Optical microcavity characterization via resonance spectra and modes

Abstract

This paper describes how resonance spectra and mode profiles can be used to characterize and quantify the mode-shaping effects in open-access plano-concave optical microcavities. The presented semi-analytic theory is based on the application of perturbation theory to the roundtrip evolution of the optical field. It includes various mirror-shape and nonparaxial effects and extends the nonparaxial theory presented by van Exter et al. (2022, Phys. Rev. A 106, 013501) and verified by Koks et al. (2022, Phys. Rev. A 105, 063502) to the common case of an anisotropic Gaussian mirror. The presented measurements and analyses of resonance spectra and mode profiles demonstrate how the different mode-shaping effects can be individually distinguished and quantified. Spin-orbit coupling, which is one of the nonparaxial effects, is prominently visible in the intriguing polarization patterns of the resonant modes, while polarization tomography yields the shape-induced birefringence and associated polarization splitting of the fundamental modes.

Figures (17)

• Figure 1: Visualization of the relative weight of three contributions to $\Delta L_{\rm fine}$ in a ternary plot, including their scaling with cavity length $L$. The blue curve visualizes a typical shift of these relative weights from dominant nonparaxial at small $L$, via partially anisotropic to dominantly aspheric at large $L$. The other curves characterize the operational regime of the microcavities in Koks2022b (orange), Benedikter2015 (red) and this work (green).
• Figure 2: Schematic setup of the experiment used to characterize a microcavity (on the left) in various ways. The HeNe-laser (633 nm) is used for measurements, while the Nd:YAG-laser (532 nm) and white light source are used for alignment and imaging. Transmission and reflection spectra are measured with an photomultiplier tube (PMT) and a (normal) photodiode (PD), respectively. Resonant mode profiles are observed with a polarization-resolving camera.
• Figure 3: Transmission spectrum, expressed as PMT voltage versus relative cavity length in nm (bottom axis) and in units of $\lambda/2$ (top axis). Each group of transmission peaks is labeled by two quantum numbers $(q, N)$ and has a detailed spectral fine structure, visible in the spectrum and mode profiles (see insets).
• Figure 4: Detailed views of the fine structure in the $(q=6 ,N)$ groups in Fig. \ref{['fig:transmission spectrum']} for $N=0$ to 3. Each group has $(N+1)$ resonant peaks, but some peaks ($1b, 2b, 2c)$ are split in two due to an observable hyperfine splitting.
• Figure 5: sin$^2(\chi_0)$, deduced from measured transverse-mode spacing $\propto \chi_0(L)$, versus cavity length $L$. The black solid line is a linear fit at short cavity length $L$. The black dashed curve is a fit based on Eq. (\ref{['eq:Gouy_scaling']}). The inset shows $z_m(r)$ of a perfect Gaussian-shaped mirror with depth $h$ (black solid curve) and two Gaussian expansions up to $r^4$ according to Eq. \ref{['eq:z']} (blue dashed curves), for $h_4 = h$ (lower curve) and $h_4=2h$ (upper curve), with the same $R_m$. The red dotted curve shows the intensity profile $I(r) \propto e^{-r^2/\gamma^2}$ of the fundamental mode at $L=R_{m}/2$.