Photoluminescence intensity is widely used to infer exciton populations, yet the detected signal inherently convolves occupancy with radiative-rate modification and collection efficiency, making quantitative inversion vulnerable to pump and system drifts. Here we realize a dual-channel self-referenced scheme enabled by two nearly degenerate quasinormal modes in a hybrid microcavity. Their shared optical path provides common-mode observables (i.e., overall spectral and intensity drift) that track global thermo-optic and pump fluctuations, while their differential-mode observables (i.e., spectral splitting and mode-contrasted emission) remain highly sensitive to local gap dielectric perturbations and dipole-dependent radiative weights. Using temperature as a control parameter in monolayer WSe$ _2 $, we exploit this common/differential-mode framework to robustly invert the relative populations of excitons with out-of-plane ($ \perp $) and in-plane ($ \parallel $) dipole transitions without external absolute calibration. At the temperature of $\sim$50 K, we obtain $ N_\perp/N_\parallel \approx 200 $, coincident with the expected accumulation in the out-of-plane-emitting dark manifold. This internally referenced approach provides a practical route to drift-tolerant, dipole-resolved population metrology in nanogap photonic systems.
The quantitative readout of exciton populations and distributions underpins the identification of exciton thermalization and non-equilibrium steady states, and further affects key physical processes such as coherence buildup [1] and condensation thresholds [2][3][4]. However, in most experiments, exciton populations are indirectly inferred from photoluminescence (PL) intensity. Under steady-state conditions, the detected signal is generally expressed as
, where N denotes the exciton populations, Γrad the radiative rate, and ηcol the collection efficiency. Any variations in Γrad or ηcol-arising from mode coupling, radiation directionality, collection numerical aperture (NA), or alignment drifts-may be misinterpreted as changes in the exciton populations. In addition, pump fluctuations and optical-path misalignment introduce common-mode intensity drift, whereas fluctuations in the dielectric environment such as temperature drift and local geometric variations may simultaneously modify resonance conditions and radiative channels, thereby further undermining the reproducibility and traceability of intensity-based inversions.
This challenge is particularly severe for out-of-plane dipoles such as spin-forbidden dark excitons, whose emission predominantly occupies high-in-plane-wave-vector (high-k∥) channels outside the detection NA, resulting in vanishingly low far-field radiation efficiency [5]. In recent years, manipulating the local density of optical states (LDOS) via micro/nanocavities [6][7][8] or near-field probes [9][10][11] has enabled the redirection of high-k∥ emission to the far field for detection. However, reliable quantification of the exciton populations remains a bottleneck: The absolute PL intensity of a single enhancement mode often superimposes contributions from various exciton states and their respective coupling pathways, making it difficult to uniquely attribute intensity variations to changes in the exciton populations alone [12,13]. In addition, drifts in pump power, mechanical stability, and collection efficiency introduce systematic errors during long-term or dynamic measurements [14,15]. These considerations motivate the development of a self-referenced detection scheme integrated within the same optical platform-one that shares common-mode perturbations yet provides a differential response via distinct radiation selectivity, thereby enabling the decoupling of instrumental drifts from intrinsic population evolution.
In our previous work, we demonstrated that a system hybridized by surface plasmon polariton (SPP) and whispering-gallery mode (WGM) serves as an efficient far-field interface [16], which is composed of a SiO2 microsphere (MS) on top of Au substrates (MS/Au, Fig. 1(a)). A dominant pair of near-degenerate quasinormal-modes (QNMs) can fold and redirect the high-k∥ emission of out-of-plane dipoles on the substrate surface into collectable angular domains for quantitative detection. Building upon this, we further find that this structure naturally emerging from the degeneracy lifting of the mode pair provides a dual-channel physical foundation for self-referenced metrology. Specifically, the common-mode quantities, including the collective intensity and global spectral shift of both modes, track pump fluctuations and slow system drifts. The differential-mode quantities encode specific information: one quantity is the spectral splitting of the two modes, which is highly sensitive to variations in the local effective dielectric environment; and the second one is their discrepancy in selective enhancement of orientated dipole transitions, which enables the inversion of the out-of-plane (OP, represented by ⊥ ) to in-plane (IP, represented by ∥) population ratio. This dual-channel self-referenced readout provides a robust pathway for the quantitative characterization of weakly radiative states under dynamic conditions.
Simulation is performed using a full-wave finite-element calculations within a Green-tensor QNM framework [17][18][19], and device fabrication follows the microsphere-assisted WSe2/Au configuration described in Ref. 16. The optical response of the WGM-SPP hybrid microcavity is governed by two nearly degenerate TM-like QNMs, denoted as QNM1 and QNM2. Although they share the same radial order and similar resonance frequencies, their field participation in the air gap between the MS and the substrate is markedly different (Fig. 1(a) and 1(b)). In firstorder perturbation theory [20,21], the resonance shift scales with the field-energy weight in the perturbed region; therefore, the spatial distributions of |E| 2 determine the relative dielectric sensitivities of the two modes. Because the field intensity of both QNMs is predominantly confined to the MS-substrate air gap, their sensitivity is governed by the gap field distribution (Fig. 1(c) and 1(d)). For example, at the immediate substrate surface, the |E| 2 intensity of QNM1 is nearly twice that of QNM2 (Fig. 1(e)).
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