Interactions in Crystals by a Lagrangian Approach

9315907纳尔逊这笔续期将继续使用拉格朗日方法对晶体对外场的电磁响应进行理论研究。将探讨四个主题。(1)研究一种全新的求解有界介质中波传播问题的数学方法。这种方法在没有边界的波矢空间中工作，因此不使用边界条件。(2)研究半空间物质激子共振附近的光学反射率的新解。(3)使用Grassmann代数的自旋的宏观拉格朗日公式将被用来探索磁性介质的性质。(4)研究了物质介质中电磁能量流矢量的形式。这项研究是在被称为晶体物理的固体物理领域进行的。采用宏观方法确定了外加磁场和电场及其相互作用对晶体性质的影响。因此，可以了解光学和磁特性，并预测新的现象。这些新现象可以通过实验加以验证，并使用更微观的方法进行更详细的研究。除了它的根本利益，这项工作可能对光子学领域也很重要。***

9315907 Nelson This grant renewal will continue theoretical studies of the electromagnetic response of crystals to external fields using a Lagrangian approach. Four topics will be explored. (1) An entirely new mathematical method of solving wave propagation problems in bounded media will be studied. This method operates in wavevector space where there are no boundaries and so uses no boundary conditions. (2) A new solution for the optical reflectivity near an exciton resonance of a half-space of matter will be studied. (3) A macroscopic Lagrangian formulation of spin using Grassmann algebra will be used to explore the properties of magnetic media. (4) Finally, research will be conducted on the form of the electromagnetic energy flow vector in a material medium. %%% The research proposed is in an area of solid state physics called crystal physics. A macroscopic approach is taken to determine the effects of external magnetic and electric fields, and their interactions, on the properties of crystals. Thus, optical and magnetic properties can be understood and new phenomena predicted. These new phenomena can then be verified by experiment and studied in more detail using more microscopic approaches. In addition to its fundamental interest, the work may be of importance to the field of photonics. ***