Mathematical studies in rigorous grating theory

Electromagnetic Field Enhancement in Small Gaps: A Rigorous Mathematical Theory

This paper is concerned with the field enhancement when an electromagnetic wave passes through subwavelength metallic gaps. We focus on a particular configuration when there is extreme scale difference between the wavelength of the incident wave, the thickness of metal films, and the size of gap apertures. Based upon a rigorous study of the perfect electrical conductor model for the transverse ...

Shadow Theory of Diffraction Grating

This paper deals with a new formulation for the diffraction of a plane wave by a periodic grating. As a simple example, the diffraction of a transverse magnetic wave by a perfectly conductive periodic array of rectangular grooves is discussed. On the basis of a shadow hypothesis such that no diffraction takes place and only the reflection occurs with the reflection coefficient −1 at a low grazi...

Institute for Mathematical Physics Quantum Dots a Survey of Rigorous Results a Survey of Rigorous Results

Rigorous Theory of Interaction Between Nuclear Particles

In this chapter a double tensor index k implies summation from 1 to 4. There is no classical way to treat the spin and charge variables of elementary particles. ' Therefore we represent matter by a set of complex wave fields p„. The quantities J, and S„& occurring in (1.1) are formed from matrices j„and s„A, . if I =0. Eq. (1.3) takes the form of Dirac's equation for a particle with inherent ma...

Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds

This paper is concerned with the problem of predicting the effective rate constant k associated with diffusion-controlled reactions in media composed of static and reactive traps (sinks) which are generally distributed randomly throughout a region containing reactive particles. The effective equation for diffusion-controlled reactions is derived using the method of homogenization. This leads to...