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]. 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]. 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 [3–5]. A number of applications such as sensing [6, 7], all-optical signal processing [8] and optical manipulating [9] have also been reported based on the slot platform.

Another technology that rivals silicon photonics is their surface plasmon polariton (SPP) based counterparts leveraging electromagnetic waves coupled to electron oscillations at the metal/dielectric interface [10]. Apart from offering two-dimensional nanoscale mode confinement, SPP structures involving metallic features also facilitate simultaneous transport and control of light and electric signals on the same chip [10]. By combining metallic waveguides with silicon components, the confinement capability of SPP structures can be further improved [11, 12]. However, the associated modal losses of these metal-silicon waveguiding configurations are substantially increased compared to the metal-low-index-dielectric cases. A promising strategy to overcome this limitation is by employing a hybrid guiding scheme that introduces an additional low-index buffer layer between the high-index structure and the metallic surface [13]. Owing to the strong interaction between the plasmonic and dielectric modes, the hybridized SPP mode exhibits a strong localization near the low-index gap with ultra-low propagation loss. This hybrid concept has successfully reconciled the conflict between low loss propagation and truly subwavelength mode confinement that widely exists in traditional SPP waveguides [14]. Due to the nice optical performance of hybrid plasmonic structures, they enable a number of intriguing applications in nanolasers [15, 16], active waveguides [17–19], compact passive optical components [20–30], enhanced optical forces [31–33], nonlinear light enhancement [34] as well as light focusing [35] and concentration [36].

In most of the previously reported hybrid plasmon polariton waveguides (HPPWs), a single high-index dielectric nanowire, made of GaAs [13, 37–39], CdS [15, 40, 41], Si [42–56], ZnS [57], Ge [58] or InGaAsP [17], is widely utilized as the dielectric element to couple with the metallic structure. It has been shown that by adding nanoscale high-index dielectric slabs symmetrically near each side of a metal stripe [59, 60], the formed hybrid structures could have much lower modal loss than their conventional hybrid counterparts, due to the unique symmetric configurations with high-index contrast near the metallic components. This symmetric hybrid concept represents an important step toward ultra-low-loss plasmon waveguiding in conjunction with tight field confinement, since it holds the advantages of enabling extremely low propagation loss even comparable to that of the long-range plasmonic waveguides [61, 62], and meanwhile capable of achieving strong light confinement down to the subwavelength scale. Several modified symmetric hybrid plasmonic waveguides have been reported since then [63–67]. Furthermore, the applications of these symmetric configurations in directional coupling [68] and optical parametric amplification [69] have also been demonstrated. Here in this paper we report another type of symmetric hybrid plasmonic guiding scheme by integrating silicon slot waveguides with plasmonic nanostructures. The presented hybrid waveguide can be realized through metallic filling inside the slot region, which makes it compatible with standard fabrication techniques and also facilities its further applications in building much more complex photonic devices, such as those incorporating bending and other features. These properties are also marked advantages over our previously proposed nanowire-embedded silicon slot structure [70]. In addition, compared with our previously studied symmetric hybrid planar waveguide whose metal stripe has been set wide enough (e.g. typically on the order of several microns) to support guided long-range plasmonic modes [59], the size of the metal nanoridge in the presented configuration can be significantly smaller (e.g. ~a few to tens of nanometers), which enables further reduction of the propagation loss. In the following sections, based on continuous mapping of key geometric parameters, comprehensive investigations on the guiding properties of the presented hybrid waveguide will be conducted at the telecom wavelength. In addition, through three-dimensional (3D) finite element method (FEM) simulations, we reveal that the guided plasmonic modes can be efficiently excited using end-fire method or directly launched by focused laser beams. These investigations are expected to lay important ground work for the further applications of the hybrid structure.

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

The architecture concept of the proposed platform is shown schematically in Fig. 1, which consists of an inverse metallic ridge right embedded inside a silica-coated silicon slot waveguide. A possible way to fabricate the waveguide is to form a vertical silicon slot waveguide by using electron-beam lithography and etching [3]. After the deposition of the oxide buffer, the silver layer can be then deposited inside the slot region assisted by another electron-beam lithography process with ultrahigh alignment precision, which is similar to that adopted in the realization of conventional HPPW with a vertical air gap [33]. In the following, the optical characteristics of the hybrid configurations are investigated at λ = 1550 nm using a FEM based software COMSOL⁠^TM⁠. The permittivities of air, SiO⁠₂⁠, Si and Ag are ε⁠_c⁠ = 1, ε⁠_g ⁠ = 2.0851, ε⁠_d⁠ = 12.0826 and ε⁠_m⁠ = −129 + 3.3i [13], respectively. The modal properties of the hybrid waveguide are analyzed by the eigenmode solver using the 2D Perpendicular Wave package in the RF module. Convergence tests are done to ensure that the numerical boundaries and meshing do not interfere with the solutions.

 

Fig. 1 (a) 3D layout of the hybrid plasmonic waveguide. (b) Cross-sectional view of the geometry. The top and bottom widths of the metallic ridge are w_mt and w_mb respectively, while the bottom width of the slot is w_sb. The height of the metal ridge is denoted as h_m. The silicon rail has a top width of w_rt, a bottom width of w_rb and a total height of h. The sidewall angle of the silicon rail is denoted as θ, whereas t and g are the thicknesses of the silicon planar layer and the gap between the metal ridge and the silicon rail.

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Electric field distributions of the symmetric and asymmetric fundamental quasi-TE hybrid slot modes supported by a typical configuration with parameters chosen as w_sb = 100 nm, w_rt = 200 nm, w_rb = 300 nm, h = h_m = 250 nm, g = 30 nm, t = 0 nm are shown in Fig. 2. 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.

 

Fig. 2 (a)-(b) 2D E_x 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 E_x profiles of the hybrid modes along the violet dash-dotted lines shown in the 2D field plots.

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By fixing h, w_rt and t at 250 nm, 200 nm and 0 nm respectively, we start carrying out detailed investigations on the dependence of the modal properties on the slot width, sidewall angle, the thickness of the gap layer as well as the height of the metal ridge, which include the real part of the modal effective index (n_eff = Re(N_eff)), propagation length (L), normalized mode area (A_eff/A₀) and the confinement factor (Γ). The propagation length (L) is obtained by L = λ/[4πIm(N_eff)]. Γ is defined as the ratio of the power inside the gap region (shown in the inset of Fig. 3(b)) to the total power of the waveguide. The effective mode area (A_eff) is calculated using

 

Fig. 3 Properties of the symmetric hybrid mode for various w_sb. (a) Modal effective index (n_eff). (b) Propagation length (L). (c) Normalized mode area (A_eff/A₀). (d) Confinement factor (Γ). The inset in (a) shows the |E| distribution for a typical waveguide with w_sb = 50 nm and g = 40 nm, where the metal ridge has turned into an inverted triangular wedge due to the relatively large gap size and small slot width. The considered gap region for the calculation of the confinement factor is highlighted in the inset of (b). The inset in (d) depicts the dependence of Γ on the gap thickness for a fixed slot width, where the red, blue and green lines correspond to w_sb = 50 nm, 100 nm and 150 nm, respectively.

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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]:

Firstly, we consider the structure with a fixed sidewall angle (set the same as that in Fig. 2), while changing the bottom width of the slot and thickness of the gap to control the modal properties. In the simulations, the height of the metal ridge is set at h_m = 250 nm, corresponding to a complete metallic filling of the slot region. Owing to the enhanced optical confinement caused by the widened metal ridge with the increased w_sb, the effective index, confinement factor as well as the modal loss monotonically increase with the widened slot width for a fixed gap, whereas the mode area exhibits a slight decrease during this process, as shown in Fig. 3. Within the range of the considered physical dimensions, subwavelength mode area along with low propagation loss (L ~tens to hundreds of microns) and tight field confinement inside the gap region can be realized simultaneously. Simulations also reveal that the modal loss can be further reduced by adopting thicker silica gap layers, while the corresponding waveguides are still capable of maintaining subwavelength field confinement. Here it is worth noting that, the confinement factor would demonstrate a non-monotonic trend when the gap thickness continuously increases, indicating the existence of an optimal gap thickness in terms of the confinement inside the gap region. It is also illustrated from the inset of Fig. 3(d) that, the critical gap size (corresponding to the largest confinement factor) increases when the slot width of the hybrid waveguide is getting larger.

The calculated modal properties for various sidewall angles are shown in Fig. 4, where the top width of the silicon rail w_rt is fixed at 200 nm and the slot width w_sb is set at 100 nm to ensure both reasonable modal loss and tight confinement inside the gap. Both the silicon rails and the metal ridge heights are set at 250 nm during the investigations. Due to the enhanced confinement inside the silicon rails and reduced power within the slot region, monotonic increases in n_eff and A_eff along with a continuous decrease in Γ can be observed at larger θ. By contrast, the propagation length demonstrates a more complicated trend, which decreases first before it increases when the sidewall angle is getting larger, as seen in Fig. 4(b). The non-monotonic optical behavior of the propagation length can be attributed to the combined effects of the metallic ridge and the silicon rails, which heavily influence the overall loss of the guided plasmonic mode. For sidewalls with relatively gentle slopes, the large sizes of the Si rails greatly enhance the dielectric-like feature of the hybrid mode, thereby resulting in the mitigation of the modal loss, as seen from the rising trend of L near 30 deg. When θ is very small, the rapidly decreased metal size becomes the dominant factor, which leads to the dramatic reduction of the modal loss. While for moderate sidewall angles, neither the dielectric-like-feature is strong nor the metallic component is small, consequently the loss of the hybrid mode is relatively large, which corresponds to a shortened propagation distance. Similar to Fig. 3, continuously increasing the gap thickness could lead to further reduction of the modal loss as well as non-monotonic trend of the confinement factor (see the inset of Fig. 4(d)). Due to the greatly weakened field confinement in the slot region for silicon rails with gentle slopes, the decreasing trend of Γ is more significant at larger θ. It is also illustrated in Fig. 4 that both ultra-low-loss and subwavelength mode size can be realized, with propagation distance exceeding the millimeter-range, which is much larger than that of the standard hybrid waveguide for similar degrees of confinement [13].

 

Fig. 4 Dependence of the modal properties on the sidewall angle (w_sb = 100 nm). (a) Modal effective index (n_eff). (b) Propagation length (L). (c) Normalized mode area (A_eff/A₀). (d) Confinement factor (Γ). The insets in (a) and (b) show the field distributions for typical configurations (θ = 0 deg, g = 40 nm for (a) and θ = 30 deg, g = 20 nm for (b)), while the inset in (d) depicts the dependence of Γ on g for a fixed θ, where red, blue and green lines correspond to θ = 0 deg, 15 deg and 30 deg, respectively.

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Finally, we investigate the effect of partial metallic filling in the slot region on the guided mode's properties. In the simulations, the slot width w_sb and the sidewall angle θ are set at 100 nm and 0 deg respectively to guarantee simultaneous realization of low propagation loss and tight field confinement. The calculated modal properties are shown in Fig. 5 for different gap widths as the metal height h_m varies from 25 nm to 250 nm. It is illustrated that the propagation loss of the symmetric hybrid slot mode can be further reduced through adopting shallower metallic ridges, while the corresponding mode size can be maintained at the subwavelength scale simultaneously. Such strong field confinement can be attributed to the closely spaced silicon rails on both sides of the metal nanoridge, which confine and store a large portion of the mode energy between them, as also seen in the corresponding electric field distribution shown in the inset of Fig. 5(c). It is also worth noting that, due to the gradually shrinked gap region between the metal ridge and the adjacent silicon rails, the confinement factor inside the gap experiences a continuous decrease as h_m gets smaller. It is found that within the range of the considered parameters in Fig. 5, the symmetric hybrid slot mode features simultaneously subwavelength mode confinement and ultra-long-range propagation length over several millimeters, indicating much lower propagation loss achieved than the previously reported conventional hybrid waveguides with comparable degrees of confinement [13, 57]. Moreover, the propagation length could even exceed the centimeter range simply by adopting larger gap sizes, while the corresponding structure is still capable of retaining tight mode confinement. Numerical simulations also reveal that for waveguides with small gap sizes, non-monotonic modal properties are observed when the height of the metal ridge decreases below ~20 nm. Since the corresponding modal behaviors are much more complicated than what is studied here, it deserves further investigations in our future studies.

 

Fig. 5 The effect of partial metallic filling on the modal properties (w_sb = 100 nm, θ = 0 deg). (a) Modal effective index (n_eff). (b) Propagation length (L). (c) Normalized mode area (A_eff/A₀). (d) Confinement factor (Γ). The insets in (c) shows the electric field distribution for a typical configuration (h_m = 100 nm), while the inset in (d) provides the 2D cross-sectional view of the geometry and also highlights the considered gap region for the calculation of Γ.

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

To further benchmark the properties of the presented symmetric hybrid structure, we here make quantitative comparisons between the optical performances of the proposed hybrid slot waveguides (HSWs) and the conventional HPPWs [13]. In order to allow for fair comparisons between different waveguiding structures, the same materials and methods for the calculations of the propagation lengths and mode areas have been adopted. The physical dimensions of the HSWs are set the same as those in Figs. 3-5, whereas the dimensions of the HPPWs are chosen according to [13], with the diameter (d) or width (w) of the silicon nanowire fixed at 200 nm and the gap size (g) chosen as 5 nm, 10 nm, 20 nm, 30 nm and 40 nm, respectively. In Figs. 6(a)-6(c), the 2D parameter plots of the normalized mode area (A_eff/A₀) versus the propagation length (L) are introduced for the above plasmonic waveguides to enable direct comparisons of modal properties. For the proposed HSWs, by replotting the data from Fig. 3, Fig. 4 and Fig. 5, we are able to show the relationships between the mode area and the propagation distance for different geometries. As clearly illustrated in Fig. 6, the HSW is capable of achieving much longer propagation distance than its conventional HPPW counterparts with the same gap sizes (e.g. nearly two orders of magnitude larger when g = 40 nm in Fig. 6(c)), although its mode area is slightly larger than that of the corresponding HPPW. These results indicate that, compared to the HPPW, significant propagation loss reduction can be enabled by employing the HSW structure, along with rather small sacrifice in the mode confinement.

 

Fig. 6 Performance comparisons between the proposed HSWs and the conventional HPPWs, where HPPW I and HPPW II represent two configurations incorporating circular-shaped and square-shaped nanowires, respectively. (a) Comparison between the HSWs in the first set of simulations (Fig. 3) and the corresponding HPPWs with the same gap sizes. (b) Comparison between the HSWs in the second set of simulations (Fig. 4) and the corresponding HPPWs. (c) Comparison between the HSWs in the third set of simulations (Fig. 5) and the corresponding HPPWs. (d) Legends of the conventional HPPWs for (a)-(c). The insets demonstrate the electric field distributions of the fundamental plasmonic modes guided by typical HPPW structures. Left inset: HPPW I (d = 200 nm, g = 30 nm). Right Inset: HPPW II (w = 200 nm, g = 30 nm).

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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, 61–63]. 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) 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.

 

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 E_x 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.

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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.

It is well known that the plasmonic mode's confinement can be gauged using a number of different methods for the calculation of the effective mode area [71]. A statistical measure by integrating the electromagnetic field over the entire cross-section of the waveguide has been adopted in our simulations for the studies of the proposed symmetric hybrid waveguide. However, it should also be noted that, the utilization of other methods might lead to quite different mode areas and may also affect the performance comparison results between different structures. For example, by calculating the ratio of the total mode energy and the peak energy density (i.e. $A_{eff}={\displaystyle \iint W(r)dA}/\max (W(r))$) [13], the corresponding mode area is typically much smaller than that obtained using the statistical measure. Moreover, since this method heavily depends on the local field enhancement in the waveguide, the resultant mode area of the proposed symmetric hybrid waveguide might be further reduced due to the existence of the metallic nanoridge with sharp corners, whereas for their conventional hybrid plasmonic counterparts, the local enhancement is not so significant in absence of the metallic corners. This might lead to even better optical performance over the conventional hybrid structure, which has already been verified in our previous studies [65, 72, 73]. Due to the fact that the tip radius of the metal corner predominantly affects the value of the calculated mode area, this method is also quite sensitive to the geometry of the structure and the mesh near sharp corners during the simulations. In addition, the ratio of the total mode energy and the peak energy density cannot accurately reflect the true spatial extent of the considered mode. Therefore, in this respect, the statistical measure might be a better choice for the gauging of the mode confinement, which not only capable of reflecting the extent of a mode's field distribution but also leads to more consistent and stable results [48, 71]. On the other hand, in order to clearly reveal the relative energy confinement of the waveguide while also irrespective of the geometry of the structure, the definition of the area that contains a specific portion of the total modal energy could be a more reliable measure of the mode area than the aforementioned two methods [74].

The discussions in the previous sections of this paper have considered some of the practical issues related to the proposed slot-based symmetric hybrid waveguide, such as the slope of the silicon rails and the partial metallic filling effects on the guided mode properties. However, some other issues are also ignored during these investigations. One of them is the scattering loss of the silicon sidewalls during the etching process for the implementation of the slot configuration, which may increase the propagation losses of the guided plasmonic modes. The effect of the tip radius of the metal corner on the modal characteristics is another issue that needs to be considered. In a word, the tolerance of the symmetric hybrid waveguide against possible fabrication imperfections requires further investigations in future study.

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] but with narrower metal stripes or other similar metallic structures, a horizontal-type symmetric hybrid plasmonic waveguiding configuration can be formed [Fig. 8(b)]. 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, 73] [Figs. 8(e)-8(h)], and coaxial type-structures consisting of metallic nanowires with rectangular [49], circular [46, 75] or other similar cross-sectional shapes surrounded by dielectrics [Figs. 8(i)-8(j)]. Similar to the previously studied symmetric waveguiding schemes [59, 65], the symmetric hybrid modes supported by these structures could also have extremely low propagation losses in conjunction with subwavelength mode sizes.

 

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.

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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.