Optics for Materials Scientists

Myeongkyu Lee

• Publisher: Apple Academic Press
• Year: 2019
• ISBN:
  9780429757747
• Edition: 1
• Topic: Sciences biologiques
• Subtopic: Science générale

This new volume will help materials scientists and engineers fully comprehend the principles of optics and optical phenomena and effectively utilize them for the design and fabrication of optical materials and devices. Materials science is an interdisciplinary field at the intersection of various fields, such as metallurgy, ceramics, solid-state physics, chemistry, chemical engineering, and mechanical engineering. Thus, many physicists, chemists, and engineers also work in materials science. Many materials scientists generally do not have a strong background in optics, and this book aims to fill that gap.

The volume explains the fundamentals of optics legibly to nonspecialists and presents theoretical treatments for a variety of optical phenomena resulting from light-matter interactions. It covers thin film optics, interference lithography, and metal plasmonics as practical applications of optics for materials research. Each chapter of the book has a problem and reference section to facilitate the reader's understanding.

The book is aimed at assisting materials scientists and engineers who must be aware of optics and optical phenomena. This book will also be useful as a textbook for students in materials science, physics, chemistry, and engineering throughout their undergraduate and early graduate years.

CHAPTER 1

Electromagnetic Waves

1.1 MATHEMATICS OF WAVE MOTION

1.1.1 ONE-DIMENSIONAL WAVE EQUATION

A wave can be described as a disturbance that travels through a medium from one position to another position. In physics, waves are time-varying oscillations of a physical quantity around fixed locations. Wave motion transfers energy from one point to another. A wave can be transverse or longitudinal. Transverse waves such as electromagnetic waves occur when a disturbance generates oscillations that are perpendicular to the propagation of energy transfer. Longitudinal waves (e.g., sound waves) occur when the oscillations are parallel to the propagation direction. Waves are described by a wave equation that sets out how the disturbance proceeds over time. Consider a transverse pulsed wave traveling in the positive x-direction with a constant speed v, as shown in Figure 1.1. Since the disturbance is a function of both position and time, it can be written as

$\psi =f\left(x,t\right)\cdot$

(1.1)

We here deal with a wave whose shape does not change as it propagates through space. The shape of the disturbance at any time, say t = 0, can be obtained by holding time constant at that value.

$\psi \left(x,t\right)|{}_{t=0}=f\left(x,0\right)=f\left(x\right)\cdot$

(1.2)

Figure 1.1 shows the wave profiles at t = 0 and t = t, that is, f (x, 0) and f (x, t). They represent the shapes of the disturbance taken at the beginning and end of a time interval t. We now introduce a new coordinate x’ that is defined as

$x^{\prime }=x-\text{v}t.$

(1.3)

In this new coordinate system, the disturbance ψ = f (x´) is no longer a function of time and looks the same at any value of t as it did at t = 0 in the original stationary coordinate system. It follows from Figure 1.1 that the disturbance can be represented in terms of the variables associated with the stationary system as

$\psi \left(x,t\right)=f\left(x-\text{v}t\right).$

(1.4)

FIGURE 1.1 Profiles of a pulsed wave moving in the positive x-direction at t = 0 and t = t.

This is the most general form of the one-dimensional wave function. Equation 1.4 describes a wave propagating in the positive x-direction. The resulting expression for a wave propagating in the negative x-direction would be

$\psi \left(x,t\right)=f\left(x+\text{v}t\right).$

(1.5)

We can figure out that regardless of the shape of the disturbance, the variables x and t appear in the wave function as a single variable in the form of (x − vt) or (x + vt). If the pulsed wave depicted in Figure 1.1 propagated by vΔt for an interval Δt, we find that

$f\left[\left(x+\text{v}\Delta \text{t}\right)-\text{v}\left(t+\Delta t\right)\right]=f\left(x-\text{v}t\right).$

(1.6)

That is, the disturbance at two different variable combinations is identical, as manifest from Figure 1.2. Note that the original shape of the pul...