Thermo-Optic Coefficients of Photonic Materials: Reference Table

Scope

The thermo-optic coefficient $dn/dT$ (how refractive index moves with temperature) sets how much every filter drifts, how efficient every thermal phase shifter is, and how hard athermal design has to work. The values are scattered across decades of papers, most behind paywalls; this page collects the working numbers for the common photonic materials at telecom wavelengths and room temperature, states the formulas they plug into, and flags where "the" coefficient is actually a family of values.

The reference table

Values near 1550 nm and 300 K unless noted; sources at the end and on each material page.

Three structural facts jump out of the table. Semiconductors cluster around $+2 \times 10^{-4}$, an order of magnitude above the dielectrics. Dielectrics (silica, nitride) cluster at $+1$–$2.5 \times 10^{-5}$. And polymers sit negative at semiconductor-like magnitude, which is the entire basis of polymer-overlay athermalization.

The formulas the table feeds

Waveguide devices respond through the effective index. What a ring or MZI feels is $dn_{eff}/dT$, the confinement-weighted average over core and cladding:

$$\frac{dn_{eff}}{dT} \;\approx\; \Gamma_{core}\frac{dn_{core}}{dT} + \Gamma_{clad}\frac{dn_{clad}}{dT}$$

A silicon strip waveguide (mode mostly in Si) lands near $1.6$–$1.9 \times 10^{-4}$; a thin-core SiN guide with most of the mode in oxide can sit well below nitride's bulk value. Geometry is a thermal design variable.

Resonance and filter drift. A resonant wavelength moves as

$$\frac{d\lambda}{dT} \;=\; \frac{\lambda}{n_g}\,\frac{dn_{eff}}{dT}$$

Plugging in: silicon ring, $n_g \approx 4.2$, $dn_{eff}/dT \approx 1.8\times10^{-4}$ → ~66 pm/°C (≈ 8 GHz/°C at 1550 nm). That is the number behind every "silicon rings need heaters and servos" statement. The same arithmetic for a silica AWG gives the ~11 pm/°C familiar from athermal-package datasheets, and for SiN roughly 10–20 pm/°C depending on confinement.

Phase-shifter efficiency. A heater's $P_\pi$ scales inversely with $dn_{eff}/dT$. Silicon's big coefficient is why its thermal tuners are 5–10× more power-efficient than nitride's, the flip side of its 5–10× worse drift. There is no free lunch; there is only choosing which side of it you want.

Caveats that keep this honest

$dn/dT$ is wavelength-dependent (mildly, away from band edges), temperature-dependent (silicon's falls by roughly an order of magnitude from 300 K to below 100 K; cryogenic photonics cannot use room-temperature numbers), and for films, process-dependent: PECVD vs LPCVD nitride, silicon-rich compositions, and polymer formulations all shift coefficients tens of percent. Anisotropic crystals (LiNbO₃) have per-axis values. Quote the axis with the number. For design sign-off, measure on your platform: a ring resonance tracked over a 20 °C sweep hands you $dn_{eff}/dT$ in one afternoon, which is precisely how most published film values were obtained.

Athermal design in one paragraph

Passive athermalization balances positive-coefficient core against negative-coefficient cladding (polymer overlays on SOI, heavily silica-loaded SiN geometries) so $dn_{eff}/dT \to 0$ at the design point; mechanical athermalization (AWG packages that physically shift the fiber with a bimetal element) cancels drift without touching the optics; and active stabilization simply spends heater power to hold setpoint, the standard answer in silicon at the cost of the power budget discussed under thermo-optic phase shifters.

Per-material context lives on the materials pages, each with references: silicon, silicon nitride, fused silica, indium phosphide, gallium arsenide, and lithium niobate. Primary sources for the headline values: Frey et al. (Si, cryo-to-RT), Arbabi & Goddard (Si₃N₄/SiOₓ, microring method), Toyoda & Yabe (silica), and the compilations in Bogaerts et al. for platform-level effective values.