Inspired by my recent post on knotting of energy bands, I have been digging through my backup drive storing old files from my PhD and earlier postdocs. I was quite surprised to see how many unfinished projects I had with semi-polished write-ups. Some of the topics covered included vortex knots in modal superpositions, accelerating solutions of the Dirac equation, coupled mode theory for plasmonic optical fibres, peculiar (topological?) edge states in certain tight binding models, non-Hermitian degeneracies in photonic lattices, and more. In some cases similar ideas ended up being published later in high impact journals by others.
It would be nice to wrap up some of these unfinished projects when I
have the time. Especially, theoretical and experimental capabilities
have advanced considerably over the past several years, making some of
the research lines more feasible.
There are many reasons why projects which looked promising at first may end up being abandoned:
- Other commitments taking over, such as needing to write up the PhD thesis
- Preliminary work being trashed by reviewers, killing motivation to continue the line of research
- Neat theoretical ideas that unfortunately seem impractical to realize in any experiment
- Inability to come up with a more general theory to describe novel behaviour seen in specific examples
- Shifting research or funding agency interests
These are all temporary problems. Dead projects may be revived later. The bottom line (PhD students take note!): Keep good records. Ideally include readable figures and a discussion of your motivation. Be diligent with commenting your code in case future you needs to figure out how it works.
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