Journal of Nanomaterials

Journal of Nanomaterials / 2015 / Article

Research Article | Open Access

Volume 2015 |Article ID 897542 | 7 pages |

Ultraviolet Beam Focusing in Gallium Arsenide by Direct Excitation of Surface Plasmon Polaritons

Academic Editor: Nay Ming Huang
Received04 Sep 2014
Accepted11 Jan 2015
Published27 Jan 2015


This paper proposed that ultraviolet beam could be focused by gallium arsenide (GaAs) through direct excitation of surface plasmon polaritons. Both theoretical analysis and computer simulation showed that GaAs could be a reasonably good plasmonic material in the air in the deep ultraviolet waveband. With a properly designed bull’s eye structure etched in GaAs, the ultraviolet electric field could be enhanced to as high as 20 times the incident value, and the full-width-half-maximum (FWHM) of the light beam could be shrunk from ~48° to ~6°. As a plasmonic material, GaAs was compared to Ag and Al. Within the studied ultraviolet waveband, the field enhancement in GaAs was much stronger than Ag but not as high as Al.

1. Introduction

Surface plasmon polaritons (SPPs) refer to the coupling between the incident electromagnetic (EM) wave and the collective free electron plasma wave excited and propagating in the surface part of a specific material [110], which is usually called the plasmonic material. Mainly because of the characteristic of intensive EM field enhancement in a small area, especially in the subwavelength scale, the SPP effect has been a hot research topic for years and is widely applied in light beam forming [2, 3], subwavelength structure [4], plasma equipment fabrication [57], biochemical sensing [810], and other areas. So far, most SPP researches are limited to metal plasmonic materials [5, 11]. However, some researchers are also actively working on nonmetal plasmonic materials, especially semiconductors [12].

This paper proposed that ultraviolet (UV) SPPs could be directly excited in gallium arsenide (GaAs), one of the most popular semiconductor materials. Using an optimized bull’s eye periodic structure, the electromagnetic (EM) field could be enhanced and collimated in 125–261 nm range.

2. Theoretical Derivation

As we know, the SPP wave is the TM wave; using the Maxwell equations and the boundary conditions at the interface where , the following equations can be easily derived: where refers to the relative permittivity of the plasmonic material, is its real part, is the wave factor, footnote stands for direction which is the surface wave propagation direction, footnote stands for direction which is perpendicular to the interface, footnote stands for the plasmonic material, and footnote stands for the surrounding dielectric material. And refers to the relative permittivity of the surrounding dielectric medium.

Use the condition , and consider in our case; to excite the waves propagating in direction and attenuating in direction, has to be real, but and have to be imaginary; therefore the relative permittivity of the plasmonic material must satisfy the following conditions:

Equation (2) is the necessary condition to excite SPP in the plasmonic material [1, 4, 1320].

Using air as the surrounding medium (relative permittivity equals 1), the relative permittivity of GaAs was calculated and compared with (2). The relative permittivity parameters of GaAs were calculated based on the original data collected from [21]. It was found that (2) could be satisfied in the range of 125–261 nm. So we focused on this deep ultraviolet waveband for possible SPP excitation at the interface of air and GaAs.

3. Simulation and Results

Computer simulations using FDTD solutions were designed to study the SPP effect in GaAs. A classic bull’s eye structure was used in our simulation. The top view and side view of the simulated bull’s eye structure are shown in Figures 1(a) and 1(b), respectively. The plasmonic material formed a thin film with a circular aperture at the center, and a series of periodic concentric-circle shaped grooves were etched from both sides of the thin film. The groove pitch was  nm, the aperture diameter was  nm, the groove depth was  nm on each side, and the thin film thickness before etching was  nm. The original point was set at the center of the film. The surrounding medium was air. It has been well accepted that, in such a structure, surface plasmonic waves can be excited in both surfaces, and the coupling of them could lead to decent EM field enhancement and collimation, provided suitable plasmonic materials and structure parameters are used [2]. As comparison, a reference aperture-only structure with the same size but without the periodic grooves was also simulated, as shown in Figures 1(c) and 1(d).

The normalized transmission spectra at different collection angles in the far field for the bull’s eye structure and the reference structure are shown in Figures 2(a) and 2(b), respectively, and the corresponding angle dependence at 248 nm is shown in Figures 3(a) and 3(b). In the reference aperture-only structure, the full-width-half-maximum (FWHM) of the divergence angle was ~48°, and, with the bull’s eye structure, the FWHM was shrunk to ~6°, thanks to the SPP effect.

The far field projection maps of the bull’s eye structure and the reference structure at 248 nm incident wavelength are shown in Figures 4(a) and 4(b), respectively. It can be seen that, with the bull’s eye structure, the transmitted light diverges much less, and the intensity at the center is about two orders of magnitude higher. For near-field enhancement, the light intensity at the center of the exit surface is 19 times the incident light with the bull’s eye structure.

Both the reduced beam divergence and the EM field enhancement at the center are direct proofs of SPP excitation in GaAs.

4. Analysis and Comparison

As commonly known good plasmonic materials, Ag and Al were used for comparison with GaAs. The real and imaginary parts of the relative permittivity of Ag and Al were calculated based on the original refractive index data collected from [22, 23]. The calculation results were plotted in Figures 5(a) and 5(b) for comparison with GaAs. It is shown that in the waveband of interest the real part of the relative permittivity of GaAs was negative, which satisfies (2) well, while that of Ag and Al was generally positive or close to zero. This implies that in the ultraviolet waveband GaAs can be as good as or a better plasmonic material than Ag and Al.

To further examine the SPP effect of GaAs, another thing to consider is how to quantitatively evaluate the strength of it so as to compare with other materials. The quality factor of SPP, or , is a reasonable figure-of-merit to evaluate it. Physically, the quality factor stands for how well a given plasmonic material can confine the electric field and thus energy within it. For plasmonic materials, can be defined as in the following equation [2426]:

The quality factor curves of GaAs, Al, and Ag were thus calculated as shown in Figure 6. It can be seen from Figure 6 that, generally speaking, the quality factor of GaAs is better than Ag but not as good as Al in the studied waveband.

The above curve comparison provided theoretical reference of the SPP strength for GaAs, Al, and Ag. To verify it by computer simulation, it is preferred to calculate the EM field enhancement quantitatively for all the incident wavelengths in the whole band of 125–261 nm, where SPP excitation in GaAs is expected. The light intensity at 0° collection angle at the center of the exit air-film interface is a good parameter to represent the EM field enhancement effect or the SPP effect strength. However, at each incident wavelength, there exists an optimal groove pitch to achieve the highest possible electric field. So we simulated different groove pitch at one wavelength to pick up the pitch yielding the highest light intensity and then plot the curve of light intensity versus wavelength, as shown as the “Intensity-actual” curve in Figure 7, to describe the strength of SPP. The result showed that the optimal near-field light intensity could be as high as 20 times the incident light because of the SPP enhancement. The curve of GaAs was also plotted in Figure 7 for easy comparison. It can be seen that the shape and peak position of the curves match well with each other.

It is worth pointing out that an easy way to obtain the optimal groove pitch at each wavelength is to relate it with the surface plasmon resonant wave factor, which can be calculated from the following equation [4]: where is the surface plasmon resonant wave factor and is the incident wave factor. Equation (4) was used to calculate the optimal surface plasmon resonant wave factor and thus the corresponding optimal groove pitch at each incident wavelength between 125 nm and 261 nm. The simulated structure and mesh grid were scaled in proportion, and then the electric field intensity at 0° collection angle at the center of the exit air-film interface at each incident wavelength was calculated through simulation. Thus calculated intensity versus wavelength curve is also shown in Figure 7 as the “Intensity-calc” curve. Comparison of the “Intensity-actual” and “Intensity-calc” curves shows that, with the help of (4), one can conveniently estimate the peak wavelength of the SPP strength, yet the intensity could be underestimated.

A similar simulation was run for Al and Ag using the same bull’s eye structure and groove pitch optimization method. The light intensity enhancement curves at the same unit incident intensity for GaAs, Al, and Ag are shown in Figure 8 for comparison. It is shown clearly that GaAs has decent EM field enhancement effect, though not as good as Al. Ag does not show good SPP effect in the studied band. This conclusion complies well with the quality factor comparison result shown in Figure 6.

5. Conclusion

To conclude this paper, direct SPP excitation in GaAs material in ultraviolet waveband was proposed, simulated, and optimized. It was shown that, in 125–261 nm waveband, SPPs could be directly excited in GaAs, and decent beam focusing effect could be observed with the optimized bull’s eye structure. The computer simulation results match well with the theoretical analysis. How to experimentally prove and make use of these results is an interesting topic of further work.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


This work is partially supported by “the Fundamental Research Funds for the Central Universities,” no. 30920130122004. Wenhua Gu thanks the support from the “Star of Zijin” Program of Nanjing University of Science and Technology.


  1. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Physics Reports, vol. 408, no. 3-4, pp. 131–314, 2005. View at: Publisher Site | Google Scholar
  2. H. J. Lezec, A. Degiron, E. Devaux et al., “Beaming light from a subwavelength aperture,” Science, vol. 297, no. 5582, pp. 820–822, 2002. View at: Publisher Site | Google Scholar
  3. V. Kravtsov, J. M. Atkin, and M. B. Raschke, “Group delay and dispersion in adiabatic plasmonic nanofocusing,” Optics Letters, vol. 38, no. 8, pp. 1322–1324, 2013. View at: Publisher Site | Google Scholar
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature, vol. 424, no. 6950, pp. 824–830, 2003. View at: Publisher Site | Google Scholar
  5. S. Kawata, Near-Field Optics and Surface Plasmon Polaritons, Springer, Berlin, Germany, 2001.
  6. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Reports on Progress in Physics, vol. 70, no. 1, p. 1, 2007. View at: Publisher Site | Google Scholar
  7. H. Raether, Surface Plasmons on Smooth Surfaces, Springer, Berlin, Germany, 1988.
  8. N. Liu, T. Weiss, M. Mesch et al., “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Letters, vol. 10, no. 4, pp. 1103–1107, 2010. View at: Publisher Site | Google Scholar
  9. Z.-G. Dong, H. Liu, J.-X. Cao et al., “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Applied Physics Letters, vol. 97, no. 11, Article ID 114101, 2010. View at: Publisher Site | Google Scholar
  10. J. Wang, C. Fan, J. He, P. Ding, E. Liang, and Q. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Optics Express, vol. 21, no. 2, pp. 2236–2244, 2013. View at: Publisher Site | Google Scholar
  11. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Physical Review Letters, vol. 101, no. 4, Article ID 047401, 2008. View at: Publisher Site | Google Scholar
  12. J. J. Cha, K. J. Koski, K. C. Y. Huang et al., “Two-dimensional chalcogenide nanoplates as tunable metamaterials via chemical intercalation,” Nano Letters, vol. 13, no. 12, pp. 5913–5918, 2013. View at: Publisher Site | Google Scholar
  13. G. Liang, H. Liang, Y. Zhang et al., “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Applied Physics Letters, vol. 102, no. 3, Article ID 031119, 2013. View at: Publisher Site | Google Scholar
  14. I. V. Konoplev, A. R. Phipps, A. D. R. Phelps, C. W. Robertson, K. Ronald, and A. W. Cross, “Surface field excitation by an obliquely incident wave,” Applied Physics Letters, vol. 102, no. 14, Article ID 141106, 2013. View at: Publisher Site | Google Scholar
  15. J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Optics Express, vol. 21, no. 13, pp. 15490–15504, 2013. View at: Publisher Site | Google Scholar
  16. P.-Y. Chen, C. Argyropoulos, and A. Alu, “Terahertz antenna phase shifters using integrally-gated graphene transmission-lines,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 1528–1537, 2013. View at: Publisher Site | Google Scholar
  17. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Physical Review Letters, vol. 92, no. 10, Article ID 107401, 2004. View at: Publisher Site | Google Scholar
  18. M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics, Springer, Berlin, Germany, 2007.
  19. A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” Journal of Optics A: Pure and Applied Optics, vol. 5, no. 4, pp. S16–S50, 2003. View at: Publisher Site | Google Scholar
  20. K. Okamoto, S. Vyawahare, and A. Scherer, “Surface-plasmon enhanced bright emission from CdSe quantum-dot nanocrystals,” Journal of the Optical Society of America B: Optical Physics, vol. 23, no. 8, pp. 1674–1678, 2006. View at: Publisher Site | Google Scholar
  21. P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Physical Review B, vol. 6, no. 12, pp. 4370–4379, 1972. View at: Publisher Site | Google Scholar
  22. E. D. Palik, Handbook of Optical Constants of Solids: Index, Elsevier, 1998.
  23. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Applied Optics, vol. 37, no. 22, pp. 5271–5283, 1998. View at: Publisher Site | Google Scholar
  24. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Optics Express, vol. 19, no. 22, pp. 22029–22106, 2011. View at: Publisher Site | Google Scholar
  25. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Physical Review Letters, vol. 90, no. 2, Article ID 027402, 2003. View at: Google Scholar
  26. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photonics Reviews, vol. 4, no. 6, pp. 795–808, 2010. View at: Publisher Site | Google Scholar

Copyright © 2015 Senfeng Lai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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