Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

Figure 1

Schematics of a 1D array of metallic nanowires with radius $a$ and separation distance $d$ (top left). (a) Real and imaginary parts of the propagation constant of the fundamental TM mode, ${\beta }_r$ and ${\beta }_i$, respectively. Panels (b) and (c) show the transverse profile of the amplitude (top) and longitudinal component (bottom) of the electric field of unstaggered and staggered PLSs, respectively, for $\lambda =1550\mathrm{nm}$ and $n_b=3.5$. In (b) and (c), $\delta n_{\mathrm{nl}}=-0.05$ ($n_2=-4\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$) and $\delta n_{\mathrm{nl}}=0.05$ ($n_2=4\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$), respectively. The nanowires have $a=40\mathrm{nm}$ and $d=8a$.

Figure 2

Soliton width $w$ vs the nonlinear index change $\delta n_{\mathrm{nl}}$, calculated for $a=40\mathrm{nm}$ and (a) $\lambda =1550\mathrm{nm}$, $d=8a$, and (b) $\lambda =632\mathrm{nm}$, $d=4a$. The solid and dashed lines correspond to $n_b=3.5$, $n_2=4\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$ (Si) and $n_b=2.8$, $n_2=1.4\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$ (${\mathrm{As}}_2{\mathrm{Se}}_3$), respectively. The dot in (a) corresponds to the soliton in Fig. 1c.

Figure 3

Linear (a) and nonlinear (b) propagation of the PLS in Fig. 1c in the lossless plasmonic array with $n_b=3.5$, $n_2=4\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$, $\lambda =1550\mathrm{nm}$, $a=40\mathrm{nm}$, and $d=8a$. (c) propagation of the same PLS in the lossy plasmonic array.

Figure 4

Propagation of a Gaussian beam with $\lambda =1550\mathrm{nm}$ in a plasmonic array with (a) $d=6a$, (b) $d=4a$, and (c) $d=8a$. (d) The beam width vs $z$: the solid, dash-dotted, and dashed curves correspond to panels (a),(b), and (c), respectively.

Figure 5

(a) The location of the peak amplitude at the output facet of a plasmonic array with length of $150\mu \mathrm{m}$, $a=0.03\lambda$, and $d=8a$ vs $P_{\mathrm{in}}$, determined for different phase tilt $k_0$ ($\lambda =1550\mathrm{nm}$). (b) The amplitude distribution of the output plasmon field vs $P_{\mathrm{in}}$, calculated for $k_0=0.5$. In (c) and (d), the normalized transverse and longitudinal electric field of a staggered 2D PLS, respectively, calculated for $a=40\mathrm{nm}$, $d=8a$, and $\lambda =1550\mathrm{nm}$. The background material is Si.