Unified derivation of the scaling laws for electromagnetic waves, acoustic waves, and matter waves under nonorthogonal curvilinear coordinate transformations

Based on the results of the operations of del, including the gradient, the curl, and the divergence obtained under nonorthogonal curvilinear coordinate transformations, we present a derivation of the scaling laws for electromagnetic waves, acoustic waves, and matter waves in a framework that is fully unified. Our derivation approach does not involve any tensor analysis or differential element analysis and may serve as an important supplement to those derivation methods established previously. (C) 2011 Optical Society of America