Owing to the physical nature of the lasing effect, lasers cannot be as stable as a good Fabry-Perot (FP) etalon. For this reason, we stabilize our reference lasers to different types of Fabry-Perot etalons, depending on needs. The Pound-Drever-Hall is the scheme that exhibits the highest reliability, and also the most suitable to ultimate frequency stability.

The laser is frequency modulated at a suitable frequency f_m of the order of 20 MHz and several orders of magnitude higher than the FP cavity linewidth. With the scheme shown, the cavity transforms the phase modulation into amplitude modulation, which is detected by a photodiode. The control delivers a DC signal proportional to the frequency detuning of the laser vs the reference cavity.

A temperature turning point is a key element in the design of a high-stability cavity because spacer and mirrors suffer from thermal expansion. A thermal expansion ΔL/L causes a shift Δf/f=-ΔL/L= in the laser frequency. Thermal expansion also causes geometric warp, mor difficult to explain and model.

For reference, the thermal expansion is of the order of 10^-5/K for metals, and of the order of 10^-6/K for glass and ceramics. Thus, the unrealistic temperature stability of 0.1-1 nK would be necessary for a frequency stability of 10^-15.

A well designed cavity exhibits a smooth turning point. If the cavity is stabilized at the turning point T₀, the thermal expansion is proportional to (T-T₀)². As temperature stability of 10-100 μK is therefore sufficient to stabilize the laser frequency at 10^-15 level.

The femtosecond comb is the standard tool to refer the optical frequency of a laser to a reference frequency in the radio spectrum. The comb enables to transfer the accuracy of the primary standard, the 9.192631770 GHz resonance of the Cs atom, to the optical signal. Such frequency transfer is so good that the fluctuations are of parts in 10^-16 at 1 s (Allan deviation)

A femtosecond laser generates light pulses at a repetition rate f_rep≈250 MHz. These pulses are so sharp that the harmonics span over more than one octave. Beating two lines f₁ and f₂ spaced by one octave (f₂≈2f₁), it is possible to lock the difference f₂-f₁ to f₁. In this condition, the repetition rate f_rep is frequency locked to the optical frequency.

Flicker (1/f) frequency noise in the FP cavity is powered by thermal energy k_BT according to the law where f/ is the Fourier frequency, and Q is the mechanical of the material. Converting the PSD S__δL(f) into Allan deviation of the fractional frequency, we get

Digital electronics provides utmost flexibility, reconfigurability and long term stability when processing discrete time radiofrequency samples, properties sought when analyzing ultra-stable oscillator properties. Also known as software defined radio, digital processing of radiofrequency signals requires a combination of multiple skills to achieve flexible and stable instruments such as composite clocks, phase characterization bench and closed controlled phase feedback loops. Because of the complexity of adressing all fields related to digital electronics ranging from radiofrequency signal acquisition (fast analog to digital conversion) and digital pre-processing taken care of in FPGAs, to transferring to a general purpose processor (Linux kernel space drivers) and implementing user space digital signal processing algorithms, a dedicated library has been developed which is being released at https://github.com/oscimp/oscimpDigital