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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6042–6047
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Multimode interference demultiplexers and splitters in metal-insulator-metal waveguides

Yao Kou and Xianfeng Chen  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6042-6047 (2011)
http://dx.doi.org/10.1364/OE.19.006042


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Abstract

Multimode interference (MMI) effect in metal-insulator-metal (MIM) waveguides is studied in this paper. Theoretical calculation based on the self-imaging principle and the finite element method (FEM) simulation are used to analyze the effect and further guide the design of plasmonic MMI devices. We show that wavelength-selective routing and splitting with high extinction ratios can be realized in the multimode waveguides, and active control by refractive index modulation is also demonstrated.

© 2011 OSA

1. Introduction

Surface plasmon is regarded as a promising candidate for realizing chip-scale photonic integration and optical-electrical interconnection. To achieve this goal, several kinds of plasmonic waveguide-based structures, such as long range surface plasmon waveguides, dielectric-loaded waveguides, metallic nanowires and metal-insulator-metal (MIM) waveguides, have been proposed in the recent years [1

1. P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express 7(10), 329–335 (2000). [CrossRef] [PubMed]

7

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

], Among these, MIM waveguide shows a special advantage for high-density integration, because it confines most of field in the insulator layer and then helps to reduce the devices size. As a tradeoff, its initial loss is also significant [6

6. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef]

,7

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

]

In this paper, MMI effect in MIM waveguides is studied by theoretical calculation and finite element method (FEM) simulation (using COMSOL Multiphysics). With the help of the self-imaging principle, the interference property is analyzed, followed by a discussion of the plasmonic MMI devices, including demultiplexer, wavelength-selective splitter and active tunable splitter.

2. Theoretical and numerical analysis of MMI effect in MIM waveguides

As shown in the inset of Fig. 1(a)
Fig. 1 (a) The dispersion relation of the MIM waveguides (shown in the inset). (b) The field profile of the first four TM modes in a 0.8μm-wide waveguide.
, the fundamental structure of the MIM waveguides consists of an insulator layer (air) symmetrically sandwiched between metal (silver) layers. When excited with transverse magnetic field (Hy), the complex propagation constants β m of the TMm modes can be solved by [12

12. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974). [CrossRef] [PubMed]

]
κ1w=mπ+2arctan(ε1α2ε2κ1)  with  m=0, 1, 2......
(1)
where κ1=(k02ε1βm2)1/2, α2=(βm2k02ε2)1/2, k0=2π/λ, w is the waveguide width and ε1, ε2 are the dielectric constants of air (ε1 = 1) and silver, respectively. The wavelength-dependent complex dielectric constants of silver are taken from the measured values in Ref [13

13. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Inc., 1985).

]. Figure 1 illustrates the dispersion relation of the first four TM modes [Fig. 1(a)] and the corresponding mode profiles [Fig. 1(b)] at the wavelength of λ = 1.55μm. It can be seen that for a given wavelength, the fundamental TM0 mode does not exhibit a cutoff, but the number of modes supported by the waveguide increases with the width w. Moreover, as a typical feature of surface plasmon, all the modes have a clear amplitude enhancement at the air/silver boundaries, and exponentially decay towards the silver side. Through this paper the field in the multimode region are launched from single mode input MIM waveguides with a width of w s = 100nm. It should be noted that if the input position falls on the zero field point of a certain mode, the mode will not be excited [8

8. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

]. This property can be utilized to control the interference pattern in the multimode waveguides.

According to the self-imaging principle that is well known for conventional dielectric waveguides [8

8. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

], the excited modes in a multimode waveguide will interfere with each other due to their different propagation constants, and the interference pattern can be characteristic by the beat length Lπ=π/(β0β1). In order to examine the theory for the MIM waveguides, we investigate the interference between the TM0 and TM1 modes. At λ = 1.55μm, the cutoff widths for TM1, TM2 and TM3 mode is 0.72μm, 1.50μm and 2.27μm, respectively. So, for a multimode waveguide with width wm = 0.8μm [dashed line in Fig. 1(a)], the theoretical propagation constants of TM0 and TM1 mode are calculated to be β0 = 4.194μm−1 and β1 = 1.799μm−1, corresponding to Lπ1.55 = 1.312μm. To compare with the theoretical results we implement FEM simulation and observe the interference pattern [Fig. 2(a)
Fig. 2 The time-averaged poynting vector distribution in the multimode waveguides. The width of the waveguide is (a) wm = 0.8μm, (b) wm = 1.6μm and (c) wm = 4μm.
]. The waveguide length L is assumed to be infinite, and the input field is asymmetrically launched into the multimode waveguide for the purpose of efficiently exciting the TM1 mode. Owing to the MMI effect, the power couples to the opposite side of the waveguide after each beat length and form a repetitive field distribution. The averaged beat length taken from the numerical result is 1.31μm, agrees with the theoretical prediction. For λ = 1.31μm, the theoretical and simulated beat length is 1.828μm and 1.83μm, respectively. In addition, we observe the MMI effect in wider waveguides [Fig. 2(b) and 2(c)]. With specific input position, their interference pattern can also be understood by the beating of the excited modes. Then, in the following sections, we will use the self-imaging principle to guide the design of plasmonic MMI devices.

3. Design of plasmonic MMI devices in MIM waveguides

3.1 Demultiplexer based on 1 × 2 configuration

3.2 Wavelength-selective splitter based on 3 × 3 configuration

Another important element for the integrated circuits is beam splitters. Although T-type or Y-type splitters composed of single mode MIM waveguide have rather low bending loss [14

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

], a limitation is that they can only have equal split effect for all the wavelengths. Here we purpose a wavelength-selective splitter using the MMI effect. Our goal is to separate one wavelength into two equal parts while maintain another one unseparated. As shown in Fig. 4
Fig. 4 The magnetic field intensity |Hy| in the 3 × 3 coupler structure when light is (a)-(b) centre-launched from port B or (c)-(d) symmetrically launched from port A&C.
, the device configuration is based on a symmetric 3 × 3 coupler where the incident light is launched from the left single mode waveguides and output through the right ones. The width of the multimode waveguide (wm = 1.6μm) guarantees the first three TM modes are supported at both λ = 1.55μm and λ = 1.31μm. If the field is launched from the central port B [see Fig. 4(a)], the TM1 mode will not exist due to its anti-symmetric profile. In this case the interference is decided by the TM0 and TM2 modes and therefore the beat length should be given by Lπ=π/(β0β2). For λ = 1.55μm/1.31μm, we have Lπ = 1.177μm/1.663μm, agrees well with the numerical simulation [Fig. 2(b)].

As an opposite situation, if the field is symmetrically launched from port A&C, the TM1 mode can be excited but will destructively interference with itself. As a result, the beat length Lπ remains unchanged. This can be verified from Fig. 4(c) and 4(d), where the λ = 1.55μm wave couples into the central port 2, but the λ = 1.31μm wave still transmits through the side ones. The power transmittance is also shown in Table 1.

3.3 Towards active tunable splitters

As shown in Fig. 5
Fig. 5 The magnetic field intensity |Hy| in the MMI tunable splitter at the wavelength of λ = 1.55μm. The refractive index in the multimode region is (a) n = 1.5, (b) n = 1.472 and (c) n = 1.458.
, the splitter is constituted by a lateral symmetrical 1 × 3 coupler with structural parameters wm = 1.1μm and L = 11μm. It is assumed that the insulator layer of the multimode waveguide is filled with materials whose refractive index can be tuned actively, and the initial index is set as n = 1.5. Under this configuration, the interference pattern still depends on the TM0 and TM2 modes. Since Eq. (1) and (2) imply that the beat length can be changed by tuning the refractive index n, we can expect to control the power distribution at the different output ports in this way. Figure 5(a)5(c) illustrate the magnetic field intensity in the structure as the incident light with a wavelength of λ = 1.55μm is launched from the left input waveguide. When n equals to 1.5, 1.472 and 1.458, the structure functions as a 1 × 1, 1 × 3 and 1 × 2 splitter, respectively, and the corresponding transmittance is summarized in Table 2

Table 2. The transmittance at the three output ports of the tunable splitter

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. The total loss of the device is over 3 dB, which can be improved by structure optimization (e. g. adding tapper structure at the waveguide junctions). It is worth noting that the required modulation on the refractive index exceeds the maximum change in the refractive index of most electrooptic media, which are usually at the order of 10−3. However, several kinds of materials with ultralarge electro-optic coefficients (larger than 150pm/V) have also been obtained in the recent years [15

15. T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006). [CrossRef]

,16

16. E. M. McKenna, A. S. Lin, A. R. Mickelson, R. Dinu, and D. Jin, “Comparison of r33 values for AJ404 films prepared with parallel plate and corona poling,” J. Opt. Soc. Am. B 24(11), 2888–2892 (2007). [CrossRef]

]. With the development of such materials, the required index-modulation in our device (~0.05) could be achieved with an external voltage lower than 100V.

4. Conclusion

In conclusion, we have theoretically and numerically investigated the MMI effect in multimode MIM waveguides. We demonstrated that the MMI effect can be utilized to design wavelength-selective devices with high extinction ratio or active controllable devices by refractive index modulation. Considering the strong confinement ability of the MIM waveguides and the compact size of the proposed structures, it may find application in high-density photonic integration.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Contract No. 10874119), the National Basic Research Program “973” of China (Contract No. 2007CB307000), and the Foundation for Development of Science and Technology of Shanghai (Grant No. 10JC1407200).

References and links

1.

P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express 7(10), 329–335 (2000). [CrossRef] [PubMed]

2.

T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

3.

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

4.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999). [CrossRef]

5.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

6.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef]

7.

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

8.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

9.

J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes,” J. Lightwave Technol. 16(7), 1228–1239 (1998). [CrossRef]

10.

Y. J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17(20), 17471–17482 (2009). [CrossRef] [PubMed]

11.

G. Yuan, P. Wang, Y. Lu, and H. Ming, “Multimode interference splitter based on dielectric-loaded surface plasmon polariton waveguides,” Opt. Express 17(15), 12594–12600 (2009). [CrossRef] [PubMed]

12.

I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974). [CrossRef] [PubMed]

13.

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Inc., 1985).

14.

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

15.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006). [CrossRef]

16.

E. M. McKenna, A. S. Lin, A. R. Mickelson, R. Dinu, and D. Jin, “Comparison of r33 values for AJ404 films prepared with parallel plate and corona poling,” J. Opt. Soc. Am. B 24(11), 2888–2892 (2007). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optics at Surfaces

History
Original Manuscript: November 8, 2010
Revised Manuscript: January 16, 2011
Manuscript Accepted: January 20, 2011
Published: March 17, 2011

Citation
Yao Kou and Xianfeng Chen, "Multimode interference demultiplexers and splitters in metal-insulator-metal waveguides," Opt. Express 19, 6042-6047 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6042


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References

  1. P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express 7(10), 329–335 (2000). [CrossRef] [PubMed]
  2. T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]
  3. A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]
  4. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999). [CrossRef]
  5. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]
  6. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef]
  7. J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
  8. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]
  9. J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes,” J. Lightwave Technol. 16(7), 1228–1239 (1998). [CrossRef]
  10. Y. J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17(20), 17471–17482 (2009). [CrossRef] [PubMed]
  11. G. Yuan, P. Wang, Y. Lu, and H. Ming, “Multimode interference splitter based on dielectric-loaded surface plasmon polariton waveguides,” Opt. Express 17(15), 12594–12600 (2009). [CrossRef] [PubMed]
  12. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974). [CrossRef] [PubMed]
  13. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Inc., 1985).
  14. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]
  15. T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006). [CrossRef]
  16. E. M. McKenna, A. S. Lin, A. R. Mickelson, R. Dinu, and D. Jin, “Comparison of r33 values for AJ404 films prepared with parallel plate and corona poling,” J. Opt. Soc. Am. B 24(11), 2888–2892 (2007). [CrossRef]

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