## Phase Lock to an Optical Reference

There are various ways to lock a laser to another optical reference. Here, the general principle of a phase lock to an optical reference will be described. The optical reference can e.g. be a second cw laser or a frequency comb. This method allows to establish coherence between the laser and the optical reference and between the lasers which are locked to the same optical reference. By establishing a phase lock to a frequency comb, coherence between lasers separated by several hundreds of nm can be realized.

Figure 14 shows the sketch of an optical setup for the implementation of an offset phase lock. Light from the optical reference is superimposed with the laser light using a beam splitter (BS), for convenience this can also be a fibre-based beam splitter. Polarization has to be taken care of such that ideally polarizations of the comb light and of the laser light are identical. The superposition of both beams is recorded with a photodiode and gives rise to a beat signal at the difference frequency between the laser light and the optical reference. In the case of a frequency comb, the optical signal will contain beats between the laser light and many comb peaks. However, the set value for the laser frequency is typically chosen close to one peak such that beats with other peaks at higher frequencies can be filtered easily.

The PD signal is a function of the phase difference between the laser light and the optical reference under consideration. This signal is only constant if the frequency difference between the laser light and the optical reference is exactly zero. Assuming that at time t=0 this value is zero, any phase deviation will lead to a deviation of the signal from zero. It can therefore directly be used as an error signal for phase stabilization.

One disadvantage of this method is that DC noise, e.g. coming from the photodiode, is converted into frequency noise.  Instead the PD signal is mixed with a reference RF signal with frequency Ω. The signal obtained from this procedure will only be constant if the frequency difference between the laser light and the optical reference is exactly Ω. The error signal is a function of the phase difference between the laser light and the optical reference apart from the constant frequency offset. Therefore, it is a phase lock.

### TOPTICA Solution

TOPTICA offers a complete solution for locking a laser to a TOPTICA frequency comb. The DFC BC is an advanced beam combiner module. It offers the possibility to adjust the power ratio of the beams and it features a pure cw-light output. The DFC MD is a monochromatic detector for detecting the beat signal. It contains a grating-based adjustable filter to get rid of all unwanted frequency components of the beat signal. Beyond that, it features a low-noise photo detector. Error signal generation is performed with TOPTICA´s PFD. It is a phase- frequency detector and includes a tunable RF source. This package is completed by a convenient software interface which integrates all components and allows controlling the lock to the comb in an easy and straightforward way.

An offset phase lock to a second cw laser can easily be implemented using TOPTICA´s FALC pro which will be presented in more detail in the application note “PID Feedback Controllers”. For implementing an offset phase lock, the FALC pro includes a fast PID controller and a frequency mixer which combines the electronics after the PD shown in Figure 14.