Zero-dispersion wavelength

The zero-dispersion wavelength ${\lambda }_0$ is the wavelength at which the chromatic dispersion of a fiber or waveguide passes through zero: the group delay is at an extremum, so neighboring wavelengths arrive together to first order. Below ${\lambda }_0$ a conventional fiber has normal dispersion ($D<0$, ${\beta }_2>0$) and above it anomalous dispersion ($D>0$, ${\beta }_2<0$). It is a property of the guided mode, not of the glass alone: bulk fused silica has its material zero at 1273 nm (computed from Malitson's Sellmeier equation), and the negative waveguide dispersion of a step-index single-mode fiber moves the zero of standard fiber to around 1310 nm.

Dispersion near λ₀

ITU-T G.652 specifies standard single-mode fiber by ${\lambda }_0$ and the dispersion slope there, $S_0$, and gives the dispersion as

$$D(\lambda )=\frac{S_0}{4}(\lambda -\frac{{\lambda }_0^4}{{\lambda }^3})$$

with ${\lambda }_0$ between 1300 and 1324 nm and $S_0\le 0.092$ ps/(nm²·km). Close to the zero the formula is linear to good accuracy,

$$D(\lambda )\approx S_0(\lambda -{\lambda }_0)$$

For ${\lambda }_0=1310$ nm and $S_0=0.092$ the exact formula gives −3.76, −1.79, +0.09 and +1.89 ps/(nm·km) at 1271, 1291, 1311 and 1331 nm, the four lanes of 400GBASE-FR4, against −3.59, −1.75, +0.09 and +1.93 from the linear form. Because ${\lambda }_0$ itself may lie anywhere in its 24 nm window, a link design uses the worst case: $\mathrm{\mid }D\mathrm{\mid }=5.19$ ps/(nm·km) at 1271 nm for a fiber with ${\lambda }_0=1324$ nm, and 2.75 at 1331 nm for one with ${\lambda }_0=1300$ nm.

What happens at λ₀

Dispersion does not vanish at ${\lambda }_0$; its second-order term does, and the third-order term ${\beta }_3$ takes over. With $D=0$ the conversion from slope is ${\beta }_3=({\lambda }^2\mathrm{/}2\pi c{)}^2{S}_0$, which for $S_0=0.092$ at 1310 nm is 0.0764 ps³/km. For a narrow-linewidth source exactly at ${\lambda }_0$, Agrawal gives the dispersion-limited bit rate as

$$B{\left(\mathrm{\mid }{\beta }_3\mathrm{\mid }L\right)}^{1\mathrm{/}3}\le 0.324$$

which allows 354 Gb/s over 10 km and 165 Gb/s over 100 km, far beyond the second-order limit a few nanometers away. Pulses shorter than a picosecond, or wide spectra such as a multimode source, see the slope directly and are distorted asymmetrically. That is the physics behind the historical O-band choice for the first single-mode systems and behind today's datacenter optics, which run intensity modulation in the O-band where no erbium amplifier is needed and where dispersion costs little; the Datacenter Link Budget Explorer computes the per-lane dispersion from the G.652 curve.

The same absence of dispersion is what made dispersion-shifted fiber a poor choice for WDM. Four-wave mixing between channels is phase-matched when the dispersion is zero. For the degenerate product of two channels spaced $\mathrm{\Delta }\nu$ the phase mismatch is about $\mathrm{\mid }{\beta }_2\mathrm{\mid }(2\pi \mathrm{\Delta }\nu {)}^2$, and at 100 GHz spacing its coherence length $2\pi \mathrm{/}\mathrm{\Delta }\beta$ is 0.71 km in G.652 fiber at 1550 nm ($D$ = 17.46 ps/(nm·km)), 3.1 km for $D=4$ ps/(nm·km), and 125 km for $D=0.1$ ps/(nm·km). In the last case mixing products build up over the whole span. Non-zero dispersion-shifted fiber places ${\lambda }_0$ outside the C-band, usually below it, to keep a small dispersion everywhere in it, and coherent systems, which compensate any dispersion digitally, have made the large dispersion of G.652 at 1550 nm an advantage rather than a cost (see dispersion compensation).

In nonlinear optics ${\lambda }_0$ is a design parameter. Soliton propagation needs anomalous dispersion, so an optical soliton must sit above the zero of a conventional fiber; supercontinuum sources in photonic crystal fiber are usually pumped close to ${\lambda }_0$ on the anomalous side; and soliton microcombs are designed by shaping the waveguide cross-section so that the pump wavelength sees weak anomalous dispersion.

The Dispersion and Pulse Broadening Calculator computes $D$ and $S$ at any wavelength from ${\lambda }_0$ and $S_0$ with the G.652 formula, includes an O-band case among its presets, and plots $D(\lambda )$ from 1200 to 1700 nm so that the zero crossing of each fiber type can be read off.

References: ITU-T Recommendation G.652, Characteristics of a single-mode optical fibre and cable. ITU-T Recommendation G.653, Characteristics of a dispersion-shifted, single-mode optical fibre and cable. ITU-T Recommendation G.655, Characteristics of a non-zero dispersion-shifted single-mode optical fibre and cable. G. P. Agrawal, Fiber-Optic Communication Systems, 5th ed. (Wiley, 2021), chapter 2. G. P. Agrawal, Nonlinear Fiber Optics, 6th ed. (Academic Press, 2019). I. H. Malitson, "Interspecimen comparison of the refractive index of fused silica," Journal of the Optical Society of America 55, 1205 (1965). IEEE Std 802.3, clause 151 (400GBASE-FR4).