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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7549–7555
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A subwavelength coupler-type MIM optical filter

Qin Zhang, Xu-Guang Huang, Xian-Shi Lin, Jin Tao, and Xiao-Ping Jin  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7549-7555 (2009)
http://dx.doi.org/10.1364/OE.17.007549


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Abstract

A novel subwavelength surface plasmon polaritons optical filter based on an incompletely directional coupler is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. An analytical solution for the resonant condition of the structure is derived by means of the cavity theory. Both analytical and simulative results reveal that the resonant wavelengths are proportional to the length of the slit segment, inversely proportional to the antinode number of a standing wave in the segment, and are related to the slit width and the gap between the two slits. The analytical solution being consistent with the numerical simulation verifies the feasibility of the concept of the new filter structure.

© 2009 OSA

1. Introduction

2. Device structure and theoretical analysis

The optical filter structure is simply composed with a MIM directional-coupling slit-waveguide where one of the slits is only a short segment (shown in Fig. 1
Fig. 1 The basic two-dimension structure map of the SPPs coupler-type filter.
). The slits’ medium is assumed to be air whose refractive index is set to be 1. The circumambience of the slits is covered with metal Ag. The frequency-dependent complex relative permittivity of silver is characterized by the Drude model εm(ω)=εωP/ω(ω+iγ).HereωP=1.38×1016 Hz is the bulk plasma frequency, which represents the natural frequency of the oscillations of free conduction electrons; γ=2.37×1013Hz is the damping frequency of the oscillations, ω is the angular frequency of the incident electromagnetic radiation, and εstands for the dielectric constant at infinite angular frequency with a value of 3.7 [15

15. Z. Han, E. Forsberg, and S. He, “IEEE Photon. “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007). [CrossRef]

]. When incident optical wave from point O transmits along slit waveguide 1, parts of the wave is coupled into slit segment 2, where the forward and backward waves are almost completely reflected in the air-Ag interfaces at the two ends of the short waveguide segment. Parts of the waves are coupled back into slit waveguide 1. Therefore, the structure is like a resonance cavity, and standing-waves can be formed with some appropriate conditions in the short waveguide segment. Finally, the incident optical wave is converted into two parts, the reflected wave and the transmitted wave, by the structure. Defining Δϕ to be the phase delay per round-trip in the ‘cavity’, one has Δϕ=k(ω)2L+2ϕref. Where, k(ω) is the angular wavenumber of the wave in the segment at frequency ω, and L is the length of the slit-waveguide segment. ϕrefis the phase shift of a beam reflected on air-metal interface at each end of the segment. Stable standing waves can only build up constructively within the “cavity” when the following resonant condition is satisfied, based on the principle of a resonant cavity:
Δϕ=m2π.
(1)
Here, positive integer m is the number of antinodes of the standing SPPs wave. Consideringk(ω)=2πλneff, one can get the resonant wavelengths to be
λm=2neffLmϕref/π,
(2)
where, neff is the effective index of the slit-waveguide segment in coupling with another slit waveguide, λ and λm are vacuum wavelengths of the wave. From Eq. (2), it can be concluded as following: 1) The ratio of λ1:λ2:λ3is equal to 1:2:3, as the term of ϕref/π is very small. 2) The resonant wavelengths are all proportional to the length L of the “resonant cavity” segment, but with different slope factor of 1/m. 3) The wavelengths of λmare all proportional to the effective index neff. Because neff is correlated inversely with the width of a MIM waveguide [8

8. B. Wang and G. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005). [CrossRef]

,16

16. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef] [PubMed]

] (that is, neffdecreases with the increase of the width), one can expect that resonant wavelengths are also correlated inversely with the width W. 4) As a directional coupler structure, the effective index neffof the waveguide segment also depends on the coupling strength of the MIM coupler. Therefore there is a certain relation between the effective index neffand the gap between the two coupling waveguides, and the resonant wavelengths are dependent on the gap in some way.

3. Simulation experiment and results

To verify the above filtering concept and its theoretical analysis, the FDTD method with perfectly matched layer absorbing boundary condition is used to simulate the MIM coupling structure. In the following simulations, the grid sizes in the x and the z directions are chosen to be 5nm and 5nm. The length of waveguide 2 is assumed to be L. The fundamental TM mode of the plasmonic waveguide is excited by dipole source at location A. Time monitors, set wider than the width of the long slit waveguide in points A and B, are used to detect the reflected and transmitted powers of Pref and Ptr at the locations. The vacuum wavelength of the incident light wave is scanned to find spectrum responses of the structures. The transmittance and reflectivity of the structure are defined to be R = Pref / Pin, and T = Ptr / Pin, respectively.

At first, we keep the widths of the two waveguides having the same value of 50nm. The length L of the waveguide segment is 0.5µm. The gap between the two waveguides is set to be 20 nm. Figure 2
Fig. 2 The spectra of the transmission at location B and the reflection at location A of the new structure with the segment length of L = 0.5µm, the gap of 20nm, and the same slit-waveguide width of W = 50nm. The wavelengths of the reflection peaks appear at λ 1 = 1.57µm and λ 2 = 0.78µm
shows the spectra of the transmission and the reflection of the structure, with the wavelength-selective characteristic of a typical filter. The minimum transmittance and the maximum reflectivity occur at the wavelengths of 0.78µm and 1.57µm, respectively. For a non-coupling slit waveguide with a width of 50 nm, its effective index neff is calculated to be about 1.5, based on the neff equations in References [10

10. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for Long-Range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]

,17

17. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

]. Thus, the wavelengths of the transmittance/reflectivity extremas of the coupler-type structure are respectively given to be 0.75μm for m = 2 and 1.5μm for m = 1 with the length of L = 500 nm of the segment and a provided phase-shift of ϕref=0, according to Eq. (2).

Figures 3 (a)
Fig. 3 (a) The reflection spectra of the optical filter for different gaps, with the same slit waveguide width of 50nm and the segment length of L = 0.5µm. (b) The wavelength shifts of the two resonant peaks of the reflection spectrum with the gap between the two slit waveguides.
and 3(b) show the spectra and the peak positions of the reflectivity of the structure at different gaps, and with the fixed slit width of 50 nm and the segment length of 500 nm. It reveals that the wavelengths of the peaks shift toward short wavelength slowly with the increasing of the gap, and the bandwidths of peaks become a bit narrow at the same time. However, with the increase of the gap, the maximum transmittances are reduced owing to the fact that the loss of a MIM coupler will increase with its gap [7

7. H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

]. The phenomenon of gap-dependent peak wavelengths can be attributed to the weak dependence of the effective index neff on the gap, as mentioned in the discussion of Eq. (2). Our simulation also reveals that the filtering spectrum of the structure will be distorted badly if the gap is smaller than 18nm. It means very large coupling strength will weaken the “cavity” effect, due to large amount of the energy coupling out of the segment.

Figures 4 (a)
Fig. 4 (a) The wavelengths of the two resonant peaks of the reflection spectrum versus the segment length of L, with the given waveguide width of W = 50nm and the gap of 25nm; (b) The wavelengths of the two resonant peaks of the reflection spectrum as functions of slit-waveguide width W, with other parameters unchanged
and 4 (b) show the dependences of the peak wavelengths of the reflective spectrum (or the wavelengths of the minima of the transmitted spectrums) on length L and width W, respectively. As is revealed in Eq. (2), the wavelengths of the two reflection peaks increase linearly with the increasing of the segment length of L, and correlate inversely with the width of W. However, the change rate of the first peak wavelength is about twice of that of the second peak wavelength. Obviously, one can realize the function of selecting any wavelength using the way of changing the parameters of the device, such as the waveguide width, the length of the slit segment, or the gap between the slit waveguides.

The quality factor of Q=2πνEP=νΔνis an important parameter for a cavity. Here, E is the stored energy in the cavity, and P is the power dissipated. ν=c/λis a resonant frequency of the cavity, λ is the resonant wavelength, and c is the speed of light. Δν is the bandwidth of a resonant peak of the cavity. Figures 5(a) and (b)
Fig. 5 (a) The dependences of the quality factor on the gap with the other parameters unchanged; (b) The dependences of the quality factor on the the segment width with the other parameters unchanged.
show the dependences of the quality factor on the gap and the width of the segment, respectively. It can be seen that the quality factor increases with the increasing of the gap and the width of the segment. The increment of Q becomes small for large values of the gap and the width of the segment. The reason is that the coupling strength of the MIM coupler decreases with increasing of the gap, so that the power dissipating from the “cavity” segment decreases. The increasing of the segment width will enhance the asymmetry of the coupler, and thus the coupling strength decreases.

4. Summary

Acknowledgment

The authors acknowledge the financial support from the Natural Science Foundation of Guangdong Province, China (Grant No. 07117866).

References and links

1.

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988).

2.

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005). [CrossRef] [PubMed]

3.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]

4.

T. Lee and S. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express 13(24), 9652–9659 (2005). [CrossRef] [PubMed]

5.

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795 (2005). [CrossRef] [PubMed]

6.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyia, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004). [CrossRef]

7.

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

8.

B. Wang and G. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005). [CrossRef]

9.

W. Lin and G. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91(14), 143121 (2007). [CrossRef]

10.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for Long-Range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]

11.

A. Hossieni and Y. Massoud, “A low-loss metal-insulator-metal plasmonic bragg reflector,” Opt. Express 14(23), 11318–11323 (2006). [CrossRef] [PubMed]

12.

A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express 16(3), 1475–1480 (2008). [CrossRef] [PubMed]

13.

J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Y. Wang, B. S. Zou, and S. C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16(7), 4888–4894 (2008). [CrossRef] [PubMed]

14.

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008). [CrossRef] [PubMed]

15.

Z. Han, E. Forsberg, and S. He, “IEEE Photon. “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007). [CrossRef]

16.

X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef] [PubMed]

17.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(240.6680) Optics at surfaces : Surface plasmons
(230.4555) Optical devices : Coupled resonators
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 11, 2009
Revised Manuscript: April 10, 2009
Manuscript Accepted: April 18, 2009
Published: April 22, 2009

Citation
Qin Zhang, Xu-Guang Huang, Xian-Shi Lin, Jin Tao, and Xiao-Ping Jin, "A subwavelength coupler-type MIM
optical filter," Opt. Express 17, 7549-7555 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7549


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References

  1. H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988).
  2. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005). [CrossRef] [PubMed]
  3. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]
  4. T. Lee and S. Gray, “Subwavelength light bending by metal slit structures,” Opt. Express 13(24), 9652–9659 (2005). [CrossRef] [PubMed]
  5. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795 (2005). [CrossRef] [PubMed]
  6. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyia, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004). [CrossRef]
  7. H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]
  8. B. Wang and G. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005). [CrossRef]
  9. W. Lin and G. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91(14), 143121 (2007). [CrossRef]
  10. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for Long-Range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]
  11. A. Hossieni and Y. Massoud, “A low-loss metal-insulator-metal plasmonic bragg reflector,” Opt. Express 14(23), 11318–11323 (2006). [CrossRef] [PubMed]
  12. A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express 16(3), 1475–1480 (2008). [CrossRef] [PubMed]
  13. J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Y. Wang, B. S. Zou, and S. C. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16(7), 4888–4894 (2008). [CrossRef] [PubMed]
  14. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008). [CrossRef] [PubMed]
  15. Z. Han, E. Forsberg, and S. He, “IEEE Photon. “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007). [CrossRef]
  16. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef] [PubMed]
  17. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

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