We develop a concept for a waveguide that exploits spatial control of nonlinear surface-polaritonic waves. Our scheme includes an optical cavity with four-level N-type atoms in a lossless dielectric placed above a negative-index metamaterial layer. We propose exciting a polaritonic Akhmediev breather at a certain position of the interface between the atomic medium and the metamaterial by modifying laser-field intensities and detunings. Furthermore, we propose generating positiondependent polaritonic frequency combs by engineering widths of the electromagnetically induced transparency window commensurate with the surface-polaritonic modulation instability. Therefore, this waveguide acts as a high-speed polaritonic modulator and position-dependent frequency-comb generator, which can be applied to compact photonic chips.

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Material characteristics and input-field specifics limit controllability of nonlinear electromagneticfield interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves. Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.field [18]. In the past few decades, experimental and theoretical investigations(for an intuitive explanation of dealing with plasmonic loss for waveguide application, see [19]) report stable propagation of linear and nonlinear SPWs employing ultra-low loss metallic-type layers such as single-crystal [20] and mono-crystal [21] metallic film, structured Fano metamaterials [22], semiconductor metamaterials [23] and superconducting metamaterials [24]. These investigations reveal that plasmonic excitation and stable propagation need minimal metallic nanostructure roughness [25]. Therefore, polaritonic frequency combs, and generally space-time control of nonlinear SPWs, are unfortunately challenging due to material limitations and driving field characteristics [26-28].Propagation of an optical pulse in nonlinear media leads to the appearance of strongly localized bright and dark waves such as soliton [29], rogue waves and breathers in nearly conservative systems [30]. Bright rogue waves and breathers are highly localized nonlinear solitary waves with oscillatory amplitudes [31,32]. These waves are valuable for their applications to phase and intensity modulation schemes [33,34], as well as the formation of bound states and molecule-like behavior [35]. More generally, dissipative rogue waves and breathers [36] have potential applications to nonlinear systems such as mode-locked lasers [37] and frequencycomb generators [38]. By contrast, dark rogue waves were only observed during multimode polarized light propagation ...