Deep-subwavelength light transmission in hybrid nanowire-loaded silicon nano-rib waveguides Download: 847次
1. INTRODUCTION
The field of nanophotonics has witnessed a number of significant breakthroughs in both the fundamental and applied aspects during the past few decades due mainly to the remarkable advancements in micro/nanofabrication techniques [1]. The ever-increasing demand for small-footprint and high-performance nanophotonic devices represents a top priority in the development of next-generation optical communication systems and data centers [2,3]. As a rapidly emerging branch of nanophotonics, plasmonics, which exploit the unique optical properties of metallic nanostructures, have been widely employed for light manipulation at the subwavelength scale due to its unprecedented potential to break the fundamental diffraction limit [4,5]. Among the wide variety of guided plasmonic configurations being studied, hybrid plasmonic waveguides (HPWs), which integrate plasmonic configurations and high-index dielectric structures, have recently received particular attention [68" target="_self" style="display: inline;">–
In addition to the extensive efforts that have been devoted to various high-performance integrated nanophotonic devices and the related applications enabled by HPWs [12
A feasible strategy for mapping out a practical route toward the implementation of the hybrid concept is to construct HPWs on a silicon-on-insulator (SOI) substrate [10,12,20,22]. Silicon photonics, which hold great promise for low-cost large-scale photonic integration [31,32], can be an ideal platform to construct a variety of passive and active hybrid plasmonic devices. On the other hand, as one of the most important plasmonic guiding elements, metallic nanowires are widely utilized to build high-quality functional integrated components as well [33,34]. Therefore, combing the silicon waveguide platform with metal nanowires (i.e., “the best of both worlds”) could potentially lead to a new class of hybridized structures that not only feature outstanding guiding performance but also offer a feasible route toward realistic devices. In this paper, we show that such a goal can be realized simply by integrating a metallic nanowire with a silicon nano-rib substrate. Owing to the efficient hybridization of the nanowire plasmon polariton and the silicon nano-rib waveguide mode, the hybrid nanowire-loaded nano-rib waveguide features an extremely small mode size (down to the deep-subwavelength scale) while maintaining a reasonable propagation distance at telecommunication wavelengths. In the following, comprehensive studies of the guided mode properties will be discussed in detail and systematic comparisons between our proposed structure and the existing state-of-the-art subwavelength plasmonic waveguides will be carried out to confirm its superior optical performance. In addition, investigations concerning practical issues, such as fabrication tolerance, mode excitation, waveguide bending, and cross talk, will be conducted. Alternative configurations to the waveguide in our case study will be suggested as well, which are expected to pave the way for future design innovations.
2. WAVEGUIDE GEOMETRY AND MODAL PROPERTIES
The geometry of our proposed hybrid nano-rib structure is shown schematically in Fig.
Fig. 1. Hybrid nanowire-loaded silicon nano-rib waveguide. (a) Schematic of the 3D geometry. (b) Cross section of the configuration within the plane. The hybrid waveguide comprises a silver nanowire (with a radius of ) located above a silicon nano-rib structure on a silica substrate. An additional silica buffer layer (with a height of ) is sandwiched between the nanowire and the silicon slab, which also determines the gap size (i.e., ). The height of the silicon waveguide is , and the rib width is . The nanowire is positioned at the center (along the axis) with respect to the silicon nano-rib.
The modal properties of the hybrid nanowire-loaded nano-rib waveguides are characterized by a complex wave vector, whose parallel component defines the propagating constant with
In order to accurately account for the energy in the metallic region, the electromagnetic energy density
The normalized effective mode area is defined as the ratio of
Here, by investigating the field profile of the fundamental hybrid plasmonic mode sustained in a typical hybrid nanowire-loaded nano-rib waveguide, we are able to further reveal the strong optical confinement present in the configuration. Figure
Fig. 2. Normalized electric field distributions of the fundamental hybrid plasmonic mode supported by a typical hybrid nanowire-loaded nano-rib waveguide. The geometric parameters of the waveguide are , , , and . (a) 2D electric field profile in the plane. 1D electric field plots along the (b) and (c) directions, respectively. The 1D field profiles are evaluated at the bottom corner of the silver nanowire.
Our studies indicate that the hybridization of the nanowire plasmon and silicon photonic modes in the hybrid waveguide can be readily regulated by way of tuning its key structural parameters. Here we first look into the effect of nanowire size and thickness of the silicon slab on the waveguiding properties. In order to ensure moderate propagation loss, deep-subwavelength mode size and reasonable confinement inside the gap and silicon waveguide region,
Fig. 3. Dependence of modal properties on the radius of the silver nanowire for a silicon slab with different thicknesses ( , ): (a) modal effective index ( ); (b) propagation length ( ), inset showing schematically the considered hybrid gap region in the study; (c) normalized mode area ( ); (d) confinement factor in the hybrid gap ( ); (e) confinement factor inside the silicon region ( ); (f) FoM. The dashed black line in (a) corresponds to the refractive index of the substrate ( ).
Next, we consider the effect of the nano-rib size on the guided mode’s performance. In the calculations, the radius of the nanowire is selected as 50 nm and the thickness of the silicon slab is fixed at 40 nm to enable the simultaneous realization of strong optical confinement and moderate propagation loss. The simulation results in Fig.
Fig. 4. Dependence of the modal properties on the size of the silicon nano-rib ( , ): (a) modal effective index ( ); (b) propagation length ( ); (c) normalized mode area ( ); (d) confinement factor inside the hybrid gap ( ); (e) confinement factor within the silicon region ( ); (f) FoM. The dashed black line in (a) represents the refractive index of the substrate ( ). The inset in (d) shows schematically the hybrid gap region considered in the study.
3. FABRICATION TOLERANCE OF THE HYBRID NANOWIRE-LOADED NANO-RIB WAVEGUIDE
In the fabrication process of the proposed hybrid nanowire-loaded nano-rib waveguides, the high-precision alignment between the silver nanowire and the silicon nano-rib as well as the accurate control of the nano-rib width might present a challenge. Here we conduct further studies on the tolerance of the waveguide performance against these possible fabrication imperfections. Figure
Fig. 5. Dependence of the hybrid mode’s properties on lateral misalignments (the waveguide dimensions are , , , and ): (a) modal effective index ( ); (b) propagation length ( ); (c) normalized mode area ( ); (d) confinement factor in the hybrid gap ( ); (e) confinement factor inside the silicon region ( ); (f) FoM. The dashed black line in (a) corresponds to the refractive index of the substrate ( ). The inset in (c) displays the electric field profile for the fundamental mode in a hybrid waveguide when . The inset in (d) shows the 2D schematic of a hybrid nanowire-loaded nano-rib waveguide with a laterally displaced silver nanowire. The deviation of the nanowire with respect to the silicon nano-rib is denoted as .
Fig. 6. Dependence of the hybrid mode’s properties on (the waveguide dimensions are , , , and ): (a) modal effective index ( ); (b) propagation length ( ); (c) normalized mode area ( ); (d) confinement factor in the hybrid gap ( ); (e) confinement factor inside the silicon region ( ); (f) FoM. The dashed black line in (a) corresponds to the refractive index of the substrate ( ). The inset in (b) shows the 2D schematic of a hybrid nanowire-loaded nano-rib waveguide with a nonideal silicon nano-rib. The variation in the nano-rib width is denoted as .
4. PERFORMANCE COMPARISON BETWEEN A HYBRID NANOWIRE-LOADED NANO-RIB WAVEGUIDE AND OTHER HIGH-PERFORMANCE SUBWAVELENGTH WAVEGUIDES
Since a variety of subwavelength plasmonic waveguides have been proposed and demonstrated during recent years, it is important to compare our proposed hybrid nanowire-loaded nano-rib waveguide with those existing high-performance waveguiding configurations to further benchmark its guiding properties. Here we conduct 2D parametric studies of the normalized mode area (
Fig. 7. (a), (b) Parametric plots of normalized mode area ( ) versus normalized propagation length ( ). (a) The curves for hybrid nanowire-loaded nano-rib waveguides are obtained by replotting the results in Figs. 3(b) and 3(c) . For the hybrid nanowire-loaded nano-rib waveguide and metallic nanowire waveguide, a trajectory corresponds to a range of nanowire radius: . Arrows indicate increasing the size of the nanowire. The HPW comprises a silicon nanowire embedded in silica near a silver substrate. Its dimensions are , . (b) The curves for hybrid nanowire-loaded nano-rib waveguides are obtained by replotting the results in Figs. 4(b) and 4(c) . For the hybrid nanowire-loaded nano-rib waveguide and HPW, a trajectory corresponds to a range of nano-rib height (gap size): . Arrows indicate increasing . The radii of the HPW and the metallic nanowire waveguide are 100 and 50 nm, respectively. NW, nanowire.
The FoM of our proposed waveguide and other plasmonic configurations are calculated as well to enable a further performance comparison. Table
Table 1. Comparisons of the FoM for the Hybrid Nanowire-Loaded Nano-Rib Waveguide Studied in this Paper and Other High-Performance Subwavelength Plasmonic Waveguides
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As clearly illustrated from Table
5. WAVEGUIDE CROSS TALK, BENDS, AND MODE EXCITATION
To validate the tight confinement capability of our proposed hybrid nanowire-loaded nano-rib waveguides and reveal their suitability for compact integrations, we investigate here the cross talk between adjacent structures. In order to benchmark the performance, the cross talk between conventional metallic nanowire waveguides in an air cladding and that of the metallic nanowire-loaded SOI waveguides are considered as well. The coupling system considered in this study is shown schematically in Fig.
Fig. 8. Cross talk analysis for the proposed hybrid nanowire-loaded nano-rib waveguides, and performance comparison with metallic nanowire-loaded SOI waveguides and nanowire waveguides. (a) 3D schematic of the coupling system, which consists of two horizontally parallel hybrid nanowire-loaded nano-rib waveguides. The center-to-center separation between the waveguides is . (b) The distributions of the major component ( ) of the electric fields of the symmetric and antisymmetric modes in a typical coupling system based on hybrid nanowire-loaded nano-rib waveguides ( , , , , and ). (c)–(e) Dependence of the normalized coupling length ( ) on the waveguide separation ( ) for adjacent waveguides: (c) proposed waveguides ( , , , and ), metallic nanowire-loaded SOI waveguides ( , , and ), and nanowire waveguides ( ); (d) proposed waveguides ( , , , and ), metallic nanowire-loaded SOI waveguides ( , , and ), and nanowire waveguides ( ); (e) proposed waveguides ( , , , and ), metallic nanowire-loaded SOI waveguides ( , , and ), and nanowire waveguides ( ).
In order to quantitatively evaluate the waveguide cross talk, further calculations are performed to reveal the coupling length of two closely spaced waveguides in the system [44,45]. Based on the coupled mode theory [46], the normalized coupling lengths (
The results shown in Figs.
We also study the bending properties of the proposed waveguides, which are important features that dictate the waveguide’s potential for building complex integrated devices, such as ring resonators and
Fig. 9. (a) Dependence of the light transmission through a 90° hybrid nanowire-loaded nano-rib waveguide bend on the bend radius. The physical dimensions of the hybrid waveguide used in this study are , , , and . Transmitted electric field distributions for typical waveguide bends: (b) and (c) . The field profiles are evaluated at the center of the silicon nano-rib.
Excitation of the guided mode is another important issue to be addressed for the practical applications of the proposed hybrid waveguides. A feasible and simple strategy that can efficiently launch a hybrid plasmonic mode is highly desirable. Here we adopt the far-field illumination method [47,48], a widely employed strategy for the launching of a conventional plasmonic nanowire mode, to excite the fundamental guided mode in our hybrid waveguide. To verify this concept, 3D full-wave simulations using the COMSOL Multiphysics software package were performed to study the mode launching and propagation. A paraxial Gaussian beam is exploited as the excitation source, which is focused normally onto the terminus of the silver nanowire. Simulation results in Fig.
Fig. 10. Excitation of the fundamental plasmonic mode guided by the hybrid nanowire-loaded nano-rib waveguide. The 3D electric field profile shows that a paraxial Gaussian beam is focused normally onto the left terminus of a silver nanowire, which efficiently launches the plasmonic mode in the hybrid waveguide. In the simulations, the length of the silver nanowire is set to be 4 μm. Other structural parameters for the cross section of the configuration are , , , and . For better visibility, the silica substrate is not shown in the 3D figure. The left top figures demonstrate the 2D transmitted electric field plots in the plane ( ) and the 2D electric field profile over the cross section of the structure ( plane).
6. ALTERNATIVE CONFIGURATIONS
Besides the hybrid nanowire-loaded nano-rib waveguide study conducted in the paper, our proposed waveguide concept can also be extended to other similar configurations as well. A combination of a silicon slab with other silicon nanostructures, such as nanowedges and nanowires, can also be integrated with a metallic nanowire to form the hybrid configuration. Figure
Fig. 11. Schematic of modified hybrid nanowire-loaded nano-rib waveguides and the electrical field distributions for the fundamental guided modes. (a), (b) Hybrid nanowire-loaded nano-rib waveguides that incorporate a silicon nanowedge in between the silicon slab and the silver nanowire ( , , , and the tip angle of the wedge is 60°). (c), (d) Hybrid nanowire-loaded nano-rib waveguide with a silicon nanowire inside the gap region ( , , , and the radius of the silicon nanowire is 5 nm).
7. CONCLUSION
In summary, by integrating a metallic nanowire with a silicon nano-rib configuration, we have developed a high-performance HPW, featuring excellent guiding performance at the telecommunication wavelength of 1550 nm. Moreover, deep-subwavelength mode sizes and reasonable propagation distances can be realized simultaneously. Comparisons of the waveguide performance with state-of-art hybrid and plasmonic configurations reveal the superior guiding properties of our proposed hybrid nanowire-loaded nano-rib waveguide, which exhibits significantly stronger field confinement for similar propagation distances. Studies on the fabrication tolerance, waveguide cross talk, 90° bends, and mode excitation further confirm the suitability of the proposed waveguide for practical implementations. Offering excellent compatibility with SOI platforms, our hybrid waveguiding structure could be exploited for building future ultracompact high-performance photonic components and enabling a number of potential applications, such as nonlinear light management, biochemical sensing, and enhanced optical force. Moreover, such structures could also provide an ideal platform for the study of various intriguing optical phenomena at the deep-subwavelength scale.
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Article Outline
Yusheng Bian, Qiang Ren, Lei Kang, Taiwei Yue, Pingjuan L. Werner, Douglas H. Werner. Deep-subwavelength light transmission in hybrid nanowire-loaded silicon nano-rib waveguides[J]. Photonics Research, 2018, 6(1): 01000037.