 |
 |
 |
|
 |
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. Experimental DesignStriving towards the goal of a 3D sub 10nm high-resolution imaging technique, experimental efforts are focused on the realization of a high-resolution scanning microscope, and the design of a signal-processing module for real time data interpretation. Initial experiments were successful at pinpointing fluorescent markers with 5nm accuracy in the z-direction (see results). Current experimentation focuses on resolving multiple fluorescent markers at different heights, and developing a z-scanning spherical mirror to improve light collection and lateral resolution. MicroscopeInitial proof of concept experimental setup consisted of a flat Si/SiO2 mirror placed on the order of 10-15 wavelengths bellow the fluorescent marker. Spectra were collected from above using a low NA objective. This setup has several experimental limitations: low lateral resolution, and low light collection. Using a flat mirror we get only a few equal path lengths for a given collection angle. Hence when a high NA objective is used, the information is averaged out. In order to remedy these experimental limitations, we propose and are in process of fabricating spherical mirrors. A spherical mirror placed at an appropriate distance bellow the florescent source, with a radius that matches the sphericity of wave fronts originating from the fluorescent marker, creates a wide angle of identical path lengths. This microscope setup emulates a 4pi system since it also collects light emitted downwards.
Fig. 1: Spectral Self-interference microscope Our scanning microscope (shown in Fig. 1) will consist of a nanometer precision stage, a z-controlled spherical mirror, and a high magnification objective. Current efforts encompass the fabrication of spherical mirrors from various metallic substrates and the development of a nanometer sensitive stage. Using various techniques we have produced spherical mirrors with a radius on the order of 10um (shown in Fig. 2). The focus of current work is the improvement of optically smooth spherical micro mirrors in tandem with implementation of a nanometer precision stage.
Fig. 2: AFM image of Ni spherical micro mirror.
|
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:
| © 2007 Trustees of Boston University. All rights reserved. | Last modified April 16, 2007 at 12:00 AM EDT |