16 Projects, toolbox and connections

16.1 How Chapter 1 feeds the rest of the course

Table 16.1: Where Chapter 1 concepts reappear in the course.

Chapter 1 concept	Where it comes back
TIR, evanescent wave, Goos–Hänchen shift, Gaussian mode	Ch. 2: waveguide modes, $V$-number, directional couplers, mode-field diameter
Group index, material dispersion	Ch. 2: waveguide and chromatic dispersion, pulse spreading
Complex index, absorption coefficient	Ch. 3 and 5: band-to-band absorption, LEDs, photodiodes, image sensors
Fabry–Perot resonator, Bragg mirror, facet reflectance	Ch. 3–4: laser threshold, DFB/DBR lasers, VCSELs, SOAs with AR facets
Coherence	Ch. 3–4: LED versus laser linewidth; Ch. 5: coherent detection
Raman and Brillouin scattering	Ch. 4: Raman amplification; distributed sensing
Interference, MZI, anisotropy	Ch. 6: polarisation, electro-optic and MZI modulators
Diffraction, gratings	Ch. 2 and 6: grating couplers, AWGs, acousto-optic modulators

16.2 Mini-projects

For students who want to go further. Each reuses optolib.py and can be done in one to three weeks.

#	project	skills	difficulty
1	Thin-film design tool: extend `ol.tmm` with a merit function and optimise a broadband AR coating or a band-pass filter for 1550 nm	optimisation, TMM	★★
2	Measure $M^2$ of a lab laser with a webcam and `laserbeamsize`; compare with the datasheet	experiment, fitting	★
3	Grating coupler: find the phase-matching condition with the grating equation, then check it with `grcwa` or Meep	diffraction, RCWA	★★★
4	Fabry–Perot laser-diode spectrum: combine facet reflectance (Fresnel), cavity modes and a Gaussian gain curve	resonators	★★
5	OTDR event detection on the toy trace of Chapter 14, then on a real trace from the lab	signal processing	★★
6	Swanepoel’s method: recover $n(\lambda)$ and the thickness of a film from its transmission fringes	thin films, inverse problems	★★
7	Kramers–Kronig from measured data: compute $n(\lambda)$ of a semiconductor from its absorption spectrum and compare with the database	causality, numerics	★★★
8	Talbot and Arago in the lab: photograph the Arago spot or Talbot self-images and compare with `ol.asm_propagate`	diffraction, experiment	★★

16.3 Python toolbox

All worked examples run with the scientific core only. The packages below extend them; the “Sections” column points to where each one is most useful.

Table 16.2: Optional Python packages for Chapter 1.

Package	Install	What it is good for	Sections
`numpy`, `scipy`, `matplotlib`, `pandas`	`pip install ...`	core numerics, FFTs, special functions (Bessel $J_1$), optimisation, tables	all
`sympy`	`pip install sympy`	symbolic derivations: Fresnel coefficients, Brewster angle, Stokes relations, Lorentz model	7, 4
`pint`	`pip install pint`	unit-aware calculations (avoids nm/µm/m mistakes in exercises)	all
`refractiveindex`	`pip install refractiveindex`	refractiveindex.info database ($n$, $K$ of Si, Ge, GaN, InP, SiO₂, …)	4, 8
`tmm`	`pip install tmm`	validated transfer-matrix code: oblique incidence, coherent + incoherent layers, absorption profiles	7, 8, 11
`laserbeamsize`	`pip install laserbeamsize`	ISO 11146 beam diameters from camera images, $M^2$ fitting	2
`miepython`	`pip install miepython`	Mie scattering of spheres; Rayleigh limit	14
`LightPipes`	`pip install LightPipes`	scalar Fourier-optics propagation: apertures, lenses, Fresnel/Fraunhofer, Gaussian and higher-order beams	2, 13
`diffractsim`	`pip install diffractsim`	visual diffraction simulator (angular spectrum), polychromatic sources and colour rendering	13, 9
`poppy`, `prysm`	`pip install poppy prysm`	physical-optics propagation through imaging systems, PSFs, aberrations	13
`finesse`	`pip install finesse`	interferometers and optical cavities with Hermite–Gauss beams	2, 10, 12
`rayoptics`, `optiland`	`pip install rayoptics optiland`	sequential ray tracing, lens design, paraxial (ABCD) analysis	6, 2
`grcwa`	`pip install grcwa`	rigorous coupled-wave analysis of gratings and metasurfaces	13, 11
Meep / MPB	`conda install -c conda-forge pymeep`	FDTD (Meep) and photonic band structures (MPB)	7, 11, 12
`legume-gme`	`pip install legume-gme`	guided-mode expansion for photonic-crystal slabs	11
`colour-science`	`pip install colour-science`	spectrum → CIE colour; colours of thin films	1, 8
`gdsfactory`, `femwell`, `sax`	`pip install gdsfactory femwell sax`	photonic-IC layout, FEM mode solving, circuit simulation of MZIs, rings, gratings	10, 12

16.4 Improvements to the course

Live figures instead of screenshots. Many slides show plots from the textbook (Fresnel coefficients, Bragg-mirror spectra, Airy functions, diffraction patterns). Every one is regenerated here by a few lines of code that students can change.
“Predict, then compute.” Before moving a slider, ask the class to predict the outcome (“What happens to the Brewster angle for internal reflection?”, “Does a thicker slit give a wider or narrower pattern?”). It is quick, engaging and suited to peer instruction.
One running example through the chapter. For instance, a silicon photonics chip: phase shifter (Chapter 1), fiber coupling (Chapter 2), Si/Ge absorption (Chapter 4), MZI (Chapter 10), grating coupler (Chapter 13).
Lab connection. The three mandatory labs can reuse these notebooks to analyse their data: $M^2$ fitting, Fabry–Perot spectra, grating dispersion.

16.5 Notes for the instructor: checks on the slides

While recomputing the examples, everything matched the slides except these points:

Slide 161 (CdTe): with $n=4$, $K=6$ the reflectance formula gives $45/61=73.8\,\%$, not 72 %.
Slides 185–187 (Bragg mirror): the Ta₂O₅/SiO₂ values for $N=4$ and 12 are not printed; the formula gives 40.0 % and 90.6 %. The TiO₂ values (94.0 % and ≈ 100 %), the interchanged stack (80.8 %) and the bandwidth (74.8 nm) match.
Slides 168–169: the sodium lamp appears with two different widths (5×10¹¹ Hz and 1 GHz). Both are legitimate, but students may find the difference confusing; see Chapter 9.
Slide numbering: this companion uses the slide numbers of Chapter1_2026.pptx. Some numbers in the first draft (ch1_companion.qmd) were off by one, probably from an older version of the deck.

# Projects, toolbox and connections {#sec-ideas} ## How Chapter 1 feeds the rest of the course | Chapter 1 concept | Where it comes back | |---|---| | TIR, evanescent wave, Goos–Hänchen shift, Gaussian mode | Ch. 2: waveguide modes, $V$-number, directional couplers, mode-field diameter | | Group index, material dispersion | Ch. 2: waveguide and chromatic dispersion, pulse spreading | | Complex index, absorption coefficient | Ch. 3 and 5: band-to-band absorption, LEDs, photodiodes, image sensors | | Fabry–Perot resonator, Bragg mirror, facet reflectance | Ch. 3–4: laser threshold, DFB/DBR lasers, VCSELs, SOAs with AR facets | | Coherence | Ch. 3–4: LED versus laser linewidth; Ch. 5: coherent detection | | Raman and Brillouin scattering | Ch. 4: Raman amplification; distributed sensing | | Interference, MZI, anisotropy | Ch. 6: polarisation, electro-optic and MZI modulators | | Diffraction, gratings | Ch. 2 and 6: grating couplers, AWGs, acousto-optic modulators | : Where Chapter 1 concepts reappear in the course. {#tbl-links tbl-colwidths="[45,55]"} ## Mini-projects For students who want to go further. Each reuses `optolib.py` and can be done in one to three weeks. | # | project | skills | difficulty | |---|---|---|---| | 1 | **Thin-film design tool**: extend `ol.tmm` with a merit function and optimise a broadband AR coating or a band-pass filter for 1550 nm | optimisation, TMM | ★★ | | 2 | **Measure $M^2$** of a lab laser with a webcam and `laserbeamsize`; compare with the datasheet | experiment, fitting | ★ | | 3 | **Grating coupler**: find the phase-matching condition with the grating equation, then check it with `grcwa` or Meep | diffraction, RCWA | ★★★ | | 4 | **Fabry–Perot laser-diode spectrum**: combine facet reflectance (Fresnel), cavity modes and a Gaussian gain curve | resonators | ★★ | | 5 | **OTDR event detection** on the toy trace of @sec-scattering, then on a real trace from the lab | signal processing | ★★ | | 6 | **Swanepoel's method**: recover $n(\lambda)$ and the thickness of a film from its transmission fringes | thin films, inverse problems | ★★ | | 7 | **Kramers–Kronig from measured data**: compute $n(\lambda)$ of a semiconductor from its absorption spectrum and compare with the database | causality, numerics | ★★★ | | 8 | **Talbot and Arago in the lab**: photograph the Arago spot or Talbot self-images and compare with `ol.asm_propagate` | diffraction, experiment | ★★ | ## Python toolbox All worked examples run with the scientific core only. The packages below extend them; the "Sections" column points to where each one is most useful. | Package | Install | What it is good for | Sections | |---|---|---|---| | `numpy`, `scipy`, `matplotlib`, `pandas` | `pip install ...` | core numerics, FFTs, special functions (Bessel $J_1$), optimisation, tables | all | | `sympy` | `pip install sympy` | symbolic derivations: Fresnel coefficients, Brewster angle, Stokes relations, Lorentz model | [-@sec-fresnel], [-@sec-index] | | `pint` | `pip install pint` | unit-aware calculations (avoids nm/µm/m mistakes in exercises) | all | | `refractiveindex` | `pip install refractiveindex` | refractiveindex.info database ($n$, $K$ of Si, Ge, GaN, InP, SiO₂, …) | [-@sec-index], [-@sec-thinfilm] | | `tmm` | `pip install tmm` | validated transfer-matrix code: oblique incidence, coherent + incoherent layers, absorption profiles | [-@sec-fresnel], [-@sec-thinfilm], [-@sec-bragg] | | `laserbeamsize` | `pip install laserbeamsize` | ISO 11146 beam diameters from camera images, $M^2$ fitting | [-@sec-gauss] | | `miepython` | `pip install miepython` | Mie scattering of spheres; Rayleigh limit | [-@sec-scattering] | | `LightPipes` | `pip install LightPipes` | scalar Fourier-optics propagation: apertures, lenses, Fresnel/Fraunhofer, Gaussian and higher-order beams | [-@sec-gauss], [-@sec-diffraction] | | `diffractsim` | `pip install diffractsim` | visual diffraction simulator (angular spectrum), polychromatic sources and colour rendering | [-@sec-diffraction], [-@sec-coherence] | | `poppy`, `prysm` | `pip install poppy prysm` | physical-optics propagation through imaging systems, PSFs, aberrations | [-@sec-diffraction] | | `finesse` | `pip install finesse` | interferometers and optical cavities with Hermite–Gauss beams | [-@sec-gauss], [-@sec-interference], [-@sec-fp] | | `rayoptics`, `optiland` | `pip install rayoptics optiland` | sequential ray tracing, lens design, paraxial (ABCD) analysis | [-@sec-snell], [-@sec-gauss] | | `grcwa` | `pip install grcwa` | rigorous coupled-wave analysis of gratings and metasurfaces | [-@sec-diffraction], [-@sec-bragg] | | Meep / MPB | `conda install -c conda-forge pymeep` | FDTD (Meep) and photonic band structures (MPB) | [-@sec-fresnel], [-@sec-bragg], [-@sec-fp] | | `legume-gme` | `pip install legume-gme` | guided-mode expansion for photonic-crystal slabs | [-@sec-bragg] | | `colour-science` | `pip install colour-science` | spectrum → CIE colour; colours of thin films | [-@sec-em], [-@sec-thinfilm] | | `gdsfactory`, `femwell`, `sax` | `pip install gdsfactory femwell sax` | photonic-IC layout, FEM mode solving, circuit simulation of MZIs, rings, gratings | [-@sec-interference], [-@sec-fp] | : Optional Python packages for Chapter 1. {#tbl-toolbox tbl-colwidths="[18,24,44,14]"} ## Improvements to the course 1. **Live figures instead of screenshots.** Many slides show plots from the textbook (Fresnel coefficients, Bragg-mirror spectra, Airy functions, diffraction patterns). Every one is regenerated here by a few lines of code that students can change. 2. **"Predict, then compute."** Before moving a slider, ask the class to predict the outcome (*"What happens to the Brewster angle for internal reflection?"*, *"Does a thicker slit give a wider or narrower pattern?"*). It is quick, engaging and suited to peer instruction. 3. **One running example through the chapter.** For instance, a silicon photonics chip: phase shifter (@sec-em), fiber coupling (@sec-gauss), Si/Ge absorption (@sec-index), MZI (@sec-interference), grating coupler (@sec-diffraction). 4. **Lab connection.** The three mandatory labs can reuse these notebooks to analyse their data: $M^2$ fitting, Fabry–Perot spectra, grating dispersion. ## Notes for the instructor: checks on the slides While recomputing the examples, everything matched the slides except these points: - **Slide 161 (CdTe):** with $n=4$, $K=6$ the reflectance formula gives $45/61=73.8\,\%$, not 72 %. - **Slides 185–187 (Bragg mirror):** the Ta₂O₅/SiO₂ values for $N=4$ and 12 are not printed; the formula gives 40.0 % and 90.6 %. The TiO₂ values (94.0 % and ≈ 100 %), the interchanged stack (80.8 %) and the bandwidth (74.8 nm) match. - **Slides 168–169:** the sodium lamp appears with two different widths (5×10¹¹ Hz and 1 GHz). Both are legitimate, but students may find the difference confusing; see @sec-coherence. - **Slide numbering:** this companion uses the slide numbers of `Chapter1_2026.pptx`. Some numbers in the first draft (`ch1_companion.qmd`) were off by one, probably from an older version of the deck.