Waves entering a spatially uniform lossy medium typically undergo exponential intensity decay, arising from either the energy loss of the Beer–Lambert–Bouguer transmission law or the evanescent penetration during reflection. Recently, exceptional point singularities in non-Hermitian systems have been linked to unconventional wave propagation. Here, we theoretically propose and experimentally demonstrate exponential decay free wave propagation in a purely lossy medium. We observe up to 400-wave deep polynomial wave propagation accompanied by a uniformly distributed energy loss across a nanostructured photonic slab waveguide with exceptional points. We use coupled-mode theory and fully vectorial electromagnetic simulations to predict deep wave penetration manifesting spatially constant radiation losses through the entire structured waveguide region regardless of its length. The uncovered exponential decay free wave phenomenon is universal and holds true across all domains supporting physical waves, finding immediate applications for generating large, uniform and surface-normal free-space plane waves directly from dispersion-engineered photonic chip surfaces.

进入空间均匀有损介质的波通常会经历指数强度衰减，这是由 Beer-Lambert-Bouguer 传输定律的能量损失或反射期间的倏逝穿透引起的。最近，非厄米系统中的异常点奇点与非常规波传播有关。在这里，我们在理论上提出并通过实验证明了在纯有损介质中的指数衰减自由波传播。我们观察到高达 400 波的深度多项式波传播，伴随着在具有特殊点的纳米结构光子平板波导上均匀分布的能量损失。我们使用耦合模式理论和完全矢量电磁模拟来预测深波穿透，无论其长度如何，整个结构化波导区域都表现出空间恒定的辐射损失。未发现的指数衰减自由波现象是普遍存在的，并且适用于支持物理波的所有领域，直接从色散工程光子芯片表面生成大的、均匀的和表面法线的自由空间平面波立即得到应用。