The Pound–Drever–Hall (PDH) technique is a widely used and powerful approach for stabilizing the frequency of light emitted by a laser by means of locking to a stable cavity.
PDH locking offers one possible solution to this problem by actively tuning the laser to match the resonance condition of a stable reference cavity.
For tight locking conditions, the linewidth depends on the absolute stability of the cavity, which can reach the limits imposed by thermal noise.
[6] Prominently, the field of interferometric gravitational wave detection depends critically on enhanced sensitivity afforded by optical cavities.
Phase modulated light, consisting of a carrier frequency and two side bands, is directed onto a two-mirror cavity.
After phase shifting and filtering, the resulting electronic signal gives a measure of how far the laser carrier is off resonance with the cavity and may be used as feedback for active stabilization.
The feedback is typically carried out using a PID controller which takes the PDH error signal readout and converts it into a voltage that can be fed back to the laser to keep it locked on resonance with the cavity.
The derivative is measured via rapid modulation of the input signal and subsequent mixing with the drive waveform, much as in electron paramagnetic resonance.
Schematic of PDH servo loop to lock the frequency of a laser (top left) to a Fabry–Perot cavity (top right). Light from the laser is sent through a phase-modulator and is then directed upon the cavity. (For diode lasers, fast frequency or phase modulation can be performed by just modulating the diode current, obviating the need for an external electro-optic or acousto-optic phase modulator). The
isolator
is not involved in the PDH setup; it is present only to ensure that light from various optical components does not reflect back into the laser. The polarizing
beamsplitter
(PBS) and
λ/4 plate
act in combination to discriminate between the two directions of light travel: light traveling in the direction left to right passes straight through and on to the cavity, while light traveling in the direction right to left (i.e., from the cavity) is diverted toward the photodetector. The phase modulator is driven with a sinusoidal signal from the
oscillator
; this impresses sidebands onto the laser light. As described in the section on the PDH readout function, the photodetector signal is demodulated (that is, passed through the mixer and the low-pass filter) to produce an error signal that is fed back into the laser's frequency control port.
Simulated plots of a two-mirror Fabry–Perot cavity reflection transfer function and a PDH readout signal.
Top:
Square magnitude
R
*
R
of reflection transfer function; i.e., the reflected power.
Middle:
Phase arctan[Im(
R
)/Re(
R
)] of reflection transfer function.
Bottom:
PDH readout function
V
, with demodulation phase
φ
= π/2. The mirrors of the simulated cavity were chosen to have amplitude reflectivities
r
1
= 0.99 and
r
2
= 0.98, and the cavity length was
L
= 1 m. The phase modulation frequency of the light was chosen to be
f
m
= 23 MHz (
f
m
=
ω
m
/2π). The portion of the PDH readout function that is useful as a servo error signal is the linear region near
f
res
. The reflected power and the PDH readout function are often monitored in real time as traces on an
oscilloscope
in order to assess the state of an optical cavity and its servo loop.
