Problem assignment PHYS3035 (Electrodynamics & Optics) 2022
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Problem assignment PHYS3035 (Electrodynamics & Optics) 2022
The unit problem assignment is designed to be different from module-specific assignments. It is not designed to train you on methods specific to a given lecture module. Instead, you will be solving a physics problem that covers aspects of different modules within the unit and connect it to a real-world application. You may choose any method you like to answer questions – analytic, numerical, experimental, statistical, observational, literature review or any combination thereof - whatever you think is most appropriate, as long as it is sound science. These need not be methods you’ve seen explicitly in lectures or tutorials in this unit. When using numerical methods, feel free to use the programming language you are most comfortable with. Some questions are open ended – be curious, be creative, and see where your investigation can lead you!
The Unit Problem should take approximately 16 hours, and we expect a report of 2 typewritten pages in the format described below (3 pages if you must), including figures and references (but not including numerical code). We strongly encourage you to use the two-column format provided by the American Physical Society (APS), RevTeX 4.2 Template. To get access to this, please go to Overleaf (www.overleaf.com) and open an account. Then click New Project and select Academic Journal, under Templates. Alternatively, if you must, you can use Word. If you do so, then you need to format it such that it looks like a Physical Review article. Hand-written reports will not be accepted.
1. Technical content: 40%. The technical details must be presented in a notation consistent throughout the report.
2. Originality, curiosity and initiative: 20%. How far beyond the specified problem have you gone? For example, is there evidence of deeper connections to the relevant literature; have connections to other fields of physics been made; have applications of the research in the real world been discussed?
3. Well-structured report: 20%. All questions should be addressed in a single cohesive document, in-line with the format of scientific literature, rather than as a series of dot points each addressing a question.
4. Link with the material discussed in class: 20%. You need to make a connection between
properties of the waveguides in Table 1 of the url and the material discussed in class. You also need to add value beyond the discussion in class and the lecture notes.
As a guide, consider the following checklist for scientific formatting:
• Figures clearly showcase results and are labelled appropriately;
• Equations are appropriately included (not every single equation needs to be included);
• Figures and results are discussed in context;
• Typesetting, equations are neat and free of typographical errors;
• Appropriate referencing when needed;
Consider the problem of transmitting electromagnetic waves, in particular microwaves, through space in a hollow metal waveguide. A classic way of achieving this is to use a rectangular waveguide (think of a hollow metal pole, with a rectangular cross-section). How well do these metal pipes transmit electromagnetic energy? The advantage of these structures is that they don’t need to be filled with anything. In fact, to simplify our analysis, we can consider that they have vacuum (or air) inside. In this problem assignment we will explore the electromagnetic waves that can be transmitted by these structures.
To provide some additional material we will be making use of the specification details found at the link: https://www.rfcafe.com/references/electrical/ew-radar-handbook/ microwave-waveguide-coaxial-cable.htmfor common rectangular structures such as the WR284 design. Your class notes should help you with this assignment, however for further
relevant material please see Chapter 3.3 of David Pozar’s textbook ’Microwave Engineering’, available on Canvas.
QUESTIONS TO ANSWER
These questions should be answered in a single seamless document, without explicitly numbering answers. The questions therefore provide a framework for what to include in your text. The questions are ordered such that answering them in this order would be a natural way to progress through the problem, and so the order provides a guideline for the structure of your text. You are expected to answer the first six questions, and you are expected to answer Q10. For Q7 - Q9, you are expected to answer one out of these three questions. Question 10 is open, and you are encouraged to take your investigation in your own direction (this will particularly address the ’originality, curiosity, initiative’element of the marking scheme).
1. Provide the boundary conditions for electromagnetic waves at the interface between vacuum and the waveguide;
2. Outline how the mode cut-offs are calculated, and provide the general solution in terms of the side lengths of the waveguide;
3. Calculate the frequency cut-off for the WR284 geometry, does it agree with the result in Table 1?
4. What happens to the mode cut-offs as the geometry is changed? Plot this cut-off as a function of a changing side length. Is it possible to recover the results of a planar waveguide?
5. Plot a 2D representation of the fundamental mode. Do the results connect with a plane wave in vacuum in any way?
6. Comment on the origin of the frequency range shown in Table 1 (and displayed in Fig. 4). You are not expected to prove anything, some reasonable comment or discussion is fine.
7. Does the material the waveguides are made of have an effect?
8. Comment on the energy flow in the waveguide. Is there a maximum amount of energy that can be transmitted down the waveguide?
9. What effect will filling the waveguide with a dielectric material have?
10. Inspired by the website, the Pozar textbook, or something else, investigate further something relevant to this problem.
2022-10-08