Maxwell's macroscopic equations, the energy-momentum postulates, and the Lorentz law of force.

We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for actual (i.e., physical) models of polarization P and magnetization M , these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with the requirements of the special theory of relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. One advantage of the proposed formulation is that it sidesteps the long-standing Abraham-Minkowski controversy surrounding the electromagnetic momentum inside a material medium by simply "assigning" the Abraham momentum density E(r,t)xH(r,t)/c2 to the electromagnetic field. This well-defined momentum is thus taken to be universal as it does not depend on whether the field is propagating or evanescent, and whether or not the host medium is homogeneous, transparent, isotropic, dispersive, magnetic, linear, etc. In other words, the local and instantaneous momentum density is uniquely and unambiguously specified at each and every point of the material system in terms of the E and H fields residing at that point. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.

Surface plasmon polaritons on metallic surfaces.

A unified theoretical study of surface plasmon polaritons on flat metallic surfaces and interfaces is undertaken to clarify the nature of these electromagnetic waves, conditions under which they are launched, and the restrictions imposed by Maxwell's equations that ultimately determine the strength of the excited plasmons. Finite Difference Time Domain computer simulations are used to provide a clear picture of the electromagnetic field distribution and the energy flow profile in a specific situation. The examined case involves the launching of plasmonic waves on the entrance facet of a metallic host perforated by a subwavelength slit, and the (simultaneous) excitation of the slit's guided mode.

Optical transmission at oblique incidence through a periodic array of sub-wavelength slits in a metallic host.

Using the Bloch modes of a periodic, semi-infinite array of slits in a metallic host, we study the transmission of obliquely incident plane-waves through sub-wavelength slits. Matching the tangential E- and H-fields at the entrance facet of the periodic structure yields the complex amplitudes of the various Bloch modes, which exist and propagate within the slit array independently of each other. The computational scheme is robust, convergence is rapid, and a good match at the boundaries is obtained in every case. The regions examined in some detail include the vicinity of the Wood anomaly (where new diffraction orders appear/disappear on the horizon), the neighborhood of a point where surface plasmon polaritons (SPPs) are excited, and an ordinary situation in which the incidence angle is far from the angles that invoke Wood's anomaly or cause the excitation of SPPs. Field distributions and energy flow diagrams in and around the slits reveal the existence of transmission minima (and reflection maxima) at incidence angles associated with the excitation of SPPs.

Intersection of nonidentical optical waveguides based on photonic crystals.

An intersection based on photonic crystal coupled resonator optical waveguides is proposed and analyzed. The two waveguides are designed to have different transmission bands without overlap, which enables light in the two corresponding bands to propagate through the intersection with no cross talk and with excellent transmission. The MIT Photonic-Bands code is used to calculate the band structures of photonic crystal waveguides. The finite-difference time-domain method is used to simulate the relevant structures.