Graphene sustained nonlinear modes in dielectric waveguides

Abstract

We discuss the existence of nonlinear modes sustained by graphene layers in dielectric waveguides. Taking advantage of the almost two dimensional nature of graphene, we introduce the nonlinear effect as a parameter in the continuity equations. We then apply our modeling to a simple slab waveguide to enlighten how graphene can be used to induce huge nonlinear phase shifts at easily accessible power levels.

Active graphene plasmonic grating for terahertz beam scanning device

“…At last, we should notice that Kerr nonlinearity could also change refractive index in our graphene plasmonic grating, but the change of the refractive index caused by Kerr effect is in a lower magnitude ( n 10 3 ∆ ≈ − under the intensity of GW/cm 2 as it demonstrated in [26]). However, our device can be tuned in a large range of the effective refractive index ( n 1.5 ∆ ≈ ) by changing electrode voltages.…”

“…Therefore, the absorption of the graphene can be ignored. Meanwhile, the nonlinearity such as saturable absorption effect [25,26] occurs under high-intensity electromagnetic field, but the intensity of THz source is generally low at present. Thus the nonlinear effect of graphene can be ignored in the THz band in our following discussion.…”

Optical Guided Wave Switching

“…As a consequence, the coupling coefficient in such structures can be easily controlled in an ultrafast fashion either by means of an applied electrical signal [67] or by changing the intensity of the signal at the device input. These findings open the way to fully exploit the huge nonlinearity of graphene for all optical signal processing: from one side giving more degrees of freedom to already proposed devices [68][69][70][71][72], from the other side paving the way to new devices. Graphene can sustain surface plasmon polariton (SPP) having unique properties as compared to what we are used to with noble metals.…”

“…Graphene can sustain surface plasmon polariton (SPP) having unique properties as compared to what we are used to with noble metals. In fact a single layer of graphene can support either TE or TM polarized plasmons without suffering from huge loss [73][74][75]; moreover, as far as the TM polarization is concerned, the extremely high confinement factor is particularly favourable to explore the huge v ð3Þ nonlinearity of graphene [68,76,77]. Experimental endeavors have demonstrated the evidence of graphene plasmons by measuring the plasmon resonance of graphene nanoribbon arrays [78], and by acquiring their near field images [79,80].…”

“…Note also that this model can be easily extended into the nonlinear regime by adding a nonlinear correction to the surface conductivity as: r R ¼ r ð1Þ R þ r ð3Þ R jEj 2 E y;z [74]. Moreover, thanks to the extremely small thickness of the graphene layer, nonlinearity can be analyzed by introducing a parameter embedded into the coefficients describing the continuity of the tangential components of the electromagnetic field [68,77]. To describe SPP propagation along z, we first note that, at first order, the y dependence of the electromagnetic field can be neglected; we then look for guided modes with harmonic temporal dependence expðixtÞ and spatial variation E 1;2;3 ðx; zÞ, H 1;2;3 ðx; zÞ $ expðÀibz AE C 1;2;3 xÞ with ¼ C .…”