Glossary entry

Multimode interference (MMI) coupler

An integrated-photonic power-splitting element that uses self-imaging in a wide multimode waveguide section to distribute light between input and output ports. The standard 1×N and N×N power splitter in modern PIC platforms.

An MMI coupler consists of a wide multimode waveguide (the MMI section) with narrow single-mode input and output waveguides attached at carefully chosen positions along its short edges. Light entering through an input waveguide excites several transverse modes in the MMI section. These modes propagate with different phase velocities; at specific lengths, their interference reconstructs the input field at one or more output positions — the self-imaging effect.

For a $1 \times N$ MMI splitter, the design length is

L_{\pi} \;=\; \frac{4 n_g W_e^2}{3 \lambda_0},

where $n_g$ is the group index, $W_e$ is the effective MMI section width (including penetration of the modal field into the cladding), and $\lambda_0$ is the free-space wavelength. The $1 \times N$ splitter length is $L = 3 L_\pi / N$ for general $N$ outputs (with port placement that exploits the symmetry of the self-image pattern).

Typical specifications:

MMI type	Dimensions (SOI 220 nm)	Insertion loss
1 × 2	3 × 25 μm	0.1 – 0.3 dB
2 × 2 (3 dB coupler)	3 × 50 μm	0.2 – 0.4 dB
1 × 4	6 × 60 μm	0.3 – 0.6 dB
4 × 4	8 × 120 μm	0.4 – 0.8 dB
1 × 8	12 × 240 μm	0.5 – 1.0 dB

Advantages over directional couplers:

Broadband response: $\pm 30$ nm or more around the design wavelength with $<$ 1 dB power imbalance
Fabrication-tolerant: relatively insensitive to width and length variations
Polarization-insensitive with appropriate design
Compact for large $N$ : scales gracefully to 8×8 or 16×16

Limitations:

Higher minimum insertion loss than ideal directional couplers ( $\sim 0.1 - 0.5$ dB vs $< 0.05$ dB)
Phase relationships between outputs are fixed by geometry (90° between adjacent outputs of a 2×2)
Larger footprint than directional couplers for very small splitting ratios (e.g., 99:1 tap ratios)

MMI couplers are the workhorse splitter in silicon photonics, providing 50/50 beam-splitter functionality at modulator inputs, balanced detector inputs of coherent receivers, and 1×N tree splitters in optical phased arrays. The 2×2 MMI is also the standard building block for Mach–Zehnder interferometer arms.