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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23907–23920
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Low-loss light transport at the subwavelength scale in silicon nano-slot based symmetric hybrid plasmonic waveguiding schemes

Yusheng Bian and Qihuang Gong  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23907-23920 (2013)
http://dx.doi.org/10.1364/OE.21.023907


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Abstract

A hybrid plasmonic structure comprising a silicon slot waveguide separated from an inverse metal ridge by a thin low-index insulator gap is proposed and investigated. Owing to its symmetric hybrid configuration containing closely spaced silicon rails near the metal ridge, the fundamental symmetric hybrid slot mode supported by the structure is demonstrated to be capable of simultaneously achieving low propagation loss and subwavelength field confinement within a wide range of physical dimensions at the telecom wavelength. Comprehensive numerical investigations regarding the effects of key geometric parameters on the guided modes' properties, including the slot sizes, the shape and dimension of the silicon rails, the width of the gap region as well as the height of metallic nanoridge, have been conducted. It is revealed that the propagation distance of the symmetric mode can be more than several millimeters (even up to the centimeter range), while simultaneously achieving a subwavelength mode size and tight field confinement inside the gap region. In addition to the studies on the modal characteristics, excitation strategies of the guided hybrid modes and the conversion between dielectric slot and hybrid slot modes are also numerically demonstrated. The studied platform potentially combines the advantages of silicon slot and plasmonic structures, which might lay important groundwork for future hybrid integrated photonic components and circuits.

© 2013 Optical Society of America

1. Introduction

As one of the most fundamental building blocks for the realization of nanophotonic devices and circuits, silicon waveguides are attracting ever-increasing research interests in recently years [1

1. M. Lipson, “Guiding, modulating, and emitting light on silicon - Challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]

]. With extraordinary features such as providing high refractive index contrast and offering strong compatibility with complementary metal-oxide semiconductor (CMOS) techniques, they have been widely employed for on-chip guiding, confining and processing of light signals in photonic integrated circuits. Among various guiding schemes, silicon slot structures consisting of nanometer-scale low-index layers sandwiched between high-index silicon slabs have received particular attention [2

2. V. R. Almeida, Q. F. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

]. Owing to the unique capabilities to squeeze the optical mode size down to the scale beyond the fundamental diffraction limit, slot waveguides could facilitate enhanced light-matter interactions at the nanoscale and thereby enable the realization of various compact photonic devices [3

3. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

5

5. R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in Silicon-on-Insulator,” Opt. Express 18(24), 25061–25067 (2010). [CrossRef] [PubMed]

]. A number of applications such as sensing [6

6. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007). [CrossRef] [PubMed]

, 7

7. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]

], all-optical signal processing [8

8. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguidesx,” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]

] and optical manipulating [9

9. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]

] have also been reported based on the slot platform.

2. Geometry, field distribution and modal properties of the symmetric hybrid waveguide

Electric field distributions of the symmetric and asymmetric fundamental quasi-TE hybrid slot modes supported by a typical configuration with parameters chosen as wsb = 100 nm, wrt = 200 nm, wrb = 300 nm, h = hm = 250 nm, g = 30 nm, t = 0 nm are shown in Fig. 2
Fig. 2 (a)-(b) 2D Ex field distributions of the symmetric and asymmetric hybrid slot modes. The arrows in the 2D panels represent the orientations of the electric fields. (c)-(d) 1D Ex profiles of the hybrid modes along the violet dash-dotted lines shown in the 2D field plots.
. Both the 2D and 1D field plots reveal that the optical fields could be effectively confined inside the low-index slot region between the silicon rails and the metal ridge, along with significant local field enhancement for both two modes. The arrows in the 2D panel indicate the quasi-TE nature of the two hybrid modes. Since the symmetric hybrid slot mode has much lower propagation loss, it will be the focus of our following studies.

Aeff=(W(r)dA)2/(W(r)2dA).
(1)

A0 is the diffraction-limited mode area in free space and defined as λ2/4. In order to accurately account for the energy in the metallic region, the electromagnetic energy density W (r) is defined as [13

13. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

]:
W(r)=12Re{d[ωε(r)]dω}|E(r)|2+12μ0|H(r)|2.
(2)
In Eq. (2), E (r) and H (r) are the electric and magnetic fields, ε (r) is the electric permittivity and μ0 is the vacuum magnetic permeability.

3. Performance comparisons between the proposed symmetric hybrid waveguide and the conventional hybrid plasmonic structures

4. Studies on the excitation strategies of the guided plasmon modes

One of most important issues that needs to be addressed in the practical applications of the plasmonic waveguides is the efficient excitation of their guided modes [20

20. X. Guo, M. Qiu, J. Bao, B. J. Wiley, Q. Yang, X. Zhang, Y. Ma, H. Yu, and L. Tong, “Direct coupling of plasmonic and photonic nanowires for hybrid nanophotonic components and circuits,” Nano Lett. 9(12), 4515–4519 (2009). [CrossRef] [PubMed]

, 61

61. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

63

63. L. Chen, X. Li, G. P. Wang, W. Li, S. H. Chen, L. Xiao, and D. S. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. 30(1), 163–168 (2012). [CrossRef]

]. Here two excitation strategies are considered for the hybrid slot structure, i.e., the end-fire coupling with a dielectric slot waveguide and direct excitation employing a paraxial Gaussian beam focused normally onto the left terminus of the metal ridge, as shown schematically in Figs. 7(a)
Fig. 7 Excitation of the plasmonic mode guided by the hybrid slot configuration. (a)-(b) Two different excitation setups for the symmetric hybrid slot mode. (c)-(d) 2D electric field plot along the metallic surface (X-Z plane) for different launching methods. The insets in (c) depicts the Ex distributions of the cross-sections at the dashed-lines (1-3), whereas the insets in (d) offer detailed looks of the transmitted fields inside the hybrid waveguide and the mode conversion regions.
and 7(b). 3D FEM simulations are performed to mimic the excitation and propagation of the guided modes, where the physical dimensions for the cross-sections of the hybrid structure are set the same as that in Fig. 2 as a proof-of-concept. It is shown in Fig. 7(c) that the symmetric hybrid slot mode can be effectively excited by the dielectric slot mode, with coupling efficiency higher than ~80%. For the second strategy, when the incident polarization is perpendicular to silver ridge, the symmetric hybrid slot mode can be excited, propagate along the structure with low loss and convert to the dielectric slot mode at the output region [Fig. 7(d)]. By aligning the incident polarization parallel to the propagation direction, the asymmetric hybrid slot mode can be launched, indicating selective excitation of the hybrid modes through polarization control of the incident light.

5. Related discussions on the further investigations of symmetric hybrid structures

For the present symmetric hybrid waveguiding scheme, the following issues need to be discussed or addressed in further studies.

  • 1) Measure of the mode area for the symmetric hybrid waveguides

  • 2) Consideration of practical fabrication issues for the symmetric hybrid structure

  • 3) Alternative symmetric hybrid waveguiding structures

In addition to the symmetric hybrid plasmonic waveguide proposed in this paper, a number of alternative guiding schemes could also be employed to achieve the goal of propagation loss reduction with subwavelength mode confinement. Similar to the symmetric structure based on the vertical-type silicon slot waveguides studied here, plasmonic configurations incorporating horizontal slot structures could also enable both low-propagation loss and strong field localization. For example, by adopting a multilayer metal-dielectric structure similar to that proposed in [59

59. Y. S. Bian, Z. Zheng, X. Zhao, J. S. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express 17(23), 21320–21325 (2009). [CrossRef] [PubMed]

] but with narrower metal stripes or other similar metallic structures, a horizontal-type symmetric hybrid plasmonic waveguiding configuration can be formed [Fig. 8(b)
Fig. 8 Schematics of different symmetric hybrid guiding schemes. (a)-(b) Symmetric hybrid structures with horizontal gaps. (c)-(d) Symmetric hybrid waveguides based on vertical slots. (e)-(h) Dielectrics covered metal nanowires. (i)-(l) Metallic nanowires surrounded by dielectrics.
]. Calculations indicate that nice optical performance can be achieved within a wide range of geometric parameters for this kind of symmetric hybrid structure, even if the symmetry of the waveguide is slightly broken (e.g. the thicknesses of the upper and lower silicon layers are different). From a practical perspective, the propagation loss of the modes supported by these silicon based horizontal symmetric hybrid structures might be even smaller than their vertical hybrid counterparts, due to the greatly minimized scattering loss at the metal-dielectric interfaces. Moreover, by using Al or Cu as the metallic layer, the horizontal-type plasmonic waveguide also offers compatibility with the standard CMOS fabrication techniques, thus facilitating its further applications. In addition to the horizontal symmetric hybrid configuration, other strategies capable of forming symmetric or near-symmetric environment along with high-index contrast near the metallic waveguides could also be employed to construct symmetric hybrid guiding schemes. These waveguides include metal nanostructures covered by low-high-index dielectrics supported by low-index substrates [72

72. Y. S. Bian, Z. Zheng, X. Zhao, L. Liu, Y. L. Su, J. S. Liu, J. S. Zhu, and T. Zhou, “Dielectrics covered metal nanowires and nanotubes for low-loss guiding of subwavelength plasmonic modes,” J. Lightwave Technol. 31(12), 1973–1979 (2013). [CrossRef]

, 73

73. Y. S. Bian, Z. Zheng, X. Zhao, J. Xiao, H. T. Liu, J. S. Liu, T. Zhou, and J. S. Zhu, “Gain-assisted light guiding at the subwavelength scale in a hybrid dielectric-loaded surface plasmon polariton waveguide based on a metal nanorod,” J. Phys. D Appl. Phys. 46(33), 335102 (2013). [CrossRef]

] [Figs. 8(e)-8(h)], and coaxial type-structures consisting of metallic nanowires with rectangular [49

49. Y. Kou, F. Ye, and X. Chen, “Low-loss hybrid plasmonic waveguide for compact and high-efficient photonic integration,” Opt. Express 19(12), 11746–11752 (2011). [CrossRef] [PubMed]

], circular [46

46. D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt. 49(36), 6868–6871 (2010). [CrossRef] [PubMed]

, 75

75. Y. S. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B 27(6), 1260–1265 (2010). [CrossRef]

] or other similar cross-sectional shapes surrounded by dielectrics [Figs. 8(i)-8(j)]. Similar to the previously studied symmetric waveguiding schemes [59

59. Y. S. Bian, Z. Zheng, X. Zhao, J. S. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express 17(23), 21320–21325 (2009). [CrossRef] [PubMed]

, 65

65. Y. S. Bian, Z. Zheng, X. Zhao, Y. L. Su, L. Liu, J. S. Liu, J. S. Zhu, and T. Zhou, “Guiding of long-range hybrid plasmon polariton in a coupled nanowire array at deep-subwavelength scale,” IEEE Photon. Technol. Lett. 24(15), 1279–1281 (2012). [CrossRef]

], the symmetric hybrid modes supported by these structures could also have extremely low propagation losses in conjunction with subwavelength mode sizes.

6. Conclusion

In summary, we have reported a novel type of symmetric hybrid waveguiding structure by integrating a silica-coated silicon slot waveguide with a metallic nanoridge. The symmetric hybrid configuration enables simultaneous realization of low propagation loss, subwavelength mode size and tight field confinement inside the low-index gap region. Compared to the conventional hybrid plasmonic waveguide based on a single high-index dielectric nanowire, the presented symmetric hybrid structure exhibits much lower loss, while retaining similar degrees of confinement at the subwavelength scale. Studies on the excitation strategies of its guided modes show that by using end-fire coupling or direct launching with focused laser beams, the symmetric hybrid slot mode can be effectively excited. In addition, we also demonstrate that a number of other similar structures could also exhibit both ultra-low propagation loss and subwavelength field confinement comparable to the waveguide configuration presented here. The nice optical performance in conjunction with unique features of these symmetric hybrid guiding schemes could enable further applications in passive integrated devices, active components, nonlinear light enhancement and processing, nanoscale optical manipulation as well as photonic integrated circuits.

Acknowledgment

This work was supported by the National Key Basic Research Program of China (Grant No. 2013CB328704), the National Natural Science Foundation of China (Grants No. 11121091, No. 91221304, No. 11134001 and No. 11304004), and the Postdoctoral Science Foundation of China (2013M530462). The authors would like to acknowledge Professor Yan Li and Professor Yunfeng Xiao in Department of Physics, Peking University for useful discussions.

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I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010). [CrossRef] [PubMed]

59.

Y. S. Bian, Z. Zheng, X. Zhao, J. S. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express 17(23), 21320–21325 (2009). [CrossRef] [PubMed]

60.

B. F. Yun, G. H. Hu, Y. Ji, and Y. P. Cui, “Characteristics analysis of a hybrid surface plasmonic waveguide with nanometric confinement and high optical intensity,” J. Opt. Soc. Am. B 26(10), 1924–1929 (2009). [CrossRef]

61.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

62.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). [CrossRef] [PubMed]

63.

L. Chen, X. Li, G. P. Wang, W. Li, S. H. Chen, L. Xiao, and D. S. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. 30(1), 163–168 (2012). [CrossRef]

64.

G. X. Cai, M. Luo, Z. P. Cai, H. Y. Xu, and Q. H. Liu, “A slot-based surface plasmon-polariton waveguide with long-range propagation and superconfinement,” IEEE Photon. J. 4(3), 844–855 (2012). [CrossRef]

65.

Y. S. Bian, Z. Zheng, X. Zhao, Y. L. Su, L. Liu, J. S. Liu, J. S. Zhu, and T. Zhou, “Guiding of long-range hybrid plasmon polariton in a coupled nanowire array at deep-subwavelength scale,” IEEE Photon. Technol. Lett. 24(15), 1279–1281 (2012). [CrossRef]

66.

L. Chen, T. Zhang, X. Li, and W. P. Huang, “Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film,” Opt. Express 20(18), 20535–20544 (2012). [CrossRef] [PubMed]

67.

T. Mahmoud, M. Noghani, and S. H. Vadjed, “Analysis and optimum design of hybrid plasmonic slab waveguides,” Plasmonics 8(2), 1155–1168 (2013). [CrossRef]

68.

L. Chen, X. Li, and D. S. Gao, “An efficient directional coupling from dielectric waveguide to hybrid long-range plasmonic waveguide on a silicon platform,” Appl. Phys. B 111(1), 15–19 (2013). [CrossRef]

69.

J. Zhang, P. Zhao, E. Cassan, and X. Zhang, “Phase regeneration of phase-shift keying signals in highly nonlinear hybrid plasmonic waveguides,” Opt. Lett. 38(6), 848–850 (2013). [CrossRef] [PubMed]

70.

Y. S. Bian, Z. Zheng, P. F. Yang, J. Xiao, G. J. Wang, L. Liu, J. S. Liu, J. S. Zhu, and T. Zhou, “Silicon-slot-mediated guiding of plasmonic modes: The realization of subwavelength optical confinement with low propagation loss,” IEEE J. Sel. Top. Quantum Electron.In Press.

71.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10(10), 105018 (2008). [CrossRef]

72.

Y. S. Bian, Z. Zheng, X. Zhao, L. Liu, Y. L. Su, J. S. Liu, J. S. Zhu, and T. Zhou, “Dielectrics covered metal nanowires and nanotubes for low-loss guiding of subwavelength plasmonic modes,” J. Lightwave Technol. 31(12), 1973–1979 (2013). [CrossRef]

73.

Y. S. Bian, Z. Zheng, X. Zhao, J. Xiao, H. T. Liu, J. S. Liu, T. Zhou, and J. S. Zhu, “Gain-assisted light guiding at the subwavelength scale in a hybrid dielectric-loaded surface plasmon polariton waveguide based on a metal nanorod,” J. Phys. D Appl. Phys. 46(33), 335102 (2013). [CrossRef]

74.

S. P. Zhang and H. X. Xu, “Optimizing substrate-mediated plasmon coupling toward high-performance plasmonic nanowire waveguides,” ACS Nano 6(9), 8128–8135 (2012). [CrossRef] [PubMed]

75.

Y. S. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B 27(6), 1260–1265 (2010). [CrossRef]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Integrated Optics

History
Original Manuscript: July 26, 2013
Revised Manuscript: September 19, 2013
Manuscript Accepted: September 23, 2013
Published: September 30, 2013

Citation
Yusheng Bian and Qihuang Gong, "Low-loss light transport at the subwavelength scale in silicon nano-slot based symmetric hybrid plasmonic waveguiding schemes," Opt. Express 21, 23907-23920 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23907


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  71. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008). [CrossRef]
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  73. Y. S. Bian, Z. Zheng, X. Zhao, J. Xiao, H. T. Liu, J. S. Liu, T. Zhou, and J. S. Zhu, “Gain-assisted light guiding at the subwavelength scale in a hybrid dielectric-loaded surface plasmon polariton waveguide based on a metal nanorod,” J. Phys. D Appl. Phys.46(33), 335102 (2013). [CrossRef]
  74. S. P. Zhang and H. X. Xu, “Optimizing substrate-mediated plasmon coupling toward high-performance plasmonic nanowire waveguides,” ACS Nano6(9), 8128–8135 (2012). [CrossRef] [PubMed]
  75. Y. S. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B27(6), 1260–1265 (2010). [CrossRef]

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