Interference

Mach–Zehnder interferometer

Two beam splitters and two mirrors make a square. Light divides at the first splitter, goes round both sides, and recombines at the second. All the light leaves by one port or the other; which one depends on the difference in optical path between the two sides, to a fraction of a wavelength.

What you are looking at

Each output has a power meter. The glass plate in the lower arm adds optical path $(n-1)t$ , and tilting it adds more.

The two meters always add up to the laser’s power, less a little lost in the glass. Interference moves light between the ports; it does not destroy it.

How the bench is set up

Laser, 50:50 cube, two flat mirrors at 45°, a 3 mm glass plate with anti-reflection coatings, a second cube and two power meters.

The theory

With a phase difference $\Delta\phi$ between the arms the powers at the two outputs are

P_A = P_0\cos^2\frac{\Delta\phi}{2}, \qquad P_B = P_0\sin^2\frac{\Delta\phi}{2}.

Tilting a plate of thickness $t$ and index $n$ by $\theta$ changes its optical path by about $t\,\theta^2 (n-1)/2n$ for small angles, so a few degrees move many fringes.

What to measure

Output share cos²(Δφ/2) against the plate’s optical path

Note both meter readings, then turn the glass plate by 1° at a time with ] and watch the power swap between the outputs.
Check that the two readings always add up to the same total.

What the model leaves out

The cubes are ideal 50:50 splitters with no absorption.

Things to try

Remove the glass plate and use the piezo on one mirror instead.
Put a polariser in one arm, or a half-wave plate: the outputs stop swapping when the two arms’ polarisations no longer match.

References

E. Hecht (2017), Optics, 5th edition, Pearson.
L. Zehnder (1891), Ein neuer Interferenzrefraktor, Zeitschrift für Instrumentenkunde 11, 275.

More experiments, and how the lab works, are in the laser lab’s overview.