Pdf monochromatic nonuniqueness in planewave inverse. Such solution is known as a monochromatic plane wave. Exact solutions are presented of the kleingordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm plane electromagnetic waves and wave propagation 7. These solutions of the wave equation are called uniform plane waves the efield and the hfield as well is constant over any infinite plane that is parallel to the xy plane in more technical terms, the surfaces of constant phase are infinite planes the pattern shown above moves with a velocity equal to c c k. Maxwells wave equation in linear isotropic media, onedimensional case, counterpropagating waves, refractiveindex and the speed of light, temporal fourier transform and the complex representation for a monochromatic field, helmholtz equation, dispersion relation for planewaves. Here, k is the wave number, which is related to the wavelength of the wave by the equation 2 k. To see how monochromatic electromagnetic waves propagate in a dielectric medium suppose that the wave is a plane wave that propagates in the z direction, so that e b e, ikz. First there are changes in the image with the color. Chapter 2 the wave equation after substituting the.
In this section we address the question of the most general possible monochromatic. The conduction current in a conductor is the cause of the di. Of these, the most important examples are the electromagnetic plane waves, in which. The precise definition of the solution is quite complicated, but very instructive. Here we will consider the situation corresponding to a plane monochromatic wave in an anisotropic material. The wave is travelling in the xdirection and polarized in the zdirection. The polarization of the plane wave describes the relative direction, magnitude, and phase of the electric part of the wave. This is similar to what we had before but now the wave vector k is a complex number. It, and its modifications, play fundamental roles in continuum mechanics, quantum mechanics, plasma physics, general relativity, geophysics, and many other scientific and technical disciplines. Ee eb bb consider a monochromatic wave of frequency.
The computation of th e scattered electri c field for a tm plane wave in cident on an infinite, homogeneous dielectric c yli nder is well known and can be foun d in harrington1. Suppose we have a monochromatic plane wave of real amplitude e 0, frequency. For example, the solution to the wave equation when absorption or ampli cation takes place contains an exponential with a complex argument. So to recap, whenever i have a monochromatic wave given by e. Pdf propagation of a monochromatic electromagnetic plane. A plane wave with a fixed direction of the electric field vector e0 is termed lin. The plane wave decomposition is mathematically universal. More generally the wave can be propagating an an arbitrary direction often desc ribed by wave vector k so that the plane wave solution can be written as e. Transverse electromagnetic wave tem 6 with the refractive index n v r and the free space impedance r zf0. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. The uniform plane wave is a fundamental concept in electro magnetics and it is the simplest solution to the maxwells equation for time varying fields in an unbound, homogeneous.
Consider light propagating in a direction given by a unit vector k. Chapter maxwells equations and electromagnetic waves. Propagation of a monochromatic electromagnetic plane wave in a medium with nonsimple motion article pdf available in technical physics 445. E has only an x component, and b only a y component all the offdiagonal i. A proper derivation of the 3d wave equation would take us a bit. The wavefront shape at the observation plane is, therefore, of particular interest. The wave is polarized in the x direction by convention, we use the direction of e to specify the polarization of an. Chapter 9 treats the propagation of plane waves in vacuum and simple. Discuss the radiation pressureof a monochromatic plane wave on a. We first consider the solution of the wave equations in free space, in absence of. Monochromatic plane waves in a corrugated tube system a. Propagation of a monochromatic electromagnetic plane wave.
One of the simplest examples of a boundary value problem is that of a. Electromagnetic plane waves the real electric and magnetic fields in a monochromatic plane wave with propagation vector k. While the monochromatic planewave field is a relatively abstract quantity, it nevertheless is a very useful concept from which much of electromagnetism, and thus optics, is based. This spatial wave function originates from a separation of variables applied to the full wave function x. We shall analyze the source terms in the maxwells equations to simplify maxwells equations in a conductor. In free space, such a plane wave is not consistent with energy conservation law in the sense of classical electrodynamics. Thus the poynting vector represents the ow of energy in the same way that the current jrepresents the ow of charge. As we discussed in the last lecture, maxwell found the wave equation 2 2 2 2 1 0 e e ct n r r. In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from maxwells theory. In physics, a plane wave is a special case of wave or field. For the dielectric materials used to guide high frequency electromagnetic waves which we will mainly consider here the conductivity is typically zero, while the permeability is that of free space.
Plane electromagnetic waves and wave propagation 7. Radiation pressure of a monochromatic plane wave on a flat. Classical electromagnetism and optics c y x z e h figure 2. Wave equation and fundamental solutions wave equation. The field is often observed or measured at a planar surface along the optical axis z. Polarization 1 polarization vectors in the last lecture, we showed that maxwells equations admit plane wave solutions e e 0e i kxt, b b 0e i kxt 1 here, e 0 and b0 are called the polarization vectors for the electric and magnetic. Here the cells left and right boundaries are located a distance afrom the origin, as depicted in fig. The monochromatic assumption implies that the right hand term of 3 is null 0. Chromatic and monochromatic aberrations aberrations in optical systems can be defined as the failure to get a faithful representation of an object in the image plane. In the absence of free charge and current densities the maxwell equations are.
The wave equation is the simplest example of a hyperbolic differential equation. Here the cells left and right boundaries are located a distance afrom the origin, as depicted in. Maxwell stress tensor for a monochromatic plane wave problem 9. In free air, the instantaneous timedomain pressure at a spacetime point x,t associated with a 1d plane monochromatic traveling wave propagating e. Acoustic wave equation is obtained, combining both equations. If and have the same phase but different magnitude we have linear polarization of the field with the polarization vector making an angle with and magnitude. Monochromatic electromagnetic plane wave wikipedia. Note that a complex corresponds to a simple phase shift in the exponential. Monochromatic wave an overview sciencedirect topics. Sep 11, 2015 uniform plane wave and wave equation the basic understanding of the electromagnetic wave propagation in medium is provided by the basic concept of uniform plane wave. If we look back at our derivation of the model dielectric function, we. Uniform plane wave and wave equation the basic understanding of the electromagnetic wave propagation in medium is provided by the basic concept of uniform plane wave. We now turn to a monochromatic single color optical field. Now suppose we want a monochromatic, plane wave that travels in some.
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