The Surface Orientation Ambiguity for Single Molecules at Dielectric Interfaces

TL;DR

This paper identifies a fundamental ambiguity in modeling the emission patterns of molecules near dielectric surfaces, which can lead to incorrect orientation measurements, and proposes a finite-element modeling solution to correct this issue.

Contribution

It reveals a mathematical ambiguity in dipole emission pattern calculations near surfaces and offers a finite-element approach to accurately determine molecular orientations at interfaces.

Findings

The ambiguity causes a rotation bias in measured dipole orientations.

Finite-element modeling can resolve the ambiguity.

A correction method for orientation measurements at interfaces is provided.

Abstract

Fluorescent molecules emit light in a dipole radiation pattern that can be used to infer their orientation through defocused fluorescence microscopy. Proper measurement of the orientation requires mathematical modeling of the radiation pattern expected for a dipole in the geometry of interest, and subsequent comparison against experimental data. We point out an ambiguity in common calculations of these patterns that appears to compromise orientation measurements for molecules that are especially near to dielectric surfaces. This results in a rotation of the measured emission dipole toward the surface for near-interface molecules, which can be mistaken for a preferentially horizontal orientation among the emitters. The proper treatment for on-surface emitters requires consideration of finite-sized current elements between two dielectric media, and we show that the theoretical ambiguity can be lifted via finite-element modeling. A prescription is provided for correcting measured orientations at arbitrary interfaces.