Glossary entry

Group index (n_g)

The ratio of the speed of light in vacuum to the group velocity of a guided mode. Governs pulse propagation, resonator free spectral range, and dispersion.

The group index is defined as

n_g \;=\; \frac{c}{v_g} \;=\; n_\text{eff} - \lambda_0 \frac{d n_\text{eff}}{d \lambda_0},

where $v_g$ is the group velocity, $n_\text{eff}$ is the effective index, and $\lambda_0$ is the free-space wavelength.

For dispersive waveguides, $n_g$ differs from $n_\text{eff}$ because $n_\text{eff}$ varies with wavelength. The difference is typically larger for high-index-contrast platforms such as SOI than for low-contrast platforms such as fiber.

Typical values at 1550 nm (fundamental TE-like mode):

Platform	Cross-section	$n_\text{eff}$	$n_g$
SOI strip	220 × 500 nm	2.44	4.3
SOI rib	220 × 500 nm	2.85	3.8
Silicon nitride	200 × 800 nm	1.81	2.0
InP shallow ridge	varies	3.30	3.6
SMF-28 fiber	core 8.2 μm	1.467	1.470

$n_g$ governs:

Free spectral range of resonators: $\text{FSR}_\lambda = \lambda_0^2 / (n_g L)$
Group delay through any waveguide section: $\tau_g = n_g L / c$
Group velocity dispersion (GVD), the wavelength-derivative of $1/v_g$
Photon lifetime in resonators (combined with cavity loss)

For ring resonator design and characterization, $n_g$ is the relevant parameter — not $n_\text{eff}$ . Confusing the two is a common error in FSR-based loss extraction.

Measurement: $n_g$ can be extracted from the measured FSR of a known-length ring resonator: $n_g = \lambda_0^2 / (\text{FSR}_\lambda \cdot L)$ .