Tunable supermode converters based on $J_x$ graphene waveguide arrays with transversely linear modulation

Conventional mode converters are usually based on wave-number matching in the propagation direction. This often requires applying the periodic modulation in the longitudinal orientation. Here, we propose to construct an efficient supermode converter with only transverse modulation. By linearly changing the surface conductivity of $J_x$ graphene waveguide arrays, we build a synthetic $J_x$ lattice with linearly varying on-site potential in the modal dimension. It turns out that each supermode can fully transfer to its corresponding symmetric partner. The conversion distance of supermodes is inversely proportional to the ramp of linear modulation. In this way, tunable supermode converters can be readily implemented by modulating the surface conductivity of graphene sheets. This study may find promising applications in developing mode converters and mode-division multiplexers utilizing plasmonic waveguide arrays.

Figure 1

(a) Schematic diagram of $J_x$ graphene waveguide arrays. (b) Real parts of propagation constants for the spatial $J_x$ lattice calculated in TMM and TBA method. (c) Modal ladder and profiles of supermodes.

Figure 2

(a)−(c) Distribution of field intensity in real space for a single incidence of first, fourth, and tenth supermode in transversely modulated $J_x$ graphene waveguide arrays. (d)−(f) Corresponding phase distribution for (a)−(c). (g)−(i) Evolution of the normalized intensity for supermodes in the modal dimension.

Figure 3

(a) Relation between γ and the conversion distance $L$ obtained by simulation data and TBA method with the incident wavelength λ = 8, 10, 12 µm. (b) Tracks of average modal intensity in modal space for δ = 0.005, 0.01, and 0.015 with the excitation of fundamental mode at λ = 10 µm.

Figure 4

(a) Conversion distance and the transformation rate versus the perturbation coefficient. (b) Tracks of average modal intensity in modal space for α = 1, 2, 3, and 10 with the excitation of fundamental supermode at λ = 10 µm. (c)−(f) Corresponding dynamics of supermodes in modal space for the tracks in (b).

Figure 5

Conversion distance of supermodes (a) and the amplitude of the mode variation (b) when the number of waveguides varies. (c)−(e) Dynamics of supermodes in modal space with the number of waveguides $N$ = 20, 30, and 40 respectively.

Figure 6

(a),(b) Evolution of supermodes in modal space with (a) the second and (b) the third order nonlinear modulation. (c) Tracks of average modal intensity in modal space for the evolution of supermodes in (a) and (b).