Guided modes in a triple-well graphene waveguide: analogy of five-layer optical waveguide

Abstract

We illustrate that a triple-well potential structure on a monolayer graphene can be treated as a five-layer optical waveguide. The transfer matrix method was used to deduce the dispersion equation for the graphene waveguide. It is found that the results have the similar dispersion equation, equivalent to the transverse electric wave in dielectrics. The symmetric and antisymmetric oscillating guided modes are determined and studied in details for the triple-well potential. From the results, we conclude that the oscillating guided modes appear either in the middle well or in all three wells. The results may be helpful in designing various novel graphenebased devices, such as electronic fiber and directional coupler.

Bipolar electron waveguides in graphene

“…Rather than achieving the quantization of momentum through geometry like a nanoribbon, or nanotube does, one may instead quantize momentum via the application a quasi-onedimensional (1D) electrostatically defined potential, i.e., by using electron waveguides [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential

“…The alternative geometry of transmission through potential barriers has also been a subject of extensive research, with the majority of studies utilizing "sharp but smooth potentials", i.e., potentials which are step-like or have kinks but are assumed to be smooth on the scale of the lattice constant, so that the effects of inter-valley scattering are neglected. Supercritical transmission [50][51][52][53][54][55][56][57][58] and tunneling through barriers has been studied for a variety of one-dimensional (1D) model potentials in both massless and massive 2D Dirac systems [25,27,49,[59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] including square barrier structures such as the double barrier [76][77][78], inverted double well [79,80], asymmetric waveguides [34,43] and various other step-like structures [41,42,80]. A variety of approaches ranging from the transfer matrix method through to the WKB method have been used.…”

“…However, realistic potential profiles vary slowly over the length scale of the Dirac material's lattice constant, and discontinuous potentials have yet to be realized. Furthermore, many piecewise potentials do not result in smooth wavefunctions across the whole of configuration space due to the nontrivial nature of their boundary conditions [42,43,127]. Smooth potentials do not suffer from this problem [36,39,46,128], additionally they permit inter-valley scattering to be neglected.…”

Guided Modes in a Double-Well Asymmetric Potential of a Graphene Waveguide

“…Another analogy is the graphene-based electron waveguides [8][9][10][11][12][13][14][15][16][17][18], which will be useful for various graphene-based devices, such as electronic fiber [19]. The crux of such an electronic waveguide is the confinement of Dirac fermions in graphene.…”