Subwavelength-grating-assisted broadbandpolarization-independent directional couplerLU LIU, QINGZHONG DENG, AND ZHIPING ZHOU*State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering andComputer Science, Peking University, Beijing 100871, China*Corresponding author: zjzhou@pku.edu.cn

Received 3 February 2016; revised 9 March 2016; accepted 9 March 2016; posted 10 March 2016 (Doc. ID 258541); published 1 April 2016

This Letter presents both numerical and experimental resultsof a polarization-independent directional coupler based onslot waveguides with a subwavelength grating. The measuredcoupling efficiency is 97.4% for TE and 96.7% for TMpolarization at a wavelength of 1550 nm. Further analysisshows that the proposed subwavelength grating directionalcoupler has a fabrication tolerance of�20 nm for the gratingstructure and that the coupling efficiencies for the two polar-izations are both higher than −0.5 dB (∼89%), exceeding theentire C-band (1525–1570 nm) experimentally. © 2016Optical Society of America

OCIS codes: (130.3120) Integrated optics devices; (050.6624)

Subwavelength structures; (050.2770) Gratings.

http://dx.doi.org/10.1364/OL.41.001648

Directional couplers (DCs), consisting of two parallel wave-guides separated by a gap, play a fundamental and significantrole in many applications, such as on-chip sensors [1,2], powertaps [3], microring filters [4,5], and Mach–Zehnder (MZ)switches [6–8]. DCs are widely preferred for their straightfor-ward way of power splitting and negligibly low insertion losswhen compared with other optical splitters, for example, a mul-timode interference (MMI) coupler (typically 0.3–0.5 dB) [9].However, DCs suffer from polarization-dependent problemswhen they are extended to high-contrast systems such as siliconphotonics [10]. The beat length for TE greatly differs from thatfor TM, making the output power unequal for the two polar-izations at a certain device length, which limits the polarization-independent coupling and power splitting in silicon photonicintegrated circuits.

One solution is to use polarization diversity schemes wherepolarization splitting and rotating is applied, which increasessystem size and complexity [11,12]. Another approach is tomake the directional coupler inherently polarization insensitive,such as modifying slot waveguide parameters [10,13–15],applying multiple parallel waveguides [16], as well as resortingto plasmonic mode features [17]. Both suffer from either rel-atively large device size or present a big challenge to the currentstandard complementary metal–oxide–semiconductor (CMOS)fabrication technology.

Subwavelength gratings (SWGs) are gratings with pitchesmuch smaller than the wavelength of light propagating throughthem [18]. SWGs can be generally considered as a homogenousmedium and their equivalent material index can be tailored bychanging the duty cycle, thus providing a new degree of free-dom for the design of novel photonic components [19]. ManySWG-based devices with high performance have been reportedsuch as beam splitters [20], fiber-chip grating couplers [21],MMI couplers [22], colorless directional couplers [23], andfabrication-tolerant polarization splitters and rotators [24].

Here, we propose the use of a SWG to design a polarization-independent directional coupler (PIDC). The key to our ap-proach is to make the effective index difference between oddand even modes identical for both TE and TM modes byadjusting the grating duty cycle. Benefited from this design,polarization independence exceeding the entire C-band isdemonstrated both numerically and experimentally while thebeat length is ∼10 μm.

The proposed PIDC (Fig. 1), designed on a silicon-on-insulator (SOI) wafer with SiO2 up-cladding, consists of twosilicon slot waveguides named A and B, respectively, which arewith a certain number of grating pitches with period of Λ at theside close to the gap. The lengths of the low and high refractiveindex segment, namely, groove and ridge are a and Λ − a, re-spectively. Owning to the properties of SWGs, the inside neigh-boring parts of waveguide A and B can be considered ashomogenous medium with an effective refractive index nk,which can be modified by varying the duty cycle f � �2awd �∕�Λ�w − ws�� (the area proportion of the low-index segment inone period) [25]. Some other parameters are as follows: thewaveguide height h is 250 nm; the silicon waveguide widthis w, where the gap width is wg ; and the slot width ws is fixedto be 100 nm, which is common in many applications. Bothgrating groove a and grating depth wd are set to be 100 nm forthe ease of fabrication. Additionally, an s-bend with a radius of5 μm is attached to the output port to decouple the waveguides.

The operation principle of the conventional directional cou-pler is illustrated as follows: light is launched into one arm andexcites the even and odd supermodes of the two parallel wave-guides. The beat length of these two modes is given as [23]

Lπ �λ

2�neven − nodd�; (1)

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0146-9592/16/071648-04 Journal © 2016 Optical Society of America

where neven and nodd are the effective indices of the two modes,respectively. If neven − nodd can be made identical for TE andTM modes, the beat lengths of both polarizations are equal,leading to polarization-independent performance. Based onthis knowledge, the proposed PIDC is realized by properlytuning neven − nodd.

The 2D finite element method (FEM) and the 3D finite-dif-ference time-domain (FDTD) method were used to design thePIDC and study its characteristics. The operation free-spacewavelength is set to 1550 nm, and the refractive indices of siliconand silicon dioxide are nSi � 3.48 and nSiO2

� 1.46, respec-tively. The inside neighboring parts of waveguides A and B areconsidered as homogenous media. When nk decreases (i.e., a gra-ting structure is introduced into a conventional slot waveguide),the beat lengths for both polarizations get longer, but the twocurves are of different slopes, as shown in Fig. 2. Thus, this pro-vides a way to manipulate the beat length Lπ by the variation ofnk, which can be achieved by the adjustment of duty cycle f .

Rytov’s formulas are used to determine the grating param-eters roughly to achieve polarization independence [26],

n2TE � n21f � n22�1 − f �1

n2TM� 1

n21f � 1

n22�1 − f �: (2)

In our case, n1 and n2 are the refractive indices of SiO2 andSi, respectively. For a grating structure with duty cycle f , if its

equivalent refractive indices for TE and TM, nTE and nTM, cansatisfy nTEk and nTMk respectively, then the f for polarizationindependence is obtained. Further, a series of 3D FDTDsimulations of PIDCs with real grating structures of varyingperiods are carried out to optimize the grating parameters.After these steps, the following parameters are chosen:w � 520 nm, wg � 230 nm, f � 0.129 (i.e., Λ � 370 nm),and the corresponding Lπ∼10 μm. It can be seen that Eq. (2) issatisfied roughly.

Further simulation is carried out to verify the polarizationindependence along the light propagation direction. Opticalenergy flux is integrated over the waveguide cross section andthe relationship between coupling efficiency and couplinglength L was obtained, which is shown in Fig. 3. The simulateddata can be well fitted as a sinusoidal function with the form ofA sin2�κ · L� φ�, which is the theoretical expression for DCcouplers [27]. The introduction of φ is to account for the modetransformation from a conventional waveguide to a SWGwave-guide. When L is small (less than 3 μm), the simulated data area little deviated from the fitted curve, while there is good agree-ment as L becomes large. This is because some distance isneeded for the slot waveguide mode to transform into a com-plete and steady SWG mode. The fitted curves for TE and TMslightly differ. However, the difference remains lower than 2%for all L. Several reasons contribute to this divergence. For TEand TM, the grating still exerts a slightly different influence onthe coupling process since for short length (e.g., one periodlong), the accuracy of Eq. (2) is low and the real effective indexwill deviate from the required nTEk (nTMk ). As a result, κ and φcould not coincide simultaneously for the two polarizations.Also, since fabrication simplicity is considered, for example,w and wg are both integral multiples of 10 nm, Lπ is not criti-cally the same for the two polarizations. Here, 10 μm for TEand 9.81 μm for TM.

For a fully coupled PIDC, the optimal length of the cou-pling region is 8.4 μm when discounting s-bend length, indi-cating a compact footprint. The grating region of waveguide Bextends until the s-bend ends to make the coupling regiontransform smoothly. A fully coupled PIDC with an s-bend ispresented in Fig. 4 as an example, with optical energy flux den-sity (Px) of TE and TMmode incidence. The input fundamen-tal TE and TM modes are launched at the input port ofwaveguide A and propagate to the output port of waveguide B.

Fig. 1. Schematics of the proposed PIDC based on slot waveguideswith a SWG. (a) 3D view, (b) zoomed-in view of the coupling region,and (c) the SWG represented as a homogenous medium waveguidewith an effective refractive index nk . The upper cladding of the silicondioxide is not shown here for clarity.

Fig. 2. Relationship between the beat length Lπ and nk at 1550 nm,when w � 520 nm and wg � 230 nm. For a certain Lπ , the corre-sponding nk for TE and TM are called nTEk and nTMk , respectively.

Fig. 3. Coupling length L dependence of coupling efficiency at1550 nm. Simulated data can be well fitted for TE, 0.983 sin2

�0.153L� 0.038�, and TM, 0.983 sin2�0.16L� 0.005�.

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The coupling efficiency is defined as PB_Out∕PA_in. As shown inFig. 5, at 1550 nm, the coupling efficiency achieves 98.0% forTE and TM, simultaneously. Furthermore, the 0.5 dB band-width, defined as the bandwidth when the coupling efficiencyfor TE and TM modes are both higher than −0.5 dB (∼89%),is as broad as 120 nm. Moreover, the coupling efficiency diver-gence between TE and TM maintains at less than 1.8%. Thisbroadband performance is much better than that of polarization-independent directional couplers which are also based on slotwaveguides, especially for the TE mode [13,15]. The transmis-sion of the bar port varies in the range of 0.3%–7.4% for TE and0.1%–8.0% for TM while the total transmission is around98.3%, indicating an insertion loss of about 0.1 dB.

For comparison, a conventional slot directional coupler wasalso simulated which is of the same parameters of the PIDC,merely excluding the grating structure. At 1550 nm, the beatlength Lπ for TE and TM are 9.76 and 7.13 μm, respectively,which can also be confirmed by Fig. 2 when nk � 3.48. Itmeans that a fully coupled DC for TE only holds a couplingefficiency of 91% for TM, indicating a distinguished couplingefficiency difference up to 9% (−0.4 dB).

Fabrication tolerance is also analyzed. Figures 6(a) and 6(b)present the normalized variation of Lπ (i.e., ΔLπ∕Lπ) as a func-tion of wd and a, respectively. For a �5% variation of Lπ, thetolerance regarding wd (a) is �20 nm for both polarizationswhile the PIDC is more sensitive to the wg variation, as shownin Fig. 6(c). For�5% (�15%) variation of Lπ, the tolerance is�10 nm (�30 nm). A conventional slot directional couplerwas also simulated which has the same parameters as thePIDC, merely excluding grating structure. Its tolerance aboutwg is similar, that is�30 nm for�16% variation of Lπ, whichindicates that the introduced grating does not bring more sen-sitivity to the directional coupler. Furthermore, our device is

expected to be less sensitive to wg variation if combined withsome fabrication tolerance-enhanced design, for example [9].

The designed directional coupler was fabricated on a SOIwafer with 250 nm thick top silicon and 2 μm thick burieddioxide. Electron-beam lithography was used to define thestructure pattern and an inductively coupled plasma etchingprocess was followed. Then, the chip was covered with a 1 μmthick silicon dioxide layer as the upper cladding by plasma-enhanced chemical vapor deposition. The top-view scanningelectron microscope (SEM) picture of the fabricated directionalcoupler is shown in Fig. 7, captured before the upper claddingwas deposited.

The experimental setup to characterize the fabricated devi-ces is as follows: a tunable CW laser is utilized as the lightsource and a digital polarization controller is used to adjust thepolarization state. Mode converters were also fabricated toefficiently transform energy between the PIDC slot waveguideand the conventional strip waveguide [28]. Light is butt-coupled into the chip and then butt-coupled out to an opticalspectrum analyzer through the coupling between the taperedlens fiber and the strip waveguide.

Figure 8(a) shows the measured transmission spectrum ofone device for TE and TM polarizations. Because of the reflec-tion of both end facets, the signal-to-noise ratio is degraded bythe Fabry–Perot effect. To suppress noise, the robust locallyweighted regression method is used to extract the trend lines[29,30], from which coupling efficiency can be derived. The

Fig. 4. Optical energy flux density (Px) in the designed PIDC for(a) TE and (b) TM at 1550 nm.

Fig. 5. Wavelength dependence of coupling efficiency.

Fig. 6. Normalized variation of Lπ as a function of (a) depth wd ,(b) groove a, and (c) gap wg at 1550 nm. Blue circle for TE and redasterisk for TM.

Fig. 7. SEM image of the fabricated directional coupler.

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trend line of TM is relatively flat and that of TE is a littlefluctuated. Besides the device’s built-in attribute, the opticalspectrum analyzer’s performance also contributes, which re-sponds better when optical power is higher. In our case, the out-put power of TE is lower than that of TM. Actually, to ensure themeasurement accuracy, three identical devices were fabricatedand each was tested two times. The mean value of their measuredresults is considered as the final result, as shown in Fig. 8(b).The measured coupling efficiency of TE and TM are 97.4%and 96.7%, respectively, at 1550 nm. In the measured range(1525–1570 nm), the difference between TE and TM is lessthan 0.4 dB, indicating that the 0.5 dB bandwidth is wider thanthe C-band. The curve of TE is redshifted, leading to low cou-pling efficiency in the wavelength range of 1525–1540 nm,which is confirmed by the output power of the TE bar portslowly decreasing as wavelength increases in Fig. 8(a). This prob-ably resulted from a slight fabrication deviation from our design.

We have proposed and fabricated a polarization-independent directional coupler based on SWG structure. TheSWG structure is carefully designed so that the beat length forboth TE and TM can be identical with high coupling effi-ciency. The measured coupling efficiency is about 97.4% forTE and 96.7% for TM at a wavelength of 1550 nm.

Broadband operation is demonstrated over a bandwidth of120 nm (1475–1595 nm) theoretically and exceeds the entireC-band (1525–1570 nm) experimentally. The device is alsocompact and has a minimum feature size of 100 nm, whichcan be easily realized by modern fabrication technology.Finally, this on-chip DC not only can be readily integrated withother optical components but also strongly consolidates thatthe concept of SWG structure could open a new windowfor the design of high-performance integrated optics devices.

Funding. National Natural Science Foundation of China(NSFC) (61120106012, 61177058).

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Fig. 8. (a) Normalized measured spectrum of one PIDC. (b) Meanvalue and the error bound of the measured spectrum of three identicaldevices. The black lines are trend lines extracted with robust locallyweighted regression (solid for TE and dashed for TM). The fittingparameter r used here is 0.25 and the efficiency difference betweenTE and TM varies by 0.027 dB (0.5%) when r changes from 0.2to 0.3. The error bound (color belts in the figure) shows the standarddeviation of the measured results.

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