Optical Phase-Locked Loops
Optical phase-locked loops synchronize the relative phases of two (laser) light fields. As a result, the two light fields have an adjustable frequency difference while the phase relation is kept constant.
- Coherent Raman transitions
Two atomic or molecular energy levels are connected via a 3rd (virtual) energy level by two coherent light fields with a defined frequency difference. To perform well-defined coherent population transfers by means of Rabi oscillations, it is important to have the relative phase of the involved lasers stable over the course of each experiment.
- Frequency combs
The repetition rate as well as the carrier envelope offset (CEO) frequency need to be well defined in order to use the comb as an “optical ruler”. The repetition rate can be directly inferred from the light and controlled by adjusting the laser cavity length. For the CEO typically, a so-called f−2f interferometer generates a beat note between the higher-frequency end of the comb spectrum with the frequency-doubled lower-frequency end, if the optical spectrum covers a frequency octave. Feedback is provided to the pump-power in order to provide corrections to keep the CEO to a defined set point.
- Coherence cloning, Laser transfer lock (laser stabilization)
Optical phase locked loops allow to transfer the coherence characteristics of one laser, e.g. its frequency/phase stability properties, to another laser, provided the bandwidth of the servo loop is high enough to cope with the noise present in the receiving laser. This way, multiple low-coherence slave lasers can be stabilized by a highly-coherent master laser.
- Coherent power combination
Synchronizing multiple lasers using OPLL allows for coherent combination of lightwaves to produce constructive and destructive interferences for phased-array optics, LIDAR, optical beam steering, etc.
The relative optical phase between the two light fields is typically detected by overlapping the fields on a beam splitter/combiner and creating a beat note at the frequency difference of the two lasers on a photodetector. From there an electrical phase-locked loop references the beat note to an RF reference oscillator of high stability. The feedback signal is then provided to a frequency or phase shifting element within the setup. This could be an element inside one of the lasers or an external element such as a frequency-shift of an acousto-optical modulator.
From a signal analysis and control perspective, the examples above can be readily understood by replacing the complex details of the optical setup with a voltage-controlled oscillator (VCO). The VCO provides an output frequency that varies dependent on what is applied to its control input. The main characteristic of the VCO is by how much the frequency is changed when the control voltage changes by a certain value. The task at hand is to compare the phase of the VCO output with a second reference oscillator by using a phase detector, i.e. a lock-in amplifier. Based on that comparison, provides a feedback to the VCO control voltage such that the VCO follows tightly the reference oscillator.
In order to have a smooth setup and stable operation the most important aspects are
- High enough servo bandwidth: Depending on the properties of the lasers and other parts of the setup, it needs to be clarified how much bandwidth is needed. Please note that more is not always better, as excess in bandwidth will typically result in more noisy lasers.
- Phase unwrap: This is absolutely crucial for convenient locking and stable operation. Most phase detectors are only capable to provide ±π/2 as available phase range for lock-in. Every distortion that exceeds that limit can end stable locking.
- Supportive user interface: Setting up the parameters that lead to first stable operation is crucial. Then, there needs to be various ways to characterize and optimize the operation.
Your benefits measuring with Zurich Instruments
- Phase unwrap over ±1024π in order to achieve a lock and robust operation. This is a key requirement!
- Depending on how much phase noise there is, you will need high servo bandwidth. For the UHFLI we achieve a servo bandwidth of up to 100 kHz.
- The PID advisor comes with a VCO model that allows to model the laser setup and calculate sensible start parameters.
- Once a lock is achieved you can further optimize the PID parameters by using the Auto-Tune routine to minimize the residual PID error.
- The LabOne Toolset consisting of Scope, Spectrum Analyzer, Sweeper and Plotter allow for an integrated analysis and monitoring of the lock quality. For instance, visualize the PID error as histogram to directly see deviations from a Gaussian indicating something in your setup is not working as expected.
- Frequency range of UHFLI (600 MHz) allows to sweep the frequency difference between the reference and locked lasers in a large span.