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By H. A. Buchdahl
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Additional resources for An Introduction to Hamiltonian Optics
At long wavelengths, we have seen in Sect. 2 that the theory of various excitations which generate a macroscopic electric field may be discussed simply and easily within the framework of electrostatic theory, when retardation is neglected. The imput is provided by specifying the nature of the frequency dependent dielectric constant (or for anisotropic materials the dielectric tensor) of the material or materials of interest. In a very similar manner, such long wavelength spin waves in a ferromagnet or antiferromagnet, where the wave vector dependencies introduced by exchange may be ignored, are described by magnetostatic theory.
Mills The short range interactions between the spins are the exchange interactions of quantum mechanical origin, w r i t t e n - J12S1 "$2 between two neighboring spins. If a spin wave is excited, and 012 is the angle between spins 1 and 2, excitation of the spin wave increases the exchange energy over that in the fully aligned ground state by J12 $2 022/2 at long wavelengths, where 012 ,~ 1. We have 012 ,,,ka o, with a 0 being the lattice constant and k the wave vector of the wave. Exchange couplings contribute a term proportional to k 2 to the spin wave frequency in the long wavelength limit.
All of our discussion of surface effects assumes that the surface is strictly parallel to the interfaces between the superlattice. Wu et al. 29, 30] explore the behavior of magnetoplasmon modes near the surface of a semiconducting superlattice, again modeled as a collection of thin quantum wells, in which the surface is normal to the interfaces. They find a rich and interesting spectrum of surface modes. 31]. In configurations where the surface is nonparallel to the interfaces, the physics will prove intriguing.
An Introduction to Hamiltonian Optics by H. A. Buchdahl