Lower Noise from Longer Lasers

Posted on 2006-08-20. Permanent link: http://www.rp-photonics.com/spotlight_2006_08_20.html

Ref.: encyclopedia articles on laser noise, quantum noise, linewidth, Schawlow-Townes linewidth, and others

Have you been aware that the intensity and phase noise level of a laser can often be reduced simply by making the laser cavity longer? This is not true e.g. for the low-frequency intensity noise arising from pump power fluctuations, but it does hold for the high frequency intensity and phase noise, including that resulting from quantum fluctuations and from cavity length changes.

The reason for that is actually quite simple. Consider some effect which affects the intensity and phase of the light circulating in the laser cavity e.g. each time it passes the laser gain medium. A longer cavity, corresponding to a longer round-trip time, then means that this disturbance will alter the intracavity light fewer times per second. This is indeed one of the reasons why e.g. single-frequency laser diodes have multi-megahertz linewidths, while solid state bulk lasers with somewhat longer cavities get down to the kilohertz region. There are other reasons, though, in particular the higher intracavity power of solid state lasers, their lower cavity losses (and thus laser gain), and their lower linewidth enhancement factor.

As an example, consider the case of quantum noise in a single-frequency laser. Here, the disturbances in each round trip are uncorrelated, so that the variance e.g. of the optical phase grows linearly with time, and the growth rate is inversely proportional to the round-trip time. The not quite trivial math shows that this leads to a linewidth which scales in proportion to the inverse square of the cavity round-trip time (see the Schawlow-Townes equation). The same kind of scaling is obtained for cavity length fluctuations, although for somewhat different reasons.

Note that in real life it often becomes more difficult to keep a cavity stable when it is made long. Also, the reduced free spectral range may then lead to mode hops, making it more difficult to obtain stable single-frequency operation. Therefore, there may be some range of cavity lengths with best noise properties. And of course there is a number of other factors which can be optimized.