We here develop a thin-shell approximation of the Mie scattering problem for a spherical core–shell structure with radial anisotropy in the shell. The solution of the full anisotropic Mie theory requires the computation of Bessel functions of complex orders, which has severely limited its application to relevant problems. The proposed thin-shell approximation removes this hurdle and is of a similar complexity to the isotropic Mie theory. We show that the predictions agree with those of the full anisotropic theory for nanoparticles with a shell thickness of the order of 1 nm or less. The approximation is therefore of great relevance to calculations of the optical properties of adsorbed molecular monolayers, for example, the optical response of dye-coated nanoparticles. In this context, we also propose a simple effective medium shell model to account for the radial anisotropy of a dye layer arising from a preferred adsorption geometry, for example, in-plane or out-of-plane. We show that the model agrees with the predictions of a simple microscopic model, but provides additional insights on how the molecular orientation in the dye layer affects its interaction with the nanoparticle, for example, with plasmon resonance of metallic particles. These simple thin-shell approximation and effective medium anisotropic shell models pave the way for further theoretical understanding of orientation and anisotropic effects in the context of dye-plasmon resonance coupling.

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We use Monte Carlo ray-tracing modeling to follow the stochastic trajectories of rays entering a cylindrical port from inside an integrating sphere. This allows us to study and quantify properties of realistic ports of non-negligible length, as opposed to the common thin-port assumption used in most theoretical treatments, where the port is simply considered as a hole in the spherical wall. We show that most practical ports encountered in integrating sphere applications cannot be modeled as thin ports. Indeed, a substantial proportion of rays entering the port can be reflected back into the sphere, with port reflectances as high as 80% demonstrated on realistic examples. This can have significant consequences on estimates of the sphere multiplier and therefore pathlength inside the sphere, a critical parameter in many applications. Moreover, a nonzero port reflectance is inevitably associated with reduced transmittance through the port, with implications in terms of overall throughput. We also discuss angular redistribution effects in a realistic port and the consequences in terms of detected throughput within a fixed numerical aperture. Those results highlight the importance of real port effects for any quantitative predictions of optical systems using integrating spheres. We believe that those effects can be exploited to engineer ports for specific applications and improve the overall sphere performance in terms of pathlength or throughput. This work carries important implications in our theoretical understanding of integrating spheres and on the practical design of optical systems using them.