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Optical Characterization and Nanophotonics Laboratory |
Principles of Spectral Self InterferenceFor many years scientists have recognized that fluorophores are often quenched when they are placed upon surfaces. Mechanisms of energy transfer, standing wave nodes in the excitation field, and destructive interference in the emission all lead to significant reductions in fluorescence. Ten years ago, Fromherz and co-workers noted that the intensity of the total fluorescence oscillates as a function of the fluorophore height above a reflecting substrate. Building upon work performed many years ago by Drexhage they utilized a convolution of the excitation standing wave and emission interference to sensitively locate the vertical position of the fluorophore in close proximity to a reflecting surface. Because the fluorophore is within ~λ of the reflecting surface, the entire spectrum of the emission is quenched or enhanced as the light undergoes constructive and destructive interference as a function of the vertical distance. Fromherz's method is based on measuring the intensity of the fluorophore for several known silicon dioxide heights in order to determine the height of the fluorophore above the dioxide layer. Spectral self-interference fluorescence microscopy is different in that the separation between the fluorophore and the reflecting substrate is much greater, on the order of 10-15 wavelengths. The longer path length difference between the direct and reflected light means only a small change in wavelength is needed to go between constructive and destructive interference. The result is spectral oscillations, or fringes, in the spectrum - a unique signature of the height of the emitter. Small height differences produce shifts in the fringes and changes in the period of oscillation (the latter are less noticeable). If the fluorescent markers are at a prescribed distance from the surface, the resulting spectrum can be calculated. Inversely, the distance above the mirror can be determined solely from the oscillations within the spectrum. Unlike fluorescence interference-contrast microscopy, it should be noted that as the height information is encoded in the spectrum, our approach is independent of the fluorophore density, emission intensity, and the excitation field strength. Green's Function FormalismIn order to analyze the spectral oscillations and to be able to determine the orientation and vertical position of a fluorophore, the radiation pattern of the fluorophore should be known. We are implementing an accurate and reliable way of finding the radiation intensity of an emitter by using
Green's functions for the stratified media. In this formalism, the electric field Green's function is written in terms of vector potential Green's functions and scalar potential Green's functions. Traditionally, these functions are represented by the Sommerfeld integrals in the spatial domain,
and by closed-form expressions in the spectral domain. Green's functions in spectral domain can be found analytically and spatial domain Green's functions are written in terms of the spectral domain Green's functions using the Sommerfeld integral: where G and As a final step, electric field is written in terms of spatial Green's functions and the radiation intensity is found using the electric field at any observation point. In this formalism, the information about the reflections from the layer interfaces is encoded in the spectral domain Green's functions that depend on the geometry and optical properties of the medium. This method is a reliable and accurate method as all the plane wave components originating from the source is taken into consideration by the nature of the formalism. Measurement of DNA conformation and orientation using SSFMThe SSFM technique maps the spectral oscillation by a fluorophore located on a layered reflection surface into a precise position determination. Analysis of the spectral oscillations (using a grating spectrometer) due to the self-interference from the direct and reflected emission yields the vertical position of that fluorophore with sub-nanometer accuracy. Assuming known orientation, e.g. randomly oriented DNA anchored to the oxide surface, it is possible to induce conformation off the DNA (single stranded vs. double stranded) on the surface based on the fluorophore – surface distance. Assuming known conformation, e.g. double stranded DNA with contour lengths shorter than the persistence length, it is possible to induce the orientation of the DNA immobilized on the surface. (Moiseev PNAS 2005). SSFM is also useful for nanometer scale characterization of other molecules, for example the characterization of a surface bound polymer or the different binding locations and orientations of DNA to a 3D binding platform (Yalcin Anal Chem, 2009).
Fig. 1: Example of SSFM Measurement Response and Setup
Fig. 2: Image Copyright 2009 ACS Publications
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are Green's functions in the spatial and spectral domains respectively, H0(2) is the Hankel function
of the second kind, and SIP is the Sommerfeld integration path. The above Sommerfeld integral cannot be integrated easily to find the spatial domain Green's function. However, when the spectral domain Green's functions are approximated in terms of complex exponentials using a technique called
generalized pencil of function (GPOF) method, the analytical evaluation of the Sommerfeld integral is possible by the Sommerfeld identity:
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