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  • Editor: Alan E. Willner
  • Vol. 38, Iss. 15 — Aug. 1, 2013
  • pp: 2783–2785
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Self-imaging generation of plasmonic void arrays

Shibiao Wei, Jiao Lin, Rong Wang, Qian Wang, Guanghui Yuan, Luping Du, Yanqin Wang, Xiangang Luo, Minghui Hong, Changjun Min, and Xiaocong Yuan  »View Author Affiliations


Optics Letters, Vol. 38, Issue 15, pp. 2783-2785 (2013)
http://dx.doi.org/10.1364/OL.38.002783


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Abstract

A plasmonic device is proposed to produce a self-imaging surface plasmon void array (2D surface bottle beam array) by the interference of two nondiffracting surface beams, namely, cosine-Gauss beams. The self-imaging surface voids are shown by full-wave calculations and then verified experimentally with an aperture-type near-field scanning optical microscope. We also demonstrate that the void array can be adjusted with flexibility in terms of the pattern and the number of voids.

© 2013 Optical Society of America

The Talbot effect, that is, the self-imaging effect, was first observed in the study of transmission gratings and arrays of holes perforated in metal films [11

11. H. F. Talbot, Philos. Mag. 9(56), 401 (1836). [CrossRef]

]. With the self-imaging effect, an optical field repeats at a regular interval known as the Talbot length. However, it has been shown that the self-imaging effect can be created by the superposition of a proper set of nondiffracting beams in free-space without periodic structures like gratings [12

12. P. Szwaykowski and J. Ojeda-Castaneda, Opt. Commun. 83, 1 (1991). [CrossRef]

]. A nondiffracting beam maintains its transverse profile as it propagates in free space. In this case, the self-imaging effect occurs when the propagation constants of the constituent nondiffracting beams are different. So the beating among different propagation constants results in periodically constructive interference and destructive interference forming the repeated optical field along the propagating direction [13

13. Z. Bouchal, Czech. J. Phys. 53, 537 (2003). [CrossRef]

]. In our study, this phenomenon is used to ensure that all the constituent SP voids in the near-field array have comparable sizes. In particular, the superposition of two nondiffracting surface waves, namely cosine-Gauss beams (CGB) [14

14. J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012). [CrossRef]

], is employed to produce the self-imaging void arrays. A nondiffracting CGB can be generated by interfering two SP plane waves at half-intersecting angle θ, shown in Fig. 1(a). The resultant 2D nondiffracting surface wave is characterized by
Ez(x,y)=E0cos(kyy)exp(y2/w02)exp(ikxx),
(1)
where E0 is a complex constant, and w0 denotes the beam waist in the y direction. kx and ky are the x and y components of the SP plane wave propagation constant ksp, respectively.

Fig. 1. Schematic of the designed structure. (a) A nondiffracting CGB is generated by interfering two SP plane waves at half-intersecting angle θ; blue solid lines represent SP line sources. (b) Arrays of plasmon bottle beams constructed by interfering two nondiffracting CGBs. The red and blue solid lines represent SP line sources with a length of D with varying half-intersecting angles θ1 and θ2. Two CGBs with varying propagating constants in the propagating direction are generated, which then interfere with each other within the overlap area, forming an array of voids. (c) Experimental setup. A Gaussian beam from a linearly polarized 633 nm laser source (x polarized), focused by an objective lens (10×, NA=0.3), normally incident on the metal surface to excite SP waves. The aperture-type near-field scanning optical microscope (NSOM) with an aluminum-coated fiber tip (tip aperture about 100 nm in diameter) is used to measure the 2D SP field distribution.

Two collinear CGBs with different half-intersecting angles θ1 and θ2 are generated simultaneously to create the self-imaging SP void array at the region where the two beams overlap with each other. The design scheme is shown in Fig. 1(b). Two SP line sources (solid red) with intersecting angle θ1 on the left-hand side generates a CGB with the propagation constant labeled kx1, while the other two SP line sources (solid blue) on the right-hand side generated another CGB with a different propagation constant kx2. It is noted that, ideally, kx1=kspcos(θ1) and kx2=kspcos(θ2). The resultant 2D amplitude distribution of the superposition can thus be expressed as
Ez(x,y)=Ez1(x,y)+Ez2(x,y)=E1cos(ky1y)exp(y2/w02)exp(ikx1x)+E2cos(ky2y)exp(y2/w02)exp(ikx2x).
(2)

We show the self-imaging property (periodicity in the propagation direction) of the field by considering the variation of the on-axis (y=0) intensity. Also, the propagation constant of SP waves can be expressed in terms of its real and imaginary components as ksp=ksp+iksp. The approximation E1E2=E0 is used in Eq. (2), while the half-intersecting angles θ1 and θ2 are small. Therefore we have the on-axis intensity component distribution of SP waves expressed as
I(x,0)=Ez(x,0)Ez*(x,0)=|E0|2{exp(2kx1x)+exp(2kx2x)+2cos[(kx1kx2)x]exp[(kx1+kx2)x]}.
(3)

The three exponents in Eq. (3) indicate the inherent Ohmic propagation loss of SP waves. The sinusoidal intensity variation represented by the third term of Eq. (3) is the result of the beating of two different propagation constants of CGBs in the x axis. Therefore, the period of the SP bottle array, depending on the cosine function in Eq. (3), is given by T=λsp/(cosθ1cosθ2) within the overlapped region along the x axis, where
λsp=λ0εd+εmεdεm
(4)
is the wavelength of SP waves. λ0 is the wavelength (633 nm) of the incident light. εd and εm are dielectric constants of the metal (Ag) and the medium (air), respectively.

Two pairs of grooves [Fig. 2(a)] with different half-intersecting angles were fabricated in a silver film on a glass substrate by focused ion beam milling to generate two CGBs with different propagating constants. The optically opaque silver film is 300 nm thick to avoid the interference caused by the directly transmitted incident light and the SP waves. In the example illustrated in Fig. 2, the half-angles θ were chosen to be 5° and 20°, respectively, and the length of grooves D was set to be 10 μm for both constituent CGBs.

Fig. 2. Arrays of voids generated by interference of two CGBs. (a) Scanning electron micrograph of the sample. (b) Finite-difference time-domain (FDTD) numerical calculation and (d) the near-field SP intensity distributions obtained from experimental measurement by NSOM. Two typical voids surrounded by high intensities are shown in (c) and (e), corresponding to areas outlined by blue frames in (b) and (d), respectively.

One can see that an array of self-imaging voids [two of them are isolated by the blue boxes and are shown in Figs. 2(c) and 2(e)] is obtained because of the self-imaging effect as a result of the interference of two nondiffracting CGBs. As a π phase jump exists between adjacent transverse intensity maxima of a CGB, there is half-period shift in the propagation direction for the intensity pattern across the y axis, which results in an intensity variation in the transverse direction. Numerical modeling of the near-field intensity distribution of the SP void array was performed with full-wave calculations based on the finite-difference time-domain (FDTD) method. The experimentally observed near-field intensity distribution [Figs. 2(d) and 2(e)] are in good agreement with the numerical calculations [Figs. 2(b) and 2(c)].

Fig. 3. Scanning electron micrograph of device with (a) D=15μm, θ1=10°, θ2=20°; (d) D=15μm, θ1=5°, θ2=30°. (b) and (e) FDTD simulation; (c) and (f) NSOM measurement. Intensity distributions of void arrays with different parameters: (b) and (c) with θ1=10°, θ2=20°, D=15μm; (e) and (f) with θ1=5°, θ2=30°, D=15μm.

In conclusion, we have shown that plasmonic voids can be generated by the self-imaging effect with a plasmonic device consisting of two pairs of intersecting grooves fabricated by focused ion beam milling on the surface of silver film. This phenomenon is based on the superposition of two nondiffraction CGBs generated by two pairs of grooves. The full-wave simulation and experimental results obtained by NSOM are in good agreement, and the results indicated that all the constituent SP voids in the near-field array had comparable sizes. Furthermore, we verified that both the pattern and the number of voids could be adjusted by simply varying the intersecting angles and the length of SP sources. This controllable property of SP void patterns could be useful toward developing plasmonic-based nanophotonics devices and planar plasmonic circuits. The 2D arrays of SP voids have great potential in the applications of near field optical trapping in terms of noninvasive manipulation [15

15. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008). [CrossRef]

,16

16. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010). [CrossRef]

], sorting 2D near-field particles [17

17. T. Cizmar, M. Siler, M. Sery, and P. Zemanek, Phys. Rev. B 74, 035105 (2006). [CrossRef]

,18

18. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, Nat. Phys. 3, 477 (2007). [CrossRef]

], and laser cooling techniques [19

19. E. S. Shuman, J. F. Barry, and D. DeMille, Nature 467, 820 (2010). [CrossRef]

,20

20. V. Vuletic and S. Chu, Phys. Rev. Lett. 84, 3787 (2000). [CrossRef]

].

This work was partially supported by the National Natural Science Foundation of China under grants 61036013, 61138003, and 11204141. X. C. Yuan acknowledges the support given by the Ministry of Science and Technology of China under grant 2009DFA52300 for China–Singapore collaborations, the National Research Foundation of Singapore under grant NRF-G-CRP2007-01, and Tianjin Municipal Science and Technology Commission under grant 11JCZDJC15200. J. Lin is the recipient of the Discovery Early Career Researcher Award funded by the Australian Research Council under project DE130100954. J. Lin acknowledges the financial support from the Defence Science Institute, Australia.

References

1.

K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996). [CrossRef]

2.

K. T. Gahagan and G. A. Swartzlander, J. Opt. Soc. Am. B 16, 533 (1999). [CrossRef]

3.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, Phys. Rev. Lett. 99, 013002 (2007). [CrossRef]

4.

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, Opt. Lett. 37, 851 (2012). [CrossRef]

5.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992). [CrossRef]

6.

J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000). [CrossRef]

7.

D. Yelin, B. E. Bouma, and G. J. Tearney, Opt. Lett. 29, 661 (2004). [CrossRef]

8.

B. P. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, Opt. Commun. 238, 177 (2004). [CrossRef]

9.

C. Alpmann, M. Esseling, P. Rose, and C. Denz, Appl. Phys. Lett. 100, 111101 (2012). [CrossRef]

10.

J. Arlt and M. J. Padgett, Opt. Commun. 281, 1358 (2008). [CrossRef]

11.

H. F. Talbot, Philos. Mag. 9(56), 401 (1836). [CrossRef]

12.

P. Szwaykowski and J. Ojeda-Castaneda, Opt. Commun. 83, 1 (1991). [CrossRef]

13.

Z. Bouchal, Czech. J. Phys. 53, 537 (2003). [CrossRef]

14.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012). [CrossRef]

15.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008). [CrossRef]

16.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010). [CrossRef]

17.

T. Cizmar, M. Siler, M. Sery, and P. Zemanek, Phys. Rev. B 74, 035105 (2006). [CrossRef]

18.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, Nat. Phys. 3, 477 (2007). [CrossRef]

19.

E. S. Shuman, J. F. Barry, and D. DeMille, Nature 467, 820 (2010). [CrossRef]

20.

V. Vuletic and S. Chu, Phys. Rev. Lett. 84, 3787 (2000). [CrossRef]

OCIS Codes
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: April 2, 2013
Revised Manuscript: June 24, 2013
Manuscript Accepted: June 24, 2013
Published: July 29, 2013

Citation
Shibiao Wei, Jiao Lin, Rong Wang, Qian Wang, Guanghui Yuan, Luping Du, Yanqin Wang, Xiangang Luo, Minghui Hong, Changjun Min, and Xiaocong Yuan, "Self-imaging generation of plasmonic void arrays," Opt. Lett. 38, 2783-2785 (2013)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-38-15-2783


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References

  1. K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996). [CrossRef]
  2. K. T. Gahagan and G. A. Swartzlander, J. Opt. Soc. Am. B 16, 533 (1999). [CrossRef]
  3. T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, Phys. Rev. Lett. 99, 013002 (2007). [CrossRef]
  4. G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, Opt. Lett. 37, 851 (2012). [CrossRef]
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992). [CrossRef]
  6. J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000). [CrossRef]
  7. D. Yelin, B. E. Bouma, and G. J. Tearney, Opt. Lett. 29, 661 (2004). [CrossRef]
  8. B. P. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, Opt. Commun. 238, 177 (2004). [CrossRef]
  9. C. Alpmann, M. Esseling, P. Rose, and C. Denz, Appl. Phys. Lett. 100, 111101 (2012). [CrossRef]
  10. J. Arlt and M. J. Padgett, Opt. Commun. 281, 1358 (2008). [CrossRef]
  11. H. F. Talbot, Philos. Mag. 9(56), 401 (1836). [CrossRef]
  12. P. Szwaykowski and J. Ojeda-Castaneda, Opt. Commun. 83, 1 (1991). [CrossRef]
  13. Z. Bouchal, Czech. J. Phys. 53, 537 (2003). [CrossRef]
  14. J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012). [CrossRef]
  15. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008). [CrossRef]
  16. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010). [CrossRef]
  17. T. Cizmar, M. Siler, M. Sery, and P. Zemanek, Phys. Rev. B 74, 035105 (2006). [CrossRef]
  18. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, Nat. Phys. 3, 477 (2007). [CrossRef]
  19. E. S. Shuman, J. F. Barry, and D. DeMille, Nature 467, 820 (2010). [CrossRef]
  20. V. Vuletic and S. Chu, Phys. Rev. Lett. 84, 3787 (2000). [CrossRef]

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