Calibrated Plane--Convex Microcavity for Room-Temperature Polaritons with Geometric \(g\)-Scaling

Abstract

We present a plane--convex open microcavity that supports room-temperature polariton spectroscopy and offers a simple geometric handle on the coupling rate. The effective length ($L_{\mathrm{eff}}$) is absolutely calibrated from the free-spectral range, and piezo tuning is performed at near-normal incidence ($k_{\parallel}!\approx!0$) to avoid angle-induced degradation. Using spin-coated PEA$2$PbI$4$ quasi-2D perovskites, we observe clear anti-crossings in reflection, with vacuum Rabi splittings up to $71~\mathrm{meV}$ (reflection) and $87~\mathrm{meV}$ (PL) near $L{\mathrm{eff}}!\approx!3~μ\mathrm{m}$. A linewidth-corrected analysis converts the apparent splitting into the coherent exciton--photon coupling rate $g$, revealing a robust geometric scaling $g \propto L{\mathrm{eff}}^{-1/2}$ across multiple longitudinal orders and spatial sites, consistent with the filled-mode thin-film limit where the transverse area cancels in the mode volume. The platform establishes a compact, broadly compatible testbed for room-temperature polaritons and provides a practical design rule: shortening $L_{\mathrm{eff}}$ is a reliable geometric lever to strengthen collective coupling in plane--convex microcavities.

Figures (5)

• Figure 1: Experimental setup and plane–convex microcavity.(a) Cross-section of the cavity: a SiO$_2$-terminated DBR on a borosilicate coverslip hosts the sample; the opposing mirror is a TiO$_2$-terminated DBR on a convex substrate bonded to a ring PZT for axial actuation. (Bottom inset) transfer-matrix field profile showing an antinode at the planar DBR surface. (b) Opto-mechanical assembly providing independent lateral (XY) translation and tip–tilt control for both mirrors, with the ring PZT setting $L_{\mathrm{eff}}$. (c) Optical layout for white-light reflectance and PL spectroscopy, assisted by a 650 nm alignment beam. A $20\times$ objective lens mode-matches the input beam to the cavity, while a spectrometer and camera record spectra and images, respectively.
• Figure 2: Alignment workflow.(a) Concept: co-monitor white-light reflection and 650 nm transmission while adjusting tip–tilt and axial position of the convex lens. (b) Camera frames at three lateral sites (A, B, C) with the cavity length tuned to three distinct values. The Newton-ring radius varies with the local gap, and 650 nm transmission appears only at resonance. The corresponding co-recorded spectra at A, B, and C are shown in (c), where the longitudinal modes appear as reflection dips. At resonance a narrow 650 nm transmission peak is observed.
• Figure 3: Plano--convex microcavity and FSR calibration.(a) Bare-cavity reflection spectra at several PZT voltages; dip spacings yield the FSR. (b) FSR (black) and derived $L_{\mathrm{eff}}$ (blue) vs. PZT bias, demonstrating continuous tuning down to $\sim$1.2 $\mu\mathrm{m}$.
• Figure 4: Energy-resolved reflectivity of the tunable microcavity.(a) PEA$_2$PbI$_4$ film on a planar DBR: excitonic absorption ($\sim$520 nm) and resonant PL ($\sim$524 nm). (b) Stacked reflection spectra while $L_{\mathrm{eff}}$ is scanned. A bare-cavity resonance in the non-absorbing region keeps a constant linewidth, indicating finesse is preserved during PZT tuning. Near $E_x$, the resonance splits into UP/LP. (c) Reflection-intensity map versus wavelength and $L_{\mathrm{eff}}$ with fitted UP/LP (blue) and coupled-oscillator branches (purple). The minimum splitting at (near) zero detuning is $\hbar\Omega_R \approx 71$ meV.
• Figure 5: Splitting and coupling vs. cavity length.(a) Coupling rate $g$ from Eq. (\ref{['eq:g_from_split']}) vs. $L_{\mathrm{eff}}$ for reflection (circles) and PL (triangles). Dashed curves are $L_{\mathrm{eff}}^{-1/2}$ fits. (b) Reflection-derived Rabi splittings vs. longitudinal order $m$. The solid line is a fit using the Savona analytic model with $g(L_{\mathrm{eff}})\propto L_{\mathrm{eff}}^{-1/2}$. Inset: FDTD simulated thickness dependence of the vacuum Rabi splitting at fixed cavity order.