One of the assignments in the Laser Diode lab states:
 

The implication is that a change in temperature will change the length of the chip and can cause an observable change in the emitted wavelength or in the mode spacing.  Let’s see if that is reasonable.

When I did the experiment I observed a changing in wavelength of about 0.8 nm for a temperature change of 4.12°C, or about 0.19 nm/°C.

Assume we have a GaAs laser with cavity length L = 300 mm.  The thermal expansion coefficient of GaAs is about 6 ´ 10^-6/°C, and the refractive index is about n = 3.5.  Assume we have a mode at 800 nm at temperature T₁.  Let’s first find the mode number.

The next highest mode, 2626, has wavelength
.

The mode spacing is thus
.

Many digits were kept in anticipation of a small effect.

Let’s increase the temperature to T₂ = T₁+ 20°C.

The change in wavelength is 800.0960 – 800 nm = 0.0960 nm, or about 0.0048 nm/°C.  The observed change of about 0.19 nm/°C is much larger than can be explained by “moving the mirrors.”

The change in mode spacing is thus –0.3047 – (-0.3046) nm = -0.0001 nm.  (Now you see why I kept so many digits.)  The resolution of the spectrometer in the lab is 0.02 nm at best.

From these calculations I conclude that
1. The change in wavelength due to change in the separation between the mirrors may be observable, but
2. it is much smaller (~40 times smaller) than the observed change, and
3. the change in mode spacing is not resolvable.

This is clearly not physically realistic, thus moving the mirrors by changing temperature to produce a change in mode spacing detectable by the spectrometer in the lab is not reasonable. 

The wavelength of the peak in the gain curve is related to the energy gap of the semiconductor, which is a function of temperature.  If the gain curve moves enough it will cause a different Fabry-Perot mode to be amplified.  Let’s see if this is a strong enough effect to explain the observed change in wavelength.

For GaAs,
.

Recall that the actual peak of the gain curve occurs for energies somewhat larger than the bandgap energy, since the peak of the electron concentration in the conduction band is somewhat above the conduction band edge, and the maximum in the density of empty states in the valence band occurs somewhat below the valence band edge.  But if the bandgap energy changes, so will the difference in energy between these maximum concentrations, by nearly the same amount.

Because of the nonlinear nature of the equation for E_g(T) I will need to work with actual temperatures, not just with changes in temperature.  Let’s assume that the peak of the gain curve was 800 nm at 18°C (291 K), and look at the effect on the peak of the gain curve of changing to 22°C (295 K).

The bandgap energy would change by
.

The energy corresponding to a wavelength of 800 nm is
.

Using the change in the bandgap energy with this gives a new peak of

Note that this is a change in the gain envelope.  A different Fabry-Perot mode would now be amplified.  To account for this we need to include the effect of temperature on the length of the laser, as well as on the energy gap.

At 22°C the length of the laser would be

The two closest modes to the new gain peak would be

and

The first gives a temperature dependence of 0.94 nm/4°C = 0.235 nm/°C.  The second gives a temperature dependence of 0.63 nm/4°C = 0.158 nm/°C.  These are comparable to and straddle to my experimentally observed change of 0.19 nm/°C.  Given that I made several assumptions (e.g. about the laser length and the initial wavelength), that are close to but not exaclty equal to the exact diode used in the experiment this is a pretty good result.