Module Content
The "Wave phenomena" module contains a number of topics:
Semester 1
- 1. Introduction and wave equations taught by Dr. Anne Green
- 2. Geometric optics taught by Dr. Lucia Hackermuller
- 3. Physical optics taught by Dr. Lucia Hackermuller
Semester 2
- 4. Fourier methods taught by Dr. Anne Green
A detailed breakdown of the module contents is below.
Letters/numbers in brackets after content are references to textbooks (details listed at bottom of page) i.e. H2.1 means Hecht section 2.1. Full details of the textbooks are given at the bottom of the page.
1. Introduction and wave equations (3 lectures)
| Lecture | Content |
|---|---|
| Intro 1 | Introduction |
| overview of module | |
| review of 1st year material | |
| I2 | Waves in 1d |
| wave equation (H2.1 & 2.2) | |
| dispersion | |
| group and phase velocities (H2.3 & 7.2) | |
| I3 | Waves in 3d |
| complex representation (H2.5) | |
| plane waves (H2.7) | |
| wave equation (H2.8) | |
| spherically symmetric waves (H2.9) |
2. Geometric optics (7 lectures + workshop)
| Lecture | Content |
|---|---|
| GO1 | Light as electromagnetic waves |
| Equation for electromagnetic waves | |
| Maxwell equations | |
| Huygen`s principle | |
| Dispersion of light | |
| Prisms | |
| GO2 | Fermat's Principle. Introduction to Geometric Optics |
| Fermat's Principle | |
| Principle of reversibility | |
| total internal reflection | |
| GO3 | Lenses (Part 1) |
| refraction at spherical surface | |
| thin and thick lenses | |
| paraxial approximation | |
| sign convention | |
| GO4 | Lenses (Part 2) |
| ray tracing | |
| complex optical systems | |
| refractive power | |
| optical aberrations | |
| W1 | Workshop (Matlab) on waves |
| GO5 | Mirrors |
| sign convention | |
| reflection on a spherical mirror | |
| ray tracing | |
| mirrors versus lenses | |
| GO6 | Optical instruments |
| human eye and vision correction | |
| microscopes | |
| telescopes | |
| GO7 | Matrix Representation |
3. Physical optics (9 lectures + 2 workshops)
| Lecture | Content |
|---|---|
| PO1 | Optical interference |
| superposition of em waves | |
| random/coherent light sources | |
| temporal and spatial coherence | |
| two-beam interference | |
| PO2 | Interference by wavefront division |
| Young`s double slit | |
| interference in thin films | |
| Lloyd's Mirror | |
| PO3 | Interference by Amplitude Division (Part 1) |
| Michelson interferometer | |
| Thin Dielectric films | |
| W2 | Workshop (Matlab) on interference |
| PO4 | Interference by amplitude division (Part 2) |
| Interference by multiple beams | |
| Fabry-Perot Interferometer | |
| PO5 | Difraction of Light |
| Huygens-Fresnel principle | |
| Fraunhofer and Fresnel difraction | |
| difraction by single and double slit | |
| PO6 | Diffraction circular apertures |
| Airy disc and resolution | |
| Babinet's principle | |
| W3 | Workshop (written) on geometric and physical optics |
| PO7 | Diffraction grating |
| difraction and interference factors | |
| spectrometers | |
| spectral resolution | |
| PO8 | Fresnel Difraction |
| Fresnel-Kirchhoff integral | |
| difraction on circular apertures | |
| Fresnel zones | |
| Revision | Recap |
(Christmas break weeks 13-16)
Mid-year assessment
Weeks 17 and 18 (non-teaching weeks)
4. Fourier methods (13 lectures + 3 workshops)
| Lecture | Content |
|---|---|
| Fourier 1 | Intro to Fourier analysis |
| what is it? | |
| applications | |
| example: square wave | |
| periodicity and harmonics | |
| essential maths | |
| F2 | Trigonometric form of Fourier Series I |
| orthogonality of sine and cos (RHB 12.1) | |
| calculation of coefficients (RHB 12.2) | |
| F3 | Trigonometric form of Fourier Series II |
| calculation of coefficients for square wave | |
| Dirichlet conditions (RHB 12.1) | |
| discontinuities (RHB 12.4) | |
| even and odd functions (RHB 12.3) | |
| analytic continuation (RHB 12.5) | |
| graphical representation | |
| W4 | Workshop (Matlab): Fourier series |
| F4 | Complex form of Fourier Series |
| calculation of coefficients (RHB 12.7) | |
| applied to square wave | |
| Parseval`s theorem (RHB 12.8) | |
| F5 | Fourier transforms I (RHB 13.1) |
| top hat example | |
| definitions | |
| F6 | Fourier transforms II |
| Dirac delta-function (RHB 13.1.3) | |
| example: FT of an infinite mono-chromatic wave train | |
| properties of Fourier transforms (RHB 13.1.5) | |
| differentiation | |
| multiplication by an exponential | |
| example: FT of a finite wave train | |
| F7 | Fourier transforms III |
| translation | |
| Fourier transform of gaussian (RHB 13.1.1) | |
| Fourier transform of an exponential | |
| Fourier transform pairs | |
| Parseval`s theorem (RHB 13.1.9) | |
| W5 | Workshop (written) on Fourier transforms |
| F8 | Convolution (RHB 13.1.7) |
| convolution theorem (RHB 13.1.8) | |
| F9 | Discrete Fourier Transforms |
| intro to discrete FTs | |
| Nyquist frequency and aliasing | |
| discrete FT and IFT | |
| F10 | Optics applications I |
| recap of plane and spherical waves | |
| Fraunhofer diffraction in terms of aperture function (RHB 13.1.2) | |
| example: single slit | |
| example: double slit | |
| F11 | Optics (and other) applications II |
| example: multiple slits | |
| 3-d Fourier transform (RHB 13.1.10) | |
| example: rectangular (2-d) aperture | |
| example: FT of the hydrogen atom | |
| W6 | Workshop (Matlab) on Fourier transforms |
| F12 | Solving differential equations I |
| ordinary differential equations | |
| pdes: general solution (RHB 20.3.3) | |
| pdes: separation of variables (RHB 21.2 and 21.2) | |
| F13 | Solving differential equations II |
| partial differential equations (pdes): Fourier transforms (RHB 21.4) | |
| Fourier revision | Intro and Fourier methods revision |
Books
The main textbooks for this module are:
FL Pedrotti, LM Pedrotti and LS Pedrotti, Introduction to Optics, 3rd edition (Pearson Prentice Hall, 2007).
E Hecht, Optics, 3rd edition (Addison Wesley Longman, 1998).
KF Riley, MP Hobson and SJ Bence, Mathematical methods for Physics and Engineering, 3rd edition (Cambridge University Press, 2006). Very comprehensive 'maths' book. Chapter 12 and 13 cover Fourier series and Fourier transforms. Available as an e-book via the library website.
In each case earlier editions contain similar (or even identical) material, however the page/section numbers may be different.
Other useful books include:
AP French, Vibrations and waves, (Nelson, 1971). Chapters 7 and 8 cover waves (and some optics).
ML Boas, Mathematical methods in the physical sciences, (Wiley, 2006).