1. Introduction

Photonic integrated circuits (PICs) represent a key topic to overpass the frequency limits of the current microelectronics technologies and keep the pace of Moore’s law [1–4]. Research in the field of PICs is taking a boost, especially because of its compatibility with the modern complementary metal-oxide semiconductor (CMOS) fabrication techniques utilizing materials such as silicon (Si) and silicon dioxide (SiO₂) [5,6]. PICs have great potentialities for prevalent use in inter- and intra-chip information communication applications [7–9] as well as in sensing [10–12]. PICs are akin to integrated electronic circuits, but in place of electronic elements, they involve optical components including optical sources, optical amplifiers, optical multiplexers and demultiplexers, and optical detectors, on a single integrated platform [1,8]. Doing extensive numerical simulations on the photonic component design before fabricating the final prototype essentially saves resources.

Optical waveguides are one of the fundamental elements in PICs [13–15]. They have the capability to transfer optical energy and signals from one optical component to another. Over the past decade, a novel waveguide approach based on silicon-on-insulator (SOI) slot waveguides has been proceeded and experimentally demonstrated to be very amenable to integration applications [16], such as electro-optical modulators [17], lasers [18], sensors [19,20], optical amplifiers [21], optical splitters [22,23], optical phase shifters [24], optical tweezers [25,26], supercontinuum sources [27], dispersion compensators [28], and so on. Followed by the first exploration of confining and guiding light within a nanometer-wide slot in 2004 [29,30], exhaustive theoretical and experimental works have been done with different designs. A slot waveguide is a kind of optical waveguides which extremely guides compact light in a low refractive index domain with subwavelength-scale via the total internal reflection. Usually, a slot waveguide is composed of two slabs or rails with high refractive index materials which are separated by a slot domain with low refractive index and subwavelength-scale, and enclosed with the low refractive index cladding materials (or surrounding materials) [14,15]. The vertical single-slot waveguide and the horizontal single-slot waveguide are two fundamental configurations. Vertical slot waveguides can well guide quasi-TE modes while quasi-TM modes can be well-guided in horizontal slot waveguides [31]. Although slot waveguides are well studied, their specific performances are influenced by numerous decisive parameters, such as morphology, operating wavelength, material properties, etc. Optimization of slot waveguides requires the basic conditions of light confinement to be achieved, light enhancement to be optimized, and single mode condition to be fulfilled, before dealing with further steps for optical communication [32–34].

Photonic crystal (PhC) devices are periodic optical nanostructures with periodicities in refractive indices [35]. Among them, the two-dimensional PhC incorporates most of the extraordinary optical properties with available and accessible fabrication means and thus has a more widespread research value [36]. They have been thoroughly inspected, both theoretically and experimentally. For example, photonic crystal fibers, first explored in 1996 at the University of Bath [37,38], are widely used in nonlinear and sensing devices and are designed to guide exotic wavelengths [39]. In the case of PICs, the design and fabrication of low propagation loss and large light confinement of optical waveguides have been readily proposed [40]. On the other hand, the use of other materials, such as gold, sapphire, titanium nitride, aluminum nitride (AlN), and silicon nitride (Si₃N₄), has been proposed for the design of optical waveguides with the ability to confine and enhance near-field modes [12]. Fu et al. demonstrated the realization of nanoscale integrated all-optical logic gates using plasmonic gold slot waveguides, hinging on the linear interference between surface plasmon polariton modes [41]. Li et al. investigated the dispersion features of slot waveguides based on AIN and SiO₂ over a wide spectral range from near-infrared to mid-infrared [42]. Other notable waveguides works with different materials include reports of the optical trapping of nanoparticles and biomolecules in Si slot waveguides [25] and in Si₃N₄ one-dimensional PhC resonators [43], ultrafast all-optical switching in horizontal Si slot waveguides at telecom wavelength [44], mid-infrared gas sensors by using silicon-on-sapphire waveguides [20], and on-chip optical amplification by using Si slot waveguides filled with erbium-doped polymers [45].

In this paper, the main objective is to explore the design of slot waveguides to achieve high light field enhancements in slot regions in the C band (1550 nm wavelength in this case), which is of special benefit for near-field optical communication. Four different configurations of slot waveguides are designed and analyzed, including conventional vertical silicon-on-insulator slot waveguides, slot waveguides using aluminum nitride, gallium nitride (GaN) and silicon nitride in slot regions, slot waveguides using photonic crystal slabs with circular air holes, and horizontal slot waveguides with aluminum nitride slots. The influences of distinct geometrical parameters on their performances for the localized field enhancement and the analysis of the effective refractive index are theoretically investigated via the finite element method. The simulation shows that, with the help of periodic air holes in slabs, and by using nitrides in slot regions, the field confinement factor is significantly increased. These waveguides can be conveniently integrated into the lab-on-a-chip devices to develop optical amplification units which may have great applications in optical communication studies.

2. Design and simulation

We first investigate three types of SOI slot waveguides, including conventional vertical slot waveguides, slot waveguides using aluminum nitride or gallium nitride or silicon nitride in slot regions, and slot waveguides using photonic crystal slabs with circular air holes, for optimization of nanoscale light enhancement at the operating wavelength of 1550 nm, as shown in Fig. 1. It can be seen that the middle slot region is sandwiched between two slabs, above the substrate. The proposed slot waveguides could be fabricated using industry-standard and advanced fabrication techniques. Here, w is the width of the high-index region of the waveguide slab, g is the width of the low-index region of the waveguide slot, and h is the height of the slot waveguide. In each PhC slab [see Fig. 1(c)], N×N circular holes with diameters of d are formed in a square lattice, and the center-to-center distance between holes is p. The material used for slabs is silicon (n_Si = 3.48) [29,46], the material used for the substrate is silicon dioxide (n_SiO2 = 1.44) [29], the holes in PhC slabs are made of air (n_air = 1), and the middle slot region is made of water (n_water = 1.33), aluminum nitride (n_AlN = 2.12) [47], gallium nitride (n_GaN = 2.317) [48] or silicon nitride (n_Si3N4 = 1.996) [49]. The cladding (or surrounding) material is water (n_water = 1.33), which is typically used as a superstrate in near-field optics [50], essentially for biological applications. The origin of the coordinate system is located at the bottom center of the slot, i.e., SiO₂–water interface. In this paper, we only consider the fundamental quasi-TE mode, because for this mode, the optical field confinement in the slot region is remarkably enhanced. The reason behind the field enhancement through the low-index slot area is the discontinuity of electric fields of the quasi-TE mode in between the two high-index slab domains [29] (and is presented later).

 

Fig. 1. Schematic structure of three slot waveguides investigated: (a) vertical slot waveguide, (b) slot waveguide with AlN as slot region, and (c) slot waveguide using PhC slabs.

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We present finite element method simulations (FEM; COMSOL Multiphysics) of designed optical waveguides to emulate and optimize their behaviors. As shown in Fig. 1, we perform mode analysis on the cross section of the optical waveguide rather than modeling the complete 3D geometry. In the modeling, we examine a total simulation domain of 4 µm × 4 µm. For the purpose of designing and developing slot waveguides for different near-field applications, it is essential to evaluate characteristic values that describe the amplification confinement and thus the interaction between light and the surrounding material. One significant figure of merit of how well the guided optical mode is delimited in a specific area is the so-called field confinement factor. The field confinement factor is also called the normalized power, which is derived as the ratio of the integrated optical power only in the slot region with respect to the integrated optical power through the complete waveguide [15,29].

3. Results and discussion

We first present numerical simulations in the vertical slot waveguide with water in the slot region. The mode field profile and the corresponding normalized electric field line plot (divided by maximum value) of the slot waveguide are highlighted in Fig. 2 at w = 160 nm, h = 500 nm, g = 50 nm. As expected, the optical mode intensity is primarily observed and concentrated in the low-index slot region, which is owing to the large discontinuity in electric fields on the slot–slab interface. The three-dimensional simulation shows that the mode profile is preserved along the waveguide (results not shown here). Figure 3 plots the dependence of the normalized power and the effective mode index with respect to different parameters of slot waveguides. Figure 3(a) shows the normalized power and Fig. 3(d) plots the effective mode index as a function of the slab width from 100 nm to 500 nm at h = 500 nm, g = 50 nm and 100 nm. For g = 50 nm, the normalized power peaks at 40.7% for the slab width is 160 nm (see Fig. 2). For g = 100 nm, the normalized power peaks of 39.3% at w = 140 nm, however, for 140 nm < w < 440 nm, the light cannot be confined into the slot region. It is not the propagating mode, it is the leaky mode. When w > 440 nm, the mode turns to be propagating mode. Hence, the w range between 140 nm and 440 nm is not feasible for the slot waveguide design. For both cases, the effective mode index shows a very similar upward trend in the simulated range and they are lying in the range between 1.4 and 3, and also, n_water < n_eff < n_Si. It could be emphasized that in our simulation, the effective mode index only has the real part, and all modes are theoretically lossless. Figure 3(b) shows the normalized power and Fig. 3(e) plots the effective mode index as a function of the slot width from 10 nm to 200 nm at w = 160 nm, h = 350 nm and 500 nm. For h = 350 nm, the normalized power varies between ∼19% and ∼34% in the investigated range and peaks of 33.9% at g = 70 nm. For h = 500 nm, the normalized power peaks of 43.3% at g = 80 nm, and for g > 80 nm, the mode turns to be leaky mode. For h = 350 nm, the wider slot experiences a smaller effective mode index. For h = 500 nm, from g = 10 nm to g = 90 nm, the effective mode index decreases, and then starts to increase after g > 90 nm. Figure 3(c) shows the normalized power and Fig. 3(f) plots the effective mode index as a function of the height of slot from 250 nm to 750 nm at g = 50 nm, w = 160 nm and 300 nm. For w = 160 nm, the normalized power increases when h gets higher and peaks of 43.3% at h = 630 nm, and for h > 630 nm, the value drops, and the mode turns to be leaky. For w = 300 nm, from h = 250 nm to h = 530 nm, the normalized power remains fairly static at approximately 16%, and for h > 530 nm, the mode is not the propagating quasi-TE mode. For both cases, the effective mode index becomes larger by increasing the height of the slot (and also the waveguide), varying from 1.55 to 2.14 for w = 160 nm, and from 2.17 to 2.73 for w = 300 nm.

 

Fig. 2. (a) Mode field distribution of vertical slot waveguide with water slot, and (b) plot of normalized electric field norm through waveguide center (w = 160 nm, h = 500 nm, g = 50 nm). Scale bar: 500 nm.

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Fig. 3. Quasi-TE mode in vertical slot waveguide: normalized power in slot versus (a) width of slab, (b) width of slot, and (c) height of slot; effective mode index versus (d) width of slab, (e) width of slot, and (f) height of slot.

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It is also interesting to consider the case where the nanoscale slot is filled with a dielectric material whose refractive index lies in between water and Si. We then show numerical simulations in slot waveguides using nitrides in slot regions. Here we explore three different materials, i.e., AlN, GaN, and Si₃N₄, which are all compatible with the industry-standard fabrication processes, for example, the complementary metal-oxide-semiconductor (CMOS) technique, and hold exquisite properties for optoelectronics, microelectronics, nonlinear and on-chip applications. It has been shown that the photonic waveguides are used for high-speed communications, because they support very large signal bandwidths. In practice, the slot region can be filled with any low-index material of interest. We also notice that the slot waveguide turns to be strip waveguide where the nanoscale slot is filled with Si. Figure 4 shows the mode field profile and the corresponding normalized electric field line plot of the slot waveguide with AlN in the slot domain at w = 500 nm, h = 500 nm, g = 50 nm. For comparison, we also provide the normalized electric field plot of the slot waveguide with 100 nm AlN slot and 50 nm water slot in Fig. 4(b). The cladding material is water. Again, the optical field confinement is primarily concentrated in the narrow slot domain. It can be visualized that there are two positions where the electric fields are enhanced in the high-index slab arms. The AlN slot can maintain deep-subwavelength optical field confinement, leading to applications tailored for the strong light–matter coupling such as nanolasers [51,52]. For all materials in the slot region, the variations of the normalized power and the effective mode index as a function of the slot width have been displayed respectively in Figs. 5(a) and 5(b), for w = h = 500 nm. The width of the slot has been varied from 30 nm to 200 nm. The improvement in the mode field enhancement and the variation of the effective mode index owing to the insertion of AlN, GaN, and Si₃N₄ dielectric material in the slot could be readily visualized. It is obvious that the field confinement factor generated from the GaN filled slot waveguide is higher than that from the AlN filled slot waveguide, and then the Si₃N₄ filled slot waveguide. The reason behind this is the larger refractive index of GaN than AlN, Si₃N₄, and water at 1550 nm, which results in more confinement of light within the slot. For example, at g = 70 nm, the normalized power is 7.91% for the GaN filled slot waveguide (highest field confinement in this figure), 6.79% for the AlN filled slot waveguide, 6.07% for the Si₃N₄ filled slot waveguide, and 2.56% for the water filled slot waveguide. It can be seen that the confinement factor in the GaN filled slot waveguide (7.91%) is about three times larger in comparison with that one of the undressed slot waveguide (2.56%). In Fig. 5(b), for all cases, the effective mode index shows a gradual decrease in the simulation range. For instance, with the GaN slot widths of 50 nm and 150 nm, the index values are 3.07 and 3.00 respectively. At a fixed slot width, the index value of the GaN slot is larger than the AlN slot, then the Si₃N₄ slot, and finally, the water slot.

 

Fig. 4. (a) Mode field distribution of slot waveguide with AlN in the slot, and (b) plot of normalized electric field norm through waveguide center (w = h = 500 nm). Scale bar: 500 nm.

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Fig. 5. Quasi-TE mode in slot waveguide with different materials in the slot: (a) normalized power versus slot width, and (b) effective mode index versus slot width.

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Next, the structural dependence of PhC slabs has been analyzed. We present numerical simulations in slot waveguides using PhC slabs with circular air holes and with water in slot regions in Figs. 6–9. Based on the analysis presented before, the width and height of the slabs are set to be 500 nm to scrutinize the overall influence of the slots and hole variances with the different waveguide parameters. The slot width has been varied from 30 nm to 200 nm in this case. The mode field profile and the corresponding normalized electric field line plot are depicted in Fig. 6 at d = 30 nm, p = 60, g = 50 nm. It can be seen that the optical mode intensity is mostly confined in the middle slot area, and part of the optical mode intensity is restricted in air holes in the slab. Figure 6(b) clearly shows the discontinuities in the electric fields on Si–water and Si–air interfaces, which are owing to the discontinuities of the refractive indices. Figure 7 shows the mode field distributions of slot waveguides using PhC slabs at d = 50 nm, p = 60 nm. Figure 8 depicts the obtained normalized power for the slot and the effective mode index with respect to the slot width and with different air hole geometries, that is, circular and square air holes, at p = 60 nm, N = 7. For square air holes, four sides have a length of 30 nm, which is equal to the circular diameter (d = 30 nm). From Fig. 8, it is clear that the square hole PhC slab is providing the largest field confinement factor and the lowest effective mode index for the entire considered range of the slot width. The reason behind this is the larger air area from the total holes. For example, at g = 50 nm, the normalized power is 6.95% and the effective mode index is 2.39 for the square hole PhC slot waveguide, 6.0% and 2.51 for the circular hole PhC slot waveguide, and 3.26% and 2.96 for the conventional slot waveguide. For three structures, the normalized power decreases as the slot width between two slabs increases. It can be seen that with the square hole PhC slabs, circular hole PhC slabs, and normal Si slabs, the effective mode index respectively lies in the range of 2.32 to 2.43, 2.45 to 2.55, and 2.92 to 2.99. We next only consider the circular air holes in slabs in the simulation because that circular holes are quite easy to fabricate, unless otherwise specified. Figure 9 plots the dependence of the normalized power and the effective mode index as a function of the slot width (from 30 nm to 200 nm) and with respect to different air hole array parameters of slabs. Figure 9(a) shows the normalized power and Fig. 9(d) plots the effective mode index with variation in hole diameter d at p = 60 nm, N = 7. Figure 9(b) shows the normalized power and Fig. 9(e) plots the effective mode index with variation in hole pitch p at d = 30 nm, N = 7. Figure 9(c) shows the normalized power and Fig. 9(f) plots the effective mode index with variation in hole number N at d = 30 nm, p = 40 nm. It can be seen that the field confinement in the slot is decreased by increasing the slot width g [Fig. 9(a)–(c)], decreasing the hole pitch p [Fig. 9(b)], increasing the hole diameter d [Fig. 9(a)], and increasing the hole number N [Fig. 9(c)]. For all cases, the effective mode index shows a downward trend in the simulated range [Figs. 9(d)–(f)]. One can also see from Fig. 9 that the air holes do affect and improve the slot waveguide performance.

 

Fig. 6. (a) Mode field distribution of slot waveguide using PhC slabs, and (b) plot of normalized electric field norm through waveguide center (w = h = 500 nm, d = 30 nm, p = 60 nm). Scale bar: 500 nm.

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Fig. 7. Mode field distribution of slot waveguide using PhC slabs (w = h = 500 nm, d = 50 nm, p = 60 nm). (a) g = 50 nm, (b) g = 100 nm, and (c) g = 150 nm. Scale bar: 500 nm.

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Fig. 8. Quasi-TE mode in slot waveguide with different geometries in the slab: (a) normalized power versus slot width, and (b) effective mode index versus slot width.

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Fig. 9. Quasi-TE mode in slot waveguide using PhC slabs with circular air holes: normalized power versus slot width and with (a) hole diameter, (b) hole pitch, (c) hole number; and effective mode index versus slot width and with (d) hole diameter, (e) hole pitch, (f) hole number.

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We also study the impacts of AlN slots and PhC slabs on the slot waveguide performance. Figure 10 shows the electrical field norm distributions of the vertical slot waveguide and the slot waveguides using PhC slabs at w = h = 500 nm, g = 100 nm. The slot material is AlN and the cladding materials is water. It can be seen that the optical energy is mostly confined inside the AlN slot and the slab air holes. The periodic air holes modify the field profile in the slabs. Figure 11 shows the variation in light confinement in the slot region and the effective mode index with respect to the slot width from 30 nm to 200 nm at w = h = 500 nm. We consider four structure designs: slot waveguides with AlN in the slot and with air/water cladding, slot waveguides with AlN in the slot, water in the cladding, and using PhC slabs (d = 30 nm, N = 7, p = 40 nm and 60 nm). It could be emphasized that the normalized optical power reaches a high level for the slot width between 60 nm and 200 nm with the PhC slabs, and reaches a high level for the slot width between 30 nm and 80 nm with the normal Si slabs without air holes. From Fig. 11(a), the normalized power peaks of 16.09% (for p = 40 nm) and 11.96% (for p = 60 nm) at g = 100 nm in the slot waveguide with AlN slot and using PhC slabs, and peaks of 7.14% (for air cladding) and 6.94% (for water cladding) at g = 50 nm in the slot waveguide with AlN slot. The result distinctly shows that with air holes in the slabs, the light mode is more concentrated in the slot region. For instance, for water cladding, at AlN slot width of 150 nm, the normalized power in the PhC slab slot waveguide [blue curve in Fig. 11(a)] is 15.56%, which is about three times higher compared to that one of the slot waveguide without holes [5.14%, red curve in Fig. 11(a)]. Figure 11(b) shows that the effective mode index decreases gradually with the decrease in the slot width in all cases. However, without air holes in slab regions, the obtained refractive index values are significantly larger as compared to that one of the PhC in the slab regions. For instance, for the slot width of 100 nm, the values of the effective mode index are 3.0 (water cladding), 2.99 (air cladding), 2.58 (p = 60 nm PhC slab) and 2.53 (p = 40 nm PhC slab), respectively. A comparison of maximum optical field confinement factor of the slot for different categories in this work is listed in Table 1.

 

Fig. 10. Mode field distribution of Si slot waveguide with AlN in the slot (w = h = 500 nm): (a) vertical slot waveguide, (b) PhC slabs at d = 30 nm, p = 40 nm, N = 7, and (c) PhC slabs at d = 30 nm, p = 60 nm, N = 7. Scale bar: 500 nm.

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Fig. 11. Quasi-TE mode in slot waveguide with AlN in the slot and using PhC slabs: (a) normalized power versus slot width, and (b) effective mode index versus slot width.

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Table 1. Field Confinement Factor of Vertical Slot Waveguide

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Finally, we consider the case of a horizontal single slot waveguide with AlN in the slot and with water in the cladding in Fig. 12. In this case [see Fig. 12(a)], w is the width of the slot waveguide, g is the height of the low-index region of the waveguide slot, and h is the height of the high-index region of the waveguide slab. The fundamental quasi-TM mode field profile and the corresponding normalized electric field line plot (divided by maximum value) are thus depicted in Figs. 12(b) and 12(c) respectively at w = 400 nm, h = 200 nm, g = 100 nm. Two middle large discontinuities in the electric fields can be observed specifically at Si–AlN interfaces, and two secondary discontinuities can be observed at Si–SiO₂ and Si–water interfaces. These result from the distinction of the refractive index. Figure 11(d) shows the normalized power and the effective mode index with respect to different slot height g varying from 30 nm to 200 nm at w = 400 nm, h = 200 nm. As shown here, the slot field confinement increases significantly from 21.46% to 48.22% with the increase in the slot height, whereas, the corresponding effective mode index decreases gradually from 2.44 to 2.14 by increasing the slot height.

 

Fig. 12. Characteristics of horizontal slot waveguide with AlN in the slot: (a) schematic structure, (b) quasi-TM mode field distribution, (c) line plot of the normalized electric field through waveguide along y-axis, and (d) normalized power and effective mode index versus slot height g. The scale bar is 400 nm in (b).

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4. Conclusion

In conclusion, the structural dependence and optimized design of four categories of silicon-on-insulator slot waveguides have been designed and analyzed, based on the FEM numerical simulations of the mode field distribution, field confinement factor, and effective refractive index at telecommunication wavelength of 1550 nm. The effects of different structural parameters are optimized, such as slot width, slab width, and air hole diameter. We demonstrate that the optical field confinement factor in the slot region can be improved over three times by the insertion of dielectric material in the slot region and by the presence of photonic crystal structure in the slab, compared to the one generated by a conventional slot waveguide. Such fascinating results may be conducive to design all-optical nanoscale devices suitable for on-chip computing applications.