1. Introduction

Silicon-on-insulator (SOI) is the main material platform for realizing on-chip photonic integrated circuits (PICs) [1–4], offering two main benefits: mature CMOS-compatible fabrication technology and high refractive index contrast, which plays a significant role in enabling compact devices. However, being highly birefringent, the SOI platform causes strong polarization dependence, which is undesirable in optical-fiber networks. Hence, polarization diversity devices including polarizers, polarization beam splitters (PBSs), and polarization rotators have been proposed to overcome this problem. Of these, PBSs, which separate transverse-electric (TE) and transverse-magnetic (TM) polarizations, are the most widely used. Over the years, many types of PBSs using various splitting mechanisms [5–18] have been reported, including adiabatic mode-evolution (AME) [5,6], multimode interference (MMI) structures [7,8], photonic crystal (PhC) [9,10], grating couplers [11,12], computationally optimized metamaterials [13], and directional couplers (DC) [14–18]. To assess a PBS, we must consider various criteria including the device footprint, polarization extinction ratio (PER), insertion loss (IL), working bandwidth (BW), and fabrication complexity. Although AME-based PBSs [5,6] are long (>200 µm) because of their use of gradually evolving geometry to obtain satisfactory performance, they have offer less stringent fabrication tolerances and broadband operation. The simpler fabrication process of MMI-based PBSs [7,8] with pure rectangular waveguides without any extra design, such as subwavelength gratings (SWGs), makes them more attractive; however, the drawback is their extremely long footprint (>1000 µm), determined by the common multiple of the self-imaging lengths [19] of TE and TM modes. PhC-based [9,10] and grating-based PBSs [11,12] achieve footprints of tens of micrometers, but the former has the disadvantages of fabrication complexity and relatively large scattering loss. Recently, a PBS with an extremely small footprint (2.4 µm × 2.4 µm) was realized using freeform metamaterials, designed using computational optimization algorithms [13]. However, optimizing a desirable device is time-consuming, and a PER of ∼10 dB within a working BW of 32 nm is still limited. By contrast, DC-based PBSs [14–18] are the most popular due to their structural simplicity, relatively small footprint, satisfactory performance, and diverse designs.

In principle, DC-based PBSs separate two polarizations by satisfying the phase-matching condition for one polarization coupling to the cross port and deviating from another propagating along the through port with negligible coupling. Accordingly, DC-based PBSs can be formed by assembling various waveguide structures (e.g., silicon wire, hybrid plasmonic, multimode interference, and nano-slot waveguides), depending on priorities in terms of device size, PER, IL, BW, and fabrication complexity. Fukuda et al. [14] reported a DC-based PBS of 7 µm × 16 µm using a coupler comprising two Si wires (strips) fabricated on a SOI wafer, calculating PER_TE (PER_TM) and IL_TE (IL_TM) to be ∼15 (10) and 0.5 (0.5) dB, respectively, in the C-band-wavelength range. Guan et al. [15] proposed an asymmetric DC-based PBS with a device footprint of 1.9 µm × 3.7 µm, comprising a Si wire and a hybrid plasmonic waveguide (HPW); the PERs of both polarizations were >12 dB, operating in a 120 nm BW. Instead of using the evanescent wave coupling between a Si wire and an HPW, they adopted an MMI coupler to achieve a small device of 1.8 µm × 2.5 µm [16]; however, the obtained PER was limited to about 10 dB over a BW of 80 nm. In addition to using conventional strip waveguides, Yue et al. [17] proposed a PBS comprising two horizontally slotted [20,21] waveguides to significantly increase coupling of the TM mode and enhance polarization dependence compared with that of a PBS comprising two Si-strip waveguides [14]. The coupling length was thus significantly reduced from ∼350 to 46.7 µm, and the calculated PERs of the two polarizations were >20 dB over only an 18 nm BW [17]. A PBS fabricated on an 8-inch Si wafer with a 2 µm silicon dioxide (SiO₂) layer displayed experimental values of 16.8 and 14.1 dB for TE and TM modes, respectively [18].

SWGs [22–28] comprising an arrangement of dielectric strips with dimensions much smaller than the wavelength have recently been used to construct various silicon photonic devices, following maturation of nanoscale pattern fabrication technology over the past decades. In principle, SWGs act as homogeneous slab waveguides with equivalent material anisotropy; the refractive index tensor can be flexibly controlled to obtain the required properties. Diffraction effects are suppressed in SWG structures because of the deep subwavelength pitches. In addition to siting SWGs in the waveguide core region [25–28], Jahani and Jacob [29–31] used them in the waveguide cladding region to reduce crosstalk. Also, Xu et al. [32] reported a similar design as that of [31] but changed two strip waveguides to two SWG-based ones to build a PBS. Throughout the introduction mentioned above, the PERs or ILs all come from simulation except the results of references [26], [31], and [32] come from actual measurements. In this work, we designed a PBS comprising horizontally slotted waveguides assisted by composite subwavelength gratings (CSWGs) between the two slot waveguides. Differing from mono-material SWGs, the CSWGs in our design consist of SiO₂ layers of the same thickness as the slot layer of the slotted waveguides. With the addition of SiO₂ layers to the top of the Si strips, the fabrication process is simplified, and the device length further reduced. The proposed PBS not only significantly reduces TE mode coupling, but also effectively enhances TM mode coupling, creating extremely strong polarization dependence. Compared with the performance of a PBS comprising a purely slotted waveguide coupler (PSWC) [17], our proposed PBS achieves around 40% reduction in device length, 13 dB improvement in PER_TM, and a better working BW.

2. Mode characteristic and coupling effect of anisotropic composite subwavelength gratings

Figure 1(a) shows a 3D-schematic diagram of the proposed PBS, comprising two horizontally slotted waveguides assisted by CSWGs (four composite strips are shown here). The slot waveguide consists of a low-index SiO₂ slot layer embedded between two high-index Si layers. A 90° angled slotted waveguide with R connected to the end of a slot waveguide effectively decouples the two waveguides. The substrate and cladding are SiO₂ and air, respectively. Zoomed in views of the cross section of the input, TE output, and TM output ports are also shown in Figs. 1(b), 1(c), and 1(d), respectively.

 

Fig. 1. (a) 3D schematic diagram and zoomed in views of the (b) input, (c) TE output, and (d) TM output ports of the proposed polarization beam splitter.

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Si widths for the slot waveguides and multiple dielectric strips are W_Si and W_cl, respectively, and the heights of Si and SiO₂ in the slot waveguides with the edge-to-edge spacing s are h_Si and t_slot, respectively. The CSWG pitch is set to Λ = W_cl + g with duty cycle ρ = W_cl /Λ, where g is the gap between the strips, and Λ is set below the subwavelength regime [22]. The TE mode with a major electric component in the x-direction is guided along the through bar connected by a curved waveguide with negligible power coupling, while the TM mode with a major electric component in the y-direction is coupled by satisfying the phase-matching condition into the cross bar with a straight geometry throughout the entire propagation. In addition, two of the four dielectric strips follow the curve of the through bar of the 90° angled waveguide for performance leverage, as shown in Fig. 1(c). To ensure the proposed design could be realized experimentally, geometry sizes of the CSWGs consisting of Si strips covered with SiO₂ layers were as per those of the slot waveguides. As a result, the required fabrication steps were almost identical to those of the PSWC conventional slot waveguide coupler, making fabrication of the proposed PBS comparatively simple. The processes involved in fabricating the proposed device are shown schematically in Fig. 2. First, the patterned hard masks of the angled TE channel, straight TM channel, and CSWGs are fabricated using high resolution electron beam lithography (EBL), then the following steps are carried out:

 

Fig. 2. Schematic of the fabrication processes for the proposed PBS.

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The relative Si and SiO₂ permittivities used were n_Si = 3.480 and n_SiO2 = 1.444 [33], respectively, at wavelength λ = 1550 nm, with relevant parameters set as follows: h_Si = 150 nm; W_cl = 75 nm; g = 50 nm; ρ = 0.6; W_Si = 400 nm; s = 550 nm. Note in particular that a dielectric strip aspect ratio of 2 substantially reduces fabrication difficulty with an SOI platform. Therefore, the geometry sizes of the proposed device can be easily realized for experimentation using modern fabrication technology. Numerical results were obtained using the boundary mode analysis feature of the commercial COMSOL Multiphysics software package, based on a rigorous finite element method. To reduce field reflection from computational window, perfectly matched layers were used to effectively absorb the outgoing light power to obtain more precise simulation results. To demonstrate the merit of the proposed design, TM (L_TM) and TE (L_TE) mode coupling lengths as a function of slot thickness, t_slot, for the PSWC and our structures were obtained, as shown in Fig. 3(a). The coupling length of a coupled waveguide, which determines the PBS device length, can be calculated using L_i = π /(β_{i, sym} – β_{i, aym}), where i is TE or TM, and β_i,sym and β_i,asym are the propagation constants of the symmetrical and anti-symmetrical modes of the i mode, respectively. The L_TM displays a dramatic decrease as t_slot increases from 0 to 50 nm. On further increase in t_slot, L_TM gradually decreases due to slight variations in TM mode confinement.

 

Fig. 3. (a) Coupling lengths of TM (L_TM) and TE (L_TE) modes and (b) the coupling-length ratio L_TE / L_TM versus slot thickness t_slot for PSWC and our structure.

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Comparing coupling lengths, the PBSs comprising two Si strips [14] (with t_slot = 0 nm) and PSWC (t_slot = 50 nm) have L_TMs values of ∼137 µm and ∼35 µm, respectively. The dramatic decrease in L_TM occurs due to the stronger polarization dependence of the slotted waveguide coupler, which increases TM mode coupling strength by embedding a low-index slot layer. It can be seen that the TM mode coupling length L_TM of the proposed structure is ∼21 µm with a 40% reduction in device length of PSWC. By comparison, TE mode coupling lengths L_TE of PSWC and our structure when t_slot = 50 nm are ∼1520 and ∼387 µm, respectively. This means that TE mode power coupling of the proposed PBS to cross bar is significantly lower than that of PSWC at the TM mode’s phase matching condition. Another index, L_TE / L_TM, referred to as the coupling length ratio, as shown in Fig. 3(b) is able to predict the maximum PER_TM (defined in the next section) and minimum IL_TE of a PBS. This is because the larger value of L_TE / L_TM implies retention of more TE power in the through bar, while TM power is completely transferred to the cross bar at its phase matching condition. For the PSWC with L_TM = 35.71 µm, the maximum value of L_TE / L_TM = 10.9 occurs with t_slot = 50 nm. By contrast, the proposed PBS with L_TM = 21.56 µm achieves L_TE / L_TM = 70.5, which is much larger, at the same t_slot.

The design principles of this PBS can be explained as follows. According to the effective-medium theory (EMT) [34], which limits the grating pitch to be much smaller than the wavelength of light, the SWG regions show equivalent material anisotropy as follows:

 

Fig. 4. Field profiles of (a) TE (E_x)- and (b) TM (E_y)- symmetrical modes of the proposed PBS, and those of (c) TE- and (d) TM-symmetrical modes of the PSWC, for t_slot = 50 nm, W_Si = 400 nm, h_Si = 150 nm, W_cl = 75 nm, g = 50 nm, and s = 550 nm. At the central plane of the slot layer (i.e., y = 175 nm from the top of the substrate), the field amplitudes along the x-direction of (a) and (c) are shown in (e), and those of (b) and (d) are shown in (f).

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For the proposed PBS, we also observe that TE field suppression (the downward arrow in Fig. 4(e)) results in weak mode coupling. In contrast, field enhancement (the upward arrow in Fig. 4(f)) of the TM field profile shows strong mode coupling. Overall, according to the index of L_TE / L_TM shown in Figs. 3(b) and the mode profiles shown in Fig. 4, introduction of the CSWGs significantly reduces device length and increases the PER_TM, as verified in the next section.

3. Propagation performance and fabrication tolerance of the proposed PBS

Based on the mode characteristics and coupling length obtained in section 2, propagation characteristics of the proposed PBS were obtained using 3D finite element method (FEM) simulations. With the same parameters as shown in Fig. 4 and R = 3 µm, the propagation Poynting vector flows of the TE and TM modes for the proposed PBS with the modified TM mode coupling length, L_cm = 20.85 µm, are shown in Figs. 5(a) and 5(b), respectively, and those for the PSWC with L_cm = 33.40 µm are shown in Figs. 5(c) and 5(d), respectively. Here, the L_cm optimized for performance differs from the L_TM calculated according to coupled waveguide systems. As mentioned above, we connected an angled waveguide at the end of the through bar guiding the TE mode to effectively decouple the two waveguides. Accordingly, the modified coupling length of L_cm is moderately shorter than the corresponding L_TM because the coupling effect remains a short distance within the angled waveguide before gradually decreasing. The difference between L_cm and L_TM is within 1 µm at R = 3 µm, regardless of slot thickness. This difference varies moderately for different values of R.

 

Fig. 5. Evolutions of the Poynting vector flow of a) TE and b) TM modes of the proposed PBS with L_TM = 21.56 µm (L_cm = 20.85 µm), and those of c) TE and d) TM modes of the PSWC with L_TM = 35.71µm (L_cm = 33.4 µm), for t_slot = 50 nm, h_Si = 150 nm, W_cl = 75 nm, gap = 50 nm, W_Si = 400 nm, and s = 550 nm.

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To assess PBS transmission characteristics, we investigated PER and IL of the TE and TM modes, as defined in Eqs. (4) and (5), respectively [18]:

 

Fig. 6. (a) PER and (b) IL versus the wavelength with t_slot = 50 nm for the proposed PBS with L_cm= 20.85 µm and the PSWC with L_cm = 33.4 µm.

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For PER_TM (PER_TE), the proposed PBS is about 12 (2–5) dB higher than that of the PSWC in the broadband of 100 (40) nm, while IL_TM values are close for the two structures. For IL_TE, the proposed structure is smaller than 0.1 dB in the entire band of 100 nm but the maximum IL_TE of the PSWC is close to 0.3 dB. It can be seen that PER_TE is significantly dependent on wavelength because of the stronger deviation of L_TM versus L_TE from their own phase-matching conditions. By contrast, PER_TM variation is moderate because of the extremely long L_TE. The proposed PBS achieves a 100 nm BW when PER_TE > 20 dB, but the PER_TE of PSWC varies from 10 dB to 18 dB. To achieve PERs >15 dB and ILs <0.1 dB for both modes, the BWs of the proposed PBS and the PSWC are 50 nm (1530–1580 nm) and 20 nm (1530–1550 nm), respectively. The results show the proposed PBS can achieve a BW greater than twice that of the PSWC.

To investigate the effects of geometry parameters on performance, PERs and ILs versus t_slot are shown in Fig. 7. The optimal PERs and ILs for both modes are within the range 40 nm < t_slot < 60 nm. We know that a thinner t_slot (<40 nm) leads to tighter mode confinement for TE (retaining more power in the through bar, resulting in higher PER_TM) and TM (coupling less power to the cross bar, resulting in lower PER_TE) modes for a slot waveguide. By contrast, the thicker t_slot results in looser mode confinement for the TE (resulting in lower PER_TM) mode but leads to a little variation in TM mode confinement. Therefore, PER_TE for the thicker t_slot (>60 nm) should show a slight increase rather than the moderate decrease. This can be explained as follows: The shorter L_TM resulting from the thicker t_slot, as shown in Fig. 3(a), causes a greater reduction in TM power, resulting in lower power scattering in the entire coupler, compared to that of the longer L_TM, although the theoretical power transfer rate is 100% at the L_TM. If we choose t_slot = 90 nm, the device length is reduced to L_cm = 13.9 µm, providing satisfactory performance of PER_TE = 24.3 dB, PER_TM = 23.1 dB, IL_TE = 0.08 dB, and IL_TM = 0.11 dB. By trading-off all PBS assessment criteria, we arrive at t_slot = 50 nm as the optimal condition with L_cm = 20.85 µm, PER_TE = 31.5 dB, PER_TM = 26.1 dB, IL_TE = 0.03 dB, and IL_TM = 0.01 dB for the PBS design parameters.

 

Fig. 7. PER (left axis) and IL (right axis) versus slot thickness, t_slot, of the proposed PBS.

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Next, the performances and L_cm versus thickness of CSWGs, h_Si, are shown in Fig. 8(a) and 8(b), respectively. We observe that thicker h_Si leads to tighter mode confinement for TE mode, resulting in higher PER_TM and lower IL_TE for a slot waveguide. For the TM mode, thicker h_Si also leads to tighter mode confinement due to effect of the slot waveguide mode [20], [21], resulting in lower PER_TE, the result is also observed from Fig. 8(b) with longer L_cm. Although the confinement of TM mode is weaker for thinner h_Si; however, it also obtains lower PER_TE. This is because the crosstalk of the TE mode increases as h_Si decreases [29–31].

 

Fig. 8. (a) PER (left axis) and IL (right axis) and (b) modified coupling length of TM mode, L_cm, versus thickness of CSWGs, h_Si, of the proposed PBS.

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On the other hand, duty cycle ρ is essential to tailoring the material anisotropy, and also influences performance of integrated photonic devices. We therefore calculated PERs and ILs for both modes versus ρ, as shown in Fig. 9(a). As mentioned in section 2, the maximum k_TE indicates tightest confinement of the TE mode occurring at ρ = 0.5, according to Eqs. (2) and (3) for single SWGs. However, in our numerical investigations, optimal PERs occur at ρ = 0.6 or 0.7, deviating a little from the theoretical prediction in [29] for SWGs. Note that PERs and ILs for TE and TM modes have opposing trends with variation of ρ. This means that PER is significantly dependent on IL. In addition, variation in TM mode coupling strength with ρ is insignificant because the major electric field, E_y, of the TM mode is parallel to the plane of the CSWGs. Therefore, the highest PER_TE is mainly dominated by the lowest IL_TE, rather than the remaining TM power in the through bar. The proposed PBS can be reduced to L_cm = 18.3 µm with moderately lower accordingly if we choose ρ = 0.8. We know that large ρ values alleviate fabrication difficulties but moderately decrease the performance to PER_TE = 28.9 dB, PER_TM = 23.3 dB, IL_TE = 0.19 dB, and IL_TM = 0.11 dB. Practically, this level of performance is satisfactory for a commercial PBS. If the duty cycle increases to 0.9, the gap between dielectric strips is about 13 nm, making the fabrication more difficult. In addition, the Lcm versus the duty cycle is also shown in Fig. 9(b) to offer the trade-off between the performance and footprint.

 

Fig. 9. (a) PER (left axis) and IL (right axis) and (b) modified coupling length of TM mode, L_cm, versus duty cycle, ρ, of the proposed PBS.

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The other critical SWG parameter is number of strips. PER and IL values versus number of strips are shown in Fig. 10(a); the practical coupling length, L_cm, versus number of strips are shown in Fig. 10(b). It can be seen that PERs and ILs increase when number of strips increases from two to four. By further increasing the number of strips to six (the strip has an aspect ratio of 3), PERs and ILs show slight variation because of their saturated mode confinements. Increasing the number of strips to six (L_cm= 20.5 µm) is not useful for reducing device length.

 

Fig. 10. (a) PER (left axis) and IL (right axis) and (b) modified coupling length of TM mode, L_cm, versus number of strips of the CSWGs

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Finally, we evaluate fabrication tolerances of the proposed PBS by investigating performance versus slot thickness variation, Δt_slot, cladding width, ΔW_cl, and thickness of CSWGs, Δh_Si, as shown in Figs. 11(a), 11(b), and 11(c), respectively. We note that PER_TM shows only slight variation with the three types of fabrication error, owing to the extremely long TE mode coupling length (L_TE = 1.5 mm). By contrast, PER_TE varies significantly with fabrication error. This is because the short L_TM leads to a large deviation from the TM mode phase-matching condition. Within the variation range Δt_slot = ±5 (10) nm, PER_TE achieves a level of >20 (15) dB and the ILs of the two modes are lower than 0.2 (0.25) dB (Fig. 11(a)).

 

Fig. 11. PER (left axis) and IL (right axis) versus variation in (a) slot thickness, Δt_slot, (b) cladding width, ΔW_cl, and (c) thickness of CSWGs, Δh_Si, of the proposed PBS.

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Thanks to modern semiconductor fabrication technology, the surface roughness of a SiO₂ layer deposited on a Si substrate can be precisely controlled to under 5 nm by deposition techniques such as plasma-enhanced chemical vapor deposition (PECVD), revealing the highest surface roughness of 4 nm, as well as physical-vapor deposition and ion-beam deposition, revealing the lowest surface roughness of 0.2 nm [35]. In fabrication processes, the width variations of SWGs and slot waveguides are correlated. Therefore, we analyze performances versus ΔW_cl = ±5 (10) nm while simultaneously altering W_Si by the same range of ΔW_Si = ±5 (10) nm. The obtained PER_TE is around 20 (12) dB and the ILs of both modes are lower than 0.2 (0.3) dB (Fig. 11(b)). In the variation range of Δh_Si= ±5 (10) nm, only PER_TE varies moderately and achieves a level of >25 (20) dB, and the ILs of the two modes are lower than 0.18 (0.2) dB (Fig. 11(c)). Achieving ΔW_cl <5 nm is expected if we require PER_TE >20 dB. Fortunately, the sidewall roughness of a Si strip can be reduced to <1 nm by adopting the mixed inductively coupled plasma-reactive ion etching (ICP-RIE) process and hydrogen annealing [36], in which the word “mixed” means that the etching and passivation processes of the conventional ICP-RIE work synchronously. Overall, the fabrication tolerance analyses for the three geometry parameters implies that Δt_slot, ΔW_cl, and Δh_Si have similar fabrication tolerances.

4. Summary

A compact, high-performance PBS is proposed, consists of two horizontally slotted waveguides with composite subwavelength gratings (CSWGs) comprising a SiO₂ slot layer over a Si strip. Introduction of the CSWGs leads to significant coupling strength suppression and enhancement of the TE and TM modes, respectively, simultaneously achieving improved PER, reduced device length, and expanded working BW. Differing from mono-material SWGs, CSWGs comprising silicon strips covered with a silicon dioxide (SiO₂) layer not only simplify the fabrication process, but further reduce the device length. Using numerical optimization, the present PBS with device length of L_cm = 20.85 µm achieved PERs of >31 dB and >26 dB for TE and TM modes, respectively, and ILs of <0.03 dB for both modes, at a wavelength of λ = 1550 nm. Working BWs of ∼50 nm for PER_TM ∼ 30 dB, PER_TE > 20 dB, and ILs < 0.1 dB were obtained for TE and TM modes. The proposed PBS can be further reduced to L_cm = 18.3 µm by selecting a duty cycle of 0.8, which moderately decreases the performance to PER_TE = 28.9 dB, PER_TM = 23.3 dB, IL_TE = 0.19 dB, and IL_TM = 0.11 dB. In terms of fabrication tolerances, PERs and ILs of >20 dB and <0.3 dB, respectively, were obtained with moderate variation in slot thickness (Δt_slot = ±5 nm), CSWG width (ΔW_cl= ±5 nm), and CSWG thickness (Δh_Si= ±5 nm). The proposed idea has application in various coupled-waveguide systems, to improve their overall performance and reduce device length for building dense photonic integrated circuits.