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.