Transmission matrix measurement of a single Mie scatterer

Abstract

Transmission matrices are valuable tools to describe and control light transport through scattering media. There are only a few cases where the transmission matrix can be compared to microscopic theories. Here we measure the polarization-complete transmission matrix of a single dielectric sphere using off-axis holography with angle scanning and reconstruct complex fields in both transmission and reflection under circular polarization. After aberration correction and angular mapping, the scattering amplitude extracted from the transmission matrix closely follows Mie theory. This work provides a calibrated benchmark for angle-resolved transmission matrix measurement and enables quantitative characterization of spherical and quasi-spherical scatterers.

Figures (9)

• Figure 1: Scattering by a single sphere. (a) Scattering plane spanned by the incident wave vector and the scattering wave vector. (b) Scattering (polar) angle $\theta$ and azimuthal angle $\phi$ in spherical coordinates. (c) Sphere on a glass substrate. In reflection, the measured field includes additional multiple reflections between the sphere and the air-glass interface.
• Figure 2: Pupil-phase aberration model with representative Zernike, edge-bias, and edge-ripple basis functions on the unit pupil.
• Figure 3: Pupil aberration estimation and correction of the measurement on the spherical particle. (a) Measured pupil phase of the co-polarized scattered field from a spherical particle for a single incident vector $\mathbf{k}_i=(6.361,\, 0.326,\, 7.620)$ µ$\mathrm{m}^{-1}$. (b) Normalized polar coordinates inside the pupil disk. (c) Theoretical Mie phase for comparison. (d) Estimated pupil aberration. (e) Phase after aberration removal. (f) Fitted aberration from the model.
• Figure 4: Condenser pupil aberration estimation. (a) Condenser and imaging objective in the measurement. (b) Sampled map of the condenser pupil phase obtained through illumination scanning. (c) Fitted condenser pupil aberration predicted by the model.
• Figure 5: Measured co-polarized component of the complex scattering amplitude in $k$-space and angle space for a single incident vector $\mathbf{k}_i=(6.361,\, 0.326,\, 7.620)$ µ m$^{-1}$. (a) Projection onto the plane spanned by $\mathbf{k}_x$ and $\mathbf{k}_y$. (b) Three-dimensional representation on the constant-$|\mathbf{k}|$ shell with the corresponding incident wave vector $\mathbf{k}_i$. (c) The same shell after rotation, so the scattering amplitude can be indexed by its angular coordinates. Complex plots: color encodes the phase and brightness encodes the magnitude kovesi2015good.