Half-wave plate
Rotates linear polarization around the configured fast axis.
Open in the canvas →In the real world
A waveplate is a slice of birefringent crystal — quartz, magnesium fluoride, calcite — in which the refractive index depends on the direction the light is polarized. Two perpendicular directions in the plate face are special: the fast axis, along which light sees the lower index and travels quicker, and the slow axis perpendicular to it. Any incoming polarization can be resolved into components along those two axes, and because the components travel at different speeds, one emerges behind the other. Nothing is absorbed; only the relative phase between the two components changes.
How much phase separates them is the retardance, and it depends on the index difference, the plate thickness, and the wavelength:
At exactly half a wave, one component is inverted relative to the other, and the effect on linear polarization is a reflection about the fast axis. The practical consequence is the one everybody uses: rotating the plate by some angle rotates the polarization by twice that angle. A plate turned 22.5° rotates the light 45°; turned 45°, it rotates it a full 90°. Because it is a phase device rather than an absorbing one, this rotation is lossless — which is exactly why a half-wave plate followed by a polarizer is the standard way to control laser power continuously without touching the laser.
On circularly polarized light the same mirror operation reverses the handedness, turning left-circular into right-circular.
Retardance depends on wavelength, so a plate is specified for one. Used far from that wavelength it is no longer half-wave and the rotation degrades. A zero-order plate is genuinely as thin as the formula demands and is relatively forgiving of wavelength, angle, and temperature; a multi-order plate is a thicker, cheaper piece that adds several whole waves on top and is correspondingly fussier. Achromatic designs combine two materials so that the retardance stays near half a wave across a broad band.
In OpticalSetup
The plate has one control that matters: the fast axis angle, on the purple canvas knob or in the inspector. Polarization is carried through the whole sketch as a Stokes vector, and the plate applies an exact 180° retardance about that axis — geometrically, a rotation of the polarization state on the Poincaré sphere.
The behaviour that follows is the real one, not an approximation of it. Linear light at 0° through a plate with its axis at 22.5° comes out at exactly 45°; set the axis to 45° and the same input comes out at 90°. Align the axis with the input polarization, or put it perpendicular, and nothing changes — a half-wave plate does nothing to light already polarized along one of its own axes. Send circular light through and the handedness flips.
Two consequences are worth knowing. The plate is lossless: it changes the state, never the intensity, so a power-control stage needs the polarizer after it to convert the rotation into attenuation. And unpolarized light passes through unchanged, which is correct rather than a shortcut — there is no preferred direction for the plate to act on. Put a polarizer before it if you want a defined state to rotate.
Polarization modulation survives the plate too: a beam being switched between two states by an electro-optic modulator keeps alternating after the waveplate, with both states rotated together, rather than having the modulation flattened away.
The retardance is exactly half a wave at every wavelength. Nothing here models Δn, the plate thickness, or their dispersion, so there is no distinction between zero-order, multi-order, and achromatic plates, and no degradation when a plate is used away from its design wavelength — in a real setup that is the single most common reason a waveplate underperforms. The plate is also perfectly lossless and perfectly aligned: no Fresnel reflection at the faces, no absorption, no sensitivity to angle of incidence or temperature, and no walk-off between the two rays inside a birefringent crystal. Its optical thickness is not modelled either, so it contributes no group-delay dispersion to a pulse.