Fig. 1. (a) Schematic of the meta-atom (unit cell) in the linear PIT metamaterial, consisting of a metal CW and a pair of metal SRRs. Geometrical parameters of the meta-atom are L=1.7, w=0.1, a=0.58, b=0.1, Px=1.6, and Py=2.4  mm. (b) SRR pair with a hyperabrupt tuning varactor mounted onto slits. (c) Possible experimental arrangement for the measurement of GHz radiation in the nonlinear PIT metamaterial. (d) Normalized absorption spectra of the CW (red), SRR pair (blue), and meta-atom of the linear PIT metamaterial (green). Adapted from Ref. [64].

Fig. 2. Numerical result of the normalized absorption spectrum of the linear PIT (Fig. 1) for (a) d=0.38, (b) d=0.24, and (c) d=0.02  mm, respectively. Analytical result given in (d), (e), and (f) is obtained from solving the model Eqs. (1) and (3) in the linear regime. Adapted from Ref. [64].

Fig. 3. Nonlinear susceptibilities of the PIT metamaterial. (a) Real and imaginary parts of the third-order susceptibility χ(3) [i.e., Re(χ(3)) and Im(χ(3))] as functions of the frequency detuning δ. (b) Real and imaginary parts of the second-order susceptibility χ(2) [i.e., Re(χ(2)) and Im(χ(2))] as functions of δ. System parameters used are given in the text. Adapted from Ref. [65].

Fig. 4. (a) 1/Vp2−1/Vg2 of χSL(3) as a function of frequency detuning δ and the coupling coefficient κ. The rectangle enclosed by purple dashed lines shows the region where the longwave–shortwave resonance occurs (i.e., Vg≈Vp). (b) Real part Re(χeff(3)) (orange solid line) and imaginary part Im(χeff(3)) (green dashed line) of the effective third-order nonlinear susceptibility χeff(3) as functions of frequency detuning δ for κ=180  GHz. Adapted from Ref. [65].

Fig. 5. Propagation of the plasmonic soliton and the interaction between two plasmonic solitons. (a) The radiation intensity |E/U0|2 of the soliton as a function of t/τ0 and z/LD. (b) The collision between two solitons. Adapted from Ref. [64].

Fig. 6. Plasmonic dromions and their collision. (a) [(b)] is the intensity profile of the shortwave |u|2 (longwave |v1|2) as a function of ξ1 and τ1 at s=0. (c1), (c2), (c3), (c4) [(d1), (d2), (d3), (d4)] are intensity profiles of the shortwave |u|2 (longwave |v1|2) during the interaction between two dromions, respectively, at s≡z/(2Ldiff)=0,1,2,3. System parameters are given in the text. Adapted from Ref. [67].

Fig. 7. (a) Double-Λ-type four-level atomic system with the atomic states |j〉 (j=1,2,3,4) coupled with two probe fields (with Rabi frequency Ωpn) and two strong control fields (with Rabi frequency Ωcn) (n=1,2). Δ3, Δ2, and Δ4 are, respectively, the one-, two-, and three-photon detunings. (b) Im(Ka+) as a function of ω for different Ωc1=Ωc2. EIT transparency window is opened near the central frequency of the probe fields (i.e., at ω=0). The blue solid curve is Im(Ka−), which always has a large absorption peak at ω=0 for arbitrary Ωc1 and Ωc2. Adapted from Ref. [67].

Fig. 8. (a) Schematic of the plasmonic metamaterial for an analog to atomic FWM, which is an array of meta-atoms. (b) The meta-atom consists of two CWs (indicated by “A” and “B”) and an SRR. For generating nonlinear excitations, four hyperabrupt tuning varactors are mounted onto the slits of the SRR. (c) The numerical result (blue dashed lines) of the normalized absorption spectrum of the EM wave as a function of frequency by taking Ey0=−Ex0, dx=dy=4.0  mm (first panel), and dx=dy=3.4  mm (second panel). (d) The numerical result (blue dashed line) of normalized absorption spectrum for Ey0=Ex0, dx=dy=4.0  mm. Red solid lines in (c) and (d) are corresponding analytical results. Details on the figure can be found in Ref. [67].

Fig. 9. (a) Linear dispersion relation of the Km+ mode (PIT mode). Im(Km+) (blue dashed line) and Re(Km+) (red solid line) are plotted as functions of ω for κ2=−κ1=50  GHz2 (first panel) and κ2=−κ1=250  GHz2 (second panel). (b) Linear dispersion relation of the Km− mode (non-PIT mode) for arbitrary κ1 (κ2=−κ1). Adapted from Ref. [67].

Fig. 10. FWM conversion efficiency η as a function of the dimensionless optical depth (κ0gf1/γ1)L for Δ1=Δ2=0 (blue dashed line) and Δ1=Δ2=5γ1 (red solid line). Inset: FWM conversion efficiency η for optical depth up to 300 for Δ1=Δ2=5γ1. Adapted from Ref. [67].

Fig. 11. (a) The meta-atom consisting of a metallic structure loaded with two varactors with capacitance CL=C0−C1(t) [CR=C0+C1(t)] on its left (right) arm. (b) Equivalent RLC circuit model of the meta-atom. The electromotive voltage V is induced by the incident signal field that is parallel to the arm. R and rt are radiation resistances, C is the capacitance between neighboring meta-atoms in the vertical direction, and L is the inductance of each metallic arm. (c) Possible experimental arrangement for measuring the propagation of the signal field and multi-mode polarition memory in the PIT metamaterial. The signal (control) field is incident along the z (x) direction. Adapted from Ref. [75].

Fig. 12. The storage and retrieval of the (3+1)-dimensional signal field. (a) The intensity patterns for the superposed LG modes [(LG)02+(LG)0−2] in the x-y plane, respectively, at the time t=0, 3τ0, 15τ0, and 27τ0. (b) The same as (a) but for the superposed LG modes [(LG)04+(LG)0−4+(LG)00+(LG)20]. (c) The same as (a) but for the superposed LG modes [(LG)06+(LG)0−6+∑p=05(LG)p0]. The first column is the patterns before storage, the second and third columns are the patterns during storage, and the fourth column is the patterns after storage. The fifth column shows the phase distribution of the input LG modes. Adapted from Ref. [75].

Fig. 13. PIT-based memory efficiency η as a function of propagation distance z and γt for storage period ts=25τ0. Red solid, blue dashed, green dotted, and purple dashed–dotted curves are for γt, taking −4.2×10−4ωr, −1×10−4ωr, 0, and 1×10−4ωr, respectively. Adapted from Ref. [75].