Negative refraction and focusing in magnetically coupled L-C loaded transmission lines

We study electromagnetic waves in circuits with one-dimensional and two-dimensional (2D) periodicities. The unit cell is composed of L-C elements, and neighboring cells are magnetically coupled. Simulations reveal passband response and are in excellent accord with dispersion relations for corresponding infinite circuits. We also consider refraction at the interface between two different 2D circuits for long wavelengths. The product of the phase and group velocities is proportional to the mutual inductance M providing the coupling. Hence, the sign of the effective refractive index is the same as the sign of M. Further, we simulate negative refraction (and focusing) of circular waves, excited by a point source, if M has opposite signs on the two sides of the border line. (C) 2007 American Institute of Physics.