Exploring spatial dispersion in helical wired media: An effective field theory approach

The propagation of electromagnetic waves in helical media with spatial dispersion is investigated. The general form of the permittivity tensor with spatial dispersion obeying the helical symmetry is derived. Its particular form describing the medium made of conducting spiral wires with pitch $2\pi/|q|$ is studied in detail. The solution of the corresponding Maxwell equations is obtained in the paraxial limit. The dispersion law of the electromagnetic field modes, their polarization, and the integral curves of the Poynting vector are analyzed. The dispersion law of photons in such a medium possesses polarization dependent forbidden bands. The widths of these gaps and their positions are tunable in a wide range of energies. If the helix angle $\alpha$ is not close to $\pi/2$ and the plasma frequency $\omega_p\ll|q|$, then there are two chiral forbidden bands. The energies of one chiral forbidden band are near the plasma frequency $\omega_p$ and the width of this gap is of order $|q|$. The other chiral forbidden band is narrow and is located near the photon energy $|q|$. In the case $\alpha\approx\pi/2$, the first chiral forbidden band becomes a total forbidden band. If, additionally, the plasma frequency $\omega_p\gg|q|$, then the second forbidden band turns into a wide polarization dependent forbidden band. For the energies belonging to this interval the photons with only one linear polarization are transmitted through the medium and the polarization plane of transmitted photons is rotated. In the nonparaxial regime, the solution of the Maxwell equations is obtained in the shortwave approximation. The dispersion law of the electromagnetic field modes, their polarization, and the integral curves of the Poynting vector are found. Scattering of the electromagnetic waves by a slab made of the helical wired medium is considered.