Probing microcavity resonance spectra with intracavity emitters

We measure the fluorescence spectrum of broadband emitters in an open optical microcavity with radius of curvature $R=17.7\left(3\right)\mu \mathrm{m}$ and finesse $F\approx 1000$. This geometry enables a combined measurement of emission spectra versus cavity length, which has several benefits over measurements at fixed wavelength or fixed cavity length alone. We demonstrate the role of the optical penetration depths on the cavity modes and provide practical working equations for its analysis. Furthermore, we show the ability to measure the coupling of cavity modes within a small scan range of the cavity length. By measuring these cavity emission spectra as a function of cavity length, we thus obtain a rich and complete picture of the optical microcavity.

Figure 1

Schematic image of the experimental setup. The microcavity (center $+$ zoom-in) is injected with either a HeNe laser ($\lambda =633$ nm) or a Nd:YAG laser ($\lambda =532$ nm). The fluorescence spectra under green off-resonant excitation are observed with either a fiber spectrometer (not shown) or a free-space spectrometer. A 10 nm bandpass filter around 532 nm (BP532) is used to filter out fluorescence that may originate from the fiber. A 550 nm longpass filter (LP550) is used to block the green laser light transmitted through the cavity.

Figure 2

Emission spectrum $P(\lambda ,L)$ of NV centers in the optical cavity: (a) horizontal line-cut of the $P(\lambda ,L)$ map for $\lambda =646$ nm, (b) false-color plot of the fluorescence spectra as a function of the cavity length, (c, black curve) typical spectrum for $q=11$ at $L\approx 3.6\mu \mathrm{m}$, (c, red curve) emission spectrum averaged over $L=3.0–5.2\mu \mathrm{m}$.

Figure 3

(a) The transverse mode splitting for the first four transverse mode groups as a function of the inverse of the free spectral range. (b) The Gouy phase converted to a “modal cavity length” such that both axes depend linearly on cavity length. The crossing with the horizontal axis yields the difference between the penetration depths. (c,d) Histograms of the deviation from the fits for the vertical axis. The horizontal axis shows the number of data points in a bin of 0.0002 for (c) and 0.0004 for (d).

Figure 4

Mode structure for transverse mode groups $N=1–4$. Each transverse mode group is fitted with 2, 3, 3, and 4 Lorentzians for $N=1$, 2, 3, and 4, respectively. The $N=2$ plot shows peak distances that correspond to the (a) and (b) labels in Table 1.

Figure 5

False color plot of the fluorescence in the $N=0$ and $N=6$ modes around their frequency degeneracy. The vertical axis indicates the cavity-length-dependent wavelength ${\lambda }_{13,0}$ at which the uncoupled $N=0$ ($q=13$) mode is resonant. The horizontal axis indicates the spectral distance $\lambda -{\lambda }_{13,0}$ from this uncoupled $N=0$ mode. The white curves follow a theoretical model of coupled modes (see text for details).

Figure 6

Effective cavity length, $L_{\mathrm{eff}}$, calculated from the free spectral range between the $N=0$ modes with $q$ and $q+1$, where $q=10–19$ are indicated with different colors. The points at a higher average frequency are more noisy because the intracavity NV centers are less bright. (a) Original data. (b) All data shifted by $q+1/2$, where $q$ is the lowest number in the labels $q=10–11, q=11–12$, etc., in (a).