Reflection Shifts in Gold Nanoparticles

Document Type : Articles


School of Engineering Science, College of Engineering, University of Tehran, Enqelab Street, Tehran, Iran


Metal nanoparticles are widely researched for the fabrication of novel low
cost and more energy efficient optoelectronic devices. Optical properties of metal
nanoparticles are known to be different from their bulk counterparts. In this paper, with
an appropriate modification of Drude model, I provide an improved dielectric function
for gold nanoparticles which accounts for particle size as well as temperature effects. The
model is consequently used to investigate Goos-Hanchen and Imbert-Fedorov reflection
shifts of an oblique linearly polarized laser beam reflected from the nanoparticles in
various temperatures. It is shown that the beam light can contribute both spatial and
angular shifts depending on its state of polarity. The maximum shifts take place at grazing
angles when the polarization of light is set at TM and 45°. Study of the light deviations'
sensitivity to the temperature indicates that reflection shifts decrease linearly at higher
temperatures except in angular out-of-plane shift Θ𝐼𝐹 . The trend is incremental for
different nanoparticle size, keeping the distinct behavior of Θ𝐼𝐹 . Such results allow more
accurate prediction of many optical phenomena involving nanoscaled gold and may serve
as a delicate method to determine nanoparticles' size.


[1 ] F. Tam and N. Halas. NPlasmon response of nanoshell dopants in organic films: a simulation study. Prog Org Coat. 47 (2003) 275–278. Available: nathan.instras .com/ResearchProposalDB/doc-102.pdf
[2 ] F. Tam, C. Moran and N. Halas. Geometrical parameters controlling sensitivity of nanoshell plasmon resonances to changes in dielectric environment. J Phys Chem B. 108, (2004) 17290–17294. Available: http:// pubs. acs. org/ doi/ abs /10.1021 /jp048499x.
[3 ] D. O’Neal, L. Hirsch et al. Photothermal tumor ablation in mice using near infrared-absorbing nanoparticles. Cancer Lett. 209 (2004) 171–176. Available:
[4 ] K. R. Catchpole, A. Polman. Design principles for particle plasmon enhanced solar cells. Appl. Phys. Lett. 93 (2008) 191113. Available: http:// aip. scitation. org/ doi/ abs/10.1063/1.3021072
[5 ] Ping-Ping Fang et al. Conductive Gold Nanoparticle Mirrors at Liquid/Liquid Interfaces. ACS Nano. 7 (10) (2013) 9241–9248. Available: http://pubs.acs. org/ doi/abs/10.1021/nn403879g; S.K. Ghosh, T. Pal. Chem. Rev. 107, (2007) 4797- 4862.
[6 ] L. Fontana et al. Gold and silver nanoparticles based networks as advanced materials for optoelectronic devices. Presented at 18th Italian National Conference on Photonic Technologies (Fotonica 2016). Available: http:// ieeexplore. document/7858049/?reload=true
[7 ] Y. Shoji, K. Kintaka et al. Low-crosstalk 2 × 2 thermo optic switch with silicon wire waveguides. Opt. Express. 18(9) (2010) 9071–9075. Available:
[8 ] M. I. Lapsley, S. S. Lin et al. An in-plane, variable optical attenuator using a fluid-based tunable reflective interface. Appl. Phys. Lett. 95(8) (2009) 083507. Available:
[9 ] T. Ochiai et al. Enhancement of self-assembly of large (>10 nm) gold nanoparticles on an ITO substrate. Appl. Phys. Express 7 (2014) 065001. Available:
[10 ] D. Wan et al. Using Spectroscopic Ellipsometry to Characterize and Apply the Optical Constants of Hollow Gold Nanoparticles. ACS nano. 3 (4) (2009) 960-970. Available:
[11 ] G. Jayaswal, G. Mistura and M. Merano. Weak measurement of the Goos-Hanchen shift. Opt. Lett. 38, 1232–1234(2013). Available: https:// www.
[12 ] W. Löffler et al. Polarization-dependent Goos–Hänchen shift at a graded dielectric interface. Opt. Commun. 283, 18, (2010) 3367–3370. Available:
[13 ] H. M. Lai, S.W. Chan et al. Nonspecular effects on reflection from absorbing media at and around Brewster's dip. J. Opt. Soc. Am., 23 (2006) 3208. Available:
[14 ] L. G. Wang et al. Negative and Positive Lateral Shift of a Light Beam Reflected from a Grounded slab. Opt. Lett. 31(8) (2006) 1124-1126. Available:
[15 ] S. Grosche, M. Ornigotti et al. Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces. Opt. Express. 16 (2015) 23. Available:
[16 ] V. J. Yallapragada, A. P. Ravishankar et al. Observation of giant Goos-Hänchen and angular shifts at designed metasurfaces. Scientific Reports. 6 (2016) 19319. Available:
[17 ] Y. Wan , Z. Zheng, W. Kong et al., Fiber-to-fiber optical switching based on gigantic Bloch-surface-wave-induced Goos-Hänchen shifts. J. Photon. 5 (2013) 7200107. Available: http:// ieeexplore. iel5/ 4563994/ 6428647/ 06384639.pdf
[18 ] X. Wang, M. Sang et al., IEEE Photonics Technology Lett. 28 (3) (2015). [19 ] M. Born and E. Wolf, Principles of Optics, 7th ed., Pergamon Press, London, 2005.
[20 ] F. Goos and H. Hanchen. Ein neuer und fundamentaler Versuch zur Total reflexion. Ann. Phys. 436 (1947) 333–346. Available: onlinelibrary. wiley. com/doi/10.1002/andp.19474360704/abstract
[21 ] C. Imbert. Calculation and Experimental Proof of the Transverse Shift Induced by Total Internal Reflection of a Circularly Polarized Light Beam. Phys. Rev. D. 5 (1972) 787. Available: 787
[22 ] F.I. Fedorov et al. On the theory of total internal reflection. SSSR. 105 (3) (1955) 465-468.
[23 ] A. Y. Qin, Y. Li et al. Measurement of spin Hall effect of reflected light. Opt. Lett. 34, (2009)2551–2553. Available: https:// www. osapublishing. org/ abstract. cfm?uri=ol-34-17-2551; V. Fedoseyev. Conservation laws and angular transverse shifts of the reflected and transmitted light beams. Opt. Commun. 282 (2009)1247–1251. Available: https:// www. sciencedirect. com/ science/article/pii/S0030401808012571
[24 ] H. M. Lai, C. W. Kwok et al. Energy-flux pattern in the Goos-Hänchen effect. Phys. Rev. E. 62 (2000) 7330. Available: https:// www. researchgate. net/.../12226103_Energy-flux_pattern_in_the_Goos-Hanchen effect
[25 ] M. Ornigotti and A. Aiello. Goos–Hänchen and Imbert–Fedorov shifts for bounded wavepackets of light. J. Opt. 15 (2013) 014004. Available:
[26 ] R. Tsekov et al. Quantifying the Blue Shift in the Light Absorption of Small Gold Nanoparticles. Available:
[27 ] O. A. Yeshchenko. Temperature effects on the surface plasmon resonance in copper nanoparticles. Ukrainian Journal of Physics. 3 (58) (2013) 249-259. Available:
[28 ] Lucia B Scaffardi and Jorge O Tocho. Size dependence of refractive index of gold Nanoparticles. Nanotechnology, 17 (2006) 1309–1315. Available:
[29 ] G. Solookinejad, M. Panahi et al. Giant Goos-Hänchen Shifts in Polaritonic Materials Doped with Nanoparticles. Plasmonics 12(3) (2017) 849-854. Available: materials-doped-with-nanoparticles/a61134/