Mississippi State University - Department of Physics: Theoretical Optics

Research in Theoretical Optics



The current topic of research in the Theoretical Optics Group is electromagnetic energy flow in the radiation field emitted by a small source.  This source can be an atom, molecule or nanoparticle, irradiated by a laser beam.  The external field induces an oscillating electric dipole moment in the particle, and electric dipole radiation is emitted (neglecting for the time being the higher order multipole moments).  Of particular interest is the emission of radiation near an interface (metal or dielectric).  We focus on fundamental aspects of the emission of radiation, on the energy flow in the optical near field (e.g., within a few wavelengths around the source), and on resulting observable effects in the far field.  The study involves numerical analysis and visualization techniques, and the advantage of considering such a relatively simple system is that analytical progress can also be made. 

Most recently (100) we have investigated the emission of radiation by an electric dipole near a mirror.  The figures below show several striking new features of the radiation pattern.  The figure on the left shows the emission pattern of the radiation emitted by a dipole oscillating parallel to the mirror surface.  The mirror is located at z = 0, so it is well outside the picture.  In both figures, a distance of 2Pi corresponds to one optical wavelength.  We found that all radiation is emitted in one direction, and for the parameters of the figure this is upward along the z-axis.  This is in sharp contrast to emission in free space by the same source, where all energy is emitted radially outward from the source, like optical rays, and rays are emitted in all directions.  The figure also shows that very close to the source some of the field lines of energy flow form closed loops, indicating that some of the energy which is emitted at one side of the dipole returns to the dipole at the other side.  As a consequence, there has to be a singular point just above the dipole, and this point is indicated by a small circle.  The distance between the dipole and the singular point is a small fraction of an optical wavelength.  The figure on the right shows energy flow lines on a smaller scale (zoomed out) for a dipole oscillating under 45º with the z-axis.  The bold line at the bottom is the mirror surface.  We see that numerous singularities are present in the flow pattern and three optical vortices appear.  This intricate energy flow pattern is due to interference between the radiation of the source and the radiation reflected at the surface.  Without the presence of the reflecting surface, all field lines would be straight lines, coming out of the dipole. 


The study of near field phenomena with nanoscale resolution (nano-photonics) requires the exact solution of Maxwell’s equations.  For radiation emitted by a small source near an interface, a closed-form solution can be obtained as an angular spectrum representation.  We have applied this technique for multipole radiation of any order to find the angular power distribution in the far field (by asymptotic analysis), but this approach can equally well be adopted for the study of the optical near field.  In the near future we intend to study radiation phenomena near interfaces using this method.  For the case of a mirror, as above, the reflected field is just the field of the image dipole, but for any other material we will need the angular spectrum representation.  In addition to reflection at the interface, part of the radiation will be transmitted into the material.  In macroscopic (geometrical) optics the process of reflection and transmission is understood in terms of ray diagrams, and Snell’s law gives the angle of refraction.  It follows from the figures above that when sub-wavelength resolution is of interest, the flow lines of energy do not even resemble optical rays (straight lines) in the near field.  We plan to study in particular the process of transmission through an interface with nanoscale resolution.  A related topic of interest will be the transmission of dipole radiation through a slab of negative index of refraction material.  Ray diagrams predict that the radiation will come to a focus both inside the medium and after exiting the layer.  The question is then whether the image that appears outside the layer has a sub-wavelength resolution or not.