1. Introduction

Photonic Integrated Circuits (PIC) combine a high number of photonic components and functions on a single chip and offer several advantages over discrete component solutions. These are scalability, better performance, increased reliability, co-integration with electronics, reduced costs and others. In particular, silicon photonics has attracted a lot of attention due to the option to make use of already existing Complementary Metal-Oxide semiconductor (CMOS) processing to fabricate PICs [1]. A high refractive index contrast between silicon (n_Si = 3.47 at the wavelength λ = 1550 nm) and silicon dioxide (n_SiO2 = 1.44 enable dense integration of optical waveguides (WGs) and other integrated passive components on PICs [2]. The high refractive index contrast combined with asymmetry in WG height and width imposes a strong waveguide birefringence [3]. A single-mode silicon strip waveguide with typical dimensions of 500 nm in width and 220 nm in height [4] can guide two fundamental polarization modes: transverse-electric-like (TE) mode with the prevailing electric field component in parallel to chip plane and transverse-magnetic-like mode (TM) with the prevailing electric field component out of plane of the chip surface. These two modes exhibit different propagation constants leading to polarization dependent performance of WGs and other components. To tackle this polarization dependency of silicon photonic devices, a polarization diversity approach can be employed [5]. A polarization beam splitter (PBS) which splits (or combines) TE and TM modes is an essential building block in the polarization diversity circuit. Polarization encoding communication systems [6] and quantum applications with polarization-encoded qubits [7] in particular, require high performance PBSs. The research of PBSs needs to take into account various performance metrics. High extinction ratio, low insertion loss and wide bandwidth for both polarizations, as well as small footprint are desired in the design of a PBS. Various approaches can be taken to achieve polarization splitting on silicon chips resulting in a wide variety of devices including multimode interferometers (MMI) [8,9], directional couplers (DC) [10], asymmetrical directional couplers [11–14], grating-assisted devices [15], subwavelength-grating and metamaterial assisted devices [15–26], as well as inversely designed structures [27]. Devices based on MMIs, DCs and asymmetrical DCs can suffer from either limited bandwidth, low extinction ratio, or large footprint. Inverse design has been shown to significantly reduce the footprint of passive silicon photonic devices that can be fabricated reliably at scale [28]. Inversely designed PBS structures can exhibit impressively small footprint, however at the cost of low extinction ratio and high losses. In recent years there have been many demonstrations of utilizing effectively anisotropic all-dielectric metamaterials to improve the performance of silicon PBS with respect to all performance metrics [29,30]. Similar concepts have been adopted in other material platforms as well [31,32]. An all-dielectric metamaterial consists of two or more periodically exchanging dielectric materials with the spatial period well below the wavelength of light. In approximation such a structure acts as a uniform anisotropic material with different refractive indices along different lateral directions [33], allowing for more control over light propagation. In case of silicon photonics, the metamaterial structure can be designed by patterning subwavelength Si ridges with either air or SiO₂-filled gaps in between. Due to anisotropy in refractive index, introduced by the metamaterial geometry, the structure exhibits strong birefringence. This enables us to achieve optical properties that cannot be obtained by conventional optical structures. Metamaterial structure can be introduced inside the waveguide core or in the cladding [34]. A so called all-dielectric metamaterial cladding, consisting of subwavelength silicon ridges along the side of the waveguide core, has been shown to reduce the coupling of TE modes between adjacent WGs [35–37] due to reduced evanescent field in the cladding. It has also been shown that introducing a metamaterial cladding structure does not significantly increase propagation losses of WGs [35]. The altered coupling effect is reversed for TM modes that exhibit stronger coupling in case of a metamaterial cladding. This effect has already been utilized to design DC PBS with small footprints and high extinction ratios [16,17]. The length of a directional coupler with metamaterial cladding is adjusted in such a way that the TM mode couples completely to the adjacent WG. The TE mode however, remains in the first WG due to coupling suppression of the metamaterial cladding. The main drawback of such a device is a rather narrow bandwidth. Different schemes have been proposed to achieve exceptionally wide bandwidth such as mode evolution approach [24], or cascaded Mach-Zehnder Interferometers (MZIs) configuration [19]. Bandwidths over 200 nm have been demonstrated at relatively large extinction ratios of around 20 dB.

In this paper we propose an improved concept of a PBS designed for a Silicon-on-Insulator (SOI) material platform with a 220 nm thick Si waveguide layer and air top cladding. As a starting point we analyze the first concept (PBS-1) where a DC with metamaterial cladding is combined with a tight WG bend with metamaterial cladding, acting as a TE polarizer [38], to increase the extinction ratio for TM mode of such constructed PBS. Furthermore, we introduce a novel structure with two compact metamaterial MZIs (PBS-2), exploiting a difference in bend radius of two parallel bent WGs to implement the phase delay in a more compact way compared to a conventional MZI structure. Such a structure has the potential to increase the bandwidth for TM mode, since it presents a compact version of a cascaded MZI configuration [39–41]. Numerical simulations based on Finite Element Method (FEM), Transfer Matrix Method (TMM) and Finite difference Time Domain (FDTD) were used in the design and to evaluate the performance of proposed devices. Simulations showed that the proposed metamaterial DC-based PBS exhibits an extinction ratio of >35 dB and insertion loss of <1 dB in the bandwidth of 163 nm for both polarizations. By employing the metamaterial compact dual MZI structure and combining it with the TE metamaterial cladding polarizer we demonstrate by simulations a PBS with a wide bandwidth of 263 nm, exhibiting a very high extinction ratio (> 35 dB) in the whole wavelength range for both polarizations. The fabricated PBS-2 device exhibits measured performance that matches well with simulations. Measurement results reveal that a wide bandwidth of >140 nm (limited by the laser tuning range) with a high extinction ratio of >30 dB were achieved for both polarizations. The insertion loss was not accurately determined, due to limitations of the measurements, however measurements still confirmed high transmission demonstrating satisfactory performance. PBS-2 also exhibits robustness to fabrication variability. A device with a minimal feature size of 100 nm is also fabricated, representing a step towards CMOS compatibility and potential mass manufacturing.

2. PBS designs and simulation methods

2.1 Metamaterial DC-based polarization beam splitter (PBS-1)

PBS-1 presents a starting point to analyse the effects of metamaterial cladding on polarization splitting and to design the improved version PBS-2. Figure 1(a) shows the geometry of the PBS-1 concept, the metamaterial DC-based polarization beam splitter, which we refer to as PBS-1.

 

Fig. 1. (a) The proposed metamaterial DC-based PBS design (PBS-1). Insert shows the basic geometry of a metamaterial DC with marked geometrical parameters of the metamaterial cladding. (b) The proposed metamaterial compact dual MZI-based PBS (PBS-2) and its main geometrical parameters. Input and output ports are denoted for both concepts. The internal port Thru_int is put in parenthesis, since it refers to the structure with excluded TE polarizer.

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The first part of the PBS-1 design presents a directional coupler (DC) with the air/Si metamaterial internal cladding between WGs. The insert in the Fig. 1 shows the basic geometry of the two WGs in the DC with the metamaterial cladding structure. Main parameters defining the geometry of the metamaterial cladding - the period P, number of Si ribs N and the fill factor ff are indicated. By carefully selecting these parameters, we can design structures exhibiting exceptionally long coupling lengths (i.e. weak coupling) for TE modes (> 1 cm) at very narrow gap widths between WG cores down to 0.5 um, as shown in our previous publication [37]. On the other hand, it turns out that, in such a structure, coupling lengths of TM modes are orders of magnitude shorter (10-20 µm, meaning large coupling rate) and the TM-mode crosstalk is even larger than in case of WGs with normal cladding. By setting the length of the DC with metamaterial cladding to the value of the coupling length for TM mode, the TM mode will fully couple to the second WG, while the TE mode will stay in the first WG with negligible coupling to the second WG. By using a metamaterial as the cladding, significantly higher peak polarization extinction ratios can be achieved compared to a DC with a normal cladding, as already reported in [16,17]. The second part of the PBS-1 presents a bent WG structure with outer-side metamaterial cladding, acting as a TE polarizer. It has to be noted that for improved polarization selectivity the width of ribs in this circular cladding decreases linearly from inner to outer side of the cladding.

PBS-1 component is designed in the following way. For the DC part the largest transmission of the TM mode has to be achieved at the Cross port, presenting the TM output. On the other hand, one has to assure that the metamaterial structure minimizes the TE mode coupling into the Cross port. Thus, the length (L) of the DC and metamaterial structure (P, N, ff) have to be optimized following this aim at a selected wavelength (central wavelength λ = 1550 nm in our case). Furthermore, the proposed geometry of the DC is chosen in such a way, that the transmitted TM mode will not experience any WG bends towards the Cross port, since the TM mode is noticeably subjugated to the bending losses as confirmed by simulations. To further reduce the remaining TM polarization at the Thru port and further increase the extinction ratio of the device, the bent TE polarizer with metamaterial cladding is brought into play. The design concept was adopted from [38]. The geometry of the TE polarizer (bend radius R_p, metamaterial structure) inside the proposed PBS component has to be designed so that most of the remaining TM mode is extracted out of the waveguide due to the presence of the metamaterial cladding structure at the outer side, while the TE mode experiences a very small bending loss despite the presence of the metamaterial cladding. This is possible because the anisotropic nature of the metamaterial structure where the condition of the total internal reflection (TIR) is relaxed to depend only on either the refractive index component in parallel to light propagation, or the refractive index component perpendicular to light propagation, affects the TE and TM mode propagation differently [42]. The bend loss of TE mode will not be significantly affected since the parallel refractive index of the cladding can be kept well below the effective refractive index of the mode. However, the TM mode can experience very high bend losses due to a small difference in effective refractive index of the mode and the perpendicular refractive index of the metamaterial cladding [38]. In order to efficiently diffract the TM mode into free space, the ff of the metamaterial cladding needs to linearly decrease when moving away from the WG core, meaning the width of Si ribs needs to decrease from the inner to the outer side of the cladding.

2.2 Metamaterial compact dual MZI-based polarization beam splitter (PBS-2)

As it will be shown later, the presented design PBS-1 can exhibit high extinction ratios and low losses, however, its bandwidth is still limited by inherent physical operation of a DC. To overcome this issue, we propose the following concept of the polarization splitter structure which includes two metamaterial compact MZI structures combined with the TE polarizer. The structure is presented in Fig. 1(b) and is referred to as PBS-2. Cascading two MZIs in a point symmetrical configuration is an effective way of achieving a coupler with broadband operation, not attainable by utilizing a single DC structure [39]. The two phase delay sections of the two MZIs cause interference for TM mode and offsets the peak coupling of TM mode in individual directional coupler segments of the MZI structures. By correctly choosing the parameters of the structure, phase compensation can be achieved for different wavelengths, resulting in a wavelength insensitive coupling of TM mode. The polarization splitter structure with a point symmetrical configuration with two cascaded MZIs [39–41] consists of DCs and WG arms with a slight difference in length that introduce a small phase delay that causes interference in the DCs. In our case the phase delays are not achieved by forming two separate arms, as in case of a MZI in a classical sense. The structure is formed from three straight sections of two WGs with metamaterial cladding acting as DCs and two bends in which the WGs remain in parallel. This results in a small path length difference between the two WGs in the bend due to a slightly different radius of the inner and outer WG. This small path length difference between WGs will introduce a small phase delay. Since the required phase delay for the operation can be small, consequently the bend section with appropriately chosen radius R_ΔL can be rather short. This further means that the coupling that occurs in this bent section is small compared to the coupling in the DC sections. This indicates that the structure can be described discretely by interchanging DCs and phase delays, or, with other words, by two cascaded MZIs. The device geometry can be significantly more compact compared to conventional devices with cascaded MZIs resulting in reduced footprint. The metamaterial cladding structure between WG cores is employed along entire structure, including MZI phase delay and directional coupler segments to ensure as little coupling of TE mode as possible. The two MZI structures as a whole therefore only act as a broadband coupler for TM mode. In Supplement 1 (section 1) the power density distribution in the structure for TE and TM mode is shown for the described compact dual MZI structure. If the top WG is excited by the TE mode, the power will remain in the top WG, whereas in case of TM mode excitation, the power concentrates in the bottom WG at the end of the structure. The geometry of the metamaterial cladding structure in between WG cores is the same as in case of the PBS-1, since it has been optimized to achieve the longest possible L_x for TE mode. By employing the described structure with two metamaterial compact MZIs, we can reduce the footprint of the device, compared to realizations where conventional MZI configuration is used. As in case of the proposed PBS-1, we also employ the TE polarizer (the same structure as in PBS-1) at the Thru output of the PBS-2 to further reduce the excess TM polarization at this (TE) output.

2.3 Simulation methods

To design and analyse the performance of the proposed concepts of polarization beam splitters numerical simulations were employed. Different simulation approaches have been applied for efficient and accurate design and analysis. The metamaterial DC cross-section geometry in the first concept and the metamaterial DC coupling section of MZIs in the second concept were designed by employing mode analysis based on Finite Element Method (FEM) in COMSOL software [43]. Mode field profiles and corresponding effective refractive indices of modes were calculated in the cross-section of WG systems. When modelling metamaterial structures, real subwavelength geometry was assumed, since this yields more accurate results compared to effective medium theory approximation assuming an equivalent anisotropic material. The coupling length (L_x) defined as the length at which all the light of certain mode couples from the excited WG to the adjacent WG, was calculated from the difference of effective refractive indices of symmetric and antisymmetric modes by means of a supermode method [44]. Such an approach can be taken, since the system of two WGs with metamaterial cladding is inherently similar to a DC with normal (air or SiO₂) cladding, consisting of two coupled single-mode WGs. The metamaterial cladding affects only the decay of the evanescent field, altering the coupling strength of TE and TM mode. The geometrical parameters of the metamaterial cladding were obtained by sweeping the ff value at various values of P and N in order to achieve the longest possible L_x at a narrow gap width between WG cores at $\lambda $ = 1550 nm. In addition, we employed 3-D Finite Difference Time Domain (FDTD) simulations, using Lumerical Inc. software [45], to account for coupling in the bent sections of a directional coupler. The geometry of the TE polarizer was chosen by following the concepts described in [38]. Its performance was assessed by performing an FDTD simulation. FDTD simulations were also used at the final stage for accurate simulations of a full geometry of the proposed PBS-1 and PBS-2.

To define selected geometry parameters in PBS-2, namely the lengths of the straight coupling sections (L₁ and L₂) and angle $\varphi $ in the two bent MZI sections, we used a transfer matrix method (TMM). The results obtained by this method are approximate, since we did not account for the coupling in the bent sections of the metamaterial MZI configuration. TMM method is therefore only used to optimize the geometrical parameters of the PBS-2 dual MZI configuration in an efficient way. The phase delay can be calculated from effective refractive index of the guided mode in the WG and the difference in bend radii of the two WGs. The formalization of the TMM method is described in Supplement 1 (section 2). FDTD is used at the final stage to determine the performance of the full structure.

Since the purpose of the PBS-2 design is to increase the bandwidth, the parameters defining its geometry (L₁, L₂ and $\varphi$) need to be optimized to maximize the transmission of TM mode through the Cross port and to maintain the TE mode to be transferred to the Thru port in a wide wavelength range. To find these parameters we employed a simulated annealing optimization algorithm [46].

The described methods were used to design the geometry of devices and to perform preliminary simulations. The performance of designed structures was evaluated in terms of TE and TM power transmissions (T), insertion loss (IL), extinction ratio (ER) and bandwidth (BW) parameters. IL and ER of a selected mode (TE or TM) in decibel scale are defined in Eq. (1) where $T_{TE}^{Thru}$, $T_{TE}^{Cross}$, $T_{TM}^{Thru}$ and $T_{TM}^{Cross}$ are TE and TM mode transmission at the specified ports. For example, $T_{TE}^{Thru}$ is defined as the TE mode power at the Thru port divided by the input TE mode power applied to the device. Please note that in result section, the transmissions are presented in the dB scale as well (T [dB] = 10 log(T)). We defined the BW parameter as the wavelength range where the IL is smaller than 1 dB and ER is larger than 35 dB, unless otherwise specified.

In all the simulations Lorentz model was used to approximate the refractive index of Si with the value of 3.47 at $\lambda $ = 1550 nm [47]. The refractive index of the buried SiO₂ layer was chosen to be constant (1.44) in the simulated wavelength range.

3. Simulation results

We design the proposed two concepts of PBS for a typical Silicon-On-Insulator (SOI) platform with Si layer thickness of 220 nm and air upper-cladding. The width of WG cores in the analysed structures was chosen to be 500 nm. The minimal feature size, referring to a minimal slot width as well as minimal Si strip width, was selected to be 50 nm making the structures amenable for fabrication with electron-beam lithography [48].

First we will present results of the design and analysis of both proposed concepts by using mode analysis, TMM and partially FDTD (for certain substructures) simulation methods. Next the results of 3-D FDTD analysis of the designed structures will be presented and final theoretical performance evaluated.

3.1 Simulations of PBS-1

Let us first focus on the DC cross-section with the metamaterial cladding structure of PBS-1. The parameters P, N and ff of the metamaterial cladding of the DC are optimized based on FEM mode analysis to achieve strong coupling for TM mode to the second WG, related to smallest possible gap width (W_gap) between WG cores, and at the same time longest coupling length for TE mode at the chosen central C-band wavelength of 1550 nm. Results were obtained by performing a sweep of the ff parameter at different values of N (2, 3, 4) and P (125 nm, 150 nm, 175 nm). The metamaterial structure is designed to be symmetrical with a constant spatial period. The metamaterial parameters therefore define the W_gap. The goal of optimization is to find a structure that exhibits a significant increase in coupling length L_x (compared to WGs without the metamaterial cladding), at the smallest possible W_gap. FEM simulations showed that the optimized geometrical parameters of the metamaterial cladding in our structure are: N = 3, P = 150 nm and ff = 0.55. This results in W_gap = 518 nm.

In Fig. 2(a) we show simulation results for the coupling length L_x of the DC with optimized metamaterial cladding and, for comparison, with normal air cladding without the metamaterial structure. We can see that L_x of the TE mode is increased and L_x of the TM mode is decreased by employing the optimized metamaterial cladding, compared to normal air cladding in the whole wavelength range (trend denoted by arrows). Thus, the difference in coupling lengths of TE and TM mode is significantly increased, presenting a good starting point for efficient separation of TE and TM mode. The coupling length for TM mode of WGs with metamaterial cladding at the wavelength of 1550 nm is 12.6 um. In Fig. 1(a) we can observe that the L_x of the TE mode around $\lambda $ = 1550 nm approaches infinity in simulation, enabling high suppression of the TE mode at the internal port Thru_int at the Thru output of the DC (considering the structure without the TE polarizer). This infinity peak occurs due to a singularity originating in the anisotropy of the metamaterial structure as already reported in [36,37]. The coupling length of TE mode remains longer than 2.3 mm in the whole simulated wavelength range and approximately three orders of magnitude longer than the coupling length of TM mode. Primarily, the length of the DC needs to be set to the coupling length of the TM mode, so that the TM mode will optimally couple to the Cross output at the chosen central wavelength of 1550 nm. However, since some coupling occurs also at the input and output bent WG segments of the DC, the length of the straight section needs to be adjusted accordingly. For this reason, we performed 3-D FDTD simulations of the bent section of the DC to get the coupling level in this section and extract the equivalent coupling length. Taking this into account we calculated that the length of the straight section of the coupler needs to be 8.23 µm (and not 12.6 µm as indicated in Fig. 2(a)) in this design.

 

Fig. 2. Simulation results of (a) coupling length of a two straight WGs in a DC with metamaterial and normal cladding for TE and TM mode as a function of wavelength. (b) TM mode transmission for the Thru_int (internal port) and Cross output port of a partial PBS-1 structure without the TE polarizer as calculated with a TMM method, (c) TE and TM mode transmission of the TE polarizer, (d) TM mode transmission for the Thru_int (internal port) and Cross output port of an optimized partial PBS-2 structure (without the TE polarizer) as calculated with a TMM method.

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In Fig. 2(b) a simulated transmission for the TM mode at the Thru_int and Cross outputs of the PBS-1 structure without the TE polarizer for applied TM mode at the input is shown. TMM method was used in calculations. Considering the geometry design for λ = 1550 nm we can see the shallow peak transmission for the Cross port at this wavelength. The transmission for the Thru_int is the lowest at this wavelength. Note that whenever we refer to the Thru_int port, the structure without the TE polarizer is assumed in simulations. From the transmission curves other parameters stated in Eq. (4) can be calculated. Results revealed that relatively limited bandwidth (BW) can be achieved at very high extinction ratio (ER) for TM mode, namely for ER > 15 dB and ER > 35 dB, the corresponding BW is 58 nm and 10 nm, respectively.

To further increase the ER of the TM mode in PBS-1, the second part of the structure, the metamaterial TE polarizer comes into the picture. To minimize the TM mode at the final Thru port of the device, the TM mode needs to be adiabatically coupled out of the WG bend into free space via the bent metamaterial cladding. The metamaterial structure is designed in such a way, that the ff parameter linearly changes from 0.83 next to the WG core to 0.17 at the outer side of the metamaterial structure at the fixed spatial period P = 300 nm. The ff values of the first and last period of the metamaterial cladding are chosen to satisfy the minimal feature size condition of 50 nm for the air gap next to WG core and the Si rib width at the outer side of the cladding. The number of periods N needs to be high enough for the TM mode to efficiently diffract into free space. Based on simulations, in our case N was selected to be 10. The bend radius R_p of the WG in the polarizer needs to be tight enough for the TM mode to experience high losses, yet not too tight to ensure high transmission for the TM mode. According to simulation tests R_p was therefore chosen to be 2.5 µm, ensuring a high ER value for TM polarization. We simulated the designed TE polarizer structure using FDTD to evaluate its performance. In Fig. 2(c) we show results for TE mode and TM mode transmission of the polarizer obtained by 3-D FDTD simulations. For reference we also show the transmission of the WG bend without the metamaterial structure indicating that the designed metamaterial outer cladding is crucial for the desired performance of the TE polarizer. The TE mode has high transmission (small IL), namely IL < 0.4 dB in the whole simulated wavelength range. The TM mode is efficiently coupled out of the WG into the free-space, by means of the metamaterial structure. The ER for TM mode for wavelengths of interest (where the TM mode IL of PBS structures is below 1 dB) is calculated from transmission characteristics and spans from 17 dB up to 28 dB. This means that the ER for TM mode of PBS structures can be significantly increased by employing a metamaterial TE polarizer at the Thru port, forming an integral part of the proposed PBS designs.

3.2 Design and analysis of PBS-2

To increase the BW, we designed the PBS-2 structure (Fig. 1(b)). The metamaterial dual compact MZI structure was designed by employing the TMM method and simulated annealing optimization algorithm. We keep the cross section of the directional coupling structure within the MZIs the same as the DC in case of the PBS-1. Here we need to optimize the lengths of straight sections (L₁ and L₂) and the angle $\varphi $ and select the radius defining the length of the two bent sections for phase delay with the aim to achieve broadband coupling of TM mode to the Cross port of the device. The middle bend radius of the two bent sections for phase delay R_ΔL is chosen to be 20 µm, large enough to ensure low losses for both modes, yet not too large to minimize the unwanted coupling that occurs in these segments and to achieve a compact footprint of the structure. Calculated optimal parameters are L₁ = 12.07 um, L₂ = 13.69 um and $\varphi $ = 12.64°. This angle $\varphi $ results in a WG length difference $\mathrm{\Delta }L = 0.225\; {\mathrm{\mu} \mathrm{m}}$. In Fig. 2(d) we show TMM results for TM mode transmission of the optimized PBS-2 structure without the TE polarizer (at Cross and Thru_int port). The calculated IL parameter from presented transmissions remains < 1 dB for the BW = 342 nm, revealing that this structure has the potential to achieve ultra-wide BW. We can see that the transmission of the Thru_int port is not as low as one would desire, the calculated ER is only around 15 dB. To increase the ER for TM mode, we employ the previously designed TE polarizer at the Thru port. The benefits of the TE polarizer can be seen in the following section where we show results of FDTD simulations assuming the complete structures of the proposed PBS-1 and PBS-2 designs. All the parameters of the designed PBS-1 and PBS-2 structures are gathered in Supplement 1 (section 3).

3.3 Detailed simulations of the complete PBS-1 and PBS-2 designs

3-D FDTD simulations were employed to get accurate simulation results of the proposed PBS-1 and PBS-2 concepts. The entire structures as presented in Fig. 1 were included in simulations. In Fig. 3 we show and compare results for TE mode and TM mode transmission of PBS-1 and PBS-2. Besides the transmissions of complete structures, we also show the transmissions in case of partial structures without the TE polarizer at the internal Thru_int and Cross port to indicate the role of the TE polarizer.

 

Fig. 3. Selected results of 3-D FDTD simulation for TE mode and TM mode transmission of PBS-1 and PBS-2 structures with (complete structure) and without the TE polarizer (partial structure). For specified ports TE and TM mode transmission as a function of light wavelength are presented: (a) TE mode transmission for the PBS-1, (b) TM mode transmission for the PBS-1, (c) TE mode transmission for the PBS-2, (d) TM mode transmission for the PBS-2.

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In Fig. 3(a) the FDTD simulation results for TE mode transmission of the PBS-1 design are shown. The results indicate that the TE mode coupling into the Cross port is, as expected from previous partial and approximate simulations, strongly suppressed. The TE mode transmission at the Cross port remains below -38 dB (without polarizer) and -34 dB (with polarizer) in the whole simulated wavelength range. This small difference at the Cross port between structures with and without polarizer occurs due to reflections induced by the polarizer. On the other hand, the TE mode transmission at the internal Thru_int and external Thru port is very high in the whole wavelength range for both cases (detailed values will be discussed when analysing the corresponding IL and ER presented in Fig. 4). This indicates that the inclusion of the TE polarizer does not significantly affect the TE mode transmission.

 

Fig. 4. 3-D FDTD simulation results of (a) insertion loss and (b) extinction ratio of the PBS-1 and PBS-2 for TE and TM mode.

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In Fig. 3(b) the results for TM mode transmission of the PBS-1 are shown. The TM mode transmission at the Cross port for the case without and with the polarizer is very high around λ = 1550 nm, however at a limited wavelength range ($\Delta \lambda $ = 163 nm for $T_{TM}^{Cross}$ > -1 dB for structure with polarizer). It can be observed that the inclusion of the polarizer does not significantly affect the TM transmission at the Cross port. However, the unwanted TM mode transmission at the external Thru port is strongly suppressed by including the polarizer, namely from –27 dB to –52 dB at $\lambda $ = 1550 nm. This indicates that inclusion of the TE polarizer significantly reduces the unwanted transmission of the TM mode at the Thru port of the proposed PBS-1 design.

In Fig. 3(c) the results for TE mode transmission of the PBS-2 structure are shown. Similar to PBS-1 design, the PBS-2 structure exhibits very high TE mode transmission at the internal Thru_int for the case without the TE polarizer as well as at the external Thru port in case of a complete structure. The TE mode coupling to the Cross port is again strongly suppressed and stays below -32 dB and -30 dB for the case without and with the TE polarizer, respectively.

In Fig. 3(d) we show the transmission of the TM mode for the PBS-2 design. The wavelength range, where $T_{TM}^{Cross}$ > -1 dB for the structure with the polarizer is $\Delta \lambda $ = 300 nm, which is much broader than in case of PBS-1 ($\Delta \lambda $ = 163 nm). The origin of this broadening is in the operation of metamaterial compact dual MZI structure as explained before.

If we compare these results to results obtained by the TMM method (shown in Fig. 2(d)), the TMM method overestimates the transmission, since it does not account for coupling and bending losses in the two curved sections of the dual compact MZI structure. FDTD simulations are therefore crucial to correctly assess the device performance. The TMM results are not shown here for comparison, since the difference is too small to be observed at the shown scale for transmission.

Based on transmission simulations we show in Fig. 4 the calculated IL (a) and ER (b) for both proposed designs. The IL for TE mode (IL_TE) remains below 0.4 dB in the whole simulated wavelength range in case of both proposed designs. For TM mode the IL (IL_TM) remains below 1 dB in the wavelength range of 1481 nm - 1644 nm for PBS-1 and 1356 nm - 1656 nm for PBS-2. The ER for TE mode (ER_TE) is higher than 35 dB in the wavelength range < 1667 nm for PBS-1 and < 1642 nm for PBS-2. The ER for TM mode (ER_TM) is higher than 35 dB in the wavelength range of 1462 nm – 1693 nm for PBS-1 and 1379 nm – 1680 for PBS-2. We define the bandwidth parameter (BW) as the narrowest wavelength range where IL is lower than 1 dB and ER is higher than 35 dB for both TE and TM mode at the same time. Following this definition, the BW for PBS-1 is 163 nm as marked in Fig. 4(a). For PBS-2 design, the BW is increased to 263 nm as marked in Fig. 4(b). In case of PBS-1 the limiting factor for BW is IL, while for PBS-2 the limiting factor is ER. FDTD simulations show that by employing the metamaterial compact dual MZI structure in the proposed PBS-2 design, optimized by using TMM, we can increase the BW by 100 nm compared to the proposed metamaterial DC-based PBS-1 design, while sustaining the IL < 1 dB and ER > 35 dB.

4. Fabrication and measurement results

The proposed PBS-2 concept was fabricated and characterized. Fabrication was carried out using 100 keV electron beam lithography (EBL) at Applied Nanotools, Inc. [49]. A SOI wafer with 2 µm thick buried oxide and 220 nm thick silicon device layer was used as the substrate. EBL patterning process followed by an inductively coupled plasma-induced reactive ion etching (ICP-RIE) process allows for fabrication of devices with minimal feature sizes down to 70 nm.

We therefore slightly modified the PBS-2 structure for fabrication to comply with requirements for minimal feature size of 70 nm. In fabricated designs we altered the ff of the metamaterial in the dual compact MZI structure from 0.55 to 0.53. The structure of the TE polarizer was also modified: the minimal ff of the metamaterial cladding was increased from 0.17 to 0.23 and the maximal ff was reduced from 0.83 to 0.76, N was changed from 10 to 9. We carried out FDTD simulations of the modified structure to check whether the performance was significantly affected. The simulated ER was found to be slightly reduced to 33 dB, while the IL remained below 1 dB in a slightly wider BW of 273 nm. Figure 5 shows scanning electron microscope images of the fabricated device. Grating couplers were employed to vertically couple light from an optical fiber to the input of the device and from the output of the device back to an optical fiber. Due to a single-etch fabrication process, subwavelength grating couplers were employed to improve the coupling efficiency and reduce reflections [50]. A tunable continuous wave (CW) laser (HP 8168F) and a power sensor (HP 81531A) were used to obtain the power transmission spectra of fabricated devices. A fiber polarization controller was also employed to adjust the polarization in the input optical fiber.

Measurements were performed in the wavelength range between 1450 nm and 1590 nm, dictated by the tuning range of the laser. Two sets of devices were fabricated: one was connected to TE mode grating couplers and the other to TM mode grating couplers. This enabled us to separately measure the TE and TM mode transmission at all ports of the device. Due to a limited bandwidth of grating couplers, we performed measurements at two different tilt angles of the optical fiber [20]. A 5° tilt angle results in a measured peak coupling efficiency of -5.92 dB at the central wavelength of 1540 nm and -14.55 dB at the central wavelength of 1557 nm for the case of TE and TM grating coupler respectively. A 12° tilt angle results in a measured peak coupling efficiency of -4.60 dB at the central wavelength of 1500 nm and -8.05 dB at the central wavelength of 1500 nm for the case of TE and TM grating coupler respectively. We set tilt angle to 12° to for the wavelength range from 1450 nm to 1525 nm and to 5° for the wavelength range from 1525 nm to 1590 nm. The measurement results shown in Fig. 6 combine the measurement results at these two tilt angles. This way more accurate results can be obtained, in contrast to performing all the measurements at a single tilt angle.

 

Fig. 5. (a) SEM image of fabricated PBS-2 device. (b) A close-up SEM image of the bent section of the metamaterial dual MZI structure. (c) A close-up of the section of the metamaterial TE-polarizer.

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Fig. 6. Measured transmission of TE and TM mode at specified ports of the PBS-2 device. Simulation results (dashed lines) are also shown for reference. (a) transmission of TE mode, (b) transmission of TM mode

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In Fig. 6(a) the results are shown for the measured TE transmission of the fabricated structure. Simulation results corresponding to the fabricated structure are also shown (dashed lines) for comparison. The measured TE mode transmission at the Thru port is above -1.5 dB in the measured wavelength range. Note that at some points the transmission exceeds 0 dB. This indicates that a certain measurement uncertainty has to be taken into account, which occurs when we normalize the measurement results to the spectrum of the grating coupler. The reason for this are fabrication imperfections of grating couplers and non-optimal alignment of optical fibers during the measurement. This makes accurate assessment of the IL difficult. Additionally, a large oscillation of measured transmission occurs at longer wavelengths, which can most likely be attributed to reflection from grating couplers, as well as a low coupling angle of 5° introducing additional reflections. The TE mode transmission at the Cross port is below -32 dB in the whole measured wavelength range. In Fig. 6(b) the results are shown for the measured TM transmission of the fabricated structure. Corresponding simulation results are also shown (dashed lines) for comparison. The TM transmission at the Cross port is higher than -1.3 dB in the measured wavelength range. Note that the transmission above 0 dB is again a result of normalization error, due to grating coupler variability and non-optimal fiber alignment. A sharp jump in transmission at 1525 nm occurs due to a change in fiber tilt angle at this wavelength in the measurements. The highest value of transmission reaches 1.3 dB indicating the measurement error. The TM transmission at the Thru port remains below -33 dB in the whole measured wavelength range. In spite of the measurement errors, results indicate high transmission of the TE mode at the Thru port of the device and the TM mode at the at the Cross port of the device. Combined with the exceptionally low measured transmission of the TE mode at the Cross port and TM mode at the Thru port, this points to good polarization splitting performance, which is in good agreement with simulation results.

We also investigated how fabrication tolerances affect the performance of the PBS-2. Results for feature size variation in the range of +/-5 nm and +/- 10 nm are shown in Supplement 1 (section 4). Results indicate that the device is robust to variations in the range of +/-10 nm, since only a slight degradation of performance was observed.

5. Discussion

Measurement results of PBS-2 for TE as well as TM mode, shown in Fig. 6, agree well with simulation results, demonstrating that fabrication of the proposed PBS-2 device is feasible and expected performance can be achieved. A slight modification of the device structure to comply with the minimal feature size of the fabrication process also did not majorly alter the performance. Measurement results confirmed that a high ER above 30 dB is achievable in the BW of at least 140 nm. Our measurements were limited by the tuning range of the laser. Simulation results reveal that the BW is possibly at least 120 nm wider. Due to measurement errors we could not accurately assess the IL, however, one can see that the measurement curves follow simulation results relatively well without any significant discrepancy in the trend. Measurement results indicate that the IL is most likely below 2 dB, however in order to accurately measure the IL, additional cascaded test structures would need to be considered in the analysis [18]. The presented measurement results still serve as a proof of concept of the proposed device.

To evaluate the properties of the proposed polarization beam splitter we present its performance parameters in comparison to other state-of-the-art demonstrations of integrated silicon photonic polarization beam splitters in Table 1. We indicate in the table which parameters refer to simulation (subscript sim) and which to the measured data (subscript exp). Results for IL, ER and BW are gathered in the table. Most of the referenced works are utilizing subwavelength structures to enhance the performance of PBSs. There have been demonstrations of PBSs of exceptionally high ERs of up to 50 dB [16] as obtained from the measurements, however the BW of such devices is very narrow. On the other hand, there have been a number of demonstrations of PBSs exceeding the measured BW of 200 nm, or in one case even 415 nm covering all the telecom bands [26]. The wide BW though, comes at the cost of lower ERs. The widest measured BW of 70 nm for an ER > 30 dB has been achieved by employing a cascaded bent DC structure [51]. Simulation results of the proposed PBS-2 structure indicate that an IL below 1 dB and ER above 35 dB can be achieved in a BW of 263 nm. The measurement results of our proposed PBS-2 device show an ER > 30 dB in a BW of at least 140 nm. Note that the IL measurement results are stated in the brackets, due to the explained measurement error.

Table 1. Summarized results for some of the current state-of-the-art polarization beam splitter demonstrations. In the first column reference number along with year of publication is shown. Simulation (subscript sim) and experimental (subscript exp) results for IL, ER and BW as well as the physical length of the structures are gathered in the table.

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The footprint of our proposed device cannot compete with the most compact PBS designs, however it is comparable to the average footprint of recent PBS demonstrations [19,24]. We believe that the performance of the PBS-2 represents a good trade-off in terms of all the performance metrics. Furthermore, we have shown that it also exhibits robustness to fabrication tolerances. The minimal feature size of the fabricated PBS-2 is 70 nm which is well within the capability of e-beam manufacturing, however, it is slightly too small for wafer-scale fabrication used in mass manufacturing. In order to test the feasibility of our proposed PBS-2 structure for mass manufacturing, we altered the design also for a minimal feature size of 100 nm. Simulation and measurement results for this structure are shown in Supplement 1 (section 5). The performance metrics for these PBS-2 structures are summarized in the first two rows of Table 1. As we can see, moving towards larger feature sizes did not significantly degrade the performance. Simulations show that only BW is slightly reduced. The only trade-off when choosing larger minimal feature sizes appears to be in the device footprint which needs to be significantly larger (108 µm).

6. Conclusion

We proposed a novel polarization beam splitter design in silicon integrated photonics by employing all-dielectric metamaterial cladding. Performance evaluations have been carried out by means of numerical simulations, as well as fabrication and measurements. As a starting point a structure is formed of a metamaterial DC and a bent metamaterial TE polarizer (PBS-1). The DC is designed to couple the TM mode to the second WG, while the metamaterial cladding contains the TE mode in the first WG. The TE polarizer is employed after the DC to diffract the unwanted excess TM polarization out of the first WG, increasing the ER of the device. Quantitative performance results of the PBS-1 are given and the role of the TE polarizer part evaluated. Since such a device still exhibits limited bandwidth, we designed a new structure formed of a metamaterial compact dual MZI structure coupled with a bent metamaterial TE polarizer (PBS-2). The dual MZI structure exhibits broadband coupling of the TM mode enabling us to achieve ultra wide bandwidth of the PBS-2. The phase delay segments of the MZIs are designed unconventionally by parallel bending of the two WGs to achieve a more compact geometry. Measurements revealed that an ER above 30 dB and a BW of at least 140 nm can be achieved for PBS-2 device. Simulation results reveal that the BW is most likely up to 120 nm wider than what was confirmed by the experiment (due to limited tuning range of the laser). We believe that the demonstrated design and performance of the PBS-2 is to be utilized in PICs for applications where high performance polarization splitting is required.