Guiding properties of asymmetric hybrid plasmonic waveguides on dielectric substrates
 Wei Wei^{1},
 Xia Zhang^{1}Email author,
 Yongqing Huang^{1} and
 Xiaomin Ren^{1}
DOI: 10.1186/1556276X913
© Wei et al.; licensee Springer. 2014
Received: 18 December 2013
Accepted: 5 January 2014
Published: 10 January 2014
Abstract
We proposed an asymmetric hybrid plasmonic waveguide which is placed on a substrate for practical applications by introducing an asymmetry into a symmetric hybrid plasmonic waveguide. The guiding properties of the asymmetric hybrid plasmonic waveguide are investigated using finite element method. The results show that, with proper waveguide sizes, the proposed waveguide can eliminate the influence of the substrate on its guiding properties and restore its broken symmetric mode. We obtained the maximum propagation length of 2.49 × 10^{3} μm. It is approximately equal to that of the symmetric hybrid plasmonic waveguide embedded in air cladding with comparable nanoscale confinement.
Keywords
Surface plasmons Hybrid plasmonic waveguides Integrated photonic devicesBackground
Surface plasmons (SP) are optically induced oscillations of free electrons at the surface of a metal and can localize the guided light far beyond the diffraction limit for electromagnetic waves in dielectric media [1, 2]. This could lead to miniaturized photonic circuits with a length scale much smaller than those currently achieved [3, 4]. Various kinds of plasmonic waveguides including metal grooves [5, 6], a chain of metal particles [7], metal stripes [8], and metal nanowires [9–11] have been proposed and investigated to realize highly integrated photonic circuits [7–12]. However, due to ohmic loss of metal [13], the propagation lengths of guided modes in plasmonic waveguides are typically short under tight confinement, which greatly limits the scope for practical applications. The main limitation of such waveguides is the tradeoff between confinement and loss. Two promising approaches, the symmetric SP mode and hybrid SP mode, are proposed to optimize the balance between propagation length and mode confinement: (1) the symmetric SP mode exhibits a lower attenuation than its asymmetric counterpart, and therefore, it is sometimes referred as to longrange SP [8]; (2) in a hybrid SP mode plasmonic waveguide, the coupling between plasmonic and waveguide modes across the gap enables ‘capacitorlike’ energy storage that allows subwavelength light propagation in nonmetallic regions with strong mode confinement [14]. Therefore, symmetric hybrid plasmonic (SHP) waveguides combining the two ideas of symmetric and hybrid SP modes can exhibit a quite long propagation length with strong mode confinement [15–20].
For practical implementations, an SHP waveguide needs to be placed on a substrate. The presence of the substrate breaks the symmetry of SP mode, leading to the dramatic decrease of propagation length. Here in this paper, by introducing an asymmetry into the SHP waveguide, we propose a novel asymmetric hybrid plasmonic (AHP) waveguide to eliminate the influence of a substrate on its guiding properties and restore its broken symmetric SP mode. Based on the combination of symmetric and hybrid SP modes, the AHP waveguide exhibits a quite long propagation length along with nanoscale mode confinement. In the following sections, with the finite element method (FEM), we investigate the guiding properties of the AHP waveguide on a substrate at a wavelength of 1,550 nm to target potential applications in telecommunications. Compared to an SHP waveguide with the same structure embedded in air cladding, the propagation length of the AHP waveguide is approximately the same along with a comparable normalized modal area. Moreover, the AHP waveguide has a horizontal slot structure featured with a horizontal low index slot, which can be convenient to be fabricated by layered deposition or thermal oxidation [21].
Methods
Results and discussion
In the first section, we investigate the guiding properties and optimize structure parameters of the SHP waveguide on a silica substrate via calculating the propagation length and normalized modal area. For further practical applications, the structure parameters of the SHP waveguide in the ideal condition (embedded in air cladding) are not investigated in detail here. We only compare the guiding properties between the AHP waveguide on a substrate and the SHP waveguide embedded in air cladding with the same structure parameters as the AHP waveguide. Then, in the second section, we propose the AHP waveguide by introducing an asymmetry into the SHP waveguide. Electromagnetic energy density profiles of an SHP waveguide embedded in air cladding, on a silica substrate, and an AHP waveguide on a silica substrate are demonstrated to compare SP mode distributions. We also investigate the guiding properties of the AHP waveguide as the height of mismatch varies. Here, it is worth mentioning that some values of the geometry parameters of the AHP waveguide considered in the study are reaching the limit where the local solutions of macroscopic Maxwell's equations may be not accurate enough for the descriptions of the electromagnetic properties. For more rigorous investigations, one needs to take nonlocal effects into account [14, 23, 24].
SHP waveguide on a substrate
AHP waveguide on a substrate
Conclusions
In conclusion, we reveal that the AHP waveguide combining the advantages of symmetric (longrange) SP mode and hybrid plasmonic waveguides is capable of supporting longrange propagation of the guided waves with nanoscale mode confinement. The proposed structure is realized by introducing an asymmetry into the SHP waveguide. Theoretical calculations show that the AHP waveguide can eliminate the effect of a silica substrate on the guiding properties of the SHP waveguide and restores the symmetry of SP mode. Thus, the AHP waveguide on a substrate can perform the same as the SHP waveguide embedded in air cladding. Considering different materials of the low index gaps in the AHP waveguide, the performance of the silicabased AHP waveguide is better than the MgF_{2}based AHP waveguide. The proposed AHP waveguide can be conveniently fabricated by existing technologies like layered deposition or thermal oxidation. This may have practical applications in highly integrated circuits as plasmonic interconnects.
Abbreviations
 AHP:

Asymmetric hybrid plasmonic
 FEM:

Finite element method
 SHP:

Symmetric hybrid plasmonic
 SP:

Surface plasmons.
Declarations
Acknowledgements
This work was supported by the National Basic Research Program of China (2010CB327605), National Natural Science Foundation of China (61077049), Program for New Century Excellent Talents in University of China (NCET080736), 111 Project of China and BUPT Excellent Ph. D. Students Foundation (CX201322).
Authors’ Affiliations
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