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enter image description here Hi. I have a question on reciprocity in optical reflection.

We have a refractive index profile (as a function of x) that continuously varies (Figure). At x=-inf and +inf, n = n1. Around x=0, the refractive index increases to n2 and then decreases again to n1. The refractive index profile, however, is asymmetric around x=0, meaning that n changes abruptly for n1 -> n2, while it changes slowly for n2 -> n1. By "abruptly" and "slowly", I meant based on the length over which the change occurs vs. the wavelength of light. In this case, which reflectivity is larger? R1 or R2? Or are they the same? Can anybody provide an intuitive explanation?

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Reciprocity applies to reflection if and only if there is no loss. (And provided there are no explicitly non-reciprocal elements/materials, like magnets.)

A simple example is a mirror with an absorber on the back. Because transmission is generally reciprocal, the transmission will be the same regardless of the surface of incidence. But the loss is not symmetric. Light incident on the absorber will be largely absorbed, while light incident on the mirror will be largely reflected. So reflection is clearly not reciprocal in this case.

If you can assume the system is lossless, since the transmission is reciprocal, then by conservation of energy, the reflection will be reciprocal as well. (Where else would the energy go?)

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  • $\begingroup$ Thanks for the clarification! $\endgroup$
    – lazybird
    Commented Feb 8, 2022 at 23:17
  • $\begingroup$ @lazybird my pleasure! Be sure to accept if you’re satisfied! $\endgroup$
    – Gilbert
    Commented Feb 9, 2022 at 3:53

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