ is the optical path difference (OPD) introduced in one arm and λ is the vacuum wavelength. A schematic shows beam splitters and mirrors; the graph plots fringe contrast versus Δ. The layout highlights how small length or index changes in one arm translate directly into intensity swings — the basis of optical sensing, some quantum optics demonstrations, and photonic modulators. Assumptions include ideal 50/50 splitters, perfect spatial mode overlap, no dispersion or polarization filtering, and a point detector. Real devices must manage vibration, thermal drift, and wavelength-dependent phase; those effects are not modeled here.
Who it's for: Undergraduate optics and photonics students learning two-beam interference, metrology, and interferometer topologies beyond the Michelson layout.
Key terms
Mach–Zehnder
Optical path difference
Interference
Beamsplitter
Coherence
Fringe visibility
Phase sensitivity
Two-beam model
Live graphs
How it works
Two-beam interferometer: recombining amplitudes with a controllable phase delay in one arm shifts output power — basis for sensing and photonics.
How does this differ from a Michelson interferometer?
Both split and recombine beams, but the Mach–Zehnder uses two separate paths that meet at a second beamsplitter. That geometry can make it easier to send each arm through different samples or modulators without sending light back toward the source, and it offers distinct output ports corresponding to complementary interference phases.
Why is the intensity periodic in Δ with period λ?
Each wavelength of OPD adds 2π to the phase difference between the arms. Because intensity depends on cos² of half the phase (for equal amplitudes), a full 2π phase cycle returns the same intensity; equivalently, the pattern repeats when Δ changes by one wavelength.
What happens if the amplitudes are not perfectly balanced?
The fringe contrast (visibility) drops. The general two-beam intensity is not symmetric about zero when one arm is weaker; minima are no longer exactly zero. This simulator fixes equal amplitudes to isolate the phase dependence.
Does the schematic include dispersion in the beamsplitters?
No. Real cube beamsplitters and coatings introduce wavelength-dependent phase; broadband sources then wash out fringes unless compensated. Here λ is a single design wavelength and materials are ideal.