Glossary entry

Mode field diameter (MFD)

The diameter of the guided mode of a single-mode fiber, equal for a Gaussian mode to the diameter at which the intensity falls to 1/e² of its peak: 9.2 µm at 1310 nm and 10.4 µm at 1550 nm for standard fiber, larger than its 8.2 µm core. It sets splice and coupling loss and, with the cutoff wavelength, the fiber's sensitivity to bending.

Fiber & telecom Integrated photonicsUpdated October 2026

The mode field diameter (MFD) is the width of the guided mode of a single-mode fiber. The fundamental mode of a step-index fiber is close to a Gaussian, $E (r) \propto \exp (- r^{2} / w^{2})$ , and for a Gaussian mode the MFD is $2 w$ , the diameter at which the field falls to $1 / e$ of its value on the axis and the intensity to $1 / e^{2}$ , 13.5% of its peak. The mode is wider than the core, since part of it travels in the cladding: Corning SMF-28, the standard single-mode fiber, has an 8.2 µm core and an MFD of 9.2 µm at 1310 nm and 10.4 µm at 1550 nm. The MFD sets the loss of a splice or a coupling, since two fibers join with little loss when their mode field diameters match, whatever their cores.

Definitions

The real mode is not exactly Gaussian: in a step-index fiber it follows a Bessel function $J_{0}$ in the core and decays exponentially in the cladding, so its width depends on how it is defined. ITU-T G.650.1 and IEC 60793-1-45 use the Petermann II definition,

MFD = 2 \sqrt{2} {[\frac{\int_{0}^{\infty} E^{2} (r) r d r}{\int_{0}^{\infty} {(d E / d r)}^{2} r d r}]}^{1 / 2},

which gives $2 w$ for a Gaussian. It is the inverse of the rms width of the far-field pattern, which is how the reference method measures it, and for a small lateral offset $d$ between two identical fibers it gives the coupled fraction as $1 - (2 d / MFD)^{2}$ , whatever the shape of the mode. For an ideal step-index fiber with the dimensions of SMF-28 at 1550 nm, computed from the exact mode, the Petermann II diameter is 10.00 µm, the diameter of the best-fitting Gaussian is 10.13 µm (which overlaps the true mode to 99.2%), and the diameter at which the intensity of the true mode falls to $1 / e^{2}$ is 9.53 µm. The definitions agree to within a few percent for standard fiber and differ more for fibers whose modes are far from Gaussian.

Estimating it from the V number

Marcuse's fit gives the radius of the best-fitting Gaussian for a step-index core of radius $a$ ,

\frac{w}{a} \approx 0.65 + \frac{1.619}{V^{3 / 2}} + \frac{2.879}{V^{6}},

accurate to about 1% for $1.2 < V < 2.4$ , where $V = 2 π a NA / λ$ is the V number. The ratio $w / a$ is also the ratio of the MFD to the core diameter:

V	MFD / core diameter
2.4	1.10
2.0	1.27
1.6	1.62
1.2	2.85

Just below the single-mode cutoff at $V = 2.405$ the mode is only 10% wider than the core, and as $V$ falls with rising wavelength it spreads rapidly into the cladding. An ideal step with SMF-28's 8.2 µm core and 0.36% index step, which gives an NA of 0.123 and $V = 2.04$ at 1550 nm, has an MFD by Marcuse's formula of 9.0 µm at 1310 nm and 10.2 µm at 1550 nm (8.8 and 10.0 µm by the Petermann II integral of the exact mode), 2 to 4% below the measured values, since real index profiles are not ideal steps. The datasheet NA of 0.14, measured from the far field at the 1% power level, overstates the index step, and with it the formula gives 9.2 µm at 1550 nm, as the calculator above notes. Both grow by about 5% per 100 nm of wavelength: the datasheet values between 1310 and 1550 nm, and the model between 1550 and 1625 nm.

Typical values

Fiber	Core diameter	MFD
Standard single-mode, SMF-28 (ITU-T G.652.D)	8.2 µm	9.2 µm at 1310 nm, 10.4 µm at 1550 nm
Non-zero dispersion-shifted, LEAF (G.655)	shaped profile	9.6 µm at 1550 nm
HI 1060, for 980 and 1060 nm	5.3 µm	5.9 µm at 980 nm, 6.2 µm at 1060 nm

The fiber values are the manufacturers' specifications. Chip-side modes are described by the same measure, taken as the diameter of the best-fitting Gaussian, although they are rarely circular or Gaussian: computed at 1550 nm, the mode of a 500 × 220 nm silicon strip waveguide is 0.46 µm across and that of a 180 nm inverse taper tip 2.6 µm, and a lensed fiber focuses to a spot 2 to 8 µm across to meet them.

Splices and coupling

Two Gaussian modes with mode field diameters $d_{1}$ and $d_{2}$ , aligned in the same plane, couple with efficiency

η = {(\frac{2 d_{1} d_{2}}{d_{1}^{2} + d_{2}^{2}})}^{2},

so a fusion splice between SMF-28 and LEAF at 1550 nm, 10.4 against 9.6 µm, loses 0.03 dB to the size difference, and one between 10.4 and 9.2 µm fibers 0.07 dB (fusion splicing). A ratio of 3 costs 4.4 dB and a ratio of 10 costs 14 dB, which is why chip couplers need spot-size converters, grating couplers or lensed fibers (mode mismatch loss). A lateral offset costs more in a small mode than in a large one: 1 µm between two SMF-28 fibers loses 0.16 dB at 1550 nm and 0.21 dB at 1310 nm. At a splice between fibers of different MFD an OTDR reads a gain from one side and an exaggerated loss from the other, and the two readings are averaged.

Bending and effective area

A mode that spreads further into the cladding is less tightly bound and loses more power at a bend, so among fibers with the same cutoff, those with a larger MFD are more sensitive to macrobending; bend-insensitive fibers reach low bend loss with a smaller MFD, a trench around the core, or both. The effective area that sets the strength of nonlinear effects is close to $π (MFD / 2)^{2}$ for standard fiber: for the ideal step at 1550 nm the exact calculation gives 76.8 µm² against 78.6 µm² from the Petermann II diameter.

The Fiber Numerical Aperture and V Number Calculator evaluates Marcuse's formula for any core and wavelength, and the Fiber Coupling Efficiency Calculator computes the overlap for any pair of mode sizes with offsets and tilts, and Coupling a Free-Space Beam into Single-Mode Fiber gives the bench procedure for matching a lens to the MFD.

Common questions

What is the mode field diameter of a fiber?

The diameter of its guided mode, which for a Gaussian mode is the diameter at which the intensity falls to $1 / e^{2}$ of its peak. For standard single-mode fiber it is 9.2 µm at 1310 nm and 10.4 µm at 1550 nm.

Why is the mode field diameter larger than the core?

Because part of the guided light travels in the cladding, as an evanescent field that decays away from the core. The fraction outside grows as the V number falls, so the MFD grows with wavelength.

How is the mode field diameter calculated?

For a step-index fiber, approximately from the V number with Marcuse's formula, $w / a \approx 0.65 + 1.619 V^{- 3 / 2} + 2.879 V^{- 6}$ , where $a$ is the core radius and MFD $= 2 w$ . For a measured or computed mode it follows from the Petermann II integral, which the standards use.

What is the difference between mode field diameter and core diameter?

The core diameter is a physical dimension of the glass; the MFD is the width of the light. For SMF-28 they are 8.2 µm and 10.4 µm at 1550 nm, and only the MFD enters the coupling and splice loss.

References: D. Marcuse, "Loss analysis of single-mode fiber splices," Bell System Technical Journal 56, 703 (1977). K. Petermann, "Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres," Electronics Letters 19, 712 (1983). ITU-T Recommendation G.650.1, Definitions and test methods for linear, deterministic attributes of single-mode fibre and cable. IEC 60793-1-45, Optical fibres, Part 1-45: Measurement methods and test procedures, Mode field diameter. Corning, SMF-28 Ultra, LEAF and HI 1060 product information sheets.