Simultaneous Measurement of the Three-Dimensional Orientation of Excitation and Emission Dipoles

The emission properties of most fluorescent emitters, such as dye molecules or solid-state color centers, can be well described by the model of an oscillating electric dipole. However, the orientations of their excitation and emission dipoles are, in most cases, not parallel. Although single molecule excitation and emission dipole orientation measurements have been performed in the past, no experimental method has so far looked at the three-dimensional excitation and emission dipole geometry of individual emitters simultaneously. We present the first experimental study, using defocused imaging in conjunction with radially polarized excitation scanning, to measure both the excitation as well as emission dipole orientations of single molecules, which allows us to sample the distribution of their mutual orientation. We find an unexpectedly broad distribution of the angle between both dipoles which we attribute to the interaction between the observed molecules and the substrate they are immobilized on.

Figure 1

Experimental setup showing the path of the excitation beam and the fluorescence emission pathways. The collimated pulsed laser ${\mathrm{TEM}}_{00}$ is passed through a linear polarizer. Any unwanted wavelengths were blocked using a clean-up filter before the beam was passed through the mode converter. Next, the beam was mode cleaned by focusing it through a $25\mu \mathrm{m}$ pinhole, resulting in a doughnut profile of radially polarized light. The beam splitter reflected this light beam into an objective which focused the light onto the sample. The inset shows the calculated longitudinal and transverse electric field components on the surface of the substrate $0.5\mu \mathrm{m}$ around the optical axis $(\text{scalebar}=200\mathrm{nm})$. The sample is first scanned with a single-photon avalanche photodetector (SPAD) as detector, to obtain excitation dipole images of the emitters. Subsequently, a replaceable mirror is switched into the detection pathway to reflect the emission onto an EMCCD camera which is displaced away from the imaging plane, to obtain defocused images of the emission dipoles.

Figure 2

Emission and excitation patterns of five Atto 655 molecules. The top row shows the excitation images, the second row the corresponding fitted patterns, the third row shows the defocused images, and the fourth row the fitted emission patterns. The scan pixel size is 50 nm and each excitation image is $25\times 25$ pixels, whereas the camera pixel size is $\sim 60\mathrm{nm}$, with each defocused image having $40\times 40$ pixels. The last row is a depiction of both the excitation (light) and emission (dark) dipole orientations, as fitted from the measurements. The $\theta$ and the $\varphi$ values indicate the orientation with respect to the $z$ and $x$ axes, shown for the first molecule. The fitted orientation angles for both dipoles are shown in Table 1.

Figure 3

Determined $\beta$ values (left) and their corresponding distribution (right) for 25 measured Atto 655 molecules on a glass surface (blue), and for 49 Alexa 488 molecules embedded into a polymer film (red). The error bars shown in the left figure were estimating using a bootstrapping algorithm. The right side shows the probability distributions with a bin width of 5°. The distributions were fitted with a Poisson distribution (solid lines) yielding a mean value of $\beta$ equal to 14.6° for Atto 655 and equal to 22.5° for Alexa 488. The results for the first five molecules of Atto 655 correspond to the five measurements shown in Fig. 2 and listed in Table 1.