Reflection-Induced Frequency Shift and Resonance in an Optical Resonator

This article investigates resonance in an optical cavity by tracking how the wavelength and frequency of light change at each reflection, through a chain of shifts that accumulate cycle by cycle -- as a follow-up to an earlier analysis of the Eisele et al. (2009) rotating optical resonator experiment (DOI: 10.5281/zenodo.21426850), which left an open question about how resonance is affected by a velocity component perpendicular to the cavity's axis. The round-trip time derived from this reflection-chain approach agrees exactly with the earlier, independent geometric analysis -- an important consistency check. However, applying the chain to a rotating two-arm apparatus predicts a frequency difference between the arms far exceeding the experimental null result of Eisele et al. (2009), sharpening rather than resolving the existing tension. The article also identifies a methodological point of general relevance: the relation f=1/t holds only for light traveling without reflection; as soon as a reflection is involved, transit time and the wave's own shifted frequency are not reciprocal quantities. A closer look at Eisele et al.'s PDH-locked apparatus shows that the quantity this article calculates has no direct counterpart in the actual, locked experiment, and that a meaningful comparison would require a full point-by-point analysis of the apparatus's three signal paths -- left to future work. Keywords: optical resonance, Doppler shift, Michelson--Morley experiment, Eisele et al. (2009), L-ARF, special relativity, absolute reference frame