Optical phase shifter

An optical phase shifter is a length of waveguide in which some applied quantity, usually heat or voltage, changes the effective index of the guided mode, so that the light emerges with a controlled extra phase. Switches, modulators, ring tuners and phased arrays all convert its phase change into a change of power, wavelength or direction. The index changes available are small, from about $10^{-5}$ to a few $10^{-3}$, so devices range from tens of micrometers to several millimeters long. At 1550 nm an effective index change of $10^{-3}$ needs 775 µm for a phase shift of π.

Phase and the π length

A change $\Delta n_\text{eff}$ over a length $L$ adds

$$\Delta\phi = \frac{2\pi\, \Delta n_\text{eff}\, L}{\lambda}$$

so the length for a π shift is

$$L_\pi = \frac{\lambda}{2\,\Delta n_\text{eff}} .$$

With $\lambda$ = 1550 nm and $\Delta n_\text{eff} = 10^{-3}$, $L_\pi$ = 775 µm; with $10^{-4}$ it is 7.75 mm. The Mach-Zehnder interferometer entry uses the same condition, $\Delta n_\text{eff} L = \lambda/2$. Only the part of the index change that overlaps the optical mode counts, so $\Delta n_\text{eff}$ is the material change weighted by that overlap.

Mechanisms

Thermo-optic. A resistive heater raises the waveguide temperature. Silicon's coefficient is large, $dn/dT \approx 1.86 \times 10^{-4}$ K⁻¹, so a 100 µm heater needs a rise of 42 K for π. The thermo-optic phase shifter entry gives $P_\pi$ of 10–30 mW in standard geometries, below 3 mW with an undercut substrate, and response times of microseconds to milliseconds.

Free carriers. In silicon the plasma dispersion effect lowers the index as electron and hole densities rise. A reverse-biased p-n junction across the waveguide (carrier depletion) reaches $V_\pi L$ of 1–3 V·cm with bandwidths of tens of gigahertz; a 3 mm single-arm shifter at 2 V·cm needs 6.7 V. Forward-biased carrier injection gives a much larger index change per volt, with $V_\pi L$ near 0.04 V·cm reported, but carriers leave only by recombining, which limits the response to about 160 MHz for a 1 ns lifetime without pre-emphasis. Both add free-carrier absorption, so the phase comes with loss, and the phase is a nonlinear function of voltage.

Pockels effect. In electro-optic crystals the index changes linearly with the applied field and without added absorption. Thin-film lithium niobate on insulator gives $V_\pi L$ of 1.5–3 V·cm and bandwidths up to about 100 GHz; barium titanate on silicon reaches 0.2–0.5 V·cm. The relation between voltage and phase is given in the half-wave voltage entry.

Mechanical and liquid crystal. MEMS shifters move a suspended waveguide or a nearby dielectric to change the evanescent overlap, holding phase with almost no static power. Liquid-crystal claddings give large index changes at low voltage, with millisecond response. Both are slower than the electrical mechanisms and less mature in foundry processes.

Figures of merit

Four numbers characterize a phase shifter: the drive needed for π ($V_\pi L$ in V·cm for voltage-driven devices, $P_\pi$ in mW for heaters), the insertion loss, often quoted as loss times $V_\pi L$ in V·dB, the speed (bandwidth or switching time) and the footprint. No mechanism leads in all four: heaters add almost no optical loss but are slow and power hungry in large numbers, depletion shifters fast but lossy, Pockels shifters fast and low loss but built in non-silicon materials.

Where phase shifters are used

Switches and modulators. In a Mach-Zehnder switch a π difference between the arms moves light from one output to the other; in a Mach-Zehnder modulator the shifter is driven with data, often push-pull so each arm supplies half the phase.

Phased arrays. An optical phased array applies a phase step $\Delta\phi$ between neighboring emitters of pitch $d$ to steer its beam to $\sin\theta = \lambda\Delta\phi/(2\pi d)$. At 1550 nm with $d$ = 2 µm, a step of π/2 steers 11.2°.

Ring tuning. A shifter inside a ring moves the resonance by $\Delta\lambda = \lambda\,\Delta n_\text{eff}/n_g$: at 1550 nm with $n_g$ = 4.2, $\Delta n_\text{eff} = 10^{-3}$ moves it 0.37 nm. A heater aligns the ring to a channel, and a junction drives a microring modulator at data rates.

Pitfalls

Phase in a heated device drifts with ambient temperature and with neighboring heaters, so circuits with many shifters need calibration and feedback. Carrier shifters change loss along with phase, which unbalances an interferometer and limits extinction. A shifter's $V_\pi L$ applies to one arm; quoting the push-pull figure halves it, and comparisons should state which is used.

Common questions

How long does a phase shifter need to be?

Divide the wavelength by twice the effective index change: 775 µm for $10^{-3}$ at 1550 nm. Thermo-optic shifters reach π in 100–300 µm because heating changes silicon's index by several $10^{-3}$; depletion shifters are usually millimeters long.

What is the difference between a phase shifter and a phase modulator?

The physics is the same. "Phase modulator" usually means a fast shifter driven with a signal, while "phase shifter" also covers slow tuning and biasing elements such as heaters.

References: G. T. Reed, G. Mashanovich, F. Y. Gardes and D. J. Thomson, "Silicon optical modulators," Nature Photonics 4, 518 (2010); R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987); L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University Press, 2015); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).