Interactions in Crystals by a Lagrangian Approach

9315907纳尔逊这批更新将继续使用拉格朗日方法的晶体的电磁响应外场的理论研究。 将探讨四个主题。 (1)本文将研究一种全新的求解有界介质中波传播问题的数学方法。 该方法在波矢量空间中操作，其中没有边界，因此不使用边界条件。(2)本文将研究半空间物质激子共振附近光反射率的一个新的解。 (3)使用格拉斯曼代数的自旋的宏观拉格朗日公式将用于探索磁介质的性质。 (4)最后，研究电磁能流矢量在物质介质中的形式。 这项研究是在固态物理学的一个领域，称为晶体物理学。 采用宏观方法来确定外部磁场和电场及其相互作用对晶体性质的影响。 因此，可以理解光学和磁性，并预测新的现象。 这些新现象可以通过实验来验证，并使用更微观的方法进行更详细的研究。 除了它的基本利益，这项工作可能是重要的光子学领域。 ***

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. ***