# MMath&Phys Mathematics and Physics / Course details

Year of entry: 2023

## Course unit details:Wave Optics

Unit code PHYS20312 10 Level 2 Semester 2 No

Wave Optics

### Pre/co-requisites

Unit title Unit code Requirement type Description
Electromagnetism PHYS20141 Pre-Requisite Compulsory
Mathematics of Waves and Fields PHYS20171 Pre-Requisite Compulsory

### Aims

To develop the concepts of wave optics and establish a firm grounding in modern optics.

### Learning outcomes

On successful completion students will be able to:

1. Use complex notation competently for wave phenomena

2. Solve problems which require the use of wave representations of electric and magnetic fields in propagating electromagnetic waves

3. Analyse simple examples of interference and diffraction phenomena

4. Explain the principles of operation of, a range of equipment used in modern optics, notably the Michelson interferometer and Fabry-Perot etalon

5. Apply the physics processes involved in producing laser radiation to solve simple problems

### Syllabus

1.  Electomagnetism
• Recap of Maxwell’s equations and the wave equation in a dielectric
• General solutions to the wave equation
• Particular solutions to the wave equation: plane & spherical waves
• Wavefronts, rays, Poynting vector; the time-averaged optical field
• Optical spectra – temporal and spatial frequencies
• Huygens’ wavelets and Fermat’s principle. Example: gravitational lenses

(2 lectures)

2.  Polarization
• Recap of polarization states; unpolarized and partially polarized light
• Polarization by reflection and scattering; Brewster’s angle.
• Polaroid and Malus’ law
• Optical anisotropy; wave equation in anisotropic media; birefringence;  o- and e-rays; double refraction
• Polarizing beamsplitters and waveplates; Faraday rotators

(5 lectures)

3.  Interference
• Conditions for interference; temporal and spatial coherence
• Young’s slits; Lloyd’s mirror; multiple slits. Extended sources, outline of radio interferometry
• The Michelson interferometer; Fourier Transform spectroscopy
• Thin films; Fabry-Perot etalon: resolution, FSR and finesse.

(6 lectures)

4.  Diffraction
• Fraunhofer diffraction: single and double slit, rectangular and circular apertures, resolution of optical instruments
• Fraunhofer diffraction as a Fourier transform; convolution
• The diffraction grating and spectrometers
• Fresnel diffraction: circular obstacles and half-period zones; straight edges

(6 lectures)

5.  Lasers
• Spontaneous and stimulated emission; absorption; Einstein coefficients
• Rate equations; population inversion and optical gain
• Optical cavities
• Steady state operation; threshold and efficiency
• An example laser system: Nd:YAG

(4 lectures)

### Assessment methods

Method Weight
Other 10%
Written exam 90%

* Other 10% Tutorial Work/attendance

### Feedback methods

Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued.

Smith, F.G. & King, T.A. Optics and Photonics - An Introduction (Wiley)

Jenkins, F.A. & White, H.E., Fundamentals of Optics, (McGraw Hill)

Lipson, S.G., Lipson, H.S. & Tannhauser, D.S., Optical Physics, (Cambridge)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Tutorials 4
Independent study hours
Independent study 70.5

### Teaching staff

Staff member Role
Neal Jackson Unit coordinator