Compact Mode Division MUX/DEMUX Using Enhanced Evanescent-Wave Coupling on Silicon-on-Insulator (SOI) Platform for 11-Tbit/s Broadband Transmission

Mode-division-multiplexing (MDM) can increase the total on-chip transmission capacity. Silicon-on-insulator (SOI) based MDM multiplexer (MUX) and demultiplexer (DEMUX) using asymmetrical directional couplers (ADCs) are promising; however, they usually require long coupling lengths for mode conversion. Here, for the first time up to the authors’ knowledge, we propose, simulate, fabricate and demonstrate a size reduced SOI based $4 \times 4$ MDM MUX and DEMUX using enhanced evanescent-wave coupling (EEC). Here, we illustrate by experiments and numerically analyses that by size reducing the ADC access coupling region, evanescent-wave coupling is enhanced. Significant coupling length reduction of ~80 % can be achieved, while similar MDM MUX and DEMUX performance can be observed. To experimentally evaluate the broadband and high-speed transmission operations of the proposed device, 48 wavelength channels each modulated by >60 Gbit/s orthogonal frequency division multiplexing (OFDM) signals are successfully mode multiplexed and demultiplexed, achieving a transmission capacity of 11.73 Tbit/s.


I. INTRODUCTION
The bandwidth demands are increasing very rapidly due to the popularity of video-based and cloud-based services. Inside the data center networks, the speeds of electronic interconnects are limited by the high heat density. Using silicon photonics (SiPh) technology can offer an increase in interconnect throughput with reduced power consumption [1]- [5]. By using the mature complementary metal oxide semiconductor (CMOS) fabrication technique, high performance and yield SiPh devices were fabricated [6]- [13]. To improve the transmission capacity of the SiPh interconnects, different multiplexing techniques have been proposed, such as The associate editor coordinating the review of this manuscript and approving it for publication was Leo Spiekman . wavelength division multiplexing (WDM), spatial division multiplexing (SDM) or polarization division multiplexing (PolDM). Among them, SDM allows signals to be transmitted in different cores [14] or different orthogonal eigenmodes in a core. The latter is also known as mode division multiplexing (MDM). Implementation of MDM systems using few-mode optical fiber (FMF) were reported. Some all-fiber MDM multiplexers (MUXs) and demultiplexers (DEMUXs) were proposed and fabricated, such as all-fiber directional mode selective couplers (MSCs) [15], [16], long period fiber grating (LPFG) [17], [18] and photonic lanterns (PLs) [19], [20]. Mode MUX/DEMUX using free-space optical setups were also reported [21].
On the contrary, deploying MDM in SiPh chip is relatively simpler, since distinct eigenmodes could be converted VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ easily by the planar waveguide structures. The MDM MUX/DEMUX based on multimode interferences (MMIs) were proposed; however, the scalability may be limited [22], [23]. MDM MUX using quasi-phase-matching and staged coupling method was also reported; however, the size was relatively large [24]. High performance MDM MUX and DEMUX based on asymmetrical directional couplers (ADCs) were proposed [25], [26]. Through phase-matching the access and bus waveguides, fundamental mode and higher order modes can be converted efficiently. By using this ADCbased MDM MUX and DEMUX, several high throughput demonstrations were reported [27]- [29]. Yet, these MDM MUX and DEMUX required relatively long coupling lengths in the directional coupler section for mode conversion.
In this work, for the first time up to the authors' knowledge, we propose, simulate, fabricate and demonstrate a size reduced semiconductor-on-insulator (SOI) based 4 × 4 mode MUX/DEMUX using enhanced evanescent-wave coupling (EEC). Traditional SOI based mode MUX/DEMUX required relatively long coupling lengths in the directional coupler section for mode conversion. In this work, we illustrate that via reducing the dimension of the ADC access coupling region, evanescent-wave coupling is enhanced. A significant coupling length reduction of ∼80 % can be achieved, while similar mode MUX/DEMUX performance can be observed. Moreover, in order to evaluate the broadband and highspeed operations of the proposed footprint reduced EEC MDM MUX and DEMUX, 48 wavelength channels, each encoded with > 60 Gbit/s orthogonal frequency division multiplexing (OFDM) signals are mode multiplexed and demultiplexed successfully by using the proposed 4 × 4 mode MUX and DEMUX. The 48 C-band wavelength channels from 1527.99 nm to 1565.50 nm under the International Telecommunication Union (ITU) dense wavelength division multiplexing (DWDM) grid are selected. Hence, transmission capacity of 11.73 Tbit/s is achieved, and the hard-decision forward-error-correction (HD-FEC) threshold (bit-error-ratio, BER 3.8 × 10 −3 ) is satisfied. Fig. 1(a) illustrates the schematic of the proposed SiPh 4 × 4 MDM MUX/DEMUX. An ADC consists of a narrow access waveguide (supporting fundamental transverse-electric, TE 0 mode) and a wide bus waveguide (supporting high order modes). Within the coupling region, fundamental TE 0 mode can be converted to higher order modes (i.e. TE 1 , TE 2 , TE 3 ) or vice versa depending on specific widths of bus waveguides satisfying the phase-matching conditions [25]. Traditionally, the smallest SOI waveguide dimension for fundamental mode transmission is 0.45 µm × 0.22 µm. By reducing the width of the ADC access width, evanescent coupling can be enhanced and the coupling length (LC) can be significantly reduced.

II. DEVICE STRUCTURES AND NUMERICAL ANALYSIS
Both proposed and traditional MDM MUX and DEMUX were fabricated by IMEC. They were put side-by-side on the same SOI wafer for comparison. Fig. 1(b) depicts the microscopic image of the proposed device with silicon waveguide thickness of 220 nm and the ADC gap of 150 nm. Fig. 1(b) is a magnified photo showing the access and bus waveguides, and the mode MUX regions of TE 0 -to-TE 1 , TE 0 -to-TE 2 , TE 0to-TE 3 . The optical signal at TE 0 mode can be coupled into and out of the MDM MUX and DEMUX via 10 o off-vertical grating coupler (GC). The bus waveguide widths supporting different higher order modes can be calculated based on the phase-matching conditions [25], [27]. Lumerical R finitedifference time-domain (FDTD) method was used to simulate the devices. For the traditional MDM MUX/DEMUX, the access waveguide width supporting TE 0 mode is 0.45 µm; while the bus waveguide widths supporting the TE 1 , TE 2 and TE 3 are 0.932 µm, 1.416 µm and 1.897 µm respectiv2ely. The corresponding coupling lengths are 17 µm, 22.5 µm and 26.4 µm respectively. For the proposed reduced footprint MDM MUX/DEMUX, the access waveguide width supporting TE 0 mode is 0.35 µm. The bus waveguide widths supporting the TE 1 , TE 2 and TE 3 are 0.740 µm, 1.132 µm and 1.535 µm respectively while the corresponding coupling lengths are reduced to 3.03 µm, 4.32 µm and 6.17 µm respectively. The cross section of the bus and access waveguides at the ADC section showing different material types is illustrated in Fig. 1(c). Table 1 summaries the coupling lengths and bus waveguide widths of the two MDM devices. In the proposed size reduced EEC MDM device, the coupling lengths are significantly reduced by 82.2 %, 80.8 % and 76.6 % in CH2, CH3 and CH4 respectively; while the bus waveguide widths are reduced by 20.6 %, 20.1% and 19.1%, respectively.    reveal similar performances in the mode crosstalk analysis. The mode crosstalk is <−20 dB within the 40 nm C-band wavelength window from 1525 nm to 1565 nm.

III. EXPERIMENTAL RESULTS AND DISCUSSION
The experimental evaluations of the traditional and proposed footprint reduced MDM MUX and DEMUX are performed. To evaluate the MDM mode crosstalk, a broadband light source using the amplified spontaneous emission (ASE) of an erbium-doped fiber amplifier (EDFA) is launched into each MUX input. Then different DEMUX outputs are measured by using an optical spectrum analyzer (OSA). For example, to measure the mode crosstalk of CH1 as shown in Fig. 6(a), the broadband light source is launched into the input port of MDM-CH1; and the optical spectra at the four output ports of MDM-CH1, MDM-CH2, MDM-CH3 and MDM-CH4 are measured. Then, the optical spectra measured at the four output ports are power normalized with respect to VOLUME 8, 2020    DEMUX. We can also observe that the mode crosstalk are <−20 dB in most of the transmission window from 1530 nm to 1565 nm. In previous study [27], the BER performance VOLUME 8, 2020 degradation is negligible if the mode crosstalk is <−18 dB. Hence, both MDM devices are good enough for the highspeed and broadband operation. Moreover, we can observe that by reduction of the coupling length by ∼80 % in the proposed device, similar mode MUX and DEMUX performance can be observed. Fig. 8 illustrates the architecture of high-speed MDM OFDM signal transmission using the proposed MDM MUX and DEMUX. The laser (LD) linewidth is <100 kHz. The output power of the LD is 6 dBm. An EDFA with noise figure of 4 dB is used to compensate the insertion loss of the MZM and the GCs of the MDM device. The optical input power to the MDM device is 8 dBm. Off-line Matlab R program is used to generate the OFDM signal. The OFDM signal is then encoded onto the optical signal emitted by the LD via a Mach-Zehnder modulator (MZM). For adjacent channels, we can employ different optical delays to de-correlate the channels.
The OFDM signal encoding process includes serialto-parallel (S/P) conversion of random data, symbol mapping (SM) to different quadrature-amplitude-modulation (QAM) levels, inverse fast Fourier transform (IFFT), parallelto-serial (P/S) conversion and cyclic prefix (CP) insertion. The generated OFDM signal is then applied to the MZM via a digital-to-analog converter, which is an arbitrary waveform generator (AWG, Tektronix AWG70001A). The AWG has a 50 GS/s sampling rate, 8 bit resolution and 20 GHz analog bandwidth. The fast-Fourier transform (FFT) size is 512 and the cyclic prefix (CP) is 16. After the mode multiplexing and demultiplexing, the OFDM signal is detected by a photodiode (PD, u2t XPDV2140R) connected to a real-time oscilloscope (RTO, Teledyne LeCroy SDA 816Zi-B). Here, the RTO acts as an analog-to-digital converter converting the analog waveform captured by the PD into digitized signals. The OFDM signal decoding process includes re-sampling, synchronization, CP removal, S/P conversion, FFT, power scaling, symbol de-mapping, and error analysis. The BER is  To further enhance the per channel data rates, bit-loading technique based on received signal-to-noise ratio (SNR) of OFDM subcarrier is implemented. 48 wavelength channels from 1527.99 nm to 1565.50 nm are chosen and coupled in and out the MDM MUX and DEMUX via 10 o off-vertical GCs. Each GC has the coupling loss of <3 dB and the optimal center wavelength at 1555 nm.
The measured bit-error ratio (BER) performances of OFDM signals multiplexed and demultiplexed by the proposed devices are illustrated in Figs. 9(a)-(d). We arbitrarily VOLUME 8, 2020 It is worth to mention that in our BER measurement experiment, our BER evaluation algorithm is to achieve the highest possible OFDM transmission data rate for each channel and at the same time satisfying the FEC threshold. To achieve a higher data rate, bit-loadings to different OFDM subcarriers are applied. However, higher OFDM data rate will decrease the receiver sensitivity. This means that for example in Fig. 9(a), the channel with a lower receiver sensitivity does not necessary mean that it performance is poorer. This is because this channel would carry a higher data rate.
We measure all the 48 wavelength channels, and their BER performances are shown in Figs

IV. CONCLUSION
MDM can increase the total on-chip transmission capacity. SOI based MDM MUX and DEMUX based on ADCs are promising; however, they usually require long coupling lengths for mode conversion. Here, for the first time, we proposed and demonstrated a size reduced SOI based 4×4 MDM MUX and DEMUX using EEC. By reducing the dimension of the ADC access coupling region, evanescent-wave coupling is enhanced. In the proposed device, the coupling lengths were significantly reduced by 82.2 %, 80.8 % and 76.6 % in CH2, CH3 and CH4 respectively; while the bus waveguide widths are reduced by 20.6 %, 20.1% and 19.1%, respectively. Similar MDM MUX and DEMUX performances were observed in the traditional and the proposed MDM devices, with mode crosstalk <−20 dB in most of the C-band window. To illustrate the broadband and high-speed operations of the proposed device, 48 wavelength channels each modulated with >60 Gbit/s bit-loaded OFDM signals were successfully mode multiplexed and demultiplexed. A total capacity of 11.73 Tbit/s signal transmission was achieved, satisfying the FEC threshold.