Mach–Zehnder interferometer
Two beamsplitters, two fully separate arms, two output ports — shown three ways: a mechanical delay, a driven phase modulator, and a phase object that turns the layout into a phase-contrast imager.
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Where a Michelson interferometer sends both arms back through the same beamsplitter, a Mach–Zehnder interferometer uses two: the first splits the beam onto two completely separate paths, each folded once by a mirror, and the second recombines them into two spatially distinct output ports. Because each arm is traversed only once — no retroreflection — the two arms can be made physically very different in length or content, which is exactly what makes the layout useful. Ludwig Zehnder proposed it in 1891 and Ludwig Mach refined it in 1892[1].
Putting anything that shifts phase or path length in one arm — a flame, a gas flow, a transparent sample, a voltage-driven phase modulator — changes how the two arms recombine, so a Mach–Zehnder interferometer converts an invisible phase difference into a visible intensity difference between its two outputs. That principle shows up at wildly different scales: wind-tunnel schlieren imaging of density gradients, single-photon "quantum eraser" experiments in quantum optics, and — as a microscopic waveguide pair on a chip — the Mach–Zehnder modulator that encodes data onto light in most fiber-optic telecommunications hardware[2].
What this setup demonstrates
One layout, two ways to put phase into an arm. Each row is the same Mach–Zehnder diamond — a laser, two beamsplitters, a mirror folding each of the two separate arms — recombining onto two cameras with their own screens. Both arms are genuinely separate ray paths: move a mirror on one and only that arm's traced path changes, exactly as on a bench.
The invariant to watch in both is that the ports are complementary. Whatever leaves one arrives at the other, and they always sum to the input — the light is redirected, never absorbed.
Row 1, a delay line. Lengthen one arm mechanically. Equal arms make one port bright and the other dark; half a wavelength (0.000266 mm at 532 nm) swaps them, and a full wavelength brings them back. It ships set to Periodic sweep, walking a micrometre back and forth at 0.1 Hz, so the two screens trade the light continuously rather than sitting on one point of the fringe. That is the interferometer as a ruler for optical path.
Row 2, a phase object. A half-wave bar across part of the beam. The arms now disagree by different amounts at different heights, so the output is not a level but a pattern, and the split follows how much of the beam the bar actually covers. That is phase contrast — and the object absorbs nothing: put a detector after it on its own and the reading is unchanged.
A third way to drive an arm is the phase modulator, which does the same swap from a voltage and at megahertz rather than by moving a stage. Its own page carries that setup.
Worth trying on both rows: give the laser a coherence length. It defaults to zero, meaning idealised, and interferes at any arm mismatch. Set a real value and sweep the delay further, and the fringes fade out where the arms are mismatched by more than that distance.
The tracer combines only phase-valid routes from this sized monochromatic CW laser. Optical path, 100%-reflective flat-mirror phase, and a unitary non-polarizing beamsplitter phase are represented. Compatible fields are grouped at the second beamsplitter before the output beams are drawn; a camera additionally integrates any remaining cross terms over its finite 1D pixels.
Temporal coherence is modelled only as a visibility envelope in the arm mismatch, set by the source's coherence length: the beam still carries a single wavelength, so the linewidth that coherence length implies is reported but never propagated, and spatial coherence is not modelled at all. This is not a general wave-optics solver either — diffraction, vibration, surface figure, and 2D sensor response are absent. Putting an optic whose carrier phase is not modeled in either arm makes the tracer fall back to conservative deposited intensity instead of inventing a fringe.