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

Institutions

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Waveform Invariance and a Contrast Law for the Two-Copy Common-Relative-Phase Superposition of a Half-Wavelength Odd-Harmonic Isolated Peak Wave

Noriaki Kihara
Zenodo (CERN European Organization for Nuclear Research)
Photorefractive and Nonlinear Optics
preprint

Waveform Invariance and a Contrast Law for the Two-Copy Common-Relative-Phase Superposition of a Half-Wavelength Odd-Harmonic Isolated Peak Wave

Noriaki Kihara
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
System Equipment (China) (CN)
Peace, Justice and strong institutions
Photorefractive and Nonlinear Optics
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.