Plasmonics | Long-Range Plasmons

What is a Long-Range Surface Plasmon (LRSP)?

An LRSP is a particular type of surface plasmon mode that is characterized by electromagnetic fields that are mostly contained in the region outside of the metal. The electric and magnetic fields of an LRSP are nearly perpendicular to the wave's direction of propagation, so that the mode can be considered "TEM-like" (Transverse Electric and Magnetic fields), with lateral confinement on the order of several wavelengths. Because of these characteristics, LRSPs can propagate the farthest of all known metallic modes--centimeter distances at infrared wavelengths and millimeters at visible wavelengths! Yet, like all plasmon modes, LRSPs remain extremely sensitive to their surrounding environment and are thus of interest for detection and sensing purposes.

Very thin metal films or metal strips can support LRSPs. In this geometry the LSRPs can be viewed as coupled states—for example, the modes for the strip geometry can be understood as arising from the coupling between individual plasmons supported by the edges and the corners of the strip. As is the case for most plasmonic structures, the LRSP mode properties are not predominantly restricted by the wavelength and thus the LRSP strip can be considered as the optical analog of the transmission line that is commonly used at microwave and radio frequencies.

In our group, we are interested in LRSP engineering. We develop quantitative numerical tools and systematic experimental protocols that will ultimately allow us to pursue a variety of new plasmonic sensors and photonic components.

Numerical Simulations of Plasmonic Transmission Lines

The properties of plasmonic transmission lines can be found using a variety of numerical simulation approaches. In one method, we make use of commercial software (HFSS by Ansoft) to compute the field structure associated with the surface plasmon modes of a planar strip. The figure above shows the simulated geometry for a straight plasmonic transmission line. Because propagation occurs along the strip in only one direction, periodic boundary conditions can be applied to reduce the simulated volume. The figure shows the typical size of a computational domain, with the thickness (t) and the width (w) the plasmonic transmission line shown. By simulating the above geometry, the mode frequencies of the plasmonic transmission line can be found as a function of the phase advance (or, equivalently, propagation constant) using the eigensolver in HFSS. HFSS has the capability of finding eigen-frequencies even in the presence of material losses (i.e., complex eigenvalues can be found). Self-consistency must be achieved between the simulated mode frequencies and the electric permittivity, which is also frequency dependent. This self-consistency is accomplished by iterating the solution: we first assume a value of the permittivity, solve for the eigenfrequency and then compare the permittivity predicted by using the computed eigenfrequency. We use our simulation method to examine some of the basic aspects of plasmonic transmission line engineering (yellow color=link to article).

The animation at the top of this page shows the propagating fields of an LRSP along a gold metal strip, as simulated using the approach described above. The plot shows the isosurface for which the electric field E=0.18Eo. [This animation is by Claudio Dellagiacoma].

Plasmon Fabrication and Experiments

We fabricate plasmonic transmission lines using standard UV lithography and e-beam metal deposition. While the fabrication in itself is not excessively difficult—at optical wavelengths, the metal is required to be on the order of ten nanometers, with the width being on the order of a few microns—the LRSP modes are extremely sensitive to the surrounding dielectric composition, which makes them very difficult to work with. The less sensitive configuration is that of a symmetric structure, where the strips are embedded in a uniform dielectric environment. In our experiments, the metal strips are made on a glass substrate and subsequently covered by a layer of index matching fluid. The index matching fluid has to be chosen carefully—a deviation in index between the upper and lower halves as small as 0.02 can result in the complete destruction of the mode.

We excite the LRSP modes using an end-fire technique. A polarization maintaining fiber coupled to a HeNe laser (λ=632 nm) illuminates one end of the strip and the microscope collects the light scattered at the other end. The strip output lights up when the electric field is parallel to the short axis of the strip. This result is as expected because the LRSP modes are mostly TM polarized.