Spatial light modulator

A spatial light modulator (SLM) is an array of individually addressable pixels that changes the phase, amplitude or polarization of the light falling on it, under computer control. The most widely used type in laboratories is the reflective liquid-crystal-on-silicon (LCoS) phase modulator: a thin layer of nematic liquid crystal sits between a cover glass and a silicon backplane of pixel electrodes, and the voltage on each pixel tilts the molecules and changes the refractive index seen by light polarized along the director. Panels commonly have 1920 × 1080 pixels or more at pitches of about 4–20 µm, a phase stroke of at least 2π at the design wavelength, and frame rates from 60 Hz to a few hundred hertz, limited by the millisecond response of the liquid crystal. Transmissive liquid-crystal panels and the binary digital micromirror device are the main alternatives.

Phase stroke and liquid-crystal thickness

For a reflective panel the light crosses the layer twice, so a full wave of phase needs $2\,\Delta n\,d = \lambda$, where $\Delta n$ is the liquid crystal's birefringence and $d$ its thickness. With $\Delta n \approx 0.2$, a panel for 1550 nm needs

$$d = \frac{\lambda}{2\Delta n} = \frac{1.55\ \mu\text{m}}{0.4} \approx 3.9\ \mu\text{m}.$$

Thicker layers give more stroke at longer wavelengths but respond more slowly, since the switching time grows roughly with the square of the thickness. Panels are therefore designed for a wavelength band, and one built for the visible may not reach 2π in the infrared.

Diffraction efficiency and steering angle

An SLM shapes beams by acting as a programmable diffractive element, which is where Fourier optics enters: a lens after the SLM forms the far field, and the SLM pattern sets what appears there. A blazed phase ramp steers the beam like a diffraction grating. Because the ramp is sampled in pixels, a ramp with $N$ phase levels per period has a first-order efficiency of

$$\eta = \operatorname{sinc}^2(1/N),$$

which is 0.41 for $N = 2$, 0.81 for $N = 4$, 0.95 for $N = 8$ and 0.99 for $N = 16$. The largest deflection comes from a two-pixel period, $\sin\theta = \lambda/(2p)$: at 1064 nm with 8 µm pixels that is about 3.8°. Practical steering stays well inside this, where more phase levels per period keep the efficiency high.

Real devices fall short of the ideal. The electric field of one pixel spreads into its neighbours (the fringing-field effect), which rounds sharp phase steps and lowers efficiency at short periods. The gap between pixels and imperfect phase response leave light in the undiffracted zero order, a bright spot on axis that experiments usually avoid by adding a small grating to shift the wanted pattern away from it.

Calibration and measurement

The voltage-to-phase response is not linear, so each panel is calibrated with a lookup table measured at the working wavelength. A common method displays two halves at different grey levels inside an interferometer or behind a double slit and records the fringe shift as one half is stepped through all grey levels. Flatness of the backplane is a second calibration: a static wavefront correction measured with an interferometer or Shack-Hartmann sensor is added to every pattern. Phase flicker, a small oscillation at the drive frequency, is measured by recording the diffracted intensity with a fast photodiode.

Applications

• Holographic beam shaping and optical tweezers, where computed phase holograms create multiple traps or custom intensity profiles.
• Adaptive optics in microscopy and ophthalmology, where the SLM corrects aberrations slowly but with many degrees of freedom.
• Femtosecond pulse shaping, with a one-dimensional SLM in the Fourier plane of a grating-and-lens pulse shaper setting the spectral phase.
• Wavelength-selective switches in ROADMs, where LCoS panels steer each wavelength channel to an output fiber.
• Structured illumination in microscopy, and prototyping of phase profiles later fixed in a metasurface.

Pitfalls

Phase-only nematic panels modulate one linear polarization; the orthogonal component passes nearly unmodulated and adds to the zero order, so the input must be aligned to the director. Average power is limited by heating of the liquid crystal and backplane; cooled high-power designs tolerate much more than standard panels, and the ratings differ widely between products. Phase wrapping at 2π is exact only at the calibrated wavelength, so broadband light sees wavelength-dependent efficiency.

Common questions

What is the difference between an SLM and a DMD?

An LCoS SLM gives continuous phase at each pixel but switches in milliseconds. A DMD gives binary amplitude, on or off, but switches at kilohertz rates. LCoS suits applications that need efficient phase control; the DMD suits applications that need speed.

Can an SLM modulate amplitude?

Yes: a phase panel between crossed or rotated polarizers, or a twisted-nematic panel, gives amplitude modulation, and amplitude can also be encoded in a phase hologram at a cost in efficiency.

References: J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).