The Pound-Drever Hall (PDH) method is a known and sophisticated method for frequency stabilization of lasers, for instance diode lasers, to a reference optical cavity, for instance Fabry-Perot cavity, in a ‘laser lock.’ In doing so, the laser linewidth is also considerably shortened.
Conversely, the length of an optical cavity can be actively stabilized to a laser using the PDH-lock. The laser can be used for precision distance control, single atom detection and second-harmonic generation. Being a phase sensitive method, the PDH detects the phase-shift of the reflected light imposed by the optical cavity. Nevertheless, a heterodyne approach is applied because it is almost impossible to measure the phase of an optical frequency directly.
Role of Electro-Optic Phase Modulator
The laser is frequency modulated by an external electro-optic phase modulator (dphi/dt = f), thus forming sidebands on the spectrum, with definite relative phases (+/- 90° relating to the carrier) (Figure 1). This modulation is a pure phase modulation. Since all interferences between carrier and sidebands cancel, beat signals detectable by a photodetector are absent despite the spectrum contains several frequency components.
Figure 1. The laser is frequency modulated by an external EOM, thus forming sidebands on the spectrum, with definite relative phases.
Alternatively, a relative phase shift is induced between each sideband and the carrier in case of light reflecting off a cavity resonance, causing a constructive interference. This means detectable beat at the modulation frequency f0. However, to detect this the photodetector needs to be fast enough. This beat signal is either sine or cosine and can be mixed down with the local oscillator to produce a dc signal with monotonic slope and zero crossing on resonance and monotonic slope.
This lock signal can be utilized in a feedback loop consisting of a PID controller (Servo) to stabilize the cavity length or the laser frequency to the zero crossing. The typical value of a modulation frequency f0 is well outside the laser noise and cavity linewidth. There is no upper limit other than the FSR of the cavity. The bandwidth of the photodetector and RF circuit imposes a practical limit. The common range of modulation frequencies is 1- 100’s of MHz.
Figure 2. Credit ESO in use
Although a modulation index of ~1 rad, i.e., 25% in each sideband, is selected for optimum signal/noise ratio, much weaker modulation < 0.1% is practical and desired in some cases, like in SHGF generation. This is due to proportional variation of the beat signal to the geometric average of the intensities in carrier and sideband sqrt(I0*I1).
This information has been sourced, reviewed and adapted from materials provided by Qubig GmbH.
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