Glossary entry

Mode mismatch loss

Optical power loss arising from imperfect spatial overlap between two propagating modes. Dominates fiber-to-fiber, fiber-to-PIC, and laser-to-fiber coupling in misaligned or geometrically dissimilar systems.

When two single-mode waveguides are joined, the transmitted power equals the squared modulus of the overlap integral between the two transverse mode profiles. For Gaussian modes, this integral has a closed form.

Size mismatch. For Gaussian modes with $1/e^2$ intensity radii $w_1$ and $w_2$ , perfectly centered and aligned:

\eta_\text{size} \;=\; \left( \frac{2 \, w_1 w_2}{w_1^2 + w_2^2} \right)^2.

The corresponding loss in dB is $-10 \log_{10} \eta_\text{size}$ .

$w_2 / w_1$	$\eta_\text{size}$	Loss
1.0	1.000	0.00 dB
1.5	0.923	0.35 dB
2.0	0.800	0.97 dB
3.0	0.600	2.22 dB
5.0	0.385	4.15 dB
10.0	0.198	7.04 dB

Lateral offset. For Gaussian modes laterally offset by distance $d$ :

\eta_\text{offset} \;=\; \exp\!\left( -\frac{2 d^2}{w_1^2 + w_2^2} \right).

For $d = w$ (one mode radius offset): $\eta \approx 0.37$ , or 4.3 dB loss.

Angular offset. For Gaussian modes with angular tilt $\theta$ :

\eta_\text{angular} \;=\; \exp\!\left( -\frac{(\pi w_b \theta)^2}{2 \lambda^2} \right),

where $w_b$ is the mode radius at the joining plane. For $w_b = 5$ μm at 1550 nm, $\theta = 1°$ : $\eta \approx 0.84$ , or 0.75 dB loss.

Total coupling efficiency multiplies the contributions: $\eta_\text{total} = \eta_\text{size} \cdot \eta_\text{offset} \cdot \eta_\text{angular} \cdot \eta_\text{Fresnel} \cdot \ldots$

For non-Gaussian modes (waveguide modes with non-circular or non-fundamental profiles), the overlap must be computed numerically. The Gaussian approximation typically gives results within 5–10% for fiber and well-confined waveguide modes.

See Fiber Coupling Efficiency Calculator for an interactive computation including all three contributions.