Wavelength temperature coefficient
The rate at which a laser's emission wavelength shifts with temperature, in nm/K. Two different physical rates exist: the gain peak follows the bandgap and moves at 0.25 to 0.5 nm/K depending on material, while a wavelength pinned by a grating or a short cavity follows the refractive index and moves at 0.06 to 0.09 nm/K. Which one a laser obeys is set by what selects its wavelength.
Every semiconductor laser's wavelength drifts with temperature, but the rate depends on what fixes the wavelength, and the two possibilities differ by a factor of five. A Fabry-Perot laser lases near the peak of its gain spectrum, and the gain peak follows the bandgap of the active material, which shrinks with temperature at a rate set by the Varshni relation for that semiconductor. A DFB, DBR, VCSEL, or grating-stabilized laser lases where its grating or cavity says, and that wavelength follows the refractive index, with the group index, since the Bragg condition or the cavity resonance is an index condition. The bandgap rate is the larger by far.
| Laser type | Wavelength | What sets | Coefficient (computed) | Typical measured range |
|---|---|---|---|---|
| GaAs / AlGaAs Fabry-Perot | 850 nm | Gain peak, meV/K | 0.26 nm/K | 0.25 to 0.30 nm/K |
| InGaAs Fabry-Perot | 980 nm | Gain peak | about 0.3 nm/K | 0.3 to 0.35 nm/K |
| InP-based Fabry-Perot | 1310 nm | Gain peak, meV/K (InP) | 0.44 nm/K | 0.4 to 0.5 nm/K |
| InGaAsP / AlGaInAs Fabry-Perot | 1550 nm | Gain peak, to meV/K | 0.5 to 0.6 nm/K | 0.4 to 0.5 nm/K |
| GaN blue Fabry-Perot | 450 nm | Gain peak, meV/K | 0.07 nm/K | 0.04 to 0.07 nm/K |
| DFB, 1550 nm | 1550 nm | Grating, , | 0.086 nm/K | 0.08 to 0.10 nm/K |
| DFB, 1310 nm | 1310 nm | Grating, , | 0.078 nm/K | 0.07 to 0.09 nm/K |
| VCSEL, 850 nm | 850 nm | Cavity resonance, , | 0.059 nm/K | 0.05 to 0.07 nm/K |
| Volume-Bragg-stabilized diode | 780 to 1064 nm | External glass grating | about 0.01 nm/K | 0.007 to 0.02 nm/K |
The computed column converts a bandgap rate to a wavelength rate through , which at 850 nm is 0.58 nm per meV of shift and at 1550 nm is 1.94 nm per meV, so the same bandgap rate produces a larger wavelength rate at longer wavelength. The measured ranges are wider than the computed values because the gain peak also moves with carrier density (band filling pushes it to shorter wavelength at higher injection), because quaternary alloys and quantum wells have their own Varshni parameters, and because the junction, not the case, sets the temperature: a laser whose junction runs 20 K above its heatsink shifts by the junction's temperature rise as well as the ambient's. That last point is what the junction-temperature measurement by wavelength shift exploits in reverse: a known coefficient turns a measured wavelength shift into a junction temperature, the method used by the junction temperature calculator and described in Measuring laser diode junction temperature.
The gap between the two rates is why Fabry-Perot lasers mode hop. The gain peak walks across the fixed comb of cavity modes at 0.3 to 0.5 nm/K while the modes themselves move at under 0.1 nm/K, so every few kelvin the lasing mode jumps to the neighbor now closer to the gain peak. In a DFB the grating and the gain peak drift apart at the same rate, and the design places the grating wavelength on the long-wavelength side of the gain peak at room temperature so that the two cross somewhere in the middle of the operating range; at the edges of a wide range the detuning costs threshold and slope, which is the reason a DFB specified over −40 to 85 °C has a wider threshold range than the same chip specified at 25 °C. Dense WDM lasers hold their wavelength with a thermoelectric cooler because 0.086 nm/K is 10.7 GHz/K at 1550 nm, and a 50 GHz grid tolerates a drift of a few GHz at most; a change of 0.1 K in the chip temperature is already 1 GHz. For uncooled coarse-WDM lasers, the 20 nm channel spacing of the CWDM grid exists precisely to swallow a 0.1 nm/K drift over a 100 K range, which is 10 nm, plus manufacturing spread.
References: I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001), for the Varshni parameters used (GaAs α = 0.5405 meV/K, β = 204 K; InP α = 0.363 meV/K, β = 162 K; GaN α = 0.909 meV/K, β = 830 K), evaluated at 300 K; L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), for the index-tuning relation and typical values. The computed column is derived from these parameters as described; the measured ranges are representative of published device data and manufacturer specifications.