High-finesse optical resonator

The experience with the CEAS experiment (Chapter 7) has made clear that an extraordinary mechanical as well as optical quality of the cavity will be the major key to an excellent detection sensitivity in NICE-OHMS. At the same time, the resonator has to be functional at cryogenic temperatures. These problems have been solved with the design shown in Figure 8.18.

All parts of the cavity body (Figure 8.18) have been machined from INVAR to provide optimal thermal stability of the cavity length. It consists of two de-tachable mirror holders and a spacer, which combines a very rigid structure with sufficient access to its interior, so that any gas injected into the experimental cell can easily enter the volume covered by the resonating light field.

INVAR caps screwed into the mirror holders lock the position of the cavity mirrors. Kapton foil between the respective cap and the mirror protects its sensitive reflective surface. Since the mirror alignment cannot be fine-tuned after installation, a good initial on-axis orientation is required to allow a later matching of the beam to the cavity mode within the restricted geometry. This is provided with Teflon rings centering the mirrors inside their holders.

The cavity length can be tuned with a low voltage piezoelectric ring actuator mounted behind one of the cavity mirrors. It pushes the mirror against the spring load of the thin-walled, flexible cap end face. The use of any glue in

OPTICAL SETUP 143

Cavity mirror

Piezo tube Teflon centering ring Invar cap

9 mm clear bore Fine thread

Figure 8.18: Resonator design. Top left: disassembled invar spacer. Top right: com-pletely assembled cavity inside the experimental cell. Bottom: layout of the mirror holder with the cavity piezo.

the complete assembly is thereby avoided, so that this design should not be susceptible to differential contraction upon cooling and thus be particularly reliable at cryogenic temperatures.

With an individual mirror curvature of 1 m, the cavity length has been picked from Table 7.1 in order to optimize the mode spacing. The maximum value compatible with the space limitations of the cryostat is L = 86.46 mm, corresponding to a free spectral range of 1.734 GHz. The chosen cavity dimen-sions lie deep inside the stable region and give an eigenmode withw0= 222.1m at 761.7 nm.

The cavity mirrors (Research Electro-Optics Inc.) have been explicitly or-dered for a specified finesse around F = 100 000 and good cavity transmission between 760 and 790 nm, with their back side AR coated for a reduction of etalon effects. An optical characterization of its actual parameters has been performed following the procedure pointed out in Section 7.1.6.

The finesse value can in principle be determined with a simple scan over a single mode, as illustrated in the top panel of Figure 8.19. The data has been recorded with an avalanche photodiode (APD) monitoring the cavity transmis-sion and is fitted to equation (7.12), which reproduces the experimental trace extremely well for F = 102 000 and v_ϕ = 84.5 s⁻¹. However, the numerical evaluation of the integral in (7.12) makes the fit procedure quite involving and together with the nonlinearity of the APD gives rise to a certain inaccuracy of

144 NICE-OHMS OF OXYGEN AT CRYOGENIC TEMPERATURES

0 10 20 30 40

0 2 4 6 8 10

0.0 0.2 0.4 0.6 0.8 1.0

Incidentpower[arb.u.]

Time [¹s]

Transmittedpower[arb.u.]

¿s= 8.24¹s 1/ switching timee ¼0.1¹s

-20 0 20 40 60

0 5 10

15 Data

Fit

Cavitytransmission[arb.u.]

Time [¹s]

Figure 8.19: Determination of the cavity finesse. Both curves have been recorded at an incident power of 1 mW in front of the cryostat and wavelengths in the atmospheric A-band of O₂ (top: 761.795 nm, bottom: 760.907 nm).

the extracted results.

A more trustworthy value for the cavity finesse is therefore instead derived from its storage time, as defined in equation (7.11). It is measured by monitoring the on-resonance cavity transmission while switching off the incident light with the help of the AOM. Typical data is displayed in the lower graph of Figure 8.19.

It demonstrates that the switching time apparently is short enough to allow a clean exponential decay in transmission, which is also not limited by the 315 ns rise time of the SRS SR560 low-noise amplifier used for signal enhancement. An average of several measurements yieldsF = 89 105±1 379, corresponding to a FWHM cavity linewidth of only 19.5 kHz.

The finesse measurement is complemented by a determination of the on-resonance cavity transmissiontand incouplingζ, as introduced in Section 7.1.6.

Values of t = 7.46 % and ζ = 40.09 % are obtained, which together with the

OPTICAL SETUP 145 finesse yield

7.96714×10⁻⁶ ≤T_in≤7.96755×10⁻⁶ 11.6384×10⁻⁶ ≤T_out≤11.6390×10⁻⁶ 50.9064×10⁻⁶ ≤Vin+Vout≤50.9071×10⁻⁶ ,

so that all essential mirror parameters are known to high accuracy. While the transmission values are within specifications, the overall loss is slightly too high, but still acceptable. In deriving the above values, it has not been necessary to account for a finite mode-matching, since values above 95 % are routinely achieved experimentally.

8.5.4 Laser-cavity locking

The most challenging aspect in realizing the stabilization of the laser frequency to the cavity length is the necessary reduction of the laser linewidth to the cavity linewidth from a few hundred kHz to 19.5 kHz. One way of accomplishing this is the use of an EOM for extremely fast, but small frequency adjustments [116].

These arise here from a constantly changing input voltage, which translates into a time-dependent phase changeϕ(t) at its output, corresponding to a temporary frequency shift∆ν = ˙ϕ/2π of the laser light.

In order to avoid a saturation of the EOM voltage for larger frequency shifts, additional actuators have to take over on longer timescales. This is achieved with the AOM on intermediate timescales for frequency shifts in the MHz range and feedback to the cavity length for DC changes of several GHz. Figure

Function generator

Figure 8.20:Error signal generation and processing for laser-cavity locking.

146 NICE-OHMS OF OXYGEN AT CRYOGENIC TEMPERATURES

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

0.0 0.4 0.8 1.2

Transmission[arb.u.]

Time [ms]

0

ErrorSignal

4 MHz

-50 0 [¹s] 50 100

-50 0 [¹s] 50 100

£10

£10

Figure 8.21:Experimental error signal and mode spectrum. The central cavity mode is accompanied by 1st and 2nd order modulation sidebands spaced by 4 MHz. Because of the short scan time, all peaks show signatures of dynamical effects, as discussed in Section 7.1.4. With sufficiently slow scanning, the error signal would take a shape similar to that shown in the bottommost panel of Figure 8.2. In practice, however, slow scan speeds lead to a distortion of the trace due to the influence of vibrations and thermal drifts on the cavity length.

8.20 schematically illustrates the distribution of feedback signals between these three elements. The inherent bandwidth capabilities of EOM 2, the AOM, and the cavity piezo constitute cross-over points for the individual feedback-paths, which had to be experimentally fine-tuned by carefully adjusting the character-istics of the respective loop amplifiers to obtain an optimal lock quality. Most of the feedback work is done by the AOM, which takes over from EOM 2 at around 500 kHz and leaves corrections below 100 Hz to the piezo.

Feedback to EOM 2 is combined with a modulation at ω_m = 4 MHz in its special driver (see Appendix E) for the generation of an according Pound-Drever-Hall error signal. It is recovered by demodulating the amplified and band-pass filtered output of the lock detector with a phase-locked local oscil-lator. Figure 8.21 shows the error signal together with corresponding cavity modes recorded in a single 4 ms scan of the cavity length. When compared to the corresponding curves in the cavity-enhanced spectroscopy experiment (Figures 7.10 and 7.12), the obtained signal quality becomes obvious.

OPTICAL SETUP 147 After appropriate low-pass filtering, the error signal is fed into the EOM and AOM loop amplifiers for suitable integration and amplification with individual bandwidths above 1 MHz. The correction voltage for the cavity piezo is obtained by integrating the resulting AOM control signal, relieving it from any larger amplitude frequency correction.