Surface Plasmons on Metal-Dielectric Waveguides

A waveguide consisting of a semi-infinite metal with a complex permittivity + i m a semi-infinite dielectric with permittivity e = e + is, where and e l are real and imaginary parts of si (z is m or d), see Fig. 2, can be treated as a limiting case of a three-layer waveguide (Fig. 1) with a metal substrate, a dielectric superstrate, and a waveguiding layer with a thickness equal to zero. 

The propagation constants of the guided modes propagating along such a structure are the solutions of Eqs. 34 and 35, which for d = 0 can be rewritten as  

This guided mode is sometimes referred as to the Fano mode [7]. As the permittivity of dielectric materials is usually positive, for the Fano mode to exist, the real part of the permittivity of the metal needs to be negative. For metals following the free-electron model [13]  

Absorption, which in reahty always exists, introduces a non-zero imaginary part into the permittivity of metals (Fig. 3, lower plot) and permits the existence of guided modes even for - e. These modes, sometimes referred as to evanescent modes [7], ej bit a very high attenuation and are therefore less practically important. In this work, we shall refer to all of the guided modes described by eigenvalue (Eq. 40) as surface plasmons (SP). 

If the real part of the permittivity of the metal is negative and its magnitude is much larger than the imaginary part the complex propa- 

---

Perturbed Surface Plasmons on Metal-Dielectric Waveguides... 

---