二维开放波导波传播问题唯一性的辐射条件
A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides
摘要：
本文研究了波导中波传播问题中Helmholtz方程解的唯一性。经典的辐射条件不适用于我们的问题，因为折射率的不均匀性在一个方向上延伸到无穷大。此外，由于波导的存在，一些波以不同的传播常数在一个方向上传播，并且幅度没有衰减。我们的主要结果提供了一个明确的条件，考虑到物理上的重要组成部分，相应的导波和非导波的唯一性，这个条件减少到经典的Sommergland-Rellich条件在相关的情况下。最后，我们还表明，我们的条件是满足的解决方案，已经在文献中，所考虑的问题。
英文摘要：
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Finally, we also show that our condition is satisfied by a solution, already present in literature, of the problem under consideration.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
