Linewidth as a Function of Integration Time
The Root-Allan variance, like the heterodyne linewidth, is a measure of the frequency stability of an oscillator. It can be interpreted as the laser spectral content over a given time interval and gives you a very accurate description of long-term laser frequency variations.* The measured Root-Allan variance for two of our lasers shows that the linewidth is narrowest (~50 kHz) at short integration times and increases with integration time. The short-time ﬂuctuations are mainly due to electrical ﬂuctuations. The long-time ﬂuctuations are mainly due to slow temperature changes, and the middle-time spikes are the result of acoustically excited mechanical resonances in the laser cavity. The curve ﬁt is based on a model that includes ﬂicker and random-walk frequency noise. The linewidth at longer time intervals can be estimated by extrapolating the line.
*F.L. Walls, and D.W. Allan, Measurements of Frequency Stability, Proc. IEEE 74, No. 1 (1986)
What is meant by instantaneous linewidth?
Besides the time dependent jitter component in the linewidth, the timeless intrinsic linewidth is determined by the cavity design. This can be measured by heterodyning on a very short time scale (less than 1 µs) with a real-time spectrum analyzer or with any spectrum analyzer by matching the resolution bandwidth to the laser linewidth. The signal strength on the spectrum analyzer will only drop if the resolution bandwidth is smaller than the heterodyned signal.