Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Abstract

In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations.

Travelling waves in nonlinear magneto-inductive lattices

“…A periodic solution is asymptotically stable if all Floquet multipliers except the trivial Floquet multiplier are strictly smaller than one in modulus. The (in)stability result obtained from calculating the monodromy matrix is also confirmed by integrating (1). Note that the physically relevant interval for the coupling parameter is |λ| < 1/2 [6].…”

“…This is due to the assumption of the nonlinearity of the capacitance of the split-ring resonators that compose the magneto-inductive materials [26]. Note that the nonlinearity is different from our previous work [1,6], where it is in the onsite potential. The present work is to study the effect of such nonlinearity.…”

Low-power threshold gas discharge by enhanced local electric field in electromagnetically-induced-transparencylike metamolecules

“…Nonlinear phenomena can then be efficiently generated by placing a nonlinear element in this small volume. To realize nonlinear metamaterials, pn junctions (or Schottky junctions) [3][4][5][6][7][8][9][10], superconductors [11,12], vanadium dioxide [13], gallium arsenide [14,15], plasma [16][17][18], and the nonlinear magnetic component of the Lorentz force in metals [19] are used in the microwave and terahertz regions, and the nonlinearity of metals and dielectrics is used in the optical region [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Frequency mixing at an electromagnetically induced transparency like metasurface loaded with gas as a nonlinear element

“…If a nonlinear element is excited by the enhanced local electromagnetic field, nonlinear phenomena can be efficiently generated. To date, various nonlinear phenomena, such as frequency conversion, 2-18 power-dependent responses, [19][20][21][22][23][24][25] and nonlinear wave propagation [26][27][28][29][30][31] have been investigated.The enhancement factor of the local electromagnetic field in a resonant metamaterial is inversely related with the losses in its unit structure. In the optical region, nonlinear dielectric resonators 7-9 would be suitable for the unit structure, since nonlinear dielectrics possess small losses.…”

“…If a nonlinear element is excited by the enhanced local electromagnetic field, nonlinear phenomena can be efficiently generated. To date, various nonlinear phenomena, such as frequency conversion, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] power-dependent responses, [19][20][21][22][23][24][25] and nonlinear wave propagation [26][27][28][29][30][31] have been investigated.…”