^{1}

^{2}

^{1}

^{2}

A full-hybrid trial-field modeling, which was proposed earlier by the authors for plasmonic structures of rectangular cross-section, has been applied to trench waveguides for channel plasmon polariton. Most of the computed results of complex propagation constant agree well with those obtained by method of lines and effective index method, though the latter two results themselves show some discrepancy. The particular aspect in which there is varying degree of disagreement among the results obtained in the above three methods is the imaginary part of the effective index seen by the plasmon-polariton.

In the field of nanophotonics, the ability of surface plasmon polariton (SPP) to beat the diffraction limit is a tremendous boon to technology and its usefulness towards achieving higher integration density in photonic integrated circuits is now well established. As such, well-confined wave guidance and improved propagation length are the key aspects being addressed by the researchers. These goals in turn have led to a number of innovations in the SPP guiding structures. Reviews of SPP guides can be found, for example, in [

The geometry of the trench SPP guide is shown in Figure

(a) Geometry of trench-CPP waveguide. (b) One half of trench-CPP guide segmented into six regions.

The parameters are chosen as in [

In this approach, we would construct the trial transverse spatial functions for

The transverse wave numbers are related to

The upper and lower functions correspond, respectively, to magnetic and electric walls at the symmetry plane

Once all six field components in each region (R1, R2, R4) are derived from the trial fields, the next task would be to apply the continuity conditions. It is not necessary to impose all the boundary conditions at all the interfaces which only overdefines the problem. We found that application of continuity of tangential field components at only the R1-R2 and R2–R4 interfaces (between two different media) yields the desired eigenvalue equations, given by (

With the chosen parameters as mentioned in Section

(a) Dispersion of the real part of the fundamental trench-CPP mode effective index with depth of the air-filled trench. (b) Dispersion of the propagation length of the fundamental trench-CPP mode with depth of the air-filled trench.

The variation of

(a) Dispersion of the real part of the fundamental trench-CPP mode effective index with trench depth for different dielectric inserts inside the trench (

(a) Dispersion of the real part of the fundamental trench-CPP mode effective index for different wavelengths of operation with depth of the air-filled trench. (b) Dispersion of the imaginary part of the fundamental trench-CPP mode effective index for different wavelengths of operation with depth of the air-filled trench.

It has been shown [

The trial-field modeling with segmented problem area is well suited for computing the complex effective index of dielectric-filled trench configuration. The results of our computation are presented in Figures

Figures

A simple and approximate yet reasonably accurate method of modeling based on full-hybrid trial field functions has been applied to trench-CPP waveguide. The technique was earlier validated by successfully applying it to metal-strip SPP guide and nanoholes of rectangular cross-section in metals [