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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 8 — Apr. 17, 2006
  • pp: 3503–3511
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Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K Lee  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3503-3511 (2006)
http://dx.doi.org/10.1364/OE.14.003503


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Abstract

In this article, we demonstrate that a subwavelength metal slit surrounded by dielectric surface gratings possesses a directional beaming effect. We propose a surface plasmon diffraction scheme to explain the three kinds of beaming conditions. The numerical simulations of the illustrative structures undertaken used a Finite Difference Time Domain (FDTD) Method and a Rigorous Coupled Wave Analysis (RCWA) Method. Our simulations were found to be consistent and in agreement with the experimental results. In comparison with other metal structures, we find that dielectric metal structures offer better performance as well as the advantage of being able to be efficiently mass produced for large volume industrial applications.

© 2006 Optical Society of America

1. Introduction

Fig.1. Atomic Force Microscope (AFM) image of a metal surface structure milled by FIB.

2. Simulation and Experimental Set-up

To further understand the details of the beaming mechanism, we first used a FDTD method to simulate the performance of the DM structure. The three simulation conditions are detailed in Fig. 2. We used three 80nm deep dielectric gratings which had a period of 465nm, 625nm, and 530nm respectively, on a 250nm thick silver film with a 230nm width slit. The incident wavelength was 633nm. Figure 3 shows the three FDTD simulation results for different periods of the DM structures of which the poynting vector SZ is in the z-direction. Unlike metal gratings, we found that the surface plasmon (SP) does not propagate along the grating profile but penetrates through the dielectric grating and propagates along the metal and dielectric interface [Fig. 3(d)]. We defined the sign of the beaming angle to be negative when the projected direction of the diffracted beam was opposite to that of the SP propagation [5

5. L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005). [CrossRef]

]. Similarly, a positive beaming angle indicates that the projected direction of the diffracted beam is the same as that of the SP propagation. The beaming angles shown in Fig. 3(a)~3(c) are negative, positive, and zero degree, respectively.

Fig. 2. FDTD simulation conditions for three DM structures. (period of Device 1 = 465m, Device 2 = 625nm and Device 3 = 530nm)

In our experimental set-up, an inverted microscope (Olympus, GX71) equipped with a transmission halogen light source with a 20nm band pass color filter (central wavelength 633nm) and a polarizer (to control the TM incident wave) was used to determine the beaming angles. A series of photographs of the transmitted light were taken by a CCD camera (Olympus, DP70) by controlling the focal plane at different heights above the sample surface.

Table 1. Design and actual geometric parameters for the three devices.

table-icon
View This Table
Fig. 3. FDTD simulations (Sz) of (a) Device 1 (b) Device 2 (c) Device 3 and (d) close-up view of the dielectric surface structures.
Fig. 4. (a) Picture of a prepared sample (three color band represent the three different periods of the DM structure) and AFM topography data of (b) Device 1 (P=465nm), (c) Device 2 (P=625nm), and (d) Device 3 (P=530nm).

The optical images shown in Figs. 5(a)~5(c) shows a series of images taken above the structure exit surface. All these images are two micrometer apart. We can see a white light dispersion from the data obtained, which implies that the surface plasmon is diffracted by the grating. To calculate the beaming angle, we placed a 20nm bandwidth red color filter before the sample [see Figs. 5(d)~5(f)]. We saw that for the red light in Device 1, the two crossover beams interfered with each other at the first 10μm, and then gradually separated after 15μm. For Device 2, the beaming angle of the red light was a positive angle. For Device 3, the beaming angle stayed very close to zero degree as only a very small divergence angle was observed. Taking into consideration that the experimental data was obtained using a 20 nm bandwidth red color filter and that the simulation was calculated by assuming a single wavelength of 633 nm, the FDTD simulations (Fig. 3) matched well to the experimental data.

To measure the beaming angle, we specified the lateral location (x-direction) of each cross-section (z-direction) and derived the regression lines. As the bandwidth for the color filter was not infinitesimal, we adopted an outer and inner boundary to define the central wavelength. By using the slope of the middle regression lines, the beaming angle was estimated to be 11.3 degrees for Device 2 (Fig. 6) and approximately zero degree for Device 3.

Fig. 5. Movies (low resolution~200KB & high resolution~1.7MB) of beaming phenomenon: (a) Device 1 [Media 1], (b) Device 2 [Media 2], (c) Device 3 [Media 3], and (d) Device 1 with filter [Media 4] (e) Device 2 with filter [Media 5], and (f) Device 3 with filter [Media 6].
Fig. 6. Calculations of the beaming angles from experimental data of Device 2 (Fig. 5(e)). (left figure indicates the definition of the coordinates)

According to the surface plasmon diffraction theory (Eq. 1) we can calculate the beaming angle for each device. Considering the case where k0 is the wave vector of light in free space, ksp is the wave vector of the surface plasmon, Λ is the period of grating, θ is the angle of incident light, and m is integer, we can obtain

ksp±m2πΛ=k0sinθ.
(1)

However as the analytical solution of ksp is difficult to derive for undulated surfaces, we instead adopted the concept of a Helmholtz reciprocal theorem and a numerical method (rigorous coupled wave algorithm, RCWA) [5

5. L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005). [CrossRef]

]. Based on these theorems, the beaming angle can be obtained from the angles exciting the surface plasmon, i.e., resonance condition, which corresponds to a minimum reflection or maximum absorption.

Our results are shown in Fig. 7. Our theoretical predications for a 633nm incident wavelength of Device 1, Device 2, and Device 3 were -10.77 degrees, 10.9 degrees, and zero degree respectively. In Table 1, the beaming angle was obtained by calculations from the experimental data and the simulations. Since the experimental results agreed well with the simulations, it might be reasonable to conjecture that a surface plasma diffraction theory may also explain the directional beaming phenomenon of a DM structure.

Fig. 7. RCWA simulations of resonance conditions for the three devices. Using Helmholtz reciprocal theorem, the minimum reflection (i.e. maximum absorption) indicates the beaming angle.

3. Discussion

Comparing DM structures to MM structures, we found that there are extra advantages of adopting DM structures. Firstly, the crystallization of metal on MM structures makes it difficult to mill a desired grating shape perfectly as the surface plasmon propagates along the metal grating profile. For DM structures, it propagates under the dielectric grating (see Fig.8). The observable difference between a MM and DM grating is the surface plasmon propagating path (red dotted line). A MM structure also suffers from a more intrinsic absorption and scattering by the metal which decreases the number of surface grooves on which the surface plasmon can “see” and broaden the beaming angle. Secondly, the intrinsic damping by metal on MM structures will affect the surface plasmon resonance condition. In Fig. 9, under the same geometric condition, we can see that the resonance angle of the DM structure is much sharper when compared to a MM structure. Thirdly, for mass production purposes, a DM structure is easier to be mass produced than a MM structure. There are available many tools to create a smooth dielectric thin film, such as using a spin coater, by chemical vapor deposition or with an evaporator machine. There are also many methods to fabricate dielectric surface gratings of precise shapes, such as with nano-imprints, e-beam lithography or a reactive ion etching system. Thus, with all of the above-mentioned merits for DM structures, we can see that DM structures offer a more feasible approach for industrial applications than that of MM structures.

Fig. 8. FDTD simulations of surface plasmon propagation path for a MM structure (left) and a DM structure (right).
Fig. 9. RCWA simulation of DM and MM structures. (Simulation parameters are detailed)

6. Conclusions

In this article, we demonstrated that a subwavelength metal slit surrounded by dielectric surface gratings can also possess a directional beaming effect. We proposed that a surface plasmon diffraction scheme can be used to explain three kinds of beaming conditions (positive angle, negative angle and zero degree). All simulations are consistent and in agreement with the experimental results. By comparing MM structures to DM structures, we found that DM structures offer better performance and have the advantage of being able to be more readily mass produced for industrial applications. With the benefits of controlling light in a microscopic world, this new mechanism as disclosed in this article has the potential to be integrated with other fields such as nanolithography [8–9

8. D. Z. Lin, L. B. Yu, C. K. Lee, C. S. Yeh, and C. L. Lin, “Simulation and fabrication of subwavelength structures for a nanometer feature enabled lens-less laser writers,” Scanning 26, I73–I77 (2004). [PubMed]

], optical storage [10

10. S. Shinada, J. Hashizume, and F. Koyama, “Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating,” Appl. Phys. Lett. 83, 836–838 (2003). [CrossRef]

], optical communication, and biosensors [11

11. D. A. Stuart, A. J. Haes, C. R. Yonzon, E. M. Hicks, and R. P. Van Duyne, “Biological applications of localised surface plasmonic phenomenae,” IEE Proc. Nanobiotechnology 152, 13–32 (2005). [CrossRef]

].

Acknowledgments

We deeply appreciate the support from the “Nano-writer and Sub-wavelength Surface Structure Design for Optical Applications” a project funded by the Materials Research Laboratory, Industrial Technology Research Institute (ITRI), Taiwan. We also appreciate the E-beam lithography system support by the Center for Information and Electronics Technologies, National Taiwan University. The authors would also like to acknowledge the financial support of this research from the National Science Council of Taiwan, through Grants NSC 93-2622-E-002-003.

References and Links

1.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944). [CrossRef]

2.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002). [CrossRef] [PubMed]

3.

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, ‘Focusing light with subwavelength aperture flanked by surface corrugations,’ Appl. Phys. Lett., 83, 4500–4502 (2003). [CrossRef]

4.

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003). [CrossRef] [PubMed]

5.

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405 (2005). [CrossRef]

6.

J. Dintinger, A. Degiron, and T. W. Ebbesen, “Enhanced light transmission through subwavelength holes,” MRS Bulletin 30, 381–384 (2005). [CrossRef]

7.

Z. B. Li, J. G. Tian, Z. B. Liu, W. Y. Zhou, and C. P. Zhang, “Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric,” Opt. Express 13, 9071–9077 (2005). http://www.opticsexpress.org/abstract.cfm?id=86076 [CrossRef] [PubMed]

8.

D. Z. Lin, L. B. Yu, C. K. Lee, C. S. Yeh, and C. L. Lin, “Simulation and fabrication of subwavelength structures for a nanometer feature enabled lens-less laser writers,” Scanning 26, I73–I77 (2004). [PubMed]

9.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4, 1085–1088 (2004). [CrossRef]

10.

S. Shinada, J. Hashizume, and F. Koyama, “Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating,” Appl. Phys. Lett. 83, 836–838 (2003). [CrossRef]

11.

D. A. Stuart, A. J. Haes, C. R. Yonzon, E. M. Hicks, and R. P. Van Duyne, “Biological applications of localised surface plasmonic phenomenae,” IEE Proc. Nanobiotechnology 152, 13–32 (2005). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(240.0240) Optics at surfaces : Optics at surfaces
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 31, 2006
Revised Manuscript: March 29, 2006
Manuscript Accepted: March 30, 2006
Published: April 17, 2006

Citation
D. Z. Lin, C.K. Chang, Y.C. Chen, D.L. Yang, M.W. Lin, J.T. Yeh, J.M. Liu, C.H. Kuan, C.S. Yeh, and C.K. Lee, "Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings," Opt. Express 14, 3503-3511 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3503


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References

  1. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944). [CrossRef]
  2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002). [CrossRef] [PubMed]
  3. F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, ‘Focusing light with subwavelength aperture flanked by surface corrugations,’ Appl. Phys. Lett.,  83, 4500-4502 (2003). [CrossRef]
  4. L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003). [CrossRef] [PubMed]
  5. L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005). [CrossRef]
  6. J. Dintinger, A. Degiron, T. W. Ebbesen, "Enhanced light transmission through subwavelength holes," MRS Bulletin 30, 381-384 (2005). [CrossRef]
  7. Z. B. Li, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, "Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric," Opt. Express 13, 9071-9077 (2005). http://www.opticsexpress.org/abstract.cfm?id=86076 [CrossRef] [PubMed]
  8. D. Z. Lin, L. B. Yu, C. K. Lee, C. S. Yeh, and C. L. Lin, "Simulation and fabrication of subwavelength structures for a nanometer feature enabled lens-less laser writers," Scanning 26, I73-I77 (2004). [PubMed]
  9. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic Nanolithography," Nano Lett. 4, 1085-1088 (2004). [CrossRef]
  10. S. Shinada, J. Hashizume, and F. Koyama, "Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating," Appl. Phys. Lett. 83, 836-838 (2003). [CrossRef]
  11. D. A. Stuart, A. J. Haes, C. R. Yonzon, E. M. Hicks, and R. P. Van Duyne, "Biological applications of localised surface plasmonic phenomenae," IEE Proc. Nanobiotechnol. 152, 13-32 (2005). [CrossRef]

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