Problem assignment PHYS3035 (Electrodynamics & Optics) 2023
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 working on a physics problem that covers aspects of different modules within the unit and
connect it to a real-world application. We will ask you to enter a question into ChatGPT and then
to comment on or critique the reply. We have found that ChatGPT’s replies are fairly good, but
definitely not perfect, and sometimes misleading or confusing.
The Unit Problem should take approximately 16 hours, and we expect a report of 2 - 3 typewritten
pages in the format described below, including figures and references. 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. Hand-written
reports will not be accepted.
The Unit problem consists of a well-defined and compulsory Part A, and an open Part B, consisting
of your own investigation on the properties of the telecommunication fibre SMF-28. The report,
covering both parts, needs to have an introduction, a description of the problem you are addressing,
your approach, results, a discussion and conclusions.
PART A–GEOMETRY
In class we considered a planar waveguide in which the mirrors consist of ideal metal. Here
we consider the somewhat more complicated geometry in which the mechanism of one of the
mirrors is Total Internal Reflection, whereas the other mirror is an ideal metal, as before. To do
this, consider again a slab of thickness d, and extending from y = 0 to y = d, and with relative
permittivity εs. The slab is sandwiched between an ideal metal for y < 0, and a medium with
relative permittivity εc < εs for y> d. The waveguide is illustrated in Figure 1. To analyze this
waveguide we can again start from Eq. (82) from the Optics notes. As in class, we only consider
TE modes.
d
ideal metal
εsd
εc
Figure 1. Schematic of the planar waveguide we are considering.
Compulsory Questions
(a) We are after modes that propagate in the z-direction (propagation constant β ) and vanish as
y→ ∞, and so the field needs to be exponentially decaying in y. Starting from Eqs. (82),
write down the general expressions of the modes’ electric field in each of the dielectrics.
(b) The mode can be found by imposing continuity of the electric and magnetic field components
that are transverse to the interface. Find the relevant magnetic field component, and impose
continuity. You should find the transcendental equation
tanκd =−κ
γ
,
where κ is defined as in the lecture notes and γ =
√
β 2− εcω2/c2. The solution of
this transcendental equation gives you β for given refractive indices, frequency and slab
thickness.
(c) Find the cut-off of the fundamental mode. What are the cut-offs of the subsequent TE-
modes?
(d) Take ns = 1.5, nc = 1.0 and d = 2 µm, and plot the effective refractive index neff ≡
β/(2π/λ ) in the wavelength range 1.4 µm ≤ λ ≤ 1.6 µm by numerically solving the
transcendental equation given in (b).
Thus your challenge is to investigate the properties of this planar waveguide. As mentioned, Part
A, consisting of questions (a)-(d) are compulsory. Parts (a)-(c) are analytic work, whereas Part (d)
is numerical.
PART B: SMF-28 FIBRE
Corning SMF-28 fibre is standard telecommunication fibre that is used around the world. The
specifications of this fibre can be found in the “spec sheet” at https://www.corning.com/
content/dam/corning/media/worldwide/coc/documents/Fiber/product-information-sheets/
PI-1424-AEN.pdf. This two-page spec sheet gives the main characteristics of SMF-28 fibre
including, for example, attenuation, bend loss, dispersion, mode-field diameter, polarisation mode
dispersion, etc.
We would like you to take one or two of the entries in the spec sheet and construct a question
about these entries which you then enter into ChatGPT. To do this you first need to open an
account at https://chat.openai.com/, which is free. You typically get a numbered list
of well-written dot points. Take one or two of these dot points, copy them into your document
along with your question, and then comment intelligently on these dot points. As mentioned, we
have found that some responses are irrelevant, some are misleading and some are plainly wrong.
As these tools become more widely used, it will become increasingly important for people with
technical expertise to be able to judge the veracity of material produced by these tools. If you find
that the dot points are correct, then perhaps elaborate more on these responses, with further details
or calculations. The bottom line is that we want you to add value to the ChatGPT responses. You
are likely to have to do some research to add the value, but that is part of the assignment.
As an example, in a laser context, rather than that of optical fibres, when asking about “three-level
lasers” the reply included the passage
Stimulated Emission: When an atom or molecule in the higher energy state (E2 or
E3) transitions to the lower energy state (E1), it can emit a photon of light with a
specific energy (frequency). This process is called stimulated emission and is a key
step in laser operation.
What is totally missing in this reply is the distinction between stimulated emission and spontaneous
emission. In other words, the passage above could equally well apply to spontaneous emission. In
2/3
your commentary you could point this out and then proceed by explaining the difference between
spontaneous and stimulated emission. For this example you do not need to do research as it was
covered in class. However, for the actual assignment we expect evidence of independent research
(with proper citations) with information that was not discussed in class.
MARKING CRITERIA
The answers to Part A will make up 50% of your overall mark. The remaining 50% will be for
your overall report (which will include Part A) and for your response to Part B. The break down
of this 50% is provided in the marking scheme below.
1. Quality of questions : 10% Are the questions you ask relevant and interesting?
2. Quality of critique: 15%. Is the critique technically correct?
3. Added value: 15% have you added value to the response , either by linking to class material
or by doing independent research?
4. Structure and presentation of the report 10%. 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.
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.