Extraordinary optical transmission

Interference pattern of double slits, where the slit width is one third the wavelength.

In optics, extraordinary optical transmission (EOT) is the phenomenon of greatly enhanced transmission of light through a subwavelength aperture in an otherwise opaque metallic film which has been patterned with a regularly repeating periodic structure. Generally when light of a certain wavelength falls on a subwavelength aperture, it is diffracted isotropically in all directions evenly, with minimal far-field transmission. This is the understanding from classical aperture theory as described by Hans Bethe.[1] In EOT however, the regularly repeating structure enables much higher transmission efficiency to occur, up to several orders of magnitude greater than that predicted by classical aperture theory. It was first described in 1998.[2][3]

## Contents

* 1 History
* 2 Applications
* 3 References

## History

This phenomenon that was fully analyzed with a microscopic scattering model is partly attributed to the presence of surface plasmon resonances[4] and constructive interference. A surface plasmon (SP) is a collective excitation of the electrons at the junction between a conductor and an insulator and is one of a series of interactions between light and a metal surface called plasmonics.[citation needed]

Currently, there is experimental evidence of EOT out of the optical range.[5] Analytical approaches also predict EOT on perforated plates with a perfect conductor model.[6][7][8] Holes can somewhat emulate plasmons at other regions of the electromagnetic spectrum where they do not exist.[9][10][11] Then, the plasmonic contribution is a very particular peculiarity of the EOT resonance and should not be taken as the main contribution to the phenomenon. More recent work has shown a strong contribution from overlapping evanescent wave coupling,[12] which explains why surface plasmon resonance enhances the EOT effect on both sides of a metallic film at optical frequencies, but accounts for the terahertz-range transmission.

Simple analytical explanations of this phenomenon have been elaborated, emphasizing the similarity between arrays of particles and arrays of holes, and establishing that the phenomenon is dominated by diffraction.[13][14][15]

## Applications

EOT is expected to play an important role in the creation of components of efficient photonic integrated circuits (PICs). Photonic integrated circuits are analogous to electronic circuits but based upon photons instead of electrons.[citation needed]

One of the most ground-breaking results linked to EOT is the possibility to implement a Left-Handed Metamaterial (LHM) by simply stacking hole arrays.[16]

EOT-based chemical and biological sensing (for example, improving ELISA based antibody detection) is another major area of research.[17][18][19][20][21][22][23][24] Much like in a traditional surface plasmon resonance sensor, the EOT efficiency varies with the wavelength of the incident light, and the value of the in-plane wavevector component. This can be exploited as a means of transducing chemical binding events by measuring a change in the local dielectric constant (due to binding of the target species) as a shift in the spectral location and/or intensity of the EOT peak. Variation of the hole geometry alters the spectral location of the EOT peak such that the chemical binding events can be optically detected at a desired wavelength.[25] EOT-based sensing offers one key advantage over a Kretschmann-style SPR chemical sensor, that of being an inherently nanometer-micrometer scale device; it is therefore particularly amenable to miniaturization.[26]

## References

1. ↑ Bethe, H. (1944). "Theory of Diffraction by Small Holes". Physical Review 66 (7–8): 163–182. doi:10.1103/PhysRev.66.163. Bibcode: 1944PhRv...66..163B.
2. ↑ T. W. Ebbesen; H. J. Lezec; H. F. Ghaemi; T. Thio; P. A. Wolff (1998). "Extraordinary optical transmission through sub-wavelength hole arrays". Nature 391 (6668): 667–669. doi:10.1038/35570. Bibcode: 1998Natur.391..667E. http://arep.med.harvard.edu/pdf/Ebbsen98.pdf.
3. ↑ Ebbesen, T. W.; Ghaemi, H. F.; Thio, Tineke; Grupp, D. E.; Lezec, H. J (March 1998). "Extraordinary Optical Transmission through Sub-wavelength Hole Arrays". Abstract from a Talk at the 1998 American Physical Society's Annual March Meeting: S15.11. Bibcode: 1998APS..MAR.S1511E.
4. ↑ H. Liu; P. Lalanne (2008). "Microscopic theory of the extraordinary optical transmission". Nature 452 (7188): 728–731. doi:10.1038/nature06762. PMID 18401405. Bibcode: 2008Natur.452..728L.
5. ↑ M. Beruete; M. Sorolla; I. Campillo; J.S. Dolado; L. Martín-Moreno; J. Bravo-Abad; F. J. García-Vidal (2005). "Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates". IEEE Transactions on Antennas and Propagation 53 (6): 1897–1903. doi:10.1109/TAP.2005.848689. Bibcode: 2005ITAP...53.1897B.
6. ↑ C.C. Chen (1970). "Transmission through a Conducting Screen Perforated Periodically with Apertures". IEEE Trans. Microw. Theory Tech. 18 (9): 627–632. doi:10.1109/TMTT.1970.1127298. Bibcode: 1970ITMTT..18..627C.
7. ↑ L. Martín-Moreno; F. J. García-Vidal; H. J. Lezec; K. M. Pellerin; T. Thio; J. B. Pendry; T.W. Ebbesen (2001). "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays". Phys. Rev. Lett. 86 (6): 1114–1117. doi:10.1103/PhysRevLett.86.1114. PMID 11178023. Bibcode: 2001PhRvL..86.1114M.
8. ↑ F. J. Garcia de Abajo, R. Gomez-Medina, and J. J. Saenz (2005). "Full transmission through perfect-conductor subwavelength hole arrays". Phys. Rev. E 72 (1 Pt 2). doi:10.1103/PhysRevE.72.016608. PMID 16090108. Bibcode: 2005PhRvE..72a6608G.
9. ↑ R. Ulrich; M. Tacke (1972). "Submillimeter waveguiding on periodic metal structure". Appl. Phys. Lett. 22 (5): 251–253. doi:10.1063/1.1654628. Bibcode: 1973ApPhL..22..251U.
10. ↑ J. B. Pendry; L. Martín-Moreno; F. J. García-Vidal (2004). "Mimicking surface plasmons with structured surfaces". Science 305 (5685): 847–848. doi:10.1126/science.1098999. PMID 15247438. Bibcode: 2004Sci...305..847P.
11. ↑ F. J. Garcia de Abajo and J. J. Saenz (2005). "Electromagnetic surface modes in structured perfect-conductor surfaces". Phys. Rev. Lett. 95 (23). doi:10.1103/PhysRevLett.95.233901. PMID 16384307. Bibcode: 2005PhRvL..95w3901G.
12. ↑ Z. Y. Fan; L. Zhan; X. Hu; Y. X. Xia (2008). "Critical process of extraordinary optical transmission through periodic subwavelength hole array: Hole-assisted evanescent-field coupling". Optics Communications 281 (21): 5467–5471. doi:10.1016/j.optcom.2008.07.077. Bibcode: 2008OptCo.281.5467F.
13. ↑ F. J. García de Abajo (2007). "Light scattering by particle and hole arrays". Reviews of Modern Physics 79 (4): 1267–1290. doi:10.1103/RevModPhys.79.1267. Bibcode: 2007RvMP...79.1267G.
14. ↑ B. Ung; Y. Sheng (2008). "Optical surface waves over metallo-dielectric nanostructures: Sommerfeld integrals revisited". Optics Express 16 (12): 9073–9086. doi:10.1364/OE.16.009073. PMID 18545619. Bibcode: 2008OExpr..16.9073U.
15. ↑ M. W. Maqsood; R. Mehfuz; K. J. Chau (2010). "High-throughput diffraction-assisted surface-plasmon-polariton coupling by a super-wavelength slit". Optics Express 18 (21): 21669–21677. doi:10.1364/OE.19.010429. PMID 21643298. Bibcode: 2011OExpr..1910429C.
16. ↑ M. Beruete; M. Sorolla; I. Campillo (2006). "Left-Handed Extraordinary Optical Transmission through a Photonic Crystal of Subwavelength Hole Arrays". Optics Express 14 (12): 5445–5455. doi:10.1364/OE.14.005445. PMID 19516710. Bibcode: 2006OExpr..14.5445B.
17. ↑ A. De Leebeeck; L. K. S. Kumar; V. de Lange; D. Sinton; R. Gordon; A. G. Brolo (2007). "On-chip surface-based detection with nanohole arrays". Anal Chem 79 (11): 4094–4100. doi:10.1021/ac070001a. PMID 17447728.
18. ↑ A. G. Brolo; R. Gordon; K. L. Kavanagh (2008). "A new generation of sensors based on extraordinary light transmission". Acc. Chem. Res. 41 (8): 1049–1057. doi:10.1021/ar800074d. PMID 18605739.
19. ↑ N. H. Mack; J. W. Wackerly; V. Malyarchuk; J. A. Rogers; J. S. Moore; R. G. Nuzzo (2007). "Optical transduction of chemical forces". Nano Lett 7 (3): 733–737. doi:10.1021/nl0629759. PMID 17309317. Bibcode: 2007NanoL...7..733M.
20. ↑ J. M. Yao; M. E. Stewart; J. Maria; T. W. Lee; S. K. Gray; J. A. Rogers; R. G. Nuzzo (2008). "Seeing molecules by eye: Surface plasmon resonance imaging at visible wavelengths with high spatial resolution and submonolayer sensitivity". Angewandte Chemie International Edition 47 (27): 5013–5017. doi:10.1002/anie.200800501. PMID 18512212.
21. ↑ P. R. H. Stark; A. E. Halleck; D. N. Larson (2005). "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology". Methods 37 (1): 37–47. doi:10.1016/j.ymeth.2005.05.006. PMID 16199175.
22. ↑ J. C. Yang; J. Ji; J. M. Hogle; D. N. Larson (2009). "Multiplexed plasmonic sensing based on small-dimension nanohole arrays and intensity interrogation". Biosens Bioelectron 24 (8): 2334–8. doi:10.1016/j.bios.2008.12.011. PMID 19157848.
23. ↑ J. Ji; J. G. O'Connell; D. J. D. Carter; D. N. Larson (2008). "High-throughput nanohole array based system to monitor multiple binding events in real time". Anal Chem 80 (7): 2491–2498. doi:10.1021/ac7023206. PMID 18307360.
24. ↑ J. C. Yang; J. Ji; J. M. Hogle; D. N. Larson (2008). "Metallic nanohole arrays on fluoropolymer substrates as small label-free real-time bioorobes". Nano Lett 8 (9): 2718–2724. doi:10.1021/nl801043t. PMID 18710296. Bibcode: 2008NanoL...8.2718Y.
25. ↑ Mehdi Tavakoli; Yousef Seyed Jalili; Seyed Mohammad Elahi (2019). "Rayleigh-Wood anomaly approximation with FDTD simulation of plasmonic gold nanohole array for determination of optimum extraordinary optical transmission characteristics". Superlattices and Microstructures 130: 454–471. doi:10.1016/j.spmi.2019.04.035. Bibcode: 2019SuMi..130..454T.
26. ↑ Lameirinhas, Ricardo A. Marques; N. Torres, Joao Paulo; Baptista, António; M. Martins, Maria Joao (2022). "A Novel Analysis for Light Patterns in Nano Structures". IEEE Photonics Journal 14 (6): 1–6. doi:10.1109/JPHOT.2022.3227429. Bibcode: 2022IPhoJ..1427429L.

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