Surface Plasmon-Polariton and Sub-wavelength imaging

For understanding the role of plasma playing in metals, plasma itself was described. Plasma was defined using notions like quasineutrality. Debye shielding, Debye length and collision length. Collective oscallation, the condition, such as a perturbation, was explored. Building on these ideas plasma frequency was dervied using fundamental laws such as conservation of charge and Gauss's law. Dispersion equation for plasma was described by concluding infinite phase velocity and no group velocity. Due to having group velocity equal to zero it was stated that collective oscillation was not a propagating wave. After which the quantization of plasma, the plasmon was described and shown over Stern and Ferfell's results.

After establishing plasma and its quantized form plasmon, the conditions for achieving a surface wave was explored. It was shown that to achieve field decaying away from the surface a purely imaginary kzwas plotted for normal imgaing kz < ko and for subwavelength imaging kx > ko using the dispersion equation for light. Applying the boundary conditions for the tangential fields the disperson equations were dervied and plotted. The dispersion equation had a stop band like structure for the lossless case between plasma frequency ωp and ωs. It was shown for a lossy case this stop band disappeared. The phase velocity and group velocity were discussed and the two different regimes of the dispersion equation was stated. Due to having fields completly bound to the surface it was stated that imaging would not work for a single interface case. From the frequency dependant nature of the fields propagation depth was discussed and it was found that metals have lower penetration depth. 

The focusing effect of flat slab was described for TE and TM mode. It was made clear that a metal slab was sufficient to achieve negative refraction for TM mode. Hence, the system would be polarization dependant. A simple relation was given between the permittivity and the width of the mediums.

The notion of space-frequency of an image was established using Fourier equations. The effect of artificially hiding some parts of the freqency domain was tested on a square image. The osberved effect was a blurred square with decaying artefacts. This idea of preserving wavenumbers (Fourier components) was applied to transfer functions dervied for symmetric slab. The transfer function was similarly derived, by applying the boundary conditions to the tangential fields. The effects of slab thickness and losses a medium had was shown on the tranfer function. Similarly, asymmetric transfer funciton was found and plotted using Matlab.

Finally, the transfer equation for 4 medium was dervied by using 3 boundary conditions. Applying these boundary conditions to the tangential field six equations were formed. After a cumbersome algebra normalized fields were found. However due to the quirky result, these results were not shown.

Suerlens as Pendry stated can form images using subwave components kx > ko, however it will be far from perfect.