Coupling of two counterpropagating modes in nonlinear split-ring resonators’ chain

•The coupling of two counterpropagating magnetoinductive waves in nonlinear SRRs chain is investigated.•Two coupled NLS equations describing the evolution of the slowly varying amplitude for the two modes are derived.•This system supports backward- and forward-propagating vector solitons of the bright–bright and dark–dark type through a cross-phase modulation.

The two coupled counterpropagating nonlinear magnetoinductive wave modes are analyzed theoretically in split ring resonator chain with Kerr nonlinear interaction. Starting from a general nonlinear lattice equation based on a quasi-discreteness approach we derive two coupled nonlinear Schrödinger equations governing the evolution of the slowly varying envelopes of these modes. It is shown that this system supports backward- and forward-propagating vector solitons of the bright–bright and dark–dark type through a cross-phase modulation.