螺旋线介质中空间色散的探索：一种有效场论方法
Exploring spatial dispersion in helical wired media: An effective field theory approach
AI总结：
该研究通过有效场论方法，推导了螺旋线介质中具有空间色散的介电张量，求解了麦克斯韦方程组，分析了电磁波模式的色散、偏振及禁带特性，并探讨了平板散射，揭示了可调谐的手性禁带和偏振旋转现象。
摘要：
研究了具有空间色散的螺旋介质中电磁波的传播。推导了满足螺旋对称性的空间色散介电张量的一般形式。详细研究了由节距为 $2π/|q|$ 的导电螺旋线构成的介质的特定形式。在近轴极限下获得了相应麦克斯韦方程组的解。分析了电磁场模式的色散律、它们的偏振以及坡印廷矢量的积分曲线。在这种介质中，光子的色散律具有依赖于偏振的禁带。这些禁带的宽度及其位置可在很宽的能量范围内调节。如果螺旋角 $α$ 不接近 $π/2$ 且等离子体频率 $ω_p\ll|q|$，则存在两个手性禁带。一个手性禁带的能量接近等离子体频率 $ω_p$，该禁带的宽度量级为 $|q|$。另一个手性禁带较窄，位于光子能量 $|q|$ 附近。在 $α\approxπ/2$ 的情况下，第一个手性禁带变为完全禁带。此外，如果等离子体频率 $ω_p\gg|q|$，则第二个禁带转变为宽的依赖于偏振的禁带。对于属于该区间的能量，只有一种线偏振的光子通过介质传播，且透射光子的偏振面发生旋转。在非近轴区域，在短波近似下获得了麦克斯韦方程组的解。找到了电磁场模式的色散律、它们的偏振以及坡印廷矢量的积分曲线。考虑了由螺旋线介质制成的平板对电磁波的散射。
英文摘要：
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 $2π/|q|$ 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 $α$ is not close to $π/2$ and the plasma frequency $ω_p\ll|q|$, then there are two chiral forbidden bands. The energies of one chiral forbidden band are near the plasma frequency $ω_p$ 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 $α\approxπ/2$, the first chiral forbidden band becomes a total forbidden band. If, additionally, the plasma frequency $ω_p\gg|q|$, 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.
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