The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
On the effective medium theory of subwavelength periodic structures
Abstract
The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelength ratios. It is shown that for large period-to-wavelength ratios near the cutoff value, no analogy between 2-D periodic structures and homogeneous media holds for highly modulated lamellar gratings.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Tables of Integrals, Series, and Products.
Bello, A. L., Gradshteyn, I. S., Ryzhik, I. M., & Jeffrey, A. (1995) · The Statistician · doi:10.2307/2348458 · Cited by 5,860
Antireflection structured surfaces for the infrared spectral region
Raguin, D. H., & Morris, G. M. (1993) · Applied Optics · doi:10.1364/ao.32.001154 · Cited by 433
Submicrometer periodicity gratings as artificial anisotropic dielectrics
Flanders, D. C. (1983) · Applied Physics Letters · doi:10.1063/1.93979 · Cited by 206
Optical elements with ultrahigh spatial-frequency surface corrugations
Enger, R. C., & Case, S. K. (1983) · Applied Optics · doi:10.1364/ao.22.003220 · Cited by 196
Convergence of the coupled-wave method for metallic lamellar diffraction gratings
Li, L., & Haggans, C. W. (1993) · Journal of the Optical Society of America A · doi:10.1364/josaa.10.001184 · Cited by 190
Artificial distributed-index media fabricated by zero-order gratings
Stork, W., Streibl, N., Haidner, H., & Kipfer, P. (1991) · Optics Letters · doi:10.1364/ol.16.001921 · Cited by 186
Antireflection effect in ultrahigh spatial-frequency holographic relief gratings
Ono, Y., Kimura, Y., Ohta, Y., & Nishida, N. (1987) · Applied Optics · doi:10.1364/ao.26.001142 · Cited by 185
Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings
Peng, S., & Morris, G. M. (1995) · Journal of the Optical Society of America A · doi:10.1364/josaa.12.001087 · Cited by 176
Antireflection surfaces in silicon using binary optics technology
Motamedi, M. E., Southwell, W. H., & Gunning, W. J. (1992) · Applied Optics · doi:10.1364/ao.31.004371 · Cited by 175
Grann, E. B., Moharam, M. G., & Pommet, D. A. (1994) · Journal of the Optical Society of America A · doi:10.1364/josaa.11.002695 · Cited by 171
Cited by
Highly improved convergence of the coupled-wave method for TM polarization
Lalanne, P., & Morris, G. M. (1996) · Journal of the Optical Society of America A · doi:10.1364/josaa.13.000779 · Cited by 958
Self-citationWaveguide sub‐wavelength structures: a review of principles and applications
Halir, R., Bock, P. J., Cheben, P., Ortega‐Moñux, A., Alonso‐Ramos, C., Schmid, J. H., Lapointe, J., Xu, D., Wangüemert‐Pérez, J. G., Molina‐Fernández, Í., et al. (2015) · Laser & Photonics Reviews · doi:10.1002/lpor.201400083 · Cited by 658
Optical properties of deep lamellar Gratings: A coupled Bloch-mode insight
Lalanne, P., Hugonin, J. P., & Chavel, P. (2006) · Journal of Lightwave Technology · doi:10.1109/jlt.2006.874555 · Cited by 198
Self-citationChen, J.-K., & Chang, C.-J. (2014) · Materials · doi:10.3390/ma7020805 · Cited by 193
Metadata
- Authors
- Lalanne, P., & Lemercier-lalanne, D.
- Venue
- Journal of Modern Optics
- Publisher
- Informa UK Limited
- Published
- 1996-10
- Volume
- 43
- Issue
- 10
- Pages
- 2063-2085
- ISSN
- 0950-0340 (ISSN-L)
- 1362-3044
- OpenAlex
- W2056893961
- Cited by
- 296
- References
- 16
- FWCI
- 4.93
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the effective medium theory of subwavelength periodic structures. https://app.cochat.ai/papers/10.1080/09500349608232871
- The paper
- Lalanne, P., & Lemercier-lalanne, D. (1996). On the effective medium theory of subwavelength periodic structures. Journal of Modern Optics. https://doi.org/10.1080/09500349608232871
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
