Progress in single molecule fluorescence experiments have enabled an in-depth characterization of fluorophores, ranging from their photophysical rates to the orientation of their emission dipole moments in three dimensions. However, one crucial spatial information remains elusive: the molecule orientation relative to its emission dipole moment. One can retrieve the latter only by the use of another non-colinear transition dipole moment. We experimentally demonstrate the optical retrieval of this information for single terrylene (Tr) molecules in a 30 nm thin para-terphenyl matrix. We show, through second-order correlation measurements at varying excitation power and polarization, that Tr molecules experience an optically induced deshelving of their triplet states, mediated by two orthogonal intra-molecular triplet-triplet absorption dipole moments. We take advantage of these two transition dipole moments to retrieve the full orientation of the Tr molecule, employing a 3-level scheme for the molecule photophysics and analytical calculations for the exciting electric field distribution. This modelling approach enables us to accurately describe both varying power and polarization measurements, giving access to the molecule's photophysical rates and to its complete orientation in three dimensions. This includes the orientation of the singlet emission dipole moment in the laboratory frame, and the orientation of the molecule plane with respect to the singlet emission dipole moment.
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