Quarter-wave plate
Applies quarter-wave retardance, producing linear, elliptical, or circular polarization from the input state.
Open in the canvas →In the real world
A quarter-wave plate is the same birefringent slice as a half-wave plate, cut half as thick. It splits the incoming polarization into components along its fast and slow axes and delays one by a quarter of a wave — 90° of phase — relative to the other.
That quarter wave is the amount that converts between linear and circular polarization rather than moving light around within either family. Two equal components 90° out of phase trace a circle as they add; the same two components in phase trace a straight line. So the plate's effect depends entirely on how the input is oriented relative to its axes:
At 45° to the fast axis, the input splits into two equal components and the plate turns linear light into circular. At 0° or 90°, all the light is already along one axis, there is no second component to delay, and the polarization passes through untouched. At any angle in between the two components are unequal and the result is elliptical — the general case, of which linear and circular are the two limits.
The conversion runs both ways, and that reversibility is what makes the plate so useful. Circular light entering a quarter-wave plate comes out linear. Pairing one with a polarizer therefore builds a simple optical gate: light passes the polarizer, becomes circular, reflects off something — which reverses the handedness — returns through the plate as linear light rotated 90° from the original, and is rejected by the polarizer it came through. That trick suppresses back-reflections in everything from optical drives to interferometers, and it is the reason quarter-wave plates turn up wherever a beam has to go out and come back along the same path.
Circular polarization is also worth having in its own right. It carries no preferred direction in the plane, so it excites molecules regardless of their orientation, and its two handednesses interact differently with chiral matter — the basis of circular dichroism spectroscopy.
In OpticalSetup
Like the half-wave plate, the quarter-wave plate exposes one control, the fast axis angle, and applies an exact retardance to the beam's Stokes vector — 90° in this case. It starts at 45°, the angle that produces circular light from a horizontally polarized input.
The full range of behaviour is there and can be read off any detector that reports polarization. Linear light at 0° with the axis at 45° comes out fully circular. Rotate the axis to 0° or 90° and the light passes through still linear. Set it to 22.5° and the output is elliptical, with the tilt of the ellipse and the amount of circularity both visible in a polarimeter's Stokes readout. Feed circular light in and linear light comes out.
Two quarter-wave plates in series with the same axis are equivalent to one half-wave plate — worth trying, because it makes concrete that retardance simply accumulates.
As with any waveplate here, the element is lossless and does nothing at all to unpolarized light, which has no defined phase relationship for the plate to act on. Establish a state with a polarizer first.
The retardance is exactly a quarter wave at every wavelength, so there is no wavelength dependence, no distinction between zero-order, multi-order, and achromatic plates, and no degradation away from a design wavelength. The plate is lossless and insensitive to angle of incidence and temperature, there is no walk-off inside the crystal, and it adds no group-delay dispersion to a pulse. The circular light it produces is mathematically perfect; a real plate leaves a small residual ellipticity that matters in sensitive polarimetry.