We shall consider here light propagation through anisotropic materials or polarizing optical elements and systems, and shall describe in brief the methods used to find the changes in light intensity and polarization introduced by these anisotropic elements.

Materials with optical anisotropy

In anisotropic materials the velocity of light propagation depends on the propagation direction. The anisotropy is connected with the structure of the material. Typical materials with optical anisotropy are transparent crystals, and the theory of light propagation through anisotropic media is usually called crystal optics [1–3]. Optical anisotropy is also observed in liquid crystals, and in some amorphous materials subjected to external forces such as mechanical or electrical forces. Stretched polymer films provide a good example. In this book we deal mainly with photoinduced anisotropy. In some materials illumination with polarized light causes selective destruction of absorbing molecules or centers, reordering of these absorbing centers, or some other changes depending on light polarization. This results in polarization-dependent changes in the absorption coefficient or/and in the refractive index of the material, that is, in optical anisotropy. The dependence of the absorbance on light polarization is called dichroism and the dependence of the refractive index on light polarization is called birefringence.

When a material is anisotropic, its dielectric permeability is a tensor, and as a consequence the wave surfaces in it are not spherical, but are ellipsoidal.

This book has one purpose: to help you understand four of the most influential equations in all of science. If you need a testament to the power of Maxwell's Equations, look around you – radio, television, radar, wireless Internet access, and Bluetooth technology are a few examples of contemporary technology rooted in electromagnetic field theory. Little wonder that the readers of Physics World selected Maxwell's Equations as “the most important equations of all time.”

How is this book different from the dozens of other texts on electricity and magnetism? Most importantly, the focus is exclusively on Maxwell's Equations, which means you won't have to wade through hundreds of pages of related topics to get to the essential concepts. This leaves room for in-depth explanations of the most relevant features, such as the difference between charge-based and induced electric fields, the physical meaning of divergence and curl, and the usefulness of both the integral and differential forms of each equation.

You'll also find the presentation to be very different from that of other books. Each chapter begins with an “expanded view” of one of Maxwell's Equations, in which the meaning of each term is clearly called out. If you've already studied Maxwell's Equations and you're just looking for a quick review, these expanded views may be all you need. But if you're a bit unclear on any aspect of Maxwell's Equations, you'll find a detailed explanation of every symbol (including the mathematical operators) in the sections following each expanded view.

Maxwell's Equations as presented in Chapters 1–4 apply to electric and magnetic fields in matter as well as in free space. However, when you're dealing with fields inside matter, remember the following points:

• The enclosed charge in the integral form of Gauss's law for electric fields (and current density in the differential form) includes ALL charge – bound as well as free.

• The enclosed current in the integral form of the Ampere–Maxwell law (and volume current density in the differential form) includes ALL currents – bound and polarization as well as free.

Since the bound charge may be difficult to determine, in this Appendix you'll find versions of the differential and integral forms of Gauss's law for electric fields that depend only on the free charge. Likewise, you'll find versions of the differential and integral form of the Ampere–Maxwell law that depend only on the free current.

What about Gauss's law for magnetic fields and Faraday's law? Since those laws don't directly involve electric charge or current, there's no need to derive more “matter friendly” versions of them.

Introduction

Underground exploration of oil, minerals and other reserves is an area of high practical interest. The technique of magneto-telluric, employing ultra low frequency (ULF) waves, has emerged as a powerful tool in this endeavour. Extremely low frequency (ELF) waves are useful for undersea exploration and submarine communication. The surface of the Earth, its cloud cover and the atmosphere can be sensed through the techniques of remote sensing, where natural emissions are detected at microwave, millimetre wave and shorter wavelengths using polar and geosynchronous satellites. In this unit, we shall study these fascinating techniques in some detail.

Magneto-Telluric Method

In this technique, one uses a dipole antenna above the surface of the Earth, to produce ULF/ELF waves, and measures the ratio of horizontal components of electric field E to magnetic field H of the wave (called wave impedance Z = E/H) on the surface of the Earth at different locations. This ratio depends on the conductivity of the Earth, σ, upto a depth δ ≃ c(2 ∈0/σω)1/2 where ω is the frequency of the wave, ∈0 is the free space permittivity and c is the velocity of Geological Seisming and Remote Sensing light in free space. By scanning Z with ω, one essentially scans σ with depth (below the surface of the Earth). As one observes Z as a function of horizontal distance on the surface of Earth, anomalies in Z are indicative of the buried ores inside the Earth, just below the location of deviation. For this purpose, one could utilise the naturally occurring electromagnetic disturbance as well.

Introduction

Newton's first law of motion, known as the law of inertia, states that a body continues to maintain its state of motion, i.e., its velocity remains constant, unless acted upon by an external force. Conversely, a frame of reference in which the law of inertia holds is called an inertial frame. Any frame, moving with constant velocity with respect to an inertial frame, is also an inertial frame. Thus, one may visualise numerous inertial frames, moving with constant velocities with respect to each other.

Newton believed that there is no preferred inertial frame in nature. The laws of nature are the same with respect to all inertial frames.

A major crisis arose, after Maxwell's equations predicted that the velocity of light in free space is c=1/√μ0∈0, where μ0=4π × 10-7 MKS is the free space permeability and ∈0= 10−9/(36π) MKS is the free space permittivity. Since μ0 and ∈0 are the same in all inertial frames, the velocity of light c, must also appear the same in all inertial frames. How could it be that the velocity of light is c, with respect to a ground observer and it is the same, with respect to an observer moving with an arbitrarily large velocity v also? This violated the law of addition of velocities. Then, it became imperative to change the very foundation of mechanics. Yet there was a suspicion that there might be a very special frame in which the velocity of light was c and it was different in other frames. This suspicion was conclusively demolished by the Michelson-Morley experiment.