Waveform Invariance and a Contrast Law for the Two-Copy Common-Relative-Phase Superposition of a Half-Wavelength Odd-Harmonic Isolated Peak Wave
Observational note. For the isolated peak wave formed by superposing constant-amplitude odd harmonics on the half-wavelength phase interval, giving two copies a common relative phase 2a applied identically to all harmonics yields, by the product-to-sum identity, psi = 2 cos(a) S_N, hence I = 4 cos^2(a) I_N. Two elementary consequences follow: (i) waveform invariance - the normalized waveform is independent of the relative phase and coincides with that of a single copy; (ii) a contrast law - the relative phase scales the squared amplitude by cos^2(a) without changing the waveform. No physical interpretation is given.
Authors
- Noriaki Kihara
Institutions
- System Equipment (China) (CN)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-26
- DOI
- https://doi.org/10.5281/zenodo.20923461
- Primary Topic
- Photorefractive and Nonlinear Optics
- Type
- preprint