We consider light propagation through a ballistic amplifying photonic honeycomb lattice below the lasing threshold. Two sublattices of the system are formed by the wave-guides with different complex dielectric permittivities, which results in the non-Hermitian Dirac equation for electromagnetic field. We reveal that there exists a critical length of the amplifying region for which the photonic lattice exhibits an amplifier to generator transition. The transmission and reflection probabilities at the normal angle of incidence are strongly enhanced at a critical length of the system. We also comment on the sensitivity of amplification to the direction of incident light and the thickness of the amplifying region.

中文翻译：

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通过放大蜂窝状光子晶格来传播光

我们考虑通过低于激光阈值的弹道放大光子蜂窝状晶格的光传播。该系统的两个子晶格由具有不同复介电常数的波导形成，这导致了电磁场的非Hermitian Dirac方程。我们揭示了存在一个放大区域的临界长度，光子晶格表现出一个放大器到发生器的跃迁。在系统的临界长度处，法向入射角的透射和反射概率会大大提高。我们还评论了放大对入射光方向的敏感性和放大区域的厚度。