1. Introduction

Photonic integrated circuits (PICs) or integrated optical circuits using photons rather than electrons to perform a wide variety of optical functions, feature high operation speed compared to traditional electronic integrated circuits. Recent advances in the density and complexity of PICs have facilitated possible integration of complete optical communication systems on a monolithic chip [1]. PICs offer an attractive solution to enable chip-scale optical interconnects and optical signal processing with relaxed latency, wide bandwidth, and high resistance to electromagnetic interferences [2–5]. In recent years, silicon photonics has become one of the most promising photonic integration platforms owing to its small footprint, low power consumption, compactness for high-density integration, and complementary metal-oxide-semiconductor (CMOS) compatible platforms for low-cost mass production [6]. Various active and passive silicon photonic devices have been reported such as lasers, modulators, (de)multiplexers and detectors [7–12]. Typical silicon photonic structures include waveguides, gratings, couplers, microring resonators, Mach-Zehnder interferometers, multi-mode interferometers, and photonic crystal nanocavities [11–13]. Among these structures, silicon waveguides are regarded as the building blocks for advanced silicon photonic devices [13]. There are several kinds of silicon waveguide structures, e.g. strip/channel waveguide, ridge/rib waveguide, hybrid plasmonic waveguide, photonic crystal waveguide, slot waveguide and subwavelength grating (SWG) waveguide. The most standard waveguides used for silicon photonics are strip waveguide and ridge waveguide, in which the light is mainly concentrated within the high-refractive-index silicon region based on the principle of total internal reflection. In addition to strip and ridge waveguides, a silicon platform, owing to its high refractive index, also enables some other novel types of waveguides replying on different guiding mechanisms, such as hybrid plasmonic waveguide, photonic crystal waveguide, slot waveguide and SWG waveguide. In the hybrid plasmonic waveguide [14–18], the guided mode based on the surface science [19], is a kind of surface enhanced supermode formed by the combined contributions from the surface plasmon polariton mode and the discontinuity of electric field at the dielectric interface, also known from the coupling between in-phase surface plasmon polariton mode and dielectric mode in the silicon. In the photonic crystal waveguide, the mode guiding mechanism is based on the photonic-crystal effect or complete photonic bandgap, i.e. the light is confined in the channel waveguide surrounded with photonic-crystal region [13].

Slot waveguide, a new type of waveguide that can confine light in a low-refractive-index region, is also based on the surface science. The slot waveguide structure is formed by a low-refractive-index submicrometer slot region (SiO₂ or air) embedded between two high-refractive-index silicon waveguides [20,21]. Due to the high refractive index contrast, modes with high intensity field at the two interfaces of the slot are formed. The overlap of the evanescent tail of the modes in the central slot leads to a greatly enhanced tight light confinement in the low-refractive-index slot region, which is also a kind of surface enhanced supermode. In contrast to the photonic crystal waveguide, the highly confined modes in the slot region are true eigenmodes and are therefore theoretically lossless, provided that these are no scattering points along the structures. Considering the tight light confinement in the SiO₂ or air slot region which has relatively lower nonlinearity compared to silicon, the slot waveguide with SiO₂ or air slot region features reduced nonlinearity and facilitates chip-scale optical interconnects. We previously demonstrated chip-scale terabit data transmission in silicon vertical slot waveguides [22]. When filling liquids into the air slot region, the slot waveguide ring resonators can be used for sensing applications with enhance sensitivity [23,24]. Additionally, when the slot region is filled with high nonlinear materials, the tightly confined light in the nano-scale slot with reduced mode area and enhanced nonlinearity, make silicon slot waveguide also suitable for efficient nonlinear optical signal processing [4,25–29].

SWG waveguide, another new type of waveguide that consists of a periodic arrangement of high and low refractive index material segments with a pitch less than one wavelength, excites a Bloch mode [30]. The subwavelength periodic structures frustrate diffraction and behave like a homogeneous medium (metamaterial). The Bloch mode can propagate through the segmented waveguide theoretically without losses caused by diffraction into radiative or cladding modes. The SWG waveguide shows unique advantages of low propagation loss, broad bandwidth and high coupling efficiency [30–32]. These brilliant peculiarities have enabled lots of SWG-based integrated devices such as couplers [32,33], microring resonators [34], true time delay line [35], polarization splitter-rotator [36], and polarizer [37]. The Bloch mode, a kind of steady-state SWG mode transmitted in the SWG waveguide, is delocalized from the silicon core, resulting in the reduced nonlinearity for chip-scale terabit data transmission in a silicon SWG waveguide [38].

Remarkably, both slot waveguide guiding slot mode and SWG waveguide guiding SWG mode delocalize most or part of mode from the silicon region. These lead to reduced nonlinearity when using SiO₂ or air as the low-refractive-index material to form the slot waveguide and SWG waveguide. To further reduce the nonlinearity, one might consider to combine the advantages of slot waveguide and SWG waveguide. In this scenario, a valuable approach would be to borrow the guiding mechanisms of both slot waveguide and SWG waveguide and form a new type waveguide with much reduced nonlinearity by further delocalizing the mode from the silicon.

In this paper, we present a subwavelength grating slot (SWGS) waveguide on silicon platform. The mode guiding mechanism (SWG slot mode) is based on the combination of surface enhanced supermode (slot mode) in a slot waveguide and Bloch mode (SWG mode) in an SWG waveguide. We study the mode properties of the SWGS waveguide, especially the greatly reduced nonlinearity when using SiO₂ and air as the low-refractive-index material. We compare in detail the nonlinearity of the SWGS waveguide with those of the strip waveguide, slot waveguide and SWG waveguide. We also optimize the SWGS waveguide with further reduced nonlinearity. Moreover, we design two types of mode converters from strip mode to slot mode and finally to SWG slot mode. The mode evolution process and mode conversion efficiency are evaluated showing favorable performance.

2. Concept of subwavelength grating slot (SWGS) waveguide

Figure 1(a) depicts a silicon-on-insulator (SOI) wafer to form various silicon waveguides. The SOI wafer considered here has a 340-nm top silicon layer and a 2-μm SiO₂ buried oxide (BOX). Shown in Figs. 1(b)-(d) are top view structures of already existing silicon-based strip waveguide, slot waveguide and SWG waveguide, respectively. Figure 1(e) depicts the top view structure of the proposed SWGS waveguide. The corresponding 3D structure is illustrated in Fig. 1(f). The silicon-based strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide employ SiO₂/air as the cladding. The SWGS waveguide borrows the idea from both slot waveguide and SWG waveguide. The mode guiding mechanism, i.e. SWGS mode, can be understood as the combination of surface enhanced supermode and Bloch mode. The high refractive index contrast and resultant electric field discontinuity at the slot boundaries (silicon-SiO₂/air) and narrow slot region lead to the surface enhanced supermode. The periodic structure of silicon-SiO₂/air with subwavelength periodicity leads to the Bloch mode. Compared to the slot waveguide with a small part of light left in the silicon region, the SWGS waveguide with periodic structure further delocalizes almost half of the residual light from silicon to SiO₂/air. Compared to the SWG waveguide with a small part of light left in the silicon region, the SWGS waveguide further delocalizes the light from the silicon and concentrate it into SiO₂/air slot region. Hence, it is expected that the proposed SWGS waveguide features greatly reduced nonlinearity due to tightly confined SWGS mode in the SiO₂/air slot region and less residual light in the silicon region.

 

Fig. 1 (a) Illustration of a silicon-on-insulator (SOI) wafer to form various silicon waveguides. (b)-(e) Top view structures of silicon-based (b) strip waveguide, (c) slot waveguide, (d) subwavelength grating (SWG) waveguide, and (e) subwavelength grating slot (SWGS) waveguide. (f) 3D structure of a SWGS waveguide.

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In the following studies, we compare the properties of four kinds of silicon waveguides, i.e. strip waveguide, slot waveguide, SWG waveguide and the proposed SWGS waveguide. SiO₂ and air are considered as the cladding. To give a relatively fair comparison, we choose the same silicon height of 340 nm (fully etched silicon layer). The slot width of slot waveguide and SWGS waveguide is set to 100 nm. The period and duty cycle (ratio of silicon block to the period) of SWG and SWGS waveguide is set to 200 nm and 50%, respectively. In the case of SiO₂ cladding, the silicon width of four kinds of silicon-based waveguide is set to 300 nm (each silicon side of slot waveguide and SWGS waveguide). In the case of air cladding, the silicon width of strip waveguide, slot waveguide and SWGS waveguide is set to 400 nm. Note that the SWG waveguide with air cladding is not considered due to its large extra confinement loss and resultant lossy propagation. Table 1 lists the typical geometric parameters of four kinds of silicon waveguides. TE polarization is considered for strip mode, slot mode, SWG mode and SWGS mode guided in the four kinds of silicon waveguides.

Table 1. Typical waveguide geometries, cladding materials and other simulation parameters

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3. Mode properties of SWGS waveguides

The mode properties of SWGS waveguides are analyzed by using the three-dimensional (3D) finite-difference time-domain (FDTD) method. We compare the mode profiles and normalized intensities along the x direction of the silicon-based strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide with SiO₂ cladding, as shown in Fig. 2. One can clearly see distinct mode features in four kinds of silicon waveguides. In a strip waveguide, as shown in Fig. 2(a), the strip mode is mainly confined in the silicon strip region. In a slot waveguide, as shown in Fig. 2(b), the slot mode is tightly confined within the narrow SiO₂ slot region with a small part of light left in the silicon region. In an SWG waveguide, as shown in Fig. 2(c) (Si segment) and 2(d) (SiO₂ segment), the SWG mode (Bloch mode) is delocalized from the silicon region, i.e. only a small part of light is left in the silicon region. In an SWGS waveguide, as shown in Fig. 2(e) (Si segment) and 2(f) (SiO₂ segment), the SWGS mode is further delocalized from the silicon region and concentrated into the SiO₂ slot region, i.e. the residual light left in the silicon region is further reduced.

 

Fig. 2 Mode profiles and normalized intensities along the x direction of the guided and propagated fundamental TE mode in (a) strip waveguide, (b) slot waveguide, (c)(d) SWG waveguide, and (e)(f) SWGS waveguide with SiO₂ cladding. (c)(e) Si segment. (d)(f) SiO₂ segment.

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We calculate the effective refractive index (n_eff) of four kinds of silicon waveguides with SiO₂ cladding. For the silicon-based SWG and SWGS waveguides with periodic structures along the propagation, the effective refractive index is calculated using the 3D FDTD method. To guarantee the calculation accuracy, we investigate the effective refractive index of the SWGS waveguide with SiO₂ cladding as a function of the mesh resolution (mesh size) at 1550 nm. As shown in Fig. 3(a), the calculated effective refractive index keeps almost unchanged when the mesh resolution is less than 30 nm. In the 3D FDTD simulations, the mesh resolution is set as 20 nm to ensure a high calculation accuracy and reliable results. Figure 3(b) shows effective refractive index as a function of wavelength for four kinds of silicon waveguides with SiO₂ cladding. The effective refractive index of strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide at 1550 nm is calculated to be 2.260, 2.225, 1.514 and 1.663, respectively.

 

Fig. 3 (a) Calculated effective refractive index of SWGS waveguide with SiO₂ cladding at 1550 nm versus mesh resolution. (b) Calculated effective refractive index of strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide with SiO₂ cladding versus wavelength. The mesh resolution is set as 20 nm.

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4. Nonlinearity of SWGS waveguides

The proposed SWGS waveguide greatly delocalizes the SWGS mode from the silicon region, holding the potential to effectively reduce the nonlinearity with SiO₂/air cladding. We study the nonlinearity of the SWGS waveguide and compare it with the strip waveguide, slot waveguide and SWG waveguide. In the calculations, the nonlinear refractive indices n₂ used for silicon and SiO₂ are 4.5 × 10⁻¹⁸ and 2.6 × 10⁻²⁰ m²/W [39], respectively. Remarkably, the efficient nonlinear coefficient, $\gamma$, depends on both mode size and confinement factor in the nonlinear guiding material [40,41]. Hence, a full-vector model that can weigh the contributions of different materials to the nonlinear coefficient is considered to achieve accurate results [42]. Using given geometric parameters and material parameters, one can calculate the effective nonlinear coefficient of the waveguide.

The effective mode area $A_{eff}$ is written by [42]

Figure 4(a) shows calculated effective nonlinear coefficient as a function of the wavelength for strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide with SiO₂ cladding. The silicon width (each side of slot waveguide and SWGS waveguide), slot width, period and duty cycle are 300 nm, 100 nm, 200 nm and 50%, respectively. One can see that the nonlinearity slightly decreases with the increase of wavelength. The lowest nonlinearity of strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide, at a wavelength of 1650 nm, is about 166.80, 55.98, 21.28 and 11.60 /W/m, respectively. As expected the SWGS waveguide with more light delocalized from the silicon region features lower nonlinearity.

 

Fig. 4 Calculated effective nonlinear coefficients of strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide with (a) SiO₂ and (b) air cladding versus wavelength.

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Figure 4(b) shows calculated effective nonlinear coefficient as a function of the wavelength for strip waveguide, slot waveguide and SWGS waveguide with air cladding. The silicon width (each side of slot waveguide and SWGS waveguide), slot width, period and duty cycle are 400 nm, 100 nm, 200 nm and 50%, respectively. The nonlinearity slightly decreases when increasing the wavelength, which is similar to the trend with SiO₂ cladding. The lowest nonlinearity at 1565 nm is about 194.82, 83.79 and 3.67 /W/m for strip waveguide, slot waveguide and SWGS waveguide, respectively. It is clearly shown that the SWGS waveguide has lower nonlinearity. Moreover, the SWGS waveguide with air cladding can further reduce the nonlinearity to an even lower value compared to that with SiO₂ cladding.

We then optimize the proposed SWGS waveguide with SiO₂ cladding as an example. The silicon height of 340 nm is kept unchanged. The waveguide design might be optimized by analyzing the dispersion relation of each unit cell [43,44]. We simply use 3D FDTD method to optimize the SWGS waveguide with further reduced nonlinearity. One can directly use the full-vector model to calculate effective nonlinearity and find the optimized one by scanning the waveguide geometric parameters (silicon width, slot width, period and duty cycle). The full-vector model based on Eqs. (1)-(3) can achieve accurate results, which however, spends relatively long computation time. Remarkably, the effective nonlinearity of the waveguide is highly dependent on the mode confinement factor in the nonlinear material (i.e. silicon). In other words, the less the mode confined in the nonlinear material, the lower the effective nonlinearity achieved. The mode confinement factor in the nonlinear material has similar trend to the effective nonlinearity. For the SWG and SWGS waveguides, it is easy to understand that smaller duty cycle also leads to lower effective nonlinearity. Consequently, we define two parameters for easy waveguide optimization. One is the mode confinement factor (Γ) defined by the ratio of power in silicon region to total power in guiding region expressed as

In addition to Tab. 1, we also compare the strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide with equal waveguide cross-section dimensions, i.e. the silicon width of the strip waveguide and SWG waveguide is set to 700 nm, which is equal to the sum of twice the silicon width (300 nm) and slot width (100 nm) of the slot waveguide and SWGS waveguide. Other waveguide geometric parameters are silicon height of 340 nm (strip, slot, SWG, SWGS), slot width of 100 nm (slot, SWGS), period of 200 nm (SWG, SWGS) and duty of 50% (SWG, SWGS). SiO₂ cladding is considered. As listed in Tab. 2, one can clearly see that the SWGS waveguide features the lowest mode confinement factor, resulting in the lowest effective nonlinearity.

Table 2. Calculated mode confinement factor for strip, slot, SWG and SWGS waveguides with equal waveguide cross-section dimensions.

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Figure 5(a) shows mode confinement factor as a function of the silicon width for SWGS waveguide with slot width of 100 nm, period of 200 nm and duty cycle of 50%. The mode confinement factor increases with the silicon width. Figure 5(b) shows mode confinement factor as a function of the slot width for SWGS waveguide with silicon width of 300 nm, period of 200 nm and duty cycle of 50%. The mode confinement factor decreases with the increase of slot width. Figure 5(c) shows mode confinement factor as a function of the period for SWGS waveguide with silicon width of 300 nm, slot width of 100 nm and duty cycle of 50%. The mode confinement factor keeps almost unchanged when varying the period. Figures 5(d) and 5(e) respectively show mode confinement factor and evaluation factor as a function of the duty cycle for SWGS waveguide with silicon width of 300 nm, slot width of 100 nm and period of 200 nm. Both mode confinement factor and evaluation factor increase with the duty cycle.

 

Fig. 5 (a)-(c) Calculated mode confinement factor Γ versus (a) silicon width, (b) slot width, and (c) period. (d)(e) Calculated (d) mode confinement factor Γ and (e) evaluation factor EF versus duty cycle. (a) slot width: 100 nm, period: 200 nm, duty cycle: 50%. (b) silicon width: 300 nm, period: 200 nm, duty cycle: 50%. (c) silicon width: 300 nm, slot width: 100 nm, duty cycle: 50%. (d)(e) silicon width: 300 nm, slot width: 100 nm, period: 200 nm.

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From Figs. 5(a)-5(e), one can clearly see that the mode confinement factor and evaluation factor and resultant effective nonlinearity can be reduced by appropriately reducing the silicon width, increasing the slot width, and reducing the duty cycle. However, greatly reducing the nonlinearity might cause extra loss. In order to achieve optimized waveguide design with greatly reduced nonlinearity while negligible extra loss, we choose the slot width of 150 nm, period of 200 nm, duty cycle of 30% and vary the silicon width from 250 to 350 nm. As shown in Fig. 6, one can clearly see that mode confinement factor reduces when reducing the silicon width. However, an extra loss is introduced when reducing the silicon width below 300 nm. Hence, we choose the silicon width of 300 nm, slot width of 150 nm, period of 200 nm and duty cycle of 30% as optimized waveguide geometric parameters.

 

Fig. 6 Calculated mode confinement factor Γ and extra loss versus silicon width (slot width: 150 nm, period: 200 nm, duty cycle: 30%).

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Using the optimized waveguide geometries (silicon width: 300 nm, slot width: 150 nm, period: 200 nm, duty cycle: 30%), we calculate the effective nonlinearity as a function of the wavelength. Uniform mesh size of 20 nm is used in the 3D FDTD calculation to be consistent with the results shown in Fig. 4. As shown in Fig. 7, an ultralow nonlinearity of 3.20 /W/m can be achieved at 1650 nm for the SWGS waveguide with SiO₂ cladding.

 

Fig. 7 Calculated effective nonlinearity of SWGS waveguide with SiO₂ cladding versus wavelength using optimized waveguide geometric parameters (silicon width: 300 nm, slot width: 150 nm, period: 200 nm, duty cycle: 30%).

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5. Compatible mode converters from strip to SWGS waveguide

In general, silicon-based strip waveguides are widely used, especially at the input and output ports of photonic integrated circuits. To incorporate the proposed SWGS waveguide in practical designs, another great challenge of compatible mode converter from strip to SWGS waveguide has to be considered. Remarkably, there exists significant mode mismatching between the strip waveguide and SWGS waveguide, resulting in huge coupling loss and limited performance when directly connecting the strip and SWGS waveguides. Here we propose two types of compatible converters which can smoothly connect the SWGS waveguide to the strip waveguide with broadband high conversion efficiency.

Figure 8 depicts different types of compatible mode converters from strip to slot, strip to SWG and strip to SWGS waveguides. Shown in Fig. 8(a) is the direct strip waveguide propagation with unchanged strip mode. Shown in Fig. 8(b) is the strip-to-slot mode converter with the guided mode gradually evolved from the strip mode (mainly in silicon region) to slot mode (mainly in SiO₂/air slot region) [45]. Shown in Fig. 8(c) is the strip-to-SWG mode converter with the guided mode gradually evolved from the strip mode (mainly in the silicon region) to SWG/Bloch mode (delocalized from the silicon region). The strip-to-SWG mode converter is designed with suitable triangle region length of 15 μm to enable low-level insertion losses of less than 0.01 dB over the wavelength range from 1490 to 1620 nm [32]. Shown in Fig. 8(d) and 8(e) are two types of strip-to-SWGS mode converters. The corresponding 3D structures are illustrated in Fig. 8(f) and 8(g), respectively. Both of the two types of strip-to-SWGS mode converters consist of two parts, i.e. part I of strip-to-slot mode converter and part II of strip-to-SWG mode converters. The type 1 and type 2 strip-to-SWGS mode converters employ different strip-to-slot converters, with type 1 based on the structure in Fig. 8(b) and type 2 based on an SWG multimode waveguide [46]. The guided mode in two types of strip-to-SWGS mode converters gradually evolves from input strip mode to slot mode and finally to output SWGS mode.

 

Fig. 8 (a)-(e) Top view structures and mode evolutions of (a) strip waveguide propagation, (b) strip-to-slot mode converter, (c) strip-to-SWG mode converter, and (d)(e) two types of strip-to-SWGS mode converters. (f)(g) 3D structures of two types of strip-to-SWGS mode converters. Both two types of strip-to-SWGS mode converters consist of two parts, i.e. part I of strip-to-slot mode converter and part II of strip-to-SWG mode converter. (d)(f) The strip-to-slot mode converter is based on (b). (e)(g) The strip-to-slot mode converter employs an SWG multimode waveguide.

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We further evaluate the operation performance of the proposed two types of strip-to-SWGS mode converters. Figure 9 shows simulated results of the type 1 strip-to-SWGS mode converter. Silicon width of 300 nm, slot width of 100 nm, period of 200 nm and duty cycle of 50% for the SWGS waveguide and a 1-μm thick SiO₂ upper cladding layer are considered. Shown in Fig. 9(a) clearly indicates the mode evolution from input strip mode to middle slot mode by part I converter and then from slot mode to finally output SWGS mode by part II converter. The mode profiles in Si segment and SiO₂ segment of propagated SWGS mode are also given. The part I of strip-to-slot converter is based on a method by tapering the strip waveguide and inserting it into the slot waveguide to convert the optical field distribution adiabatically [45]. Figure 9(b) depicts the mode evolution process when passing through the part I of strip-to-slot converter and part II of strip-to-SWG converter. Within the mode coupling region, the effective refractive indices of TE modes for both strip waveguide and slot waveguide at 1550 nm as a function of the width of the central silicon region are plotted in Fig. 9(c). The cross point, matching the effective refractive indices of these two modes, gives a suitable width (~236 nm) of central silicon region in the middle of the taper. Near the wavelength of 1550 nm, the coupling efficiency of part I is larger than 99.7%. The length of the part I converter is 15 μm. The total conversion efficiency of the type 1 strip-to-SWGS mode converter as a function of the wavelength is shown in Fig. 9(d). The overall conversion efficiency is about 99% at 1550 nm. Within a broadband wavelength range from 1450 nm to 1650 nm, the conversion efficiency from input strip mode to output SWGS mode keeps higher than 98%. From 1450 to 1850 nm the conversion efficiency varies slightly from 94% to 99%.

 

Fig. 9 Simulated results of the type 1 strip-to-SWGS mode converter. (a) 3D structure of type 1 strip-to-SWGS mode converter and mode evolution from input strip mode to middle slot mode by part I converter and then from slot mode to finally output SWGS mode by part II converter. (b) Mode evolution process when passing through the part I of strip-to-slot converter and part II of strip-to-SWG converter. (c) Effective refractive indices of strip waveguide TE mode and slot waveguide TE mode versus width of central silicon region. (d) Total conversion efficiency of the type 1 strip-to-SWGS mode converter versus wavelength.

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Figure 10 shows simulated results of the type 2 strip-to-SWGS mode converter. Silicon width of 400 nm, slot width of 100 nm, period of 200 nm and duty cycle of 50% for the SWGS waveguide and air upper cladding layer are considered. Figure 10(a) depicts the mode evolution from input strip mode to middle slot mode by part I converter and then from slot mode to finally output SWGS mode by part II converter. The mode profiles in Si segment and air segment of propagated SWGS mode are also shown. The part I of strip-to-slot converter is based on a taper-integrated SWG multimode waveguide connecting the input strip waveguide and output slot waveguide [46]. The maximum width of the SWG multimode waveguide is set as 2 μm. Figure 10(b) depicts the mode evolution process when passing through the part I of strip-to-slot converter and part II of strip-to-SWG converter. The conversion efficiency of strip-to-slot mode converter (part I) as a function of the number of 2-μm wide SWG multimode blocks is shown in Fig. 10(c). A high conversion efficiency is still available even under a small number of SWG multimode blocks. In the simulations, the number of SWG multimode blocks is chosen to be 3 and the conversion efficiency is about 90.9%. The length of the part I converter is only 3.3 μm. The total conversion efficiency of the type 2 strip-to-SWGS mode converter as a function of the wavelength is shown in Fig. 10(d). The overall conversion efficiency slightly varies between 88% and 91% within a broadband wavelength range from 1450 nm to 1650 nm.

 

Fig. 10 Simulated results of the type 2 strip-to-SWGS mode converter. (a) 3D structure of type 2 strip-to-SWGS mode converter and mode evolution from input strip mode to middle slot mode by part I converter and then from slot mode to finally output SWGS mode by part II converter. (b) Mode evolution process when passing through the part I of strip-to-slot converter and part II of strip-to-SWG converter. (c) Conversion efficiency of strip-to-slot mode converter (part I) versus number of 2-μm wide SWG multimode blocks. (d) Total conversion efficiency of the type 2 strip-to-SWGS mode converter versus wavelength.

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6. Discussion

The obtained results shown in Figs. 2-10 indicate the implementation of a new type of waveguide, i.e. SWGS waveguide. One distinct feature of the presented SWGS waveguide is its further mode delocalization from the silicon region. Consequently, when employing the low-refractive-index material with low nonlinearity as the cladding, the SWGS waveguide has the potential to greatly reduce the nonlinearity, which may find wide applications in chip-to-chip and on-chip optical interconnects. In addition to the SiO₂ cladding and air cladding, other low-refractive-index materials with low nonlinearity could be also adopted such as SU-8 polymer. There exists a trade-off between the reduced nonlinearity and extra loss. When reducing the nonlinearity to a large extent, an extra loss might be introduced. Moderate reduction of nonlinearity together with negligible extra loss could be achieved via the optimization of waveguide geometric parameters.

Besides the low nonlinearity for chip-scale data transmission, due to the feature of broadband tight light concentration, the proposed SWGS waveguide with air cladding might be also used in sensing applications. The etched region could be filled with CO₂, CH₄ and other gases as well as H₂O, NaCl solution and other liquids. When filled with different gases, the light passing through the SWGS waveguide might show different absorption curves. When filled with different liquids, the combination of SWGS waveguide and microring resonator might offer the possibility of achieving high sensing sensitivity.

Beyond chip-scale optical interconnects and chip-scale optical sensing, the SWGS waveguide might be further applied to nonlinear optical signal processing when employing low-refractive-index materials with high nonlinearity as cladding, such as silicon nanocrystal (Si-nc or Si-rich), PTS [polymer poly (bis para-toluene sulfonate) of 2, 4-hexadiyne-1, 6 diol] and other organic materials.

For the two types of strip-to-SWGS mode converters, the type 1 features broadband and ultrahigh conversion efficiency but with relatively large size. In contrast, the type 2 shows ultra-compact structure but pays penalty of slightly reduced conversion efficiency.

The proposed SWGS waveguide could be fabricated on an SOI wafer based on the well-established techniques on silicon platform, i.e. electron beam lithography (EBL) followed by inductively coupled plasma (ICP) etching. The EBL defines the device pattern and the ICP transfers the device pattern into the silicon layer of the SOI wafer. For the SWGS waveguide with SiO₂ cladding, after the ICP etching process, a silicon dioxide layer is deposited onto the wafer to encapsulate the silicon waveguide. The SWGS waveguide borrows ideas and advantages of slot waveguide and SWG waveguide. Remarkably, both slot waveguide and SWG waveguide have been successfully fabricated on silicon platform [21,30]. Hence, we believe the proposed SWGS waveguide could be fabricated based on existing mature techniques.

7. Conclusion

In summary, we design a novel SWGS waveguide formed by a slot structure and an SWG structure. It borrows ideas from the slot waveguide and SWG waveguide. The guided mode, i.e. SWG slot mode, can be understood as the combined surface enhanced supermode (slot mode) in a slot waveguide and Bloch mode (SWG mode) in an SWG waveguide. We study in detail the mode properties, effective refractive indices and effective nonlinear coefficients of four kinds of silicon waveguides, i.e. strip waveguide, slot waveguide, SWG waveguide and SWGS waveguide. The presented SWGS waveguide with SiO₂/air cladding shows distinct feature of significantly reduced nonlinearity due to the great delocalization of light from the silicon region. We use mode confinement factor and evaluation factor to optimize the SWGS waveguide by scanning the waveguide geometric parameters (silicon width, slot width, period and duty cycle). An ultralow nonlinearity of 3.20 /W/m is achieved. Additionally, we propose and simulate two types of compatible mode converters from strip mode to SWGS mode. Favorable operation performance with broadband high conversion efficiency is achieved. The obtained results of the designed SWGS waveguide with low nonlinearity imply possible applications in chip-to-chip and on-chip optical interconnects. With future improvement, 1) by filling the gases or liquids as the cladding, the SWGS waveguides may find optical sensing applications; 2) by employing low-refractive-index nonlinear materials as the cladding, the SWGS waveguide may find nonlinear optical signal processing applications.