Maxwell Optics: II. An Exact Formalism
نویسنده
چکیده
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This 8 × 8 matrix representation is used to construct the optical Hamiltonian. This has a close analogy with the algebraic structure of the Dirac equation, enabling the use of the rich machinery of the Dirac electron theory. We get interesting wavelength-dependent contributions which can not be obtained in any of the traditional approaches.
منابع مشابه
Maxwell Optics: III. Applications
A new formalism of beam-optics and polarization has been recently presented, based on an exact matrix representation of the Maxwell equations. This is described in Part-I and Part-II. In this Part, we present the application of the above formalism to the specific example of the axially symmetric graded index fiber. This formalism leads to the wavelength-dependent modifications of the six aberra...
متن کاملWavelength-Dependent Effects in Maxwell Optics
We present a new formalism for light beam optics starting with an exact eight-dimensional matrix representation of the Maxwell equations. The Foldy-Wouthuysen iterative diagonalization technique is employed to obtain a Hamiltonian description for a system with varying refractive index. Besides, reproducing all the traditional quasiparaxial terms, this method leads to additional contributions, w...
متن کاملFully stable numerical calculations for finite one- dimensional structures: mapping the Transfer Matrix method
We design a fully stable numerical solution of the Maxwell ́s equations with the Transfer Matrix Method (TMM) to understand the interaction between an electromagnetic field and a finite, one-dimensional, nonperiodic structure. Such an exact solution can be tailored from a conventional solution by choosing an adequate transformation between its reference systems, which induces a mapping between i...
متن کاملMaxwell Optics: I. An exact matrix representation of the Maxwell equations in a medium
Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...
متن کاملSolutions of the cylindrical nonlinear Maxwell equations.
Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002