Operating a near-concentric cavity at the last stable resonance

Near-concentric optical cavities of spherical mirrors can provide technical advantages over the conventional near-planar cavities in applications requiring strong atom-light interaction, as they concentrate light in a very small region of space. However, such cavities barely support stable optical modes, and thus impose practical challenges. Here, we present an experiment where we maintain a near-concentric cavity at its last resonant length for laser light at 780 nm resonant with an atomic transition. At this point, the spacing of two spherical mirror surfaces is $207\left(13\right)\mathrm{nm}$ shorter than the critical concentric point, corresponding to a stability parameter $g=-0.999962\left(2\right)$ and a cavity beam waist of $2.4\mu \mathrm{m}$.

Figure 1

Schematic of a near-concentric cavity assembly. Arrows indicate the moving directions of piezo segments.

Figure 2

Locking scheme of the near-concentric cavity setup. Red and orange lines indicate the beams from the 780-nm probe laser and 810-nm lock laser, respectively. The frequency of the probe laser is stabilized to a D2 transition of ${}^{87}\mathrm{Rb}$ by modulation transfer spectroscopy. The lock laser's sideband is locked to resonance of the transfer cavity, which in turn is stabilized to the probe laser. The frequency of the lock laser can be tuned by adjusting the sideband frequency. The near-concentric cavity is stabilized to the lock laser. All cavity locking schemes use the standard Pound-Drever-Hall technique with 20-MHz phase modulation. The cavity transmission of probe and lock lasers are separated by a dichroic mirror (DM). A camera with linear response (C) and a photodetector (PD1) are placed at the cavity transmission's 780-nm arm to observe the resonant modes. PBS, polarization beam splitter; BS, beam splitter; SMF, single-mode fibers.

Figure 3

Transverse-mode frequency spacing ($\mathrm{\Delta }{\nu }_{\mathrm{tr}}$) at different critical distance ($d$) of cavity lengths that are resonant with the 780-nm laser. The solid line is the fit based on Eq. (2). Error bars show the standard deviation of the measurement. The inset shows a typical cavity transmission spectrum and the derived $\mathrm{\Delta }{\nu }_{\mathrm{tr}}$.

Figure 4

Cavity transmission spectra, measured by detuning the cavity through small changes (few nm) in the cavity length. (a) $d=597\mathrm{nm}$. The dashed line is a fit to a sum of two Lorentzian functions modeling two resonant peaks. (b) $d=207\mathrm{nm}$. Transverse modes become degenerate and form a long tail extending out to the lower frequencies. (c) $d=-183\mathrm{nm}$. The cavity is in the unstable regime. Insets show the transmitted transverse mode profiles recorded by a (partly saturated) camera.

Figure 5

Drift of cavity alignment. Light transmitted through a cavity resonance is coupled to a single mode fiber as a mode filter. The relative transmission (before and after the single mode fiber) as a function of transverse displacement of the second cavity mirror is shown over some time without any stabilization.

Figure 6

Transverse stability of the near-concentric cavity at the last stable longitudinal resonance ($d=207\mathrm{nm}$). The slow drift of cavity transmission on the order of minutes is due to the transverse misalignment caused by temperature change, while the cavity length is locked to a probe light resonance during the measurement. Vertical arrows indicate the activation of the stabilization algorithm, where the cavity transmission recovers to the maximum value after the successful implementation of the algorithm within a few seconds.