Study of surface plasmon polaritons (SPPs) propagation through plasmonic crystals

A periodic array of air holes (diameter=200 nm, periodicity=344 nm), which are embedded in a 110 nm PMMA layer (above a 50 nm Au layer) are fabricated to form square lattices, which are called plasmonic crystals. A measuring technique, called SPP Tomography is employed. A linearly polarized He-Ne laser light ( =632.8 nm) and a set of trenches (formed by a composite of PMMA/Au-Air/Au layers) are utilized to excite three Surface Plasmon Polaritons (SPPs) beams that propagate in directions that are perpendicular to the respective sets of trenches. Further, the three SPP beams propagate toward the crystals at 45o and 90o angles of incidence, with reference to the orientation of the sides of the crystal unit cells, respectively. The SPP beam with a 45o angle of incidence continues propagating through the crystals, while the other two SPPs with a 90o angle of incidence are impeded as they start propagating through the crystals.

After magnified by a microscope (Nikon Eclipse 300 series), the surface emission (SE) image of the propagating SPP is captured by a CCD camera at a far field. From such a surface image a plot of SPP intensity, I, vs. position, x, is generated constituting an exponentially decaying function. The decay constant of such a function represents the imaginary part, designated as , of the kSPP wave vector allowing us to quantify the propagation length, Lx, of the SPP beam inside and outside the crystal area.

The effective index of refraction, neff, and kSPP values inside the crystals are determined theoretically and experimentally. The theory makes use of a filling factor and the bowing factor, . On the other hand, the experimental method employs CCD acquired Fourier Plane (FP) images. The two methods show an excellent agreement in terms of the value of neff inside the crystals, which is equal to 1.07218 confirming the merit and significance of the experimentally acquired Fourier Plane (FP) images. (kSPP inside the crystal can be calculated once neff is determined).