Laser Frequency Stabilization by Using Arm-Locking

In order to achieve the required measurement performance on LISA, the laser frequency must be stabilized to approximately 30 Hz/X[1+(1mHz/f)4]1/2 in the LISA measurement bandwidth from 0.03 mHz up to 1 Hz for the master laser in the constellation. All other lasers are offset locked to the master laser such that the Doppler shifts are taken into account and beat signals between 3 MHz and 18 MHz are produced on all detectors in the constellation. Ensuring sufficient frequency stability can be established by different methods. A straight forward approach is to use an optical cavity. It turns out that a cavity alone significantly drives the thermal stability requirements at low frequencies. Therefore, different versions of arm-locking are considered in order to provide both, frequency stabilization at low frequencies as well as at high frequencies. While it is obvious how a stable feedback loop at low frequencies can be achieved, a stable control system with noise suppression also at high frequencies can only be achieved when at least two arms are combined in the overall control approach. In the framework of this paper, the Sagnac and the Michelson locking scheme are described and it is shown that the resulting system is stable and achieves significant noise suppression at frequencies up to around 100 Hz. The theoretical results are supported by frequency and time-domain simulations. Results from the time-domain simulation are currently being used for an end-to-end simulation of the LISA measurement data chain that involves the Synthetic LISA simulator, the laser frequency noise generated from the arm-locking simulation, the digital part of the phasemeter, and the TDI data post-processing. This effort will result in a detailed understanding and quantization of additional error sources introduced at the various level of data processing.