Wiki / Wavefront Shaping / Spatial light modulator

Spatial light modulator

Reflects by default and can overlay lens-array, grating, steering, or speckle functions.

A live trace, not a picture of one — but this preview is not interactive. Open it in the canvas to move things, change parameters, and save or export your own version.

In the real world

A spatial light modulator is a programmable optic. Instead of grinding a surface into a fixed shape, it imposes a phase pattern that software can change frame by frame — so one device can act as a lens, a grating, a corrector for aberrations it measures on the fly, or a hologram that paints an arbitrary intensity pattern in a distant plane.

How liquid crystals do it

The working substance is a nematic liquid crystal: rod-shaped molecules that share a common orientation — the director — while remaining free to move past one another like a liquid. That orientational order without positional order is what makes the phase useful. Aligned rods are optically birefringent: light polarized along the director sees the extraordinary index n_e, light polarized across it sees the ordinary index n_o, and the difference is large — around 0.1 to 0.2, roughly ten times that of a quartz waveplate.

Applying a voltage across a pixel tilts the director toward the field. The index seen by light polarized along the original director slides continuously from n_e toward n_o, so the optical path through that pixel — and therefore the phase of the light leaving it — becomes a smooth function of the applied voltage:

\Gamma(V) = \frac{2\pi\,\Delta n(V)\,d}{\lambda}

Phase retardance of one pixel: the voltage-dependent index difference times the liquid-crystal layer thickness. This is the same expression as a waveplate, with Δn now under electrical control.

\Gamma_{\text{LCOS}} = 2 \times \frac{2\pi\,\Delta n(V)\,d}{\lambda}

A reflective device doubles it: light crosses the layer on the way in and again on the way out, so half the thickness achieves a full 2π stroke.

Nearly all phase-only modulators are LCOS — liquid crystal on silicon. A CMOS backplane addresses each pixel and carries a mirror beneath it, with the liquid-crystal layer above; light enters, reflects off the pixel mirror, and leaves having crossed the modulating layer twice. Pixels are a few micrometres across, the phase is quantised to 8 bits, and the device is calibrated so that its full drive range corresponds to exactly 2π at one design wavelength.

Two consequences follow from the physics and are worth knowing before you design around one. First, the input must be linearly polarized along the director: only that component is modulated, so light in the orthogonal state passes through unchanged and dilutes the pattern. Every SLM setup therefore has a polarizer in front of it. Second, liquid crystals are slow — reorientation takes milliseconds, so refresh rates are tens of hertz, not the megahertz an acousto-optic device reaches.

The zero-order problem

An SLM never modulates all the light that lands on it, and the unmodulated fraction leaves along the direction of a plain mirror — the specular, or zeroth-order, beam. It sits on the optical axis, undiffracted, while the pattern you asked for is formed around it. Several causes contribute:

Fill factor below 100%. The gaps between pixels, and the circuitry at their edges, are not modulated. That light reflects with no phase structure at all.
Front-surface reflection from the protective cover glass, which never reaches the liquid crystal.
Incomplete 2π stroke. If the calibration is off, or the device is used away from its design wavelength, the phase never wraps cleanly and a residual unmodulated component survives.
Phase quantisation and flicker from the digital drive scheme.

Together these typically leave a few per cent up to about ten per cent of the incident power in the zeroth order — which, concentrated in a single undiffracted spot, is frequently the brightest feature in the output plane. In holographic optical tweezers it is a trap nobody asked for; in a microscope it is a bright spot at the centre of the field; at high power it can damage a sample outright.

The standard remedy is to steer the useful light away from it. Adding a linear phase ramp — a blazed grating — to the displayed hologram deflects the whole pattern off-axis, leaving the zeroth order behind on the axis where it can be removed with a beam block at an intermediate focus. Careful per-wavelength calibration of the 2π lookup table reduces the residue at the source, and slightly tilting the device separates the cover-glass reflection from the modulated beam.

In OpticalSetup

The SLM is reflective by default, matching an LCOS device, with a Transmissive toggle for the less common transmissive kind. Its active size sets how much of a beam it intercepts, and the blue handle resizes it on the canvas.

What it does to light is set by a stack of optical function layers, applied in order — up to four:

Lens array — divides the aperture into lenslets of a chosen count and focal length, so one beam becomes several focused spots. Each lenslet is tracked separately, so beams do not blend between them.
Grating — a programmable diffraction grating with a chosen line density and list of orders, which is how a real SLM steers and splits.
Beam steer — a plain angular deflection, the simplest thing a phase ramp does.
Speckle / diffuser — scatters into a cone, standing in for a random phase pattern.

The zeroth order, on a toggle

Because the undiffracted beam is a real and often dominant feature of any SLM setup, it is available here rather than quietly ignored — but it is off by default, so a teaching diagram is not cluttered by a stray beam nobody asked about.

Turn on 0th-order reflection and set the fraction (0.1, ten per cent, by default — a realistic figure for a good device) and the element splits its output: that fraction leaves along the plain specular direction, exactly where a mirror would send it, while the patterned light carries the rest. With a grating layer on a device at 45°, you can watch the two separate — the diffracted beam steered by the pattern, the zeroth order going straight on, and the balance between them shifting as you change the fraction.

The toggle correctly does nothing on an unpatterned SLM. With no layers configured the device is simply a mirror, and there is no diffracted order for a "zeroth" to be measured against.

This makes the standard mitigation something you can actually draw: add a grating layer to steer the useful light off-axis, then put a beam dump in the path of the zeroth order and terminate it.

Simplified vs. reality

No phase map is computed. The layers are geometric ray operations chosen to stand in for what a hologram does, not a diffraction calculation over a pixel array — so there is no pixel pitch, no fill factor, no 8-bit quantisation, no 2π stroke, and no wavelength dependence of Δn. The zeroth-order fraction is a number you set, not one derived from the fill factor and calibration that actually cause it. The polarization requirement is not enforced either: a real device modulates only the component along its director, whereas this one acts on any input state, so a sketch will not warn you about the missing polarizer. Grating orders share the light evenly rather than following a blaze, and the millisecond response and frame rate of a real liquid crystal are not represented at all — the pattern here changes instantly.