2846 Vol. 45, No. 10 / 15 May 2020 /Optics Letters Letter

Design and experimental demonstration of asilicon multi-dimensional (de)multiplexer forwavelength-, mode- and polarization-division(de)multiplexingYu He, Yong Zhang, Hongwei Wang, Lu Sun, AND Yikai Su*State Key Lab of AdvancedOptical Communication Systems andNetworks, Department of Electronic Engineering,Shanghai Jiao TongUniversity, Shanghai 200240, China*Corresponding author: yikaisu@sjtu.edu.cn

Received 10 February 2020; revised 5 April 2020; accepted 5 April 2020; posted 8 April 2020 (Doc. ID 390015); published 14 May 2020

Leveraging the physical dimensions of an optical carrier(e.g., wavelength, mode, or polarization) allows significantscaling of the transmission capacity for optical communica-tions. Here we propose a scheme for implementing on-chipsilicon (de)multiplexers with simultaneous wavelength-,mode-, and polarization-division (de)multiplexingcapability. The device is constructed by using cascadedsubwavelength grating (SWG)-based contra-directionalcouplers. To verify the feasibility of the proposed structure,we perform a proof-of-concept experiment of an 8-channel(de)multiplexer with two wavelengths, two modes, and twopolarizations. The insertion losses are lower than 6.6 dB andthe crosstalk values are below −18.7 dB at around 1540 nmand 1550 nm for all the eight channels. © 2020 OpticalSociety of America

https://doi.org/10.1364/OL.390015

Multiplexing technologies in silicon photonic integratedcircuits have attracted much attention due to their compactfootprints and the compatibilities with the complementary-metal-oxide-semiconductor (CMOS) fabrication processes[1]. Currently, most on-chip devices employ only one or twophysical dimensions of an optical carrier such as wavelength [2],mode [3–6], or polarization state [7–10]. Scaling towards morephysical attributes of an optical carrier can effectively increasethe transmission capacity and is therefore highly desired.

Recently, there have been some reports of on-chipwavelength- and mode-division multiplexing (WDM-MDM)technologies [11–16]. Polarization-division multiplexing(PDM) has also been introduced in combination with WDM[17] or MDM [18–20] to achieve a higher capacity. However,to the best of our knowledge, no (de)MUX with simultaneousWDM-MDM-PDM capability has been reported.

In this Letter, we propose an on-chip silicon (de)multiplexercapable of (de)multiplexing wavelength-, mode-, andpolarization-channels simultaneously, by using a bus waveguideside coupled to multiple subwavelength grating (SWG)-basedcontra-DCs [21]. The SWG contra-DC is the key building

block, which possesses the advantages of flat-top passband, highdesign flexibility, and single-band operation. We first design thestructural parameters of the contra-DCs to satisfy the phase-matching conditions for each mode on different polarizationstates. Then the operation wavelengths of the contra-DCsare adjusted by tuning the periods of the SWG structures.The multi-dimensional (de)multiplexer with simultaneousWDM-MDM-PDM capability is therefore implemented bycascading multiple contra-DCs designed for each channel. Toverify the feasibility of the structure, we perform a proof-of-concept experiment of an 8-channel (de)multiplexer with twowavelengths (1540 and 1550 nm), two polarizations, and twomodes (TE0, TE1, TM0, TM1). Measured results indicate thatthe insertion losses (ILs) for all the eight channels are lowerthan 6.6 dB, and the crosstalk values are below−18.7 dB. Morewavelength channels or higher-order mode (de)multiplexingcan be achieved by cascading more contra-DCs to further scalethe transmission capacity.-

The schematic of an SWG-based contra-DC is shown inFig. 1. An SWG waveguide (WG1) with a period of 3 and aduty cycle of δ, is placed along a strip bus waveguide (WG2),to form the coupling region. The interaction of the modes inthe two waveguides can be described by the mode couplingequations [22]:

Fig. 1. Schematic configuration of the SWG-based contra-DC.

0146-9592/20/102846-04 Journal © 2020Optical Society of America

Letter Vol. 45, No. 10 / 15May 2020 /Optics Letters 2847

daBloch

dz=−iβBlochaBloch + iκa p

da p

dz=−iβpa p − iκaBloch, (1)

where aBloch and a p are the amplitudes of the forward propagat-ing Bloch mode in WG1 (βBloch) and the backward-propagatingspatial mode p in WG2 (βp ), respectively.κ is the coupling coef-ficient. We assume that κ = 2κ0f (z) with f (z) describing theperiodic structural variations of the grating along the z axis andκ0 is the normalized coupling coefficient. By introducing therelation: a = Ae−iBjz, Eq. (1) can be approximated as

d ABloch

dz= iκ0e iεz A p

d A p

dz=−iκ0e−iεz ABloch, (2)

with ε= βBloch + βp − 2π/3. The solutions of these equationscan be found in Ref. [22]. When the phase matching conditionis satisfied:

ε= 0⇒ βBloch + βp −2π

3= 0⇒

n p + nBloch

2=λc

23, (3)

where λc is the operation wavelength of the contra-DC. Thepower coupling ratio can be expressed as∣∣∣∣ A p(Drop)

ABloch(Input)

∣∣∣∣2

= tanh2(κ0L c ). (4)

With a sufficiently long coupling length L c , the injectedBloch mode is completely converted to a backward-propagatingspatial mode p in WG2. An SWG-wire transition taper witha 20-µm-length is used to convert the injected TE0 or TM0mode in the silicon nanowire waveguide to a Bloch mode in theSWG [23]. For an accurate controlling of L c , an SWG wave-guide bend with a 10-µm curvature radius and a trapezoidalsegment design is used to separate or combine the two wave-guides with a negligible bending loss. The structural parametersof the trapezoidal segments are designed by following rulesprovided in Ref. [24] and optimized through iterative devicefabrications and characterizations. We calculate the effectiverefractive indices of the waveguide modes using a finite differ-ence eigenmode (FDE) solver and plot the dispersion curveswith phase-matching conditions for different mode couplingsas shown in Fig. 2(a)–2(d). The phase-matching condition issatisfied at the cross-point of the two curves in each subplot,where the Bloch mode (nBloch) on TE- or TM-polarizationstate in WG1 can be contra-directionally coupled to a selectivewaveguide mode (n p ) in WG2 at 1550 nm. Due to the highindex asymmetry, the co-directional coupling is effectivelysuppressed.

The SWG-based contra-DCs designed for each modechannel are optimized by using the 3D finite-difference time-domain (FDTD) method. The simulation window dimensionis 300× 3 µm2 with a mesh size of 25 nm in both directions.We simulate the demultiplexing processes by launching spatialmodes into the Drop port and monitoring the output powerat the Input port. The simulated electric field distributions forthe TE0-, TM0-, TE1-, and TM1-mode DEMUX processes

Fig. 2. Calculated dispersion curves of the guided modes withphase-matching conditions for the (a) TE0-TE0, (b) TM0-TM0,(c) TE0-TE1, (d) TM0-TM1 mode couplings at 1550 nm, respectively.

at 1550 nm are shown in Fig. 3(a)–3(d), respectively. High-efficiency contra-directional couplings between the spatialmodes in WG2 and the Bloch modes in WG1 can be observed.The 3-dB bandwidth can be described as [22]:

1λ∝1

L∣∣ d

dλ (|β1 + β2|)∣∣ . (5)

To achieve a narrow reflection bandwidth for multiple wave-length channels, all the contra-DCs are designed to operate ina weak-coupling regime [21], with large gap values (350 nm–500 nm) and long coupling lengths (L c = 300 µm). The

Fig. 3. Simulated electric field distributions (E x component) forthe (a) TE0-, (c) TE1-mode DEMUX, and electric field distribu-tions (E y component) for the (b) TM0-, (d) TM1-mode DEMUX at1550 nm.

2848 Vol. 45, No. 10 / 15May 2020 /Optics Letters Letter

Fig. 4. Simulated transmission responses of the DEMUX stages forall eight wavelength channels with incident lights on (a) TE0, (b) TE1,(c) TM0, (d) TM1 mode, respectively. The numbers denote the periodsof the SWGs designed for each wavelength channel (unit: nm).

Fig. 5. Schematic of the proposed eight-channel multi-dimensionalMUX.

operation wavelength of the contra-DC can be shifted by tun-ing 3 of the SWG waveguide. We simulate the transmissionspectra of the contra-DCs designed for each mode channel withdifferent period values, as shown in Fig. 4(a)–4(d), respectively.Note that only DEMUX stages were included in simulationsfor fast evaluation. Eight wavelength channels in C-band witha 6-nm channel spacing are employed to maintain a reasonablecrosstalk below −20 dB. The numbers in each subplot denotethe period values used for the corresponding contra-DCs. Theoverall insertion losses for all channels are lower than 1.5 dBaccording to the simulations. Therefore, by cascading SWG-based DCs designed for each channel, the WDM-MDM-PDM(de)multiplexing can be achieved.

To verify the feasibility of the proposed scheme, we perform aproof-of-concept experiment of an 8-channel (de)multiplexerwith two wavelengths, two modes, and two polarizations, asshown in Fig. 5. Structural parameters of the contra-DCs used

for each mode channel at 1540 nm and 1550 nm are detailed inTable 1. Adiabatic tapers with a 0.8◦ angle are used to smoothlyconnect the bus waveguides of the contra-DCs with differentwidths [3]. Note that the correspondence between the opera-tion wavelengths and the periods of the contra-DCs in Table 1slightly differs from that in Fig. 4. This can be attributed to therelatively low mesh accuracy we used in our simulations forfast evaluations (level 1). A finer mesh setting can be used toget a more accurate estimation of the contra-DCs’ operationwavelengths.

The devices were fabricated on a silicon-on-insulator (SOI)wafer with a 220-nm-thick silicon on top of a 3-µm SiO2buried oxide. Waveguides and gratings were patterned usingelectron beam lithography (EBL, Vistec EBPG 5200+) andfully etched by inductively coupled plasma (ICP) etching. A2-µm-thick SiO2 cladding layer was then deposited on top ofthe devices by plasma-enhanced chemical vapor deposition(PECVD, Oxford). The microscope image of a fabricated 8-channel (de)multiplexer is shown in Fig. 6(a). Eight contra-DCsare used as MUXes with their input ports denoted as I1 ∼ I8.Fundamental TE or TM modes are injected from these portsand coupled to selective spatial modes in the bus waveguide.After a 207-µm-long multimode waveguide transmissionincluding two multimode bus waveguides with a 25-µmlength and a 180-deg waveguide bend with a 50-µm curva-ture radius, signals are demultiplexed by the correspondingcontra-DCs and selectively dropped at eight output ports(O1 −O8). The footprint of the total (de)multiplexer is lessthan 2870.4× 104.0 µm2. The minimum feature size of thedevice is relatively small (108 nm) due to the introduction of thetrapezoidal segments in the curved waveguide region. Though itstill can be stably fabricated by using EBL and ICP etching [4].Figure 6(b)–6(e) show the scanning electron microscope (SEM)photos of the coupling regions of the contra-DCs designed forTE0, TM0, TE1, and TM1 modes, respectively.

To characterize the fabricated device, we used a tunablecontinuous wave (CW) laser (Keysight 81960A) to inject asignal from a selected input port (Ii ), and collect data fromall the eight output ports (O1 −O8) using an optical powermeter. Grating couplers are employed to couple the TE- andTM-polarized lights into and out of the chip. The periods ofthe TE and TM grating couplers are 630 nm and 1080 nm,respectively, with the same filling factor of 48%. Both gratingcouplers have an etching depth of 70 nm. The coupling lossesof the TE- and TM-polarized gratings are 6.2 and 7.0 dB/facetwith a 3-dB bandwidth of 50 nm [7]. Measured transmissionresponses and crosstalk values of the fabricated device are shownin Fig. 6(g). The transmission spectra are normalized to thestraight waveguides with grating couplers fabricated on the samechip. The insertion losses, including MUX and DEMUX stages,are 2.7 dB, 2.3 dB, 6.6 dB, 5.5 dB, 6.5 dB, 3.9 dB, 5.6 dB and

Table 1. Structural Parameters of the SWG-based Contra-DCs

Channel wstrip (µm) wSWG (µm) gap (nm) L c (µm) δ

3 (nm) at1540 nm 1550 nm

TE0 0.5 0.5 350 300 50% 361 365TE1 1.0 0.6 350 300 60% 334 338TM0 0.5 0.5 500 300 50% 458 463TM1 1.1 0.7 500 300 60% 451 456

Letter Vol. 45, No. 10 / 15May 2020 /Optics Letters 2849

Fig. 6. (a) Microscope photo of a fabricated eight-channel (de)multiplexer. SEM images of the coupling regions of the SWG-based contra-DCs forthe (b) TE0, (c) TM0, (d) TE1, (e) TM1 mode channels, respectively. (f ) SEM image of the SWG-Wire transition taper. (g) Measured transmissionresponses at the 8 output ports of the mode DEMUX (denoted as Oi , i= 1∼ 8), when the light is injected from input ports I1 − I8, respectively.

4.9 dB for the eight channels, respectively. The relatively largeILs and some observed splits in the passband can be attributedto the misalignments between the operation wavelengths ofthe MUX and DEMUX stages, which were induced by thedeviations of the duty cycle and waveguide width during thefabrication process. The overall crosstalk values are lower than−18.7 dB. The sidelobes in the measured spectra can be furtheroptimized by employing the apodized SWG-based structure[25]. By cascading more contra-DCs, the device can be scaledto a multi-dimensional (de)multiplexing structure with morewavelength channels [26] and higher-order modes. This comesat the cost of larger device footprint, more fabrication time andhigher cost, and lower yield with more channel count.

In summary, we have proposed a scheme for on-chip multi-dimensional (de)multiplexing of WDM-MDM-PDMsignals. As a proof-of-concept experiment, an eight-channel(de)multiplexer on two wavelengths, two polarizations, and twomodes has been demonstrated. The overall insertion losses arelower than 6.6 dB and the crosstalk values are below−18.7 dBat around 1540 nm and 1550 nm. Scaling the number of modesand the wavelength channels can be expected based on the buswaveguide architecture.

Funding. Key Technologies Research and DevelopmentProgram (2019YFB1803602); National Natural ScienceFoundation of China (61835008, 61975115).

Disclosures. The authors declare no conflicts of interest.

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