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I included a derivation for the effective length of a ring resonator in my thesis. However, I'd like to cite the original reference I used when deriving this expression.

Screenshot of effective length result

However, I can't find the reference anymore. The above is a screenshot of the equation in the reference--I had it saved in my Notion document while writing my thesis, but I didn't write down where I'd screenshotted it from. Does anyone know where this screenshot might have come from? There are also these screenshots, which I believe came from the same source:

Transmission equations for ring resonator

It appears as though these come from lecture or course notes, or possibly a thesis, rather than a paper, but I'm not sure. References I've already ruled out: Saleh & Teich, Fundamentals of Photonics(2nd ed.), Little et al., JLT (1997), Heebner & Ibrahim, Optical Microresonators (2008), Bogaerts et al., Laser Photonics Rev. (2012), Rabus, Integrated Ring Resonators: A Compendium (2007), Yariv & Yeh, Photonics (2007). Can anyone help?

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