Glossary entry

Thermo-optic phase shifter

A resistive heater over a waveguide that tunes optical phase through the temperature dependence of refractive index. Slow but simple and lossless at DC, and the trim-and-bias workhorse of photonic integrated circuits.

Integrated photonicsUpdated October 2026

Every interferometric photonic circuit needs phase control: to bias Mach–Zehnders, align ring resonances to channels, and trim away fabrication variation. The thermo-optic phase shifter delivers it with nothing more than a resistor: metal or doped-silicon heater above (or beside) the waveguide, current through the heater, local temperature rise, index shift $Δ n = (d n / d T) Δ T$ , phase shift $Δ ϕ = 2 π Δ n_{e f f} L / λ$ .

Material contrast explains where the technique shines. Silicon's thermo-optic coefficient is large ( $d n / d T \approx 1.8 \times 10^{- 4} K^{- 1}$ ), so a silicon phase shifter reaches $π$ with modest heating: $P_{π}$ of 10–30 mW in standard geometries. Silicon nitride's coefficient is an order smaller ( $\approx 2.4 \times 10^{- 5}$ ), so nitride circuits pay proportionally more power for the same phase, the flip side of nitride's prized thermal stability.

Figures of merit: $P_{π}$ (power for π), response time, and optical loss (near zero, since the heater sits outside the mode; its one clean advantage over carrier-based phase shifters, whose free carriers absorb). Response is thermal-diffusion limited: microseconds to milliseconds, fine for bias and configuration, useless for data.

The figures of merit follow from three quantities. The temperature rise for a π shift over a heater of length $L$ is $Δ T_{π} = λ / (2 L d n_{e f f} / d T)$ ; the power to hold it is $P_{π} = G_{t h} Δ T_{π}$ with $G_{t h}$ the thermal conductance from heater to core; and the response time is $τ = C_{t h} / G_{t h}$ with $C_{t h}$ the heat capacity of what must warm. Their product $P_{π} τ = C_{t h} Δ T_{π}$ does not depend on $G_{t h}$ at all, which is the trade in one line: undercutting the substrate lowers $G_{t h}$ , lowering $P_{π}$ and raising $τ$ by the same factor.

Platform	$d n / d T$ (K $^{- 1}$ )	$Δ T_{π}$ for the stated length	Typical $P_{π}$	Typical response
Silicon, 100 µm heater	$1.86 \times 10^{- 4}$	42 K	10 to 30 mW	1 to 10 µs
Silicon, 300 µm heater	$1.86 \times 10^{- 4}$	14 K	10 to 30 mW (longer, cooler)	1 to 10 µs
Silicon, undercut	$1.86 \times 10^{- 4}$	as above	0.5 to 3 mW	100 µs to 1 ms
Silicon nitride, 1 mm heater	$2.45 \times 10^{- 5}$	32 K	50 to 300 mW	10 to 100 µs
Silica (PLC), 5 mm heater	$1.0 \times 10^{- 5}$	16 K	100 to 500 mW	about 1 ms

The $Δ T_{π}$ column is computed from the coefficient and length at 1550 nm; the power and response columns are representative of published devices and vary with cladding thickness and heater geometry. The same arithmetic applied to a ring, where the requirement is a full free spectral range rather than π, is worked in Thermal tuning and locking of ring resonators. Efficiency engineering is thermal engineering: undercut/suspended structures that block heat leakage to the substrate push $P_{π}$ below 1 mW at the cost of slower response and mechanical delicacy; folded waveguides under one heater trade length for power.

System-level realities dominate at scale. A circuit with hundreds of shifters at tens of mW each spends watts on standing still, often the largest single term in a PIC's power budget. Thermal crosstalk couples neighboring shifters (heat does not respect layout boundaries), so dense meshes need calibration matrices and feedback, with on-chip monitors closing the loop. And since ambient temperature moves the whole chip, thermo-optic bias points are servoed, not set-and-forgotten.

Alternatives when heat won't do: plasma-dispersion (fast, lossy), Pockels-effect platforms (LNOI), and MEMS or stress-optic tuners for low-power hold.

Applied to rings rather than interferometer arms, the same heater physics is worked in Thermal tuning and locking of ring resonators.

References: K. Padmaraju and K. Bergman, "Resolving the thermal challenges for silicon microring resonator devices," Nanophotonics 3, 269 (2014). P. Dong et al., "Thermally tunable silicon racetrack resonators with ultralow tuning power," Opt. Express 18, 20298 (2010). A. Arbabi and L. L. Goddard, "Measurements of the refractive indices and thermo-optic coefficients of Si₃N₄ and SiOₓ using microring resonances," Optics Letters 38, 3878 (2013). L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University Press, 2015).