Reconciliation of generalized refraction with diffraction theory
Open accessAbstract
When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position-dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell's law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.
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Transmission through a space-variant metalstripe metasurface results in part of the incident light being redirected (diffracted), similar to blazed gratings.
“Particularly, early work has considered transmission through a space-variant metalstripe metasurface[11, 12], which results in part of the incident light being redirected (i.e., diffracted), similar to the functionality of blazed gratings[13].”
From Plasmonic metagratings for simultaneous determination of Stokes parameters (2015) · cites this paper as [11]
By combining a metalstripe metasurface with a linear polarizer and performing two successive measurements, or by Fourier transforming the transmitted near-field when a quarter-wave plate is placed in front of the metasurface, it is possible to determine the Stokes parameters.
“For example, by combining the metasurface with a linear polarizer and performing two successive measurements[11, 14] or, alternatively, by Fourier transforming the transmitted near-field when a quater-wave plate is placed in front of the metasurface [12], it is possible to determine the Stokes parameters.”
From Plasmonic metagratings for simultaneous determination of Stokes parameters (2015) · cites this paper as [11]
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Negative Refraction Makes a Perfect Lens
Pendry, J. B. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.3966 · Cited by 12,159 · see citing works
Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction
Yu, N., Genevet, P., Kats, M. A., Aieta, F., Tetienne, J.-P., Capasso, F., & Gaburro, Z. (2011) · Science · doi:10.1126/science.1210713 · Cited by 10,361 · see citing works
Broadband Light Bending with Plasmonic Nanoantennas
Ni, X., Emani, N. K., Kildishev, A. V., Boltasseva, A. E., & Shalaev, V. M. (2011) · Science · doi:10.1126/science.1214686 · Cited by 1,503 · see citing works
Smith, D. R., Mock, J. J., Starr, A. F., et al. (2005) · Physical Review E · doi:10.1103/physreve.71.036609 · Cited by 385 · see citing works
Self-citationLalanne, P., Aştilean, S., Chavel, P. H., et al. (1998) · Optics Letters · doi:10.1364/ol.23.001081 · Cited by 329 · see citing works
Diffraction efficiencies of thin phase gratings with arbitrary grating shape
Magnusson, R., & Gaylord, T. K. (1978) · Journal of the Optical Society of America · doi:10.1364/josa.68.000806 · Cited by 155 · see citing works
Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths
Tsai, Y.-J., Larouche, S., Tyler, T., et al. (2011) · Optics Express · doi:10.1364/oe.19.024411 · Cited by 47 · see citing works
Self-citationAnalysis of a Gradient Index Metamaterial Blazed Diffraction Grating
Smith, D. R., Tsai, Y.-J., & Larouche, S. (2011) · IEEE Antennas and Wireless Propagation Letters · doi:10.1109/lawp.2011.2179632 · Cited by 12 · see citing works
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Flat optics with designer metasurfaces
Yu, N., & Capasso, F. (2014) · Nature Materials · doi:10.1038/nmat3839 · Cited by 5,984 · see citing works
Planar Photonics with Metasurfaces
Kildishev, A. V., Boltasseva, A., & Shalaev, V. M. (2013) · Science · doi:10.1126/science.1232009 · Cited by 3,110 · see citing works
Broadband High-Efficiency Half-Wave Plate: A Supercell-Based Plasmonic Metasurface Approach
Ding, F., Wang, Z., He, S., Shalaev, V. M., & Kildishev, A. V. (2015) · ACS Nano · doi:10.1021/acsnano.5b00218 · Cited by 474 · see citing works
Gap plasmon-based metasurfaces for total control of reflected light
Pors, A., Albrektsen, O., Radko, I. P., & Bozhevolnyi, S. I. (2013) · Scientific Reports · doi:10.1038/srep02155 · Cited by 368 · see citing works
Plasmonic metasurfaces for efficient phase control in reflection
Pors, A., & Bozhevolnyi, S. I. (2013) · Optics Express · doi:10.1364/oe.21.027438 · Cited by 334 · see citing works
Plasmonic metagratings for simultaneous determination of Stokes parameters
Pors, A., Nielsen, M. G., & Bozhevolnyi, S. I. (2015) · Optica · doi:10.1364/optica.2.000716 · Cited by 13 · see citing works
- Authors
- Larouche, S., & Smith, D. R.
- Affiliations
- Duke University (US)
- ORCID
- Larouche, Stéphane
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2012-06-12
- Volume
- 37
- Issue
- 12
- Pages
- 2391
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W2055887225
- Cited by
- 253
- References
- 8
- Citations by year
- 2026: 11 · 2025: 12 · 2024: 15 · 2023: 18 · 2022: 21 · 2021: 14 · 2020: 21 · 2019: 16 · 2018: 20 · 2017: 26 · 2016: 28 · 2015: 18 · 2014: 17 · 2013: 15 · 2012: 1
- FWCI
- 6.29
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Multidisciplinary University Research Initiative (W911NF-09-1-0539)
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Materials Science › Surfaces, Coatings and Films › Optical Coatings and Gratings
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
- Keywords
- diffraction gratings, blazed gratings, Snell's law, oblique incidence, phase continuity, refractive index discontinuity, electromagnetic wave propagation
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