Mode hop

A mode hop is a sudden change of a laser's wavelength from one longitudinal mode of its cavity to a neighboring one. A laser runs on the mode with the highest net gain, and when a change of temperature, drive current or optical feedback moves the gain spectrum or a wavelength filter relative to the cavity modes, a neighbor eventually has more gain and the laser switches to it. The wavelength then jumps by one mode spacing, ${\lambda }^2\mathrm{/}(2n_{g}L)$ for a cavity of length $L$ and group index $n_g$: 1.11 nm for a 300 µm InGaAsP chip at 1550 nm, 0.05 nm for an external cavity laser with 23.6 mm of optical length. Between hops the wavelength follows the cavity modes, which move far more slowly with temperature than the gain peak does, so a Fabry-Perot laser's wavelength rises with temperature in a staircase.

Hop size and spacing

Computed at 1550 nm with a group index of 3.6 for the chips:

In an InGaAsP Fabry-Perot laser near 1550 nm the gain peak moves with temperature at about 0.5 nm/K, following the bandgap, while the cavity modes move at 0.086 nm/K, following the refractive index (wavelength temperature coefficient). The gain peak therefore gains on the modes at about 0.41 nm/K. In the 300 µm chip it passes one mode spacing every 2.7 K, so the wavelength rises by 0.23 nm along one mode and then jumps by 1.11 nm; in the 1 mm chip the jumps are 0.33 nm every 0.8 K. Averaged over many steps the wavelength follows the gain peak. Drive current does the same through self-heating.

In different lasers

• Fabry-Perot lasers hop as described. Many run on several modes at once, sharing the power among them in proportions that change with current and temperature, and the shifting shares show up as mode partition noise when the light passes through a dispersive fiber.
• DFB lasers select one mode with a grating whose Bragg wavelength moves at the same 0.086 nm/K as the cavity modes, so temperature does not move the selection relative to the modes, and the laser stays on one mode across its rated range; qualification tests confirm it (DFB characterization workflow). A DFB can still hop to the mode at the other edge of the grating's stop band, or to a Fabry-Perot mode formed by its facets, when the gain peak has moved far from the Bragg wavelength or when spatial hole burning at high current changes the balance between modes. A quarter-wave phase shift in the grating and anti-reflection-coated facets make the selection robust.
• DBR lasers are tuned by current in the Bragg section. The lasing mode hops by one cavity mode spacing each time the Bragg peak moves by about that much, unless a phase section shifts the cavity modes in step with it.
• External cavity lasers tune smoothly only when the cavity length changes in proportion to the wavelength; otherwise they hop every mode spacing, 6.35 GHz in the example above. Residual reflection from the gain chip's facet adds modes of its own.
• Optical feedback from an external reflection forms a compound cavity with additional modes, and a laser without an optical isolator can hop among them as the path length drifts (optical feedback regimes).

Signs of a hop

The wavelength, read on a wavemeter or an optical spectrum analyzer, jumps by one mode spacing. The L–I curve often shows a small step or kink, since the two modes have slightly different losses. Close to the boundary the two modes have nearly equal net gain, so the side-mode suppression ratio falls towards 0 dB and the laser may alternate between them, which raises its low-frequency intensity noise. The hop often occurs at a different temperature or current on the way up than on the way down, because the lasing mode, by saturating the gain, holds down the gain available to its neighbor. A map of wavelength against both current and temperature shows the mode-hop-free regions as bands.

Avoiding them

A laser stays on one mode when its operating point is held inside a mode-hop-free region of that map, with a thermoelectric cooler and a stable current source; when its wavelength filter moves with the cavity modes, as in a DFB laser; or when filter and cavity are tuned together, as in an external cavity laser with a correctly placed pivot or a DBR laser with a phase section. An isolator removes hops caused by feedback. In swept-wavelength measurements a hop of the source appears as a step in the measured spectrum, which can be mistaken for a feature of the device under test (ring resonator Q extraction).

Common questions

What is a mode hop in a laser?

A sudden jump of the lasing wavelength from one longitudinal mode of the cavity to the next, by one mode spacing, when a neighboring mode comes to have more gain than the lasing one.

What causes mode hopping?

A change that moves the gain spectrum or a filter relative to the cavity modes: temperature and current, which move the gain peak about five times faster than the modes in a Fabry-Perot laser near 1550 nm, tuning of a filter without the cavity length, or optical feedback.

How large is a mode hop?

One mode spacing, ${\lambda }^2\mathrm{/}(2n_{g}L)$: about 1.1 nm for a 300 µm diode laser chip at 1550 nm, 0.33 nm for a 1 mm chip and 0.05 nm for an external cavity laser a few centimeters long.

How is mode hopping prevented?

By holding temperature and current where the laser is known to stay on one mode, by using a laser whose filter moves with its cavity modes, such as a DFB laser, by tuning filter and cavity length together, and by isolating the laser from reflections.

References: L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, 1988). G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).