The Pound-Drever-Hall (PDH) technique for stabilizing lasers

There are numerous applications that benefit from noise suppression and stabilization of the laser operating parameters.
Well-known applications include interferometric gravitational wave detection (cf. 2017 Nobel Prize in Physics awarded to key contributors to the LIGO project) and spectroscopic probing of quantum states in atomic physics, optical frequency standards and quantum computing.

One of the most powerful active laser stabilization techniques is the Pound-Drever-Hall technique, where the emission frequency of the laser light is locked to the resonance of a stable, high finesse cavity. This technique is named after Robert Pound, Ronald Drever and John L. Hall. The PDH technique was first described in the journal Applied Physics B in 1983, “Laser Phase and frequency stabilization using an optical resonator”. This paper has been quoted over 2,000 times according to Thomson Reuter’s in 2017.

“The PDH scheme has incredible robustness and really has emerged as the dominant locking mechanism. Today, all these years later, we are still using it to try and make ultrastable lasers with linewidths of a few millihertz” . Dr Jun Ye, NIST.

“The PDH technique was a very elegant and robust way to get such an error signal, in a very clean way. There were also other techniques that were more exotic, but in my honest opinion, the PDH technique definitely was, by far, the most reliable” . Pr Sylvain Gigan, Laboratoire Kastler Brossel.

The PDH technique uses common optical heterodyne spectroscopy and RF electronics. The frequency of the laser is measured with an Etalon or a Fabry-Perot Cavity, and the measurement is used to feedback to the laser to suppress frequency deviations of the laser.

Benefits include the decoupling of the frequency measurement from the laser’s intensity, as well as the response time, which could be faster than the cavity’s response time.
For more technical details, RAM and PDH

Choosing a good Phase Modulator for PDH

An example of PDH set-up is given from fig. 2.
When the laser’s frequency matches the cavity’s FSR (integer multiple) perfectly, the reflected beam and the leakage beam have the same amplitude and exactly 180° out of phase. The two beams interfere destructively, and reflected beam vanishes.

Given the narrow linewidth of the laser sources of interest and the modulation depth required, iXblue has developed a comprehensive series of optimized Phase Modulators for implementing the PDH technique.

From any other phase modulators, we can distinguish advantages of LN-0.1 Series:

• Adapted to low frequencies: DC coupled to 200 MHz modulation frequency.
  The need of LiNb0₃ modulators  dedicated to low frequencies.
• Dedicated to a given wavelength range.
• Very low Driving voltage Vπ.
• Low Insertion Loss (LIL option).
• High Input Impedance to improve the modulation efficiency.
• High Polarization Extinction Ratio (PER) for the NIR versions.
• Low Parasitic Intensity Modulation.
• Patented Design for Residual Amplitude Modulation (RAM) Mitigation (EP3009879A1).

Real-world advantages Low Frequencies Phase Modulators

Common high bandwidth travelling wave electro-optical modulators designed and developed for optical communication application has load resistance termination at the end of the RF line to reduce electrical RF reflections. When operated at low frequencies, these high bandwidth phase modulators experience significant electrical current travelling in the RF microwave line. This causes localized heating by the Joule effect.

Cycles of heating and thermal dissipation becomes a problem when the frequencies become lower and become comparable to the time constant of thermal effects. As a result, the physical properties of the electrodes, waveguides are changing during heating and cooling.

Thermal effects are suppressed by using high input impedance load (10 kΩ) or an open electrode line (1 MΩ). iXblue’s LN-0.1 Phase Modulators for PDH are tested and demonstrated to be able to maintain performance covering a large temperature range (-40°C to +85°C) and during temperature variations.

^{Fig. 3: Electrical Modulation Signals and Measured Optical Intensity Signals.
Left: Response @ 50 Hz showing the thermal effects. Top (Modulation signal) Bottom (Intensity signal).
Right: Response @ 50 Hz: thermal effects disappeared due to unloaded capacitive electrodes. Top (Modulation signal) Bottom (Intensity signal).}

When implementing the PDH technique with an Electo-Optic Modulator, RAM is invariably generated causing distortions to the error signal and unintended frequency shift during environmental perturbations. When instabilities of the systems have been progressively reduced to extremely low levels, it becomes increasingly important to suppress or mitigate the frequency instabilities caused by RAM. Dedicated low frequency Phase Modulators from iXblue for PDH are designed and optimized to mitigate RAM.

RAM can be strongly reduced by a permanent DC voltage corresponding to a global negative Refractive index variation, cancelling the deep Electrical induced waveguide.
A 5-15 V DC voltage is sufficient to mitigate RAM by > 10dB. The LN-0.1 series embeds an high impedance internal RF load which will be not damaged by a permanent DC signal.