Optical Phase-Locked Loops
Optical phase-locked loops (OPLLs) synchronize the relative phases of two (laser) light fields. As a result, the two fields have an adjustable frequency difference while their phase relation remains constant. Examples of popular applications of OPLLs are:
Coherent Raman transitions
Two atomic or molecular energy levels are connected through a third (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 stabilize the relative phase of the involved lasers over the course of each experiment.
The repetition rate as well as the carrier envelope offset (CEO) frequency need to be well-defined to use a frequency 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, a so-called f−2f interferometer typically generates a beat note between the higher-frequency end of the comb spectrum and the frequency-doubled lower-frequency end (if the optical spectrum covers a frequency octave). Feedback is provided to the pump power to keep the CEO to a defined setpoint.
Coherence cloning, laser transfer lock (laser stabilization)
Optical phase-locked loops make it possible to transfer the coherence characteristics of one laser, e.g. its frequency or phase stability properties, to another laser provided that the bandwidth of the servo loop is high enough that it can handle the noise present in the receiving laser. In fact, multiple low-coherence slave lasers can be stabilized with a highly coherent master laser.
Coherent power combination
Synchronizing multiple lasers using an OPLL allows for the coherent combination of light waves to produce constructive and destructive interferences for phased-array optics, LIDAR and optical beam steering, among others.
The relative optical phase between the two light fields is typically detected by overlapping the fields on a beam splitter or combiner, 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 a radio-frequency oscillator with high stability. The feedback signal is then fed to a frequency- or phase-shifting element within the setup. The latter can be an element inside one of the lasers or an external element such as 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 depending on what is applied to its control input. The main characteristic of the VCO is the amount by which the frequency varies 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 with 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. For smooth and stable operation, the most important aspects to consider are:
- High servo bandwidth: depending on the properties of the lasers and of other parts of the setup, it is necessary to know how much bandwidth is required. More is not always better, as bandwidth excess typically results in noisier lasers.
- Phase unwrap is absolutely crucial for convenient locking and stable operation. Most phase detectors can only provide ±π/2 as the accessible phase range for locking. Every distortion that exceeds that limit can be a source of instability.
- Supportive user interface: setting up the parameters that lead to stable operation is a key step.
The Benefits of Choosing Zurich Instruments
- Phase unwrap over ±1024π enables robust operation.
- Depending on the amount of phase noise, you will need a high servo bandwidth. The UHFLI Lock-in Amplifier guarantees a servo bandwidth of up to 100 kHz.
- The PID Advisor comes with a VCO model that allows you to model the laser setup and calculate sensible starting parameters.
- Once locking is achieved, you can optimize further the PID parameters with the Auto-Tune routine to minimize the residual PID error.
- The LabOne® toolset consisting of Scope, Spectrum Analyzer, Sweeper and Plotter enables an integrated analysis and monitoring of the locking quality. For instance, you can visualize the PID error as a histogram to spot deviations from a Gaussian, which indicate that something in your setup does not work as expected.
- The frequency range of the UHFLI (600 MHz) allows you to sweep the frequency difference between the reference and the locked lasers over a large range.
- Klenner, A. et al. Phase-stabilization of the carrier-envelope-offset frequency of a SESAM modelocked thin disk laser. Opt. Express 21, 24770 (2013)