Simulation of a High-Performance Polarization Beam Splitter Assisted by Two-Dimensional Metamaterials.

It is challenging to simultaneously consider device dimension, polarization extinction ratio (PER), insertion loss (IL), and operable bandwidth (BW) to design a polarization beam splitter (PBS) that is extensively used in photonic integrated circuits. The function of a PBS is to separate polarizations of light, doubling the transmission bandwidth in optical communication systems. In this work, we report a high-performance PBS comprising two-dimensional subwavelength grating metamaterials (2D SWGMs) between slot waveguides. The 2D SWGMs exhibited biaxial permittivity by tailoring the material anisotropy. The proposed PBS showed PERs of 26.8 and 26.4 dB for TE and TM modes, respectively, and ILs of ~0.25 dB for both modes, with an unprecedented small footprint of 1.35 μm × 2.75 μm working at the wavelength λ = 1550 nm. Moreover, the present structure attained satisfactory PERs of >20 dB and ILs of <0.5 dB within an ultrabroad BW of 200 nm.

1. Introduction

To accomplish photonic integrated circuits (PICs) [1,2,3,4], a popular material platform is the silicon on insulator (SOI). There are two primary merits of using the SOI platform: matured semiconductor fabrication technology and the high-index contrast of the refractive index, thereby significantly rendering the devices compact. However, the SOI platform’s highly birefringent property leads to significant polarization dependence, which is undesirable for an optical-fiber network. To resolve this problem, polarization management components, including polarization rotators [5,6,7,8], polarizers [9,10,11,12,13], and polarization beam splitters (PBSs) [14,15,16,17,18,19,20], were proposed. Among them, PBSs are the most popular for separating two orthogonal polarizations, the transverse-electric (TE) and the transverse-magnetic (TM), because of effectively using the two polarizations in transmitting optical signals. The overall performance of a PBS is evaluated by several criteria, such as device footprint, polarization extinction ratio (PER), insertion loss (IL), operable bandwidth (BW), and fabrication tolerances. Most PBSs are based on the directional coupler (DC) type because they can be flexibly designed by adopting diverse structures (e.g., silicon (Si) strip, plasmonic waveguide, multimodal interference effect, and slot waveguides) depending on the selected priorities of the device size, PER, IL, and BW. The authors in [14] proposed a DC-type PBS on a coupler consisting of Si strips. In [15], the authors reported an asymmetric DC-type PBS comprising a Si strip and a hybrid plasmonic waveguide (HPW). They also used an MMI coupler between a Si strip and an HPW to obtain a device footprint of 1.8 × 2.5 μm2 [16]. Yue et al. [17] designed a PBS consisting of horizontal slot waveguides [21,22] to enhance TM mode coupling compared to that of a PBS consisting of an Si-strip coupler [14], remarkably shrinking the coupling length from a few hundreds to a few tens of micrometers. However, the PERs of the TE and TM modes are >20 dB over a narrow range of about 18 nm BW [17]. In experiments, the PBS [17] exhibited PERs of 16.8 for TE mode and 14.1 dB for TM mode [18]. Kim et al. [19] reported a 7.5 μm long PBS assisted by a bridged Si waveguide to achieve high PERs over the full C-band wavelength range. They then reported a PBS using a three-waveguide directional coupler [20], showing extremely high PERs of ~40 dB, but with a coupler length of about 29.4 μm.

In recent years, subwavelength-grating metamaterials (SWGMs) [23,24,25] comprising periodically arranged dielectric strips have been widely adopted to build PICs owing to the maturated development of nanoscale-pattern fabrication technology. SWGMs can be considered to be equivalent anisotropic waveguide structures approximated by effective medium theory (EMT) [26,27], and their permittivity tensors can be flexibly engineered to achieve the desired optical properties. As a result, many applications utilizing tailorable anisotropy SWGMs were reported, including waveguide couplers [28,29], low-loss fiber-to-chip couplers [30,31], spectral-filtering devices [32,33], and polarization management [34,35,36,37,38]. In polarization devices, Halir et al. [34] fabricated a beam splitter based on MMI showing it to be three times more compact and with a lower phase error than that of its conventional counterpart. SWGMs were placed between two strip waveguides by Xu and Xiao [35] to reduce TM mode coupling and increase TE mode coupling. Liu et al. [36] embedded SWGMs in a coupler comprising two strip wires to attain BW broadening by altering the effective index of the even mode. Xu and Shi [37] fabricated an ultrasharp multimode waveguide bending assisted by SWGM mode converters to inhibit intermodal coupling. Adopting tilted SWGMs, Luque-González et al. [38] reported a PBS with 72 nm BW, IL < 1 dB, PER > 15 dB, and device length of 14 μm.

Instead of locating SWGMs in the waveguide-core region [34,35,36,37,38], some research groups [39,40,41] theoretically proposed and experimentally adopted SWGMs in cladding regions to reduce crosstalk between Si-strip waveguides by engineering the depths of evanescent waves called extreme skin-depth (e-skid) waveguides. Li et al. [42] realized a PBS adopting cascaded dual-core tapers. Mao et al. [43] reported a PBS with ultrabroad BW > 420 nm using tapered SWGM and slot waveguides, with ILs < 0.8 dB and PERs > 10.9 dB. Mia et al. [44] reported adiabatically tapered e-skid to form a PBS capable of operating at a large BW of 250 nm; however, the device length of 100 μm led to severe limitations for building densely integrated photonic circuits. Zhang et al. [45] experimentally demonstrated an e-skid-based PBS with the performance of BW > 80 nm, PERs > 20 dB, ILs < 1 dB, and 14 μm long device length. Xu et al. [46] discovered a PBS that extended SWGMs in both core and cladding regions. The PBS was designed to function as an MMI coupler for TM mode, but as two isolated waveguides for TE mode. Inspired by the idea [47] of e-skid waveguides that are implemented by SWGMs in parallel and perpendicular directions to engineer evanescent wave allowing, we present a PBS consisting of a two-dimensional SWGMs (2D SWGMs) between two slot waveguides to extend the applications of conventional one-dimensional SWGMs (1D SWGMs). The present PBS dramatically reduces (enhances) the mode couplings of TE (TM) mode, thus concurrently achieving an extremely short PBS with high PERs, low ILs, and ultrabroad BW. The dependences of geometrical dimensions on device performance are analyzed in detail. The spectral response was also investigated to show the broadband operation. Lastly, we address fabrication tolerance to validate the robustness of the proposed PBS.

2. Mode Characteristic and Coupling Effect with Anisotropic SWGMs

Figure 1a–c show the 3D diagram with the TE (E) and TM (E) mode profiles in the incident plane, the top view, and the cross-section in the xy plane, respectively, of the proposed PBS. Slot waveguides on a SiO2 substrate comprised a SiO2 slot layer sandwiched with high-index Si strips in which the TE channel was connected to a bent waveguide with a radius of curvature (R) at the end in order to effectively decouple the two slot waveguides. In the slot waveguides with width WS, the thicknesses of the slot layers and Si layers were t and hSi, respectively. The height and width of Si strips (copper red) were 2hSi + t and WS, respectively. The pitch of SWGMs in the x direction was set to Λ = WCl + g with duty cycle ρ = WCl /Λ, where WCl is the width of the Si strips, and g is the gap between Si strips. Edge-to-edge spacing between slot waveguides is s. Likewise, the pitch of SWGMs in the z direction was set to be Λ = L + LSiO2 with duty cycle ρ = LSiO2/Λ, where L is the gap between SiO2 grating (dull blue).

Figure 1

(a) 3D diagram with TE (E) and TM (E) mode profiles in the incident plane; (b) top view; (c) schematic of calculating the resultant effective permittivity ε of 2D SWGMs, which is obtained by sequentially estimating the 1D SWGMs in the z (ε) and x directions (ε) on the basis of EMT between slot waveguides; (d) cross-section in xy plane of the present PBS.

Before analyzing the proposed design, the fabrication processes are schematically illustrated in Figure 2. (1) A negative photoresist (PR) film (purple) was deposited to pattern the lower Si strips with a hard mask defining the patterns of the proposed structure on a SiO2 substrate (blue); then PR exposure and development were conducted. (2) The proposed structure was formed by etching SiO2 and lifting off the PR film. (3) A Si film was deposited by chemical vapor deposition, and the Si layer was planarized by chemical mechanical polishing (CMP). (4) Depositing a positive PR (green) to pattern the SWGMs with another mask was followed by PR exposure and development, SiO2 slot layer deposition using thermal oxidation, and a CMP was conducted. (5) Similar to Step 4 but with a different mask. (6) After SiO2 reactive ion etching, the PR film was lifted off. (7) The upper Si strips and SWGMs were deposited, and a CMP was carried out. (8) A positive PR was deposited with the same mask as that in Step 1, followed by PR exposure and development. (9) After Si etching, the positive PR film was lifted off to reach the desired structure. Lastly, the SiO2 regions between the SWGMs could be formed with the procedures of SiO2 deposition, PR deposition, patterning the 2D SWGMs with a mask, SiO2 etching, and lifting off the PR.

Figure 2

Schematic diagram of the fabrication processes of the designed PBS.

The working principle of the present PBS is that we propagated TE mode with major electric field E along the bar, while TM mode was coupled with a major electric field E under the phase matching condition (PMC) into the cross, as shown in Figure 1a. Using the EMT [26,27], the proposed 2D SWGMs displayed an equivalent material anisotropy ε by considering the permittivity of Si, εSi and ε as follows (see Figure 1c): where ε, ε, and ε denote permittivity in the x, y, and z directions, respectively. In this work, ε = diag [ε, ε, ε] denotes the equivalent anisotropic permittivity of the SWGMs consisting of SiO2 strips and air gaps along the z direction, as shown below: where εSiO and εair denote the permittivity of SiO2 and air, respectively. Differing from the previous reports [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] using one-dimensional SWGMs, ε in Equation (1) showed biaxial anisotropy, thus more flexibly tuning the optical characteristics. To design a PBS here, the mode characteristics of the TE and TM modes had to be obtained in advance. After that, the coupling length of a coupled waveguide for a specific mode measuring the distance required to completely transfer power from one waveguide to another can be computed by L = λ/{2(n − n)} [48], where i denotes TE or TM. n and n denote the effective indices of the even and odd modes, respectively.

First, we analyzed the mode characteristics of the present design. The relative permittivity of Si and SiO2 was εSi = 12.110 and εSiO = 2.085 [49], respectively, at λ = 1550 nm. The chosen parameters were WSi = 400 nm, WCl = 75 nm, g = 50 nm (i.e., ρ = 0.6), hSi = 150 nm, La = 100 nm, LSiO2 = 150 nm (i.e., ρ = 0.6), s = 550 nm, and four Si strips between slot waveguides. First, we obtained the anisotropic ε = diag [1.285, 1.285, 1.206] according to Equations (5) and (6). Next, the resultant biaxially anisotropic ε = diag [1.851, 2.815, 2.805] could be obtained according to Equations (2)–(4). With the obtained ε in the region between slot waveguides and using COMSOL Multiphysics 6.0 (COMSOL Inc., Burlington,VT, USA), the coupling length of TM mode Lc,TM and the coupling-length ratio of TE and TM modes LTE/Lc,TM versus ts for the present PBS and the conventional SWs [17,18] are shown in Figure 3. The larger value of LTE/Lc,TM implies that more TE power is retained in the bar while TM power is completely transferred to the cross. LTE was far larger than Lc,TM due to better TE mode confinement; thus, a PBS’s length is determined by a shorter Lc,TM. For conventional SWs [17], Lc,TM (dull blue dotted line) varied from 82.42 to 32.19 μm for ts for 10 and 60 nm, respectively, and LTE/Lc,TM (copper red dotted line) was only 9.16 at ts = 60 nm. In contrast, the proposed structure not only shrunk Lc,TM (dull blue solid line) to 10.69 and 3.15 μm for ts = 10 and 60 nm, respectively, but also improved LTE/Lc,TM (copper red solid line) to 891 at ts = 60 nm. Results demonstrate that the device length and PER of a PBS based on a two-SW can be significantly reduced and improved, respectively, by locating the proposed 2D SWGMs between the two SWs.

Figure 3

(left axis) Coupling length of TM mode LTM TM and (right axis) coupling-length ratio Lc,TE/Lc, versus ts for the present PBS and the SWs.

Further 3D calculations of mode and propagation characteristics are outlined in the next section. For observing the mode coupling, the even TE and TM field contours of the present structure are exhibited in Figure 4a,b, respectively, and those of the SWs are exhibited in Figure 4c,d, respectively.

Figure 4

Field contours of the even modes of (a) TE and (b) TM and those of (c) TE and (d) TM of the SWs for WSi = 400 nm, ts = 60 nm, hSi = 150 nm, WCl = 75 nm, g = 50 nm, s = 550 nm, and λ = 1550 nm. (e) Field amplitudes at the central lines of the slot along the x directions of (a,c); (f) field amplitudes at the central lines of the slot along the x directions of (b,d).

By adding 2D SWGs in the middle region of conventional SWs, the decaying rates of evanescent wave of the TE and TM modes are considerably suppressed (i.e., larger LTE/Lc,TM) and enhanced (i.e., shorter Lc,TM), respectively. In addition, the relative field amplitudes of the TE and TM modes along the line denoted in the inset of Figure 4e are shown in Figure 4e,f, respectively. The above results can be explained by the decay constant of the TE mode kTE that can be adjusted by the ε ratio according to the dispersion relation [39], and the ε > ε condition is always fulfilled. Therefore, 2D SWGMs significantly reduce crosstalk compared to an isotropic cladding with ε = 1. In contrast, the decay constant of the TM mode, kTM, depends on the ε < 1 ratio, leading to weaker mode confinement.

3. Performance Dependences on Duty Cycle, Wavelength, and Fabrication Tolerance

Device performance dependences on geometry parameters, wavelength response, and fabrication tolerance proceeded by executing 3D simulations. To assess the transmission performance of a PBS, we analyze the PERs and ILs of both modes, which are formulated in Equations (7) and (8), respectively: where P denotes the input power, P( denotes the TE (TM) mode power at the bar (cross), and P( is the TE (TM) mode power at the cross (bar). By adopting R = 3 μm and the same parameters displayed in Figure 4, the y component of the magnetic field (H) and total power (|P|) evolutions of TE mode are shown in Figure 5a,c, respectively, and the y component of the electric field (E) and total power (|P|) evolutions of TM mode are shown in Figure 5b,d, respectively.

Figure 5

y components of (a) magnetic field of the TE mode and (b) electric field of the TM mode, and the total power evolutions of the (c) TE and (d) TM modes of the present structure with device length LD = 2.75 μm (i.e., the practical Lc,TM with optimal performance) for ts = 60 nm, hSi = 150 nm, WCl = 75 nm, WSi = 400 nm, g = 50 nm, s = 550 nm, and λ = 1550 nm.

In Section 2, the calculated Lc,TM at t = 60 nm was 3.15 μm on the basis of equivalent permittivity ε. The practical Lc,TM to obtain optimal performance is device length LD = 2.75 μm, which was shorter than the calculated Lc,TM in Section 2 because the coupling continued a short distance from the entrance of the bent waveguide and then gradually decreased. At device length LD = 2.75 μm, the obtained results were PERTE = 26.81 dB, PERTM = 26.48 dB, ILTE = 0.16 dB, and ILTM = 0.19 dB. By contrast, conventional SWs [17] with Lc,TM = 34.6 μm achieved PERTE = 25.5 dB, PERTM = 14.8 dB, ILTE = 0.07 dB, and ILTM = 0.06 dB. Results show that the proposed PBS not only considerably reduced the proposed PBS’s length by about 12 times when compared to the conventional SWs [17], but also achieved superior PERs, particularly for PERTM. Although the ILs of the current design were higher than those of the SWs, values of <0.2 dB were still acceptable. Considering the effect of duty cycles, we show the PERs and ILs versus ρ in Figure 6a. The optimal PERs and ILs of both modes appeared in the interval of ρ = 0.4 to 0.6. Once the condition of ρ > 0.6 had been reached, PERs and ILs dramatically degraded because a larger ρ decreases (increases) the value of ε (ε) leading to smaller (larger) kTE (kTM), simultaneously increasing the crosstalk of both modes. The higher PERs are also reflected in lower ILs. Although optimal PERs and ILs were at ρ = 0.4 or 0.5 here, the device length was LD = 6.50 or 4.15 μm, respectively. Considering compactness, we chose ρ = 0.6 to investigate the subsequent analyses, and PERs and ILs versus ρ are exhibited in Figure 6b.

Figure 6

(left axis) PER and (right axis) IL of both modes as functions of duty cycles (a) ρx and (b) ρz at the same parameters as those in Figure 4.

The ILs of the TE and TM modes slightly increased, ranging from ρ = 0.2 (LD = 2.9 μm) to 0.8 (LD = 2.55 μm), and PERTE and PERTM slightly varied as ρ varies. Differing from the major effect of ρ, ρ plays a finetuning role on device performance and length. Regarding to the number of Si strips (N), the PERs and ILs versus N (at the condition of ρ =0.6 and ρ = 0.6) are shown in Figure 7. The proposed PBS achieved optimal performance when N = 4 was chosen. Further increasing N resulted in moderately varying performance. The performance of TM mode dramatically worsened as N decreased. This result can be attributed to t Λ being increasingly away from the condition of Λ << λ, causing the increase in scattering loss that resulted from the grating structure [21].

Figure 7

(left axis) PER and (right axis) IL of both modes as a function of the number of Si strips, N between slot waveguides at the same parameters as those in Figure 5.

To assess the BW of the present PBS, the PERs and ILs as a function of wavelength are shown in Figure 8a,b, respectively. PERTM (ILTM) significantly decreased (increased) as the wavelength moved away from the target wavelength of λ = 1550 nm because the short Lc,TM was more sensitive than the extremely long Lc,TE to deviation from the PMC. By contrast, the PERTE and ILTE of the shorter (longer) than λ = 1550 nm wavelengths were higher (lower) and lower (higher), respectively. This can be explained by the guided modes with shorter (longer) wavelengths leading to shorter (longer) evanescent wave tails, thus reducing (increasing) crosstalk between waveguides. The working BW of both modes with PERs > 20 dB and ILs < 0.5 dB ranged from λ = 1440 to 1650 nm (>200 nm).

Figure 8

(a) PER and (b) IL versus wavelength at the same parameters as those in Figure 4.

To show our design’s superiority, we compared its overall performance with that of SWGM-based PBSs, as shown in Table 1. The footprint of the proposed structure was the smallest PBS compared with the reported PBSs [19,20,42,43,44,45,46], rendering it more beneficial in constructing a highly dense photonic component.

Table 1

Performance comparison of SWGM-based PBSs.

Structure	Footprint (μm2)	PERs (dB)	ILs (dB)	BW (nm)
[19]	1.7 × 12.25	22.5	1.8	>100
[20]	2.41 × 29.4	39.0	0.35	>100
[42]	2.5 × 33.6	20	0.3	270
[43]	1.3 × 4.6	10.9	0.8	420
[44]	2.75 × 100	20	1.2	250
[45]	2.5 × 14	20	1	80
[46]	1.9 × 12.25	20	1	200
This work	1.35 × 2.75	20	0.5	200

In addition to analyzing performance dependence on duty cycles and number of Si strips, as shown in Figure 6 and Figure 7, respectively, we investigated severe geometries ts and WCl to assess fabrication tolerance. Performance versus variations in Si strip width ΔWCl and slot thickness Δts is shown in Figure 9a,b, respectively. PERTM significantly depended on the two fabrication errors (ΔWCl and Δts) because of the extremely short Lc,TM = 2.75 μm of the TM mode. As shown in Figure 9a, PERTM decreased to ~17 dB (from ~26 dB), and ILTM increased to ~0.4 dB (from ~0.2 dB) while ΔWCl > 5 nm or Δts > 10 nm. Within the variation range of ΔWCl < 3 nm or Δts < 5 nm, PERTM maintained values of >20 dB and ILTM < 0.25 dB. In contrast, PERTE and ILTE showed slight variations in ΔWCl and Δts due to the exceptionally long Lc,TE = 891 μm of TE mode.

Figure 9

(left axis) PER and (right axis) IL as functions of variations in the (a) Si strip width ΔWCl and (b) slot thickness Δt of the present structure.

Another essential fabrication error, angled sidewall, frequently occurs in etching processes that typically do not have a perfect 90° sidewall. In the present structure, the crucial parts are SWGMs due to their larger aspect ratio compared to that of the slot waveguides. Therefore, we now discuss the sidewall effect of the SWGMs on device performance. The width difference between the bottom and top of the SWGMs is Wsw, as shown in Figure 10a, and the PERs and ILs of both modes are shown in Figure 10b. PERTE (PERTM) and ILTE (ILTM) showed slight (significant) dependences on Wsw due to the extremely weak (strong) coupling strength induced by the 2D SWGMs. PERTM decreased to about 14.2 (9.8) dB, and ILTM increased to about 0.62 (1.25) dB, while Wsw increased to 5 (10) nm.

Figure 10

(a) Cross-sectional diagram in xy plane and zooned-in view of a SWGM, where Wsw denotes the difference between the bottom and top of the SWGMs. (b) PER and IL versus Wsw.

4. Conclusions

An ultracompact and broadband PBS comprising slot waveguides assisted by in between 2D SWGMs was proposed to increase the integration density and transmission bandwidth of photonic devices. The proposed 2D SWGMs served as both a barrier to suppress TE mode coupling and bridging to improve TM mode coupling by carefully engineering the duty cycles of the SWGMs. The numerical results of the proposed PBS showed PERs of 26.8 and 26.4 dB for TE and TM modes, respectively, and ILs of ~0.25 dB for both modes, with a compact PBS of 1.35 μm × 2.75 μm. Moreover, the present PBS achieved satisfactory performance while operating in a BW of 200 nm. Fabrication tolerance analyses showed that the PERTM maintained superior values of >20 dB and ILTM < 0.25 dB within the variation range of clad width ΔWCl < 3 nm or slot thickness Δts < 5 nm.