Glossary entry

Effective index (n_eff)

The ratio of the free-space propagation constant to the guided-mode propagation constant of a waveguide. Quantifies how slowly the guided phase advances compared to plane-wave propagation in vacuum.

The effective index of a guided mode is defined as

n_\text{eff} \;=\; \frac{\beta \, c}{\omega} \;=\; \frac{\beta \, \lambda_0}{2\pi},

where $\beta$ is the mode propagation constant, $\omega$ is the angular frequency, $c$ is the speed of light, and $\lambda_0$ is the free-space wavelength. The phase velocity of the guided mode is $v_p = c / n_\text{eff}$ .

For a confined mode, $n_\text{eff}$ lies between the cladding and core indices: $n_\text{clad} < n_\text{eff} < n_\text{core}$ . Higher confinement corresponds to $n_\text{eff}$ closer to $n_\text{core}$ .

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

Platform	Cross-section	$n_\text{eff}$
SOI strip	220 × 500 nm	2.44
SOI rib (slab + 220 nm strip)	220 × 500 nm	2.85
Silicon nitride	200 × 800 nm	1.81
Silicon nitride (thick)	800 nm	1.95
InP shallow ridge	varies	$\sim$ 3.30
SMF-28 fiber	core 8.2 μm	1.467

$n_\text{eff}$ is wavelength-dependent — different wavelengths see different effective propagation conditions. The wavelength derivative defines the group index, which governs pulse propagation and resonator FSR.

$n_\text{eff}$ enters all phase-matching conditions: the Bragg condition for DFB lasers and gratings, the grating-coupler design equation, and the resonance condition for ring resonators ( $n_\text{eff} \, L = m \lambda_0$ , where $L$ is round-trip length and $m$ is an integer).