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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 1 — Jan. 3, 2011
  • pp: 224–229
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Manipulation of surface plasmon polaritons by phase modulation of incident light

G. H. Yuan, X.-C. Yuan, J. Bu, P. S. Tan, and Q. Wang  »View Author Affiliations


Optics Express, Vol. 19, Issue 1, pp. 224-229 (2011)
http://dx.doi.org/10.1364/OE.19.000224


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Abstract

Manipulation of surface plasmon polaritons (SPP) by phase modulation of incident light beams is proposed with analytical and numerical verifications when an optical vortex (OV) beam is employed as an example. Fundamental functionalities of a plasmonic chip such as in-plane focusing, coupling and multiplexing of SPP by sequentially varying the topological charge of OV beam are demonstrated. Complementary to the manually-controlled optical-path-different technique reported in literature, the proposed method reveals a direct phase transform from OV beam to SPP with dynamic and reconfigurable advantages.

© 2010 OSA

1. Introduction

An OV beam is well known for its phase singularity and nonuniform wavefront. Mathematically, the electric field of OV beam can be described as [12

12. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009). [CrossRef]

]
E(r,θ,z)(2rw)lLpl(2r2w2)exp(r2w2)exp{i[Φ(z)+kr22R+lθ]}
(1)
where Lpl(x) is the associated Laguerre polynomials, p and l are radial and azimuthal numbers, Φ(z)=(2p+l+1)tan1(z/z0) is the Gouy phase shift and z0=πw02/λ is the Rayleigh distance. The last phase term exp(ilθ) is of special interest to us. Phase values around a loop encircling the axis of the beam change by l times 2π. In the beam centre, the phase can take on any value between 0 and l times 2π, resulting in formation of phase singularity and hollow intensity profile in the transversal plane. The integer l is also known as the topological charge. Experimentally, an OV beam can be generated by passing a Gaussian beam through a computer generated hologram or a spiral phase plate with a transmission function exp(ilθ) [13

13. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221 (1992), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/ol/abstract.cfm?URI=ol-17-3-221. [CrossRef] [PubMed]

, 14

14. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]

]. In the aspect of excitation of SPP, such a natural phase of OV beam will provide much ease for sequentially shifting the initial phase of SPP by changing the topological charges. Therefore, an OV beam is a good candidate for dynamically focusing and multiplexing of SPP into multiple DLSPPWs in combination with a subwavelength arc-shaped slit as shown below.

2. Dynamic manipulation of SPP with OV beam

We use the FullWAVE module of the commercial RSOFT software [15] to implement FDTD simulations of SPP focusing and multiplexing. A schematic is illustrated in Figs. 1(a)
Fig. 1 Schematic configuration of SPP phase modulation with OV beam which is focused by the objective lens onto the subwavelength slit: (a) top view and (b) side view. (c) Typical phase map of OV beam of topological charge l = 20. (d) Normalized |Etotal|2 distribution of focused SPP generated by x-polarized OV beam of l = 20 taken from 100 nm above the silver surface. The radius, width and opening angle of the arc are 6 μm, 240 nm and 72° respectively. White arrow indicates center of the focus.
and 1(b). An OV beam polarized along the x direction and focused by an objective lens illuminates the arc-shaped slit perforated through the 200-nm-thick silver film from the substrate side. At 633 nm wavelength in free-space, dielectric constant of silver is εm = −15.89 + 1.078i. The propagation constant of SPP along the Ag/air interface is kspp = (1.033 + 0.00234i)k0, resulting in the SPP wavelength of 613 nm and propagation length of 21.5 μm. For an OV beam with topological charge l, the SPP emitted from the two ends of the 72° arc slit has a total phase difference of . A conventional Gaussian beam can be seen as a special case of l = 0, thereby the initial SPP excited along the arc are in-phase and will constructively be interfered in the centre, resulting in a bright focal spot in the central point. However, for an OV beam carrying a nonuniform wavefront exp(ilθ), this nonzero phase difference alters the SPP interference pattern and produces an angular displacement of the focal spot. Figure 1(c) gives a typical phase map of the OV beam of l = 20. The phase distribution is divided into 20 parts in the azimuthal direction, and linearly increases from 0 and 2π in each part anticlockwise. For positive topological charges, since SPP generated in the upper part of the slit has a phase delay relative to that of the lower part and a shorter optical path is required to compensate such phase difference, the diffraction angle of the focal spot is positive to ensure the constructive interference condition and vice versa. Figure 1(d) shows FDTD simulation result of the SPP focus for l = 20, where the radius and width of the arc-shaped slit are 6 μm and 240 nm respectively. A bright focal spot is formed at the 5.67 μm distance away from centre of the slit with a diffraction angle about 19.7°. The full width at half maximum (FWHM) along and across the focal spot are 1.6 μm and 0.424 μm, respectively.

If the OV phase mask is coded with different topological charges, either positive or negative, diffraction angle of the focal spot can dynamically be tuned in a wide range. The larger the topological charge, the greater the diffraction angle. We have sequentially shifted the focal spot away from the centre by using different topological charges ranging from −40 to 40. For instance, the diffraction angle for l = −20 and l = 40 is −19.7°and 41.2° respectively, as shown in Figs. 2(a)
Fig. 2 Normalized |Ez|2 distribution generated by OV beam of (a) (b) l = −20 and (c) (d) l = 40. The displayed area is 10μm × 12μm. (a) (c) are FDTD simulation results, and (b) (d) are the results from theoretical model. White arrow indicates center of the focus. (e) Dependence of diffraction angle of the focal spot on the topological charges for R = 6 μm.
and 2(c). It is also seen that the shape of the focal spot does not show apparent degradation when varying the topological charges. Further investigation indicates that the diffraction angle is approximately proportional to the topological charge at fixed geometrical parameters. For R = 6 μm as an example, the diffraction angle increases 1.028 degree when the topological charge is increased by 1, corresponding to 107 nm shift of the focal spot in the lateral direction. Moreover, it is worthy to emphasis that the phase difference and sequent deflection of the focal spot in our paper and reference [10

10. A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91(8), 083115 (2007). [CrossRef]

] originate from two different mechanisms: the former comes from the intrinsic helical phase of optical vortex beam, while the latter roots in the inclining of incident Gaussian beam. Using the same wavelength (532 nm), arc angle (120°), arc radius (5 μm), slit width (175 nm) and similar total phase differences (8.67π corresponding to charge 13 and 8.974π corresponding to 16° incident angle), it is calculated that the diffraction angle of the focal spot is 10.95° and 11.3° in our case and reference [10

10. A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91(8), 083115 (2007). [CrossRef]

], respectively. Hence, our simulation and theoretical work can indirectly be verified by the experiment.

This phenomenon can be interpreted by Huygens-Fresnel principle. The longitudinal plasmonic field near the focal point is attributed to the superposition of the initial SPP which are excited along the arc, and it can be expressed as
Ez(r,ϕ,z)=θ0/2θ0/2E0(r)cosθeilθekzzeikspp|rR|dθ
(2)
where E0(r) is the initial amplitude of SPP along the circle, the ‘cosθ’ term originates from the projection of x-polarized electric field to the p-polarized radial component, R is the circle radius, (r,ϕ) denote the observation point in cylindrical coordinate, kspp and kz are the transversal and longitudinal wave vectors, respectively. It is noted that the spherical wavefront phase factor exp(-ikR2/f) coming from the focus of the objective lens is neglected here, because it is a constant in our configuration. Figures 2(b) and 2(d) show the calculated results of normalized |Ez|2 distribution generated by OV beam of l = −20 and 40 from the theoretical model. Both the direction and shape of the focal spots are in good agreement with the FDTD simulations in Figs. 2(a) and (c). The deviation in the adjacent areas of the slit is due to the fact that the nonplasmonic quasicylindrical waves which are generated several wavelengths away from the slit in the model are not taken into account [16

16. B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, “Efficient generation of surface plasmon by single-nanoslit illumination under highly oblique incidence,” Appl. Phys. Lett. 94(1), 011114 (2009). [CrossRef]

].

3. Multiplexing SPP into DLSPPWs

Next, we couple the focused SPP into dielectric waveguide arrays fabricated on the silver film. The detailed arrangement is shown in the inset of Fig. 3(d)
Fig. 3 The multiplexing of SPP into dielectric-loaded surface plasmon waveguides with 1.3 μm center-to-center separation using OV beams of topological charges (a) l = −20, (b) l = 1, (c) l = 20 and (d) l = 40. The displayed area is 12μm × 12μm. The detailed arrangement is shown in the inset of Fig. 3(d). Blue colour is the PMMA and light gray is the Ag surface. The thickness and width of the PMMA stripe are both 250 nm.
. The DLSPPWs have attracted increased interests of optics community because of their relatively low bend and propagation loss, compatibility with different thermal-optical, electrical-optical and nonlinear Kerr materials for the development of active plasmonic components [17

17. A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]

]. The dielectric medium is assumed to be PMMA with thickness 250 nm and refractive index 1.49, which can easily be spin-coated onto the silver film in the experiment. The centre-to-centre seperation between adjacent waveguides is 1.3 μm. By using the OV beams with discrete topological charges of −20, 1, 20 and 40, the optical energy near the focal spot are efficiently coupled into the second to the fifth waveguide channels from the bottom as shown in Figs. 3(a) to 3(d) respectively, despite of the PMMA stripe as narrow as 250 nm. The 250-nm-thickness PMMA film only sustains TM0 mode whose effective index is 1.587, and the FWHM across the focal spot is as small as 302 nm. The biggest difference between positive- and negative-charge optical vortex beams is that they possess opposite chirality, anticlockwise for positive charges and clockwise for negative charges. It is flexible to dynamically adjust the coupling channel using optical vortex beams with appropriate charge values and signs.

4. Unidirectional excitation and focus of SPP

Due to rotational symmetry of the setup, the OV beam emanates from the objective lens and converges toward the geometric focus. Therefore, SPP can unidirectionally be excited and then focused with properly chosen slit width and focal angle of incident OV beam [18

18. H. Kim and B. Lee, “Unidirectional surface plasmon polariton excitation on single slit with oblique backside illumination,” Plasmonics 4(2), 153–159 (2009). [CrossRef]

]. The ratio of optical energy of SPP propagating to the two opposite directions of the slit is strongly dependent on the two parameters of a fixed thickness Ag film. The result is depicted in Fig. 4(a)
Fig. 4 (a) The dependence of the ratio of optical energy in the two opposite directions on the slit width and incident angle (in logarithm scale). (b) An example of unidirectional excitation and focus of SPP by OV beam of l = 20. The slit width is 400 nm, and the incident angle is 20°. White arrow indicates center of the focus.
in logarithmic scale. The upper limit of the incident angle is 42°, which is determined by the numerical aperture (NA = 1) of the objective lens. Obviously, there are two regions where the SPP are efficiently and unidirectionally excited. Especially when the slit width is around 400 nm, there are a wide range of feasible incident angles from 9.5° to 37°, where the ratio of optical energy of the two opposite propagating SPP is over 100. Absolute value of the electric field intensity in the left side of the slit also possesses a peak in this range which is not shown here. Figure 4(b) gives an example of unidirectional excitation and focus of SPP. In comparison with the result in Fig. 1(d), it is obviously seen in Fig. 4(b) that the SPP propagating to the rightward direction are efficiently blocked, and almost all of SPP propagate and are focused in the left side of the slit. As a result, the focusing efficiency of SPP can further be improved and the possible background noise caused by the random scattering from the adjacent plasmonic components will be reduced.

5. Conclusions

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grant No. (10974101 and 60778045), Ministry of Science and Technology of China under Grant no.2009DFA52300 for China-Singapore collaborations and National Research Foundation of Singapore under Grant No. NRF-G-CRP 2007-01.

References and links

1.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

2.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

3.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

4.

A. Polman, “Applied physics. Plasmonics applied,” Science 322(5903), 868–869 (2008). [CrossRef] [PubMed]

5.

Q. Wang, X.-C. Yuan, P. Tan, and D. G. Zhang, “Phase modulation of surface plasmon polaritons by surface relief dielectric structures,” Opt. Express 16(23), 19271–19276 (2008), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/oe/abstract.cfm?URI=oe-16-23-19271. [CrossRef]

6.

L. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). [CrossRef] [PubMed]

7.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005). [CrossRef]

8.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhenolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit coupler for surface plasmons,” Nat. Phys. 3(5), 324–328 (2007). [CrossRef]

9.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88(17), 171108 (2006). [CrossRef]

10.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91(8), 083115 (2007). [CrossRef]

11.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010). [CrossRef]

12.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009). [CrossRef]

13.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221 (1992), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/ol/abstract.cfm?URI=ol-17-3-221. [CrossRef] [PubMed]

14.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]

15.

http://www.rsoftdesign.com/

16.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, “Efficient generation of surface plasmon by single-nanoslit illumination under highly oblique incidence,” Appl. Phys. Lett. 94(1), 011114 (2009). [CrossRef]

17.

A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]

18.

H. Kim and B. Lee, “Unidirectional surface plasmon polariton excitation on single slit with oblique backside illumination,” Plasmonics 4(2), 153–159 (2009). [CrossRef]

19.

E. Chung, Y. H. Kim, W. T. Tang, C. J. R. Sheppard, and P. T. C. So, “Wide-field extended-resolution fluorescence microscopy with standing surface-plasmon-resonance waves,” Opt. Lett. 34(15), 2366–2368 (2009), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/ol/abstract.cfm?URI=ol-34-15-2366. [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Optics at Surfaces

History
Original Manuscript: August 16, 2010
Revised Manuscript: October 7, 2010
Manuscript Accepted: October 19, 2010
Published: December 22, 2010

Citation
G. H. Yuan, X.-C. Yuan, J. Bu, P. S. Tan, and Q. Wang, "Manipulation of surface plasmon polaritons by phase modulation of incident light," Opt. Express 19, 224-229 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-224


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References

  1. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]
  2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  4. A. Polman, “Applied physics. Plasmonics applied,” Science 322(5903), 868–869 (2008). [CrossRef] [PubMed]
  5. Q. Wang, X.-C. Yuan, P. Tan, and D. G. Zhang, “Phase modulation of surface plasmon polaritons by surface relief dielectric structures,” Opt. Express 16(23), 19271–19276 (2008), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/oe/abstract.cfm?URI=oe-16-23-19271 . [CrossRef]
  6. L. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). [CrossRef] [PubMed]
  7. W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005). [CrossRef]
  8. F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhenolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit coupler for surface plasmons,” Nat. Phys. 3(5), 324–328 (2007). [CrossRef]
  9. Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88(17), 171108 (2006). [CrossRef]
  10. A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91(8), 083115 (2007). [CrossRef]
  11. B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010). [CrossRef]
  12. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009). [CrossRef]
  13. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221 (1992), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/ol/abstract.cfm?URI=ol-17-3-221 . [CrossRef] [PubMed]
  14. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]
  15. http://www.rsoftdesign.com/
  16. B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, “Efficient generation of surface plasmon by single-nanoslit illumination under highly oblique incidence,” Appl. Phys. Lett. 94(1), 011114 (2009). [CrossRef]
  17. A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]
  18. H. Kim and B. Lee, “Unidirectional surface plasmon polariton excitation on single slit with oblique backside illumination,” Plasmonics 4(2), 153–159 (2009). [CrossRef]
  19. E. Chung, Y. H. Kim, W. T. Tang, C. J. R. Sheppard, and P. T. C. So, “Wide-field extended-resolution fluorescence microscopy with standing surface-plasmon-resonance waves,” Opt. Lett. 34(15), 2366–2368 (2009), http://www.opticsinfobase.org.ezlibproxy1.ntu.edu.sg/ol/abstract.cfm?URI=ol-34-15-2366 . [CrossRef] [PubMed]

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