J. Eur. Opt. Society-Rapid Publ. 22, 53( 2026) 521
Fig. 2. Computed lumen refractive index n core( k) for healthylike( H), borderline( B), and cancer-like( C) exosomes based on the Barer relation and protein / NA concentration bands. p n eff ðkÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffi e eff ðkÞ: ð5Þ
This procedure is applied to the healthy-like, borderline, and cancer-like lumen compositions defined above, thereby
yielding three effective refractive indices n ðHÞ eff ðÞ k, n ðBÞ eff ðkÞ, and n ðCÞ eff ðkÞ.
The retrieved indices are consistent with the expected extracellular vesicle( EV) optical responses and fall within the experimentally observed EV index range( 1.37 – 1.40 in the visible) reported by nanoparticle tracking analysis and flow cytometry [ 16, 26, 42, 53 ].
Figure 3 shows the resulting effective refractive indices for the three exosome classes at the wavelengths of interest. Cancer-derived exosomes systematically exhibit a slightly higher n eff than healthy-like exosomes, with borderline exosomes( gray shaded area in the Fig. 2) populating the intermediate range. These distinct ERI bands form the basis for the single-exosome classification strategy pursued in this work, where the exosomes, modeled as homogeneous spheres with the retrieved n eff, areplacedinthenearfield of uncoated, PS- and CsPbI 3-coated silica microresonators to calculate the corresponding resonant wavelength shifts.
4
Modeling and simulation
All models are built in Comsol Multiphysics, which relies on the Finite-Element Method( FEM). The proposed biosensor is a silica microresonator( microdisk, 30 lm radius) with a 100 nm coating, placed in an aqueous medium. Light is coupled into the microdisk via a single-mode optical fiber( SMF), consisting of a silica core of 500 nm radius and a Teflon cladding of 2 lm thickness, designed and optimized in our previous works [ 37, 38 ]. A two-dimensional modeling approach was used, and the input power applied in the SMF optical fiber was 1 W / m for all models. A schematic representation of the modeled microresonator is shown in Figure 4.
Fig. 3. Effective refractive indices n eff of healthy-like( H), borderline( B), and cancer-like( C) exosomes retrieved from the full-wave Comsol Multiphysics simulations.
In order to ensure the accuracy of the results and explicitly account for the effect of light coupling into the microresonator, all simulations are performed in a full-wave drivenmode configuration. To the best of our knowledge, we are the first group to demonstrate such full-field driven-mode simulations of coated WGM microresonators [ 37, 38 ]. Three modeling scenarios are investigated: an uncoated microdisk, which provides the baseline for all comparisons; a PS-coated microdisk; and a CsPbI 3-coated microdisk. In each case, the coupling distance d x, the distance from the fibercoretothe microresonator, is optimized to maximize the coupling efficiency. Specifically, we choose a d x that maximizes the transmitted power T while maintaining a high quality factor Q f.
For every model, the relevant figures of merit are extracted, namely the resonance wavelengths k res, the transmitted power T, the quality factor Q f, the mode volume V mode, and the electric-field at the sensing location | E |. These quantities are used to quantify and compare the sensing functionality of the biosensor in the uncoated, PScoated, and CsPbI 3-coated cases. Afterwards, a single exosome is placed in the immediate vicinity of the microresonator equator for the three health states – healthy( H), borderline( B), and cancerous( C) – and the corresponding resonance wavelength shifts Dk res are calculated. By immediate vicinity, we mean that, in each case, the exosome is positioned in direct, tangential contact with the microresonator boundary at the equator, on the right-hand side of the resonator in Figure 4. This enables a direct assessment of the sensing performance of uncoated and nanocoated microresonators for single-exosome classification.
It is worth mentioning that such multiscale full-wave driven-mode simulations( microresonator in the micrometer regime, coating and exosome in the nanometer regime) require an extremely well-designed and fine mesh, in particular in the fiber – microresonator coupling region, and around the coating and exosome. To ensure accuracy and consistency, the same meshing strategy is used for all models. This requirement results in 1,766,528 mesh elements