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Journal of the Optical Society of America B

Single-molecule orientations determined by direct emission pattern imaging

M. Andreas Lieb, James M. Zavislan, Lukáš Novotný

Published Jun 1, 2004• 425 citations
Publisher

Abstract

We demonstrate a new method of determining the three-dimensional dipole orientations of single molecules by direct imaging of the emission patterns in the back focal plane of a high-numerical-aperture objective lens. We compare the reconstructed emission-dipole orientations with a previously established method of absorption-dipole mapping. We find that, for a given number of emitted photons, emission pattern imaging provides better accuracy (1°–2°) than absorption-dipole mapping of single molecules. Compared with some other methods for emission-dipole mapping, the presented method is (1) less sensitive to optical aberrations and adjustment and (2) data analysis is simplified because radiation patterns can be expressed in a simple analytical form.

DOI
10.1364/josab.21.001210

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We demonstrate a new method of determining the three-dimensional dipole orientations of single molecules by direct imaging of the emission patterns in the back focal plane of a high-numerical-aperture objective lens. We compare the reconstructed emission-dipole orientations with a previously established method of absorption-dipole mapping. We find that, for a given number of emitted photons, emission pattern imaging provides better accuracy (1°–2°) than absorption-dipole mapping of single molecules. Compared with some other methods for emission-dipole mapping, the presented method is (1) less sensitive to optical aberrations and adjustment and (2) data analysis is simplified because radiation patterns can be expressed in a simple analytical form.
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We present direct imaging of the emission pattern of individual chromium-based single photon emitters in diamond and measure their quantum efficiency. By imaging the excited state transition dipole intensity distribution in the back focal plane of high numerical aperture objective, we determined that the emission dipole is oriented nearly orthogonal to the diamond-air interface. Employing ion implantation techniques, the emitters were engineered with various proximities from the diamond-air interface. By comparing the decay rates from the single chromium emitters at different depths in the diamond crystal, an average quantum efficiency of 28% was measured.
Stimulated emission (StE) remains relatively unused as an image-forming signal despite having potential advantages over fluorescence in speed, coherence, and ultimately resolution. Several ideas for the radiation pattern and directionality of StE remain prevalent, namely, whether a single molecule would radiate StE itself in a pure dipole pattern, or whether its emission direction depends on the driving field. Previous StE imaging has been carried out in transmission, which would collect signal either way. Here, we introduce the StE driving field (the probe) at an angle, using total internal reflection to avoid incident probe light and its specular reflections in our detection path. In this non-collinear detection configuration that also collects some fluorescence from the sample, we observe fluorescence depletion even in the spectral window where an increase in detected signal from StE would be expected if StE radiated like a simple classical dipole. Because simultaneous direct measurement of the fluorescence represents a calibration of the potential size of StE were it spatially patterned like a classical dipole emitter, our study clarifies a critical characteristic of StE for optimal microscope design, optical cooling, and applications using small arrays of emitters.
Photons emitted from a single emitter are promising candidates for an efficient single-photon source, which is essential for many novel nano- and quantum-optical applications. As a photon source having a larger flux and high reliability is highly desirable. In this paper, we quantitatively studied the dependencies of the numbers of photons emitted and collected from single terrylene molecules on different experimental conditions, the refractive index of the substrate and the numerical aperture of the collection lens. Also, back-focal plane images are used to visualize the emission pattern of a single emitter.
Precisely measuring the three-dimensional position and orientation of individual fluorophores is challenging due to the substantial photon shot noise in single-molecule experiments. Facing this limited photon budget, numerous techniques have been developed to encode 2D and 3D position and 2D and 3D orientation information into fluorescence images. In this work, we adapt classical and quantum estimation theory and propose a mathematical framework to derive the best possible precision for measuring the position and orientation of dipole-like emitters for any fixed imaging system. We find that it is impossible to design an instrument that achieves the maximum sensitivity limit for measuring all possible rotational motions. Further, our vectorial dipole imaging model shows that the best quantum-limited localization precision is 4%-8% worse than that suggested by a scalar monopole model. Overall, we conclude that no single instrument can be optimized for maximum precision across all possible 2D and 3D localization and orientation measurement tasks.