Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Chapter 19:
Advanced Concepts

19.1 Wave Equation

An electromagnetic wave is governed by three important features: the spatial curvature of the electric field ∇2E, the temporal curvature of the electric field Ë, and the temporal slope of electric current density J, which may also be considered the acceleration of electric current density. These parameters are expressed in the wave equation as follows:

E = μ(ε0 Ë, + J),

where μ is the magnetic permeability and ε0 is the electric permittivity.

The ∇ operator defines the gradient as

∇ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k

where i, j, and k are unit vectors. The ∇2 operator defines the Laplacian as

2 = (∂2/∂x2)i + (∂2/∂y2)j + (∂2/∂z2)k.

The temporal versions of the spatial operators are

Á = (∂/∂t)A


Ä = (∂/∂t2)A.

Online access to SPIE eBooks is limited to subscribing institutions.

Back to Top