pith:5KPP72Q2
Scattering Symmetries in Diffraction Gratings
A global scattering matrix combined with symmetry representations yields an invariance condition that constrains the sub-scattering matrices between every pair of diffraction orders.
arxiv:2603.16555 v2 · 2026-03-17 · physics.optics
Add to your LaTeX paper
\usepackage{pith}
\pithnumber{5KPP72Q2FX62RQZB2GSA6XUYUZ}
Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge
Record completeness
Claims
We develop a formalism to determine the scattering symmetries of diffraction gratings supporting multiple diffraction orders. The approach is based on constructing a global scattering matrix that connects all incident and scattered diffraction channels and on introducing matrix representations of spatial symmetry operations acting on the field amplitudes. From these representations, we derive an invariance condition that directly constrains the sub-scattering matrices associated with each pair of diffraction orders.
That spatial symmetry operations can be faithfully represented as linear matrix transformations acting directly on the vector of all diffraction-channel amplitudes without additional constraints arising from the specific grating geometry, material dispersion, or evanescent-field coupling.
A new matrix-based formalism derives invariance conditions on sub-scattering matrices from spatial symmetries and reciprocity for diffraction gratings supporting multiple orders.
References
Formal links
Receipt and verification
| First computed | 2026-05-18T02:45:04.786639Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
ea9effea1a2dfda8c321d1a40f5e98a65895f723297d0d9111f4cfad9713aaec
Aliases
· · · · ·Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/5KPP72Q2FX62RQZB2GSA6XUYUZ \
| jq -c '.canonical_record' \
| python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ea9effea1a2dfda8c321d1a40f5e98a65895f723297d0d9111f4cfad9713aaec
Canonical record JSON
{
"metadata": {
"abstract_canon_sha256": "ee2489711140fff46b77a854fd1e81f8431f6ddcd63a579b65e9e87a5f30001d",
"cross_cats_sorted": [],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"primary_cat": "physics.optics",
"submitted_at": "2026-03-17T14:18:44Z",
"title_canon_sha256": "bf5363057510f709c43516b6ab56aa8cacbe59a8798fad146cbd772300e6a77f"
},
"schema_version": "1.0",
"source": {
"id": "2603.16555",
"kind": "arxiv",
"version": 2
}
}