Perturbed Surface Plasmons on Metal-Dielectric Waveguides

Perturbed Surface Plasmons on Metal-Dielectric Waveguides 

A change in the surface plasmon propagation constant induced by a surface refractive index change occurring within a layer with a thickness h can be calculated by substituting the perturbation of the permittivity profile Eq. 55 and the field distribution of the surface plasmon Eq. 48 into Eq. 53. After a straightforward mathematical manipulation we obtain  

Re yd 0). For the perturbation of the effective index of the surface plasmon, this equation yields  

The perturbation of the effective index of a surface plasmon depends exponentially on the thickness of the layer within which the refractive index change occurs. For a thicknesses much larger than the penetration depth of the surface plasmon (h Ipd = 1/ Re /d ) the exponential term can be neglected and Eq. 60 simplifies to Eq. 57. For refractive index changes occurring within a layer thinner than the penetration depth of the field of fhe surface plasmon (h Ipd = 1/ Re /d ). the expressions for the perturbations in the propagation constant and the effective refractive index can be reduced to  

If the real part of the permittivity of the metal is much larger than the imaginary part e the sensitivity of the effective index of a surface 

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