The primary textbook for Physics 4380/5380 is:

Hecht, Eugene

Optics, 3d ed., Addison Wesley Longman, 1998.

A secondary textbook is listed which will serve as an additional resource for advanced projects in Physics 5380:

Guenther, Robert D.

Modern Optics, John Wiley & Sons, 1990.

The following book provides many illustrations of optical transform techniques in optics. Furthermore, many graphs were prepared using the computer program MATLAB.

Wilson, Raymond G.

Fourier Series and Optical Transform Techniques in Contemporary Optics: An Introduction John Wiley & Sons, 1995.

The chapters listed below are those in the textbook by Hecht.  Topics will be chosen from the following sections.

2  Wave Motion 11

2.1  One-dimensional Waves 11
2.2  Harmonic Waves 15
2.3  Phase and Phase Velocity 18
2.4  The Superposition Principle 21
2.5  The Complex Representation 23
2.6  Phasors and the Addition of Waves 24
2.7  Plane Waves 26
2.8  The Three-dimensional differential wave equation 29
2.9  Spherical Waves 30
2.10  Cylindrical Waves 33

     Problems p. 34

3  Electromagnetic Theory, Photons, and Light 37

3.1  Basic Laws of Electromagnetic Theory 38
3.2  Electromagnetic Waves 43
3.3  Energy and Momentum 46
3.4  Radiation 57
3.5  Light in Matter 66
3.6  The Electromagnetic-Photon Spectrum 73
3.7  Quantum Field Theory 80

     Problems p. 81

4  The Propagation of Light  85

4.1  Introduction 85
4.2  Rayleigh Scattering 85
4.3  Reflection 95
4.4  Refraction 100
4.5  Fermat's Principle 105
4.6  The Electromagnetic Approach 109
4.7  Total Internal Reflection 121
4.8  Optical Properties of Metals 127
4.9  Familiar Aspects of the Interaction of Light and Matter 131
4.10 The Stokes Treatment of Reflection and Refraction 135
4.11 Photons, Waves, and Probability

      Problems 4.1, 4.37, 4.51, 4.53, 4.54, 4.58, 4.69

5  Geometrical Optics 148

5.1  Introductory Remarks 148
5.2  Lenses 149
5.3  Stops 173
5.4  Mirrors 177
5.5  Prisms 189
5.6  Fiber Optics 195
5.7  Optical Systems 203
5.8  Wavefront Shaping 231

     Problems p. 238

7  The Superposition of Waves 285

7.1  The Addition of Waves of the Same Frequency 286
7.2  The Addition of Waves of Different Frequency 295
7.3  Anaharmonic Periodic Waves 300
7.4  Nonperiodic Waves 305

      Problems 7.6, 7.35, 7.37, 7.39, 7.42

8  Polarization 319

8.1  The Nature of Polarized Light 319
8.2  Polarizers 326
8.3  Dichroism 327
8.4  Birefringence 330
8.5  Scattering and Polarization 340
8.6  Polarization by Reflection 342
8.7  Retarders 346
8.8  Circular Polarizers 352
8.9  Polarization of Polychromatic Light 353
8.10 Optical Activity 355
8.11 Induced Optical Effects - Optical Modulators 360
8.12 A Mathematical Description of Polarization 366

      Problems 8.1, 8.2, 8.3, 8.6, 8.7, 8.13, 8.15, 8.20, 8.25, 8.27, 8.35, 8.45, 8.48, 8.51, 8.52, 8.53, 8.57, 8.62

9  Interference 377

9.1  General Considerations 378
9.2  Conditions for Interference 381
9.3  Wavefront-Splitting Interferometers 384
9.4  Amplitude-Splitting Interferometers 392
9.5  Types and Localization of Interference Fringes 407
9.6  Multiple-beam Interference 409
9.7  Applications of Single and Multilayer Films 418
9.8  Applications of Interferometry 423

      Problems 9.1, 9.5, 9.10, 9.14, 9.19, 9.25, 9.34, 9.35, 9.40, 9.41, 9.45

10  Diffraction 433

10.1  Preliminary Considerations 433
10.2  Fraunhofer Diffraction 442
10.3  Fresnel Diffraction 476
10.4  Kirchhoff's Scalar Diffraction Theory 501
10.5  Boundary Diffraction Waves 505

      Problems 10.8, 10.11, 10.18, 10.23, 10.27, 10.34, 10.40, 10.55

11  Fourier Optics 512

11.1  Introduction 512
11.2  Fourier Transforms 512
11.3  Optical Applications 523

      Problems 11.2, 11.8, 11.11, 11.18, 11.24, 11.27

12  Basics of Coherence Theory 554

12.1  Introduction 554
12.2  Visibility 556
12.3  The Mutual Coherence Function and the Degree of Coherence 563
12.4  Coherence and Stellar Interferometry 567

     Problems p. 572

COMPUTER PROJECTS

1. Superposition of Two Waves
2. Energy Density in Electric Field
3. Refraction and Snell's Law
4. Spherical Mirrors
5. Interference of Two Point Sources
6. Single-slit Diffraction

Here is an example of the transforms described in Wilson's book. The MATLAB program computes the spatial frequency spectrum of a square aperature of side L.

The computer program, specam.m, which generated this plot is shown below.

% specam.m Compute the spatial frequency spectrum of a square
%           aperture of side L.
clear all; help specam.m;  % Clear memory; print header

%@ Initialize variables
%
NGrid = 100;            % Number of grid points for plots
xMax = 5;              % Values plotted from x= -xMax to x= xMax
yMax = xMax;           % Values plotted from y= -yMax to y= yMax
for i=1:NGrid
  xPlot(i) = -xMax + (i-1)/(NGrid-1)*(2*xMax); % x values to plot
  yPlot(i) = -yMax + (i-1)/(NGrid-1)*(2*yMax); % y values to plot
end

%@ Loop over all grid points and evaluate E(x,y) on grid
for i=1:NGrid
 y = yPlot(i);
 for j=1:NGrid
   x = xPlot(j);   
 
   %@ Compute amplitude of electric field at the grid point
   EPlot(i,j) = sin(pi*x)*sin(pi*y)/(pi*pi*x*y);
  
 end
end

%@ Plot contours of constant electric potential
clf;  figure(gcf);    % Clear figure; bring figure window forward
mesh(xPlot,yPlot,EPlot);  % Plot electric amplitude in contour/mesh plot
xlabel('x, Spatial frequency');  
ylabel('y, Spatial frequency'); 
zlabel('Spectral amplitude');
title('Fourier Transform of a Square Aperature');
hold off;

Students are encouraged to learn to write and use computer programs in MATLAB and/or Maple for problem solving.

If you have questions or comments about the course, please contact me at the e-mail address: dcwold@ualr.edu.

If you plan to take Physics 4380/5380, I'd like to know which mathematics courses you are taking this semester. Let me know what I can do to help you to learn more physics.

Course descriptions are available for all physics courses: Physics Course Descriptions.