Goos–Hänchen effect

Short description: Optical phenomenon

Ray diagram illustrating the physics of the Goos–Hänchen effect

The Goos–Hänchen effect, named after Hermann Fritz Gustav Goos (1883 - 1968) and Hilda Hänchen (1919 - 2013), was first theorized by Isaac Newton (1643 - 1727),[1][2][3][4] and is an optical phenomenon in which a finite-width beam of light undergoes a small lateral shift when totally internally reflected. The shift arises because a bounded beam comprises a continuous distribution of plane wave components with differing wave vectors. The Fresnel reflection coefficients are both polarization and angle dependent, so each plane wave component acquires a different phase shift upon reflection. The superposition of these phase-shifted components displaces the reflected beam's centroid along the interface. The magnitude of the shift is small, and it depends on the beam's polarization state, the wavelength, and the angle of incidence[5]. It is among the most studied non-specular reflection phenomena in optics.[6]

Acoustic analog of the Goos–Hänchen effect is known as Schoch displacement.[7]

## Contents

* 1 Description
* 2 Research
* 3 Generation of giant Goos–Hänchen shift
* 4 References

## Description

This effect occurs because the reflections of plane wave components of a finite-sized beam undergo different phase shifts. A finite-width beam can be expressed as a superposition of plane waves via a Fourier decomposition.

ψ(x,z)=12π∫−∞∞Φ(kx)e−i[kxx+z(k12−kx2)]dkx

where Φ(kx) is the angular spectrum of the beam. Each value of kx represents a plane wave in the direction of kx. Without loss of generality k1 lies in the x-z plane.

Under total internal reflection, each plane-wave component reflects according to the Fresnel equations where |r(kx)|=1 but acquires a phase shift χ(kx) where

χ(kx)=−2tan−1[m(k12−kx2)1/2(kx2−k22)1/2]

with m=n22/n12 for the polarization parallel to the plane of incidence and m=1 for polarization perpendicular to the plane of incidence. Taylor expanding χ(kx) to first order about kx=k1sin⁡(θi) it can be shown that the reflected beam is laterally displaced along the interface by

Δ=−dχdkx|kx=k1=sin⁡(θi)

Which is the standard Artmann result.[8]

## Research

This effect continues to be a topic of scientific research, for example, in the context of nanophotonics applications. A negative Goos–Hänchen shift was shown by Walter J. Wild and Lee Giles.[9] Sensitive detection of biological molecules is achieved based on measuring the Goos–Hänchen shift, where the signal of lateral change is in a linear relation with the concentration of target molecules.[10] The work by M. Merano et al.[11] studied the Goos–Hänchen effect experimentally for the case of an optical beam reflecting from a metal surface (gold) at 826 nm. They report a substantial negative lateral shift of the reflected beam in the plane of incidence for a p polarization and a smaller positive shift for the s polarization case.

## Generation of giant Goos–Hänchen shift

It is known that the value of lateral position Goos–Hänchen shift is only 5–10 μm at a total internal reflection interface of water and air, which is very difficult to be experimentally measured.[12][13] In order to generate a giant Goos–Hänchen shift up to 100 μm, surface plasmon resonance techniques were applied based on an interface between metal and dielectric.[14][15][16] The electrons on the metallic surface are strongly resonant with the optical waves under specific excitation condition. The light has been fully absorbed by the metallic nanostructures, creating an extreme dark point the resonance angle. Thus, a giant Goos–Hänchen position shift is generated by this singular dark point at the totally internally reflected interface.[17] This giant Goos–Hänchen shift has been applied not only for highly sensitive detection of biological molecules, but also for the observation of photonic spin Hall effect, which is important in quantum information processing and communications.[18][19]

## References

1. ↑ Caloz, Christophe, ed (2006). Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. Hoboken, N.J: John Wiley & Sons. pp. 50. ISBN 978-0-471-66985-2. https://books.google.com/books?id=ICPI2XDxOacC&pg=PA50.
2. ↑ de Haan, Victor-O.; Plomp, Jeroen; Rekveldt, Theo M.; Kraan, Wicher H.; van Well, Ad A.; Dalgliesh, Robert M.; Langridge, Sean (8 January 2010). "Observation of the Goos-Hänchen Shift with Neutrons" (in en). Physical Review Letters 104 (1). doi:10.1103/PhysRevLett.104.010401. ISSN 0031-9007. https://link.aps.org/doi/10.1103/PhysRevLett.104.010401.
3. ↑ Camley, Robert E., ed (2017). Solid State Physics: 68. Solid State Physics (1st ed.). Cambridge, MA: Academic Press. pp. 122. ISBN 978-0-12-811992-1. https://books.google.com/books?id=oeDWDgAAQBAJ&pg=PA122.
4. ↑ Ul Haq, Iqra Zia; Syed, Aqeel A.; Naqvi, Qaisar Abbas (2020). "Observing the Goos–Hänchen shift in non-integer dimensional medium" (in en). Optik 206. doi:10.1016/j.ijleo.2019.164071. https://linkinghub.elsevier.com/retrieve/pii/S0030402619319709.
5. ↑ Ghatak, A. (1978). Contemporary Optics. Optical Physics and Engineering Ser. New York, NY: Springer. ISBN 978-1-4684-2358-7.
6. ↑ Wan, Yuhang; Zheng, Zheng; Kong, Weijing; Zhao, Xin; Liu, Ya; Bian, Yusheng; Liu, Jiansheng (9 April 2012). "Nearly three orders of magnitude enhancement of Goos-Hanchen shift by exciting Bloch surface wave" (in en). Optics Express 20 (8): 8998. doi:10.1364/OE.20.008998. ISSN 1094-4087. https://opg.optica.org/oe/abstract.cfm?uri=oe-20-8-8998.
7. ↑ Atalar, Abdullah (1978). "An angular‐spectrum approach to contrast in reflection acoustic microscopy". Journal of Applied Physics 49: 5130–5139. doi:10.1063/1.324460.
8. ↑ Artmann, Kurt (January 1948). "Berechnung der Seitenversetzung des totalreflektierten Strahles" (in en). Annalen der Physik 437 (1-2): 87–102. doi:10.1002/andp.19484370108. ISSN 0003-3804. https://onlinelibrary.wiley.com/doi/10.1002/andp.19484370108.
9. ↑ Wild, Walter J.; Giles, C. Lee (1982). "Goos-Hänchen shifts from absorbing media". Physical Review A 25 (4): 2099–2101. doi:10.1103/physreva.25.2099. Bibcode: 1982PhRvA..25.2099W. http://clgiles.ist.psu.edu/papers/PhysRevA-1982.pdf.
10. ↑ Jiang, Li; Zeng, Shuwen; Xu, Zhengji; Ouyang, Qingling; Zhang, Dao‐Hua; Chong, Peter Han Joo; Coquet, Philippe; He, Sailing et al. (August 2017). "Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection" (in en). Small 13 (30). doi:10.1002/smll.201700600. ISSN 1613-6810. https://onlinelibrary.wiley.com/doi/10.1002/smll.201700600.
11. ↑ Merano, M.; Aiello, A.; 't Hooft, G. W.; van Exter, M. P.; Eliel, E. R.; Woerdman, J. P. (2007). "Observation of Goos Hänchen Shifts in Metallic Reflection". Optics Express 15 (24): 15928–15934. doi:10.1364/OE.15.015928. PMID 19550880. Bibcode: 2007OExpr..1515928M.
12. ↑ Snyder, A. W. (1976). "Goos-Hänchen shift". Applied Optics 15 (1): 236–238. doi:10.1364/AO.15.000236. PMID 20155209. Bibcode: 1976ApOpt..15..236S. https://www.osapublishing.org/ao/abstract.cfm?uri=ao-15-1-236.
13. ↑ Renard, R. H. (1964). "Total reflection: A new evaluation of the Goos–Hänchen shift". Journal of the Optical Society of America 54 (10): 1190–1197. doi:10.1364/JOSA.54.001190. https://www.osapublishing.org/josa/abstract.cfm?uri=josa-54-10-1190.
14. ↑ Yin, X. (2006). "Goos-Hänchen shift surface plasmon resonance sensor". Applied Physics Letters 89 (26): 261108. doi:10.1063/1.2424277. Bibcode: 2006ApPhL..89z1108Y. https://aip.scitation.org/doi/10.1063/1.2424277.
15. ↑ Parks, A. D. (2015). "Weak value amplification of an off-resonance Goos–Hänchen shift in a Kretschmann–Raether surface plasmon resonance device". Applied Optics 54 (18): 5872–5876. doi:10.1364/AO.54.005872. PMID 26193042. Bibcode: 2015ApOpt..54.5872P. https://www.osapublishing.org/ao/viewmedia.cfm?uri=ao-54-18-5872&seq=0.
16. ↑ Zeng, S. (2020). "Plasmonic metasensors based on 2D hybrid atomically thin perovskite nanomaterials". Nanomaterials 19 (7): 1289–1296. doi:10.3390/nano10071289. PMID 32629982.
17. ↑ Wang, Y. (2021). "Targeted sub-attomole cancer biomarker detection based on phase singularity 2D nanomaterial-enhanced plasmonic biosensor". Nano-Micro Letters 13 (1): 96–112. doi:10.1007/s40820-021-00613-7. PMID 34138312. Bibcode: 2021NML....13...96W.
18. ↑ Bliokh, K. Y. (2015). "Spin–orbit interactions of light". Nature Photonics 9 (12): 796–808. doi:10.1038/nphoton.2015.201. Bibcode: 2015NaPho...9..796B. https://www.nature.com/articles/nphoton.2015.201.
19. ↑ Yin, X. (2015). "Photonic spin Hall effect at metasurfaces". Science 339 (6126): 1405–1407. doi:10.1126/science.1231758. PMID 23520105. https://www.science.org/doi/10.1126/science.1231758.

Books

* de Fornel, Frédérique (2001) (in en). Evanescent Waves: From Newtonian Optics to Atomic Optics. Berlin: Springer. pp. 12–18. ISBN 978-3-540-65845-0.
* Goos, F.; Hänchen, H. (1947). "Ein neuer und fundamentaler Versuch zur Totalreflexion". Annalen der Physik 436 (7–8): 333–346. doi:10.1002/andp.19474360704. Bibcode: 1947AnP...436..333G.
* Delgado, M.; Delgado, E. (2003). "Evaluation of a total reflection set-up by an interface geometric model". Optik 113 (12): 520–526. doi:10.1078/0030-4026-00205. Bibcode: 2003Optik.113..520D.

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Goos–Hänchen effect. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Goos–Hänchen_effect&oldid=4369582"