Wave Propagation in Periodic Structures
E675973
"Wave Propagation in Periodic Structures" is a foundational scientific monograph by Léon Brillouin that systematically develops the theory of wave behavior in periodically structured media, underpinning modern solid-state physics and band theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Wave Propagation in Periodic Structures canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7603300 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wave Propagation in Periodic Structures Context triple: [Léon Brillouin, notableWork, Wave Propagation in Periodic Structures]
-
A.
Bloch waves
Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
C.
Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
-
D.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
-
E.
Rayleigh waves
Rayleigh waves are a type of surface seismic wave that travel along the ground with a rolling motion, causing both vertical and horizontal ground displacement.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wave Propagation in Periodic Structures Target entity description: "Wave Propagation in Periodic Structures" is a foundational scientific monograph by Léon Brillouin that systematically develops the theory of wave behavior in periodically structured media, underpinning modern solid-state physics and band theory.
-
A.
Bloch waves
Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
C.
Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
-
D.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
-
E.
Rayleigh waves
Rayleigh waves are a type of surface seismic wave that travel along the ground with a rolling motion, causing both vertical and horizontal ground displacement.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
nonfiction book
ⓘ
physics book ⓘ scientific monograph ⓘ |
| appliesTo |
crystalline solids
ⓘ
multi-dimensional periodic structures ⓘ one-dimensional periodic structures ⓘ |
| author | Léon Brillouin NERFINISHED ⓘ |
| contribution |
formalized treatment of waves in infinite periodic lattices
ⓘ
introduced rigorous analysis of allowed and forbidden frequency bands ⓘ laid foundations for modern band theory ⓘ provided a systematic theory of wave behavior in periodically structured media ⓘ underpinned theoretical framework of solid-state physics ⓘ |
| field |
mathematical physics
ⓘ
physics ⓘ solid-state physics ⓘ wave physics ⓘ |
| historicalSignificance |
classic reference in solid-state theory
ⓘ
early comprehensive treatment of waves in periodic media ⓘ |
| influenced |
crystal lattice dynamics
ⓘ
electronic band structure calculations ⓘ phononic crystals theory ⓘ photonic crystals theory ⓘ semiconductor physics ⓘ solid-state physics ⓘ |
| language | English ⓘ |
| mainSubject |
Bloch waves
ⓘ
Brillouin zones NERFINISHED ⓘ acoustic waves in periodic structures ⓘ band theory ⓘ dispersion relations ⓘ electromagnetic waves in periodic structures ⓘ electron waves in crystals ⓘ energy bands ⓘ forbidden bands ⓘ lattice periodicity ⓘ periodic media ⓘ wave propagation ⓘ wave scattering ⓘ |
| namedAfter | Léon Brillouin NERFINISHED ⓘ |
| relatedTo |
Brillouin scattering
NERFINISHED
ⓘ
Brillouin zone NERFINISHED ⓘ |
| usesConcept |
Bloch theorem
NERFINISHED
ⓘ
Fourier analysis ⓘ eigenvalue problems ⓘ periodic boundary conditions ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Wave Propagation in Periodic Structures Description of subject: "Wave Propagation in Periodic Structures" is a foundational scientific monograph by Léon Brillouin that systematically develops the theory of wave behavior in periodically structured media, underpinning modern solid-state physics and band theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.