Ultra-Compact Ultra-Broadband Two-Mode Transverse-Electric Based SWG Multiplexer Demonstrated at 64 Gbps

We designed and experimentally demonstrated an ultra-compact and ultra-broadband two-mode de-multiplexer based on a subwavelength grating (SWG) asymmetrical coupler (ADC) on a silicon-on-insulator (SOI) platform. The device consists of a cascaded strip waveguide tapered to a multimode segment and a SWG-based single-mode waveguide. Tapering the strip waveguide in multi-segments guarantees a high fabrication tolerance with a wider wavelength range of operation. The parameters of the periodic structure are chosen to meet the Bragg condition and phase-match the TE1 mode of the strip waveguide. These features produce a faster mode evolution with a shorter coupling length of only 8.5 μm and an entire mode division multiplexing (MDM) link (Mux and Demux) of only 55 μm. The MDM link operates over a wide wavelength range, covering the entire S-, C-, and L-bands. The insertion loss (IL) and crosstalk (CT) achieved at 1550 nm are better than 1 dB and −18 dB, respectively. The device also has low fabrication sensitivity to deviations in the waveguide's parameters. Additionally, the transmission performance of the link is demonstrated at 1550 nm wavelength using non-return-to-zero (NRZ) on-off keying (OOK) modulation, where clear eye diagrams are obtained at 64 Gbps.

(PIC). With the boom of 5G wireless networks and cloud services came a high demand to scale the optical data transmission capacity [1], [2]. Hence, optical modules with a high density of optical processing capabilities are required. Therefore, diverse multiplexing schemes such as wavelength-and polarizationdivision multiplexing (WDM and PDM, respectively) have been extensively investigated [3], [4], [5], [6], [7]. However, these schemes are limited by the number of wavelength channels of the WDM system or to only 2 degrees of freedom in the case of PDM multiplexing. Waveguide mode-division multiplexing (MDM) offers unprecedented bandwidth scaling that can mitigate the communication bottleneck in high-density on-chip interconnects since each mode of a single wavelength becomes an individual data transfer channel. Hence, higher attention is drawn to MDM schemes [8], [9], [10], [11], [12], [13].
Mode (de)multiplexers are key components for constructing an MDM link. Diverse schemes have been explored to realize it on the silicon-on-insulator (SOI) platform, such as multimode interferometers (MMI) [14], [15], [16], asymmetric Y-junctions [17], [18], asymmetric directional couplers (ADC) [8], [19], [20], ADCs with hybrid plasmonic waveguides (HPW) [21], [22], [23], and adiabatic couplers (AC) [24], [25], [26]. MMIbased couplers have high fabrication tolerance but are complex in structure with a long device footprint, while asymmetric Y-junctions introduce high insertion losses. Adiabatic couplers have a wide bandwidth and low fabrication sensitivity, but the coupling length must be long enough to ensure adiabatic mode evolution. Although the use of tapered ADCs brings the advantage of a higher fabrication tolerance, they still require long coupling lengths. When it comes to ADCs with HPWs, the use of metals makes the footprint smaller, but this comes at the cost of high insertion losses.
Mode multiplexers that combine adiabatic couplers with subwavelength gratings (SWGs) have been recently theoretically analyzed and experimentally demonstrated [27], [28]. Adding a periodic SWG structure with specific parameters to phase-match the higher-order modes on the strip waveguide drives a quicker mode evolution, making the device ultra-compact. They also offer broadband wavelength operation and have the advantage of being able to manage more higher-order optical modes. Despite their improved manufacturing tolerance and outstanding bandwidth operation, their footprint (> 50 µm for a single multiplexer device) remains very large for dense integration. Therefore, a compact mode multiplexer with wideband operation is desired.
In this work, we propose and experimentally demonstrate an ultra-compact (25 µm) and ultra-broadband (200 nm) SWGbased two-mode (de) multiplexer on an SOI platform. The device achieves state-of-the-art performance due to our novel device configuration, in which a cascaded tapered strip waveguide is combined with an SWG-based waveguide. The performance of the device was also tested at 64 Gbit/s non-return-to-zero (NRZ) data transmission. The paper is organized as follows, Section II will present the device design and operation principle. The device performance and fabrication are discussed in Sections III and IV, respectively. The transmission characteristics of the MDM link for NRZ modulated signals are demonstrated in Section V. Finally, Section VI concludes the paper. Fig. 1 shows a schematic of the proposed SWG-based multiplexer. The asymmetrical coupler comprises a section of an SWG-based single-mode waveguide (access waveguide) spaced by a constant gap (G) from a second single-mode waveguide (bus waveguide) that is tapered (cascaded) to a multimode waveguide. The access waveguide has a width Wb1 and tapered to Wb2 through three sections of lengths Lb1, Lb2, and Lb3. This arrangement avoids any back coupling and diffracts any remaining light in the single-mode waveguide. A taper length of Lb1 is used before the coupling region to efficiently transition the TE0 mode into the periodic region with low loss. The SWG is defined with a grating pitch Λ and a duty-cycle f. The Lb2 section denotes the length of the coupling region whereas the Lb3 region denotes the length of the terminator section. The bus waveguide has an initial width Wa1 that is tapered up to Wa2 with a length La1, followed by a second adiabatically tapered section up to Wa3 with a length La2. The device operates based on a mode coupling across the two waveguides due to the phase-matching condition. The effective refractive index of TE0 mode in the access waveguide is phase matched to effective refractive index of TE1 in the bus waveguide where its state is preserved, while the fundamental TE injected in the bus waveguide remains as TE0 due to phase mismatch and passes through with low crosstalk.

II. DEVICE DESIGN AND OPERATING PRINCIPLE
For the SWG-based waveguide, widths of Wb1 = 400 nm tapered to Wb2 = 200 nm are chosen with a length Lb3 = 3.9 µm. The Lb1 section is 9.8 µm long (including the tapered non segmental section), the gap (G) is 100 nm, and Lb2 is 8.5 µm long. According to the effective medium theorem (EMT) [29], [30], [31], the SWG can be described as a periodic structure that behaves as a homogeneous medium with an equivalent effective refractive index determined by the duty cycle. Its structure offers the ability to locally reduce and engineer the refractive index without changing its material composition. The equivalent refractive n eq index is calculated using (1) below, where n si = 3.47 and n sio2 = 1.44 are the refractive indices of silicon and silicon dioxide, respectively.
The grating pitch Λ is chosen to be 200 nm to be smaller than the Bragg period (Λ Bragg = λ/2n B ) to effectively suppress the diffraction effect. The duty cycle f = Λ/a must take into consideration the minimum fabrication feature size, and it is set to 65%, where a is the width of the silicon segment of the grating.
The phase matching condition between the TE0 mode in the access waveguide and the TE1 mode in the bus waveguide is shown in Fig. 2 (calculated using the Mode Solver Solutions). Here, the width Wa is found to phase match the access waveguide width Wb1, centered at 1550 nm. However, this phase match condition used in typical asymmetrical directional couplers (ADCs) can be rapidly broken by any slight fabrication deviations in the design parameters [32]. Additionally, the TE1 mode suffers a much higher change in the effective index (n eff ) with the waveguide width variation compared to the access waveguide TE0. This results in a high sensitivity to variations in fabrication. Also, phase-matching condition is satisfied only for narrowband.
To mitigate these limitations, we introduce a multi-section tapered ADC, where the bus waveguide is tapered around the initially found phase matching width. In this scenario, when design variations occur, a phase match condition can still be found at different positions along the taper, creating a constant high conversion efficiency and high fabrication tolerance. This leads to an efficient implementation of high-order mode multiplexing with a higher operating wavelength range.
In our proposed design, the bus waveguide has a starting width of Wa1 = 450 nm, and it is separated from the access waveguide with an S-bend to avoid crosstalk between both input ports. The first section of the strip waveguide in the coupler region is tapered from Wa1 to Wa2 = 570 nm with a taper length La1 = 1 µm. This taper, sufficiently long to originate a mode evolution, is introduced to allow the phase-matching condition to happen at lower wavelengths, increasing the device bandwidth with low fabrication sensitivity. A second section tapered to Wa3 = 655 nm is added following the previous taper, to phase match higher wavelengths. The +/−60 nm width variation is chosen so that strong coupling is always allowed to happen for the entire L-and C-bands, which stabilizes higher-order modes in the waveguide.
The remaining parameter to be determined is the taper length, La2. The combination of an SWG-based waveguide with tapered ADCs relaxes the sensitivity around the coupling length necessary for high conversion efficiency. The SWG periodicity effectively delocalizes the field of the guided optical modes such that their evanescent fields have higher interaction with the cladding, hence, creating a strong coupling within shorter lengths. In order to maximize the coupling efficiency and stabilize the mode in the higher-order waveguide, the taper length La2 is determined using finite-difference time-domain (FDTD) 3D simulations, where the transmission response is evaluated for different length values. As shown in Fig. 3, increasing the taper length to a certain value improves the mode conversion efficiency (TE0 -> TE1) between the two waveguides. As such, La2 is chosen to be 4.5 µm long.

III. DEVICE PERFORMANCE
The FDTD 3D simulations were carried out to evaluate the MDM (de)-multiplexer performance centered at 1550 nm wavelength. The simulated light propagation is shown in Fig. 4(a) and (b) for both input/output I1/O1 and I2/O2 ports, respectively. In this design, light coupled to port I1 remains as TE0 throughout the different sections of the device and exits the (de)multiplexer at port O1, while light coupled as TE0 into port I2 is adiabatically coupled to the TE1 mode and back coupled as TE0 to port O2, whereas any remaining light will travel to O1 as crosstalk.   (IL) and crosstalk (CT), expressed as: CT = − 10 log 10 P Oi P x , x = 2, 1 where P Oi is the output power of the desired mode with regarding to respective input (I1/O1 or I2/O2), P in is the total input power in the fundamental TE0 mode and P x relates to the power of the remaining interfering modes. As a result of this design-specific characteristics, the performance of the (de) multiplexer shows to have low wavelength dependency. Analyzing the data transmitted on the complete MDM link with light input from port 1, the IL in I1/O1 and CT in I1/O2 are better than 0.12 dB and −21 dB, respectively. The corresponding values for the case when the light is coupled to input 2, ports I2/O2 and I2/O1 present an IL less than 0.4 dB and a CT less than −20 dB, respectively. To evaluate the device's sensitivity to fabrication variations, the mode conversion loss TE0-TE1 and the crosstalk TE0-TE0 are analyzed. The most crucial parameters to be considered are the waveguide width, coupling gap, and grating duty cycle. A reasonable waveguide width fabrication error in current processes is Δ = +/−10 nm. In a realistic scenario, both bus and access waveguides widths are changed simultaneously to a maximum deviation of Δ. In line with this, we keep a constant center-to-center distance between both waveguides. As such, the width deviations will change the gap accordingly. Fig. 6(a) and (b) depict the tolerance of coupling efficiency K TE0-TE1 between the bus and access waveguides and the CT in the bus waveguide, respectively, simulated at 1550 nm. A maximum variation of ∼0.03 dB from the optimized design of K TE0-TE1 is observed for the entire MDM link. As well, the CT shows low sensitivity to the width variation, with a maximum degradation of ∼1 dB.
As for the SWG, the analysis is done keeping a constant distance between each periodic block or a constant grating pitch. Fig. 6(c) and (d) show the simulated coupling efficiencies K TE0-TE1 and the CT deviations, respectively. The coupling coefficient is defined as |t TE1 | 2 / |t 0 | 2 , where |t TE1 | 2 is the measured transmitted power to the TE1 output port (downstream from the mode converter) and |t 0 | 2 is the power of a reference waveguide in the same die (including coupling losses to the chip and losses through the setup). In the worst-case scenario, a degradation of K TE0-TE1 to < 0.6 dB is seen for the entire MDM link. On the other hand, the CT shows no deterioration with the deviations. It is noteworthy to explain that for a wider width of a, better coupling efficiency and a better CT are obtained; however, such width values violate the minimum waveguide spacing allowed in this fabrication process.

IV. FABRICATION AND CHARACTERIZATION
The proposed two-mode multiplexer was fabricated on a SOI platform with a 220 nm thick silicon layer and a 2 µm thick box oxide, through the NanoSOI process at Applied Nanotools Inc. The fabrication is based on direct-write 100 KeV electron beam lithography technology; using hydrogen silsesquioxane (HSQ) resist and an anisotropic ICP-RIE etch process with chlorine. A plasma-enhanced chemical vapor deposition (PECVD) process, based on tetraethyl orthosilicate (TEOS) was used to deposit a 2.2 µm oxide cladding. Fig. 7 shows scanning electron microscope (SEM) images of the fabricated device.
Experimental characterization of the device is performed through edge coupling. Lensed fibers are used to couple light to the silicon chip, which is mounted on a temperature-controlled stage. The optical transmission response is measured using a  tunable Keysight 8100B laser source (C-band) and a Keysight N7744A optical detector sensor. The light polarization of the laser source is adjusted with an external polarization controller in order to maintain the TE0 polarization. The fabricated MDM link exhibits a high performance for a broadband operation of 200 nm around the C-band. The measured TE0-TE0 (I1O1) insertion loss and crosstalk (I1O2) at 1550 nm wavelength are 0.9 dB and −18.7 dB (see Fig. 8(a)), respectively. Additionally, for the TE0-TE1-TE0 mode conversion, the (I2O2) and TE0-TE0 crosstalk (I2O1) [ Fig. 8(b)], the measured maximum IL and CT are 2.3 dB and −18.6 dB, respectively. In optical telecommunications systems, such as fiber-to-the-home (FTTH) systems, such crosstalk levels may be sufficient. As can be seen when comparing with simulations, the experimental results align very well. The discrepancy in insertion loss can be attributed to the measurement setup error tolerance. Process variations limit crosstalk by breaking the optimum design points, resulting in non-ideal coupling/decoupling. Table I shows a comparison between our device performance and that of previously reported similar multiplexers on the SOI platform. The device length here is referring to a single stage (Mux or Demux). As noted, our device achieves record compactness with a length of 25 µm (entire MDM link [Mux+Demux] is 55 µm) while maintaining high performance and an ultrabroadband response. Additionally, our device shows a simple design with very low sensitivity to fabrication variations. In comparison, most previously reported mode multiplexers had to sacrifice either footprint or operation bandwidth to improve the remaining metrics of the device. Furthermore, some of the reported designs lack experimental validation.

V. SYSTEM DEMONSTRATION
The fabricated device was further characterized using an amplitude modulated signal. The setup is shown in Fig. 9. A Keysight 64 Gbaud M8045A pattern generator was used to generate an NRZ-OOK 40 and 64 Gbit/s pseudorandom binary sequence (PRBS) of 2 31 -1 length. A Thorlabs LN05S 40 GHz intensity Mach-Zehnder modulator was used for signal modulation of a tunable laser centered at 1550 nm. The modulator is DC-biased at 3.5 V, adjusted for performance optimization, and driven by an SHF S807C RF amplifier. A polarizationmaintaining booster optical amplifier (Thorlabs S9FC1004P) was used to pre-amplify the optical signal before it was coupled to the silicon chip. Polarization controllers are also added before the modulator and after the amplifier to maintain TE-polarized light in the setup and improve the signal quality. Fig. 10(a) and (b) show the input and the pre-amplified optical signal modulated at 40 and 64 Gbps, respectively. The output signal is then amplified using a polarization-insensitive semiconductor optical amplifier (Thorlabs S7FC1013S). The optical signals that correspond to the input/output pairs of I1/O1 and I2/O2 (see Fig. 6) are then amplified and captured by a Keysight Infinium DCA-X 86100D widebandwidth oscilloscope. Fig. 10

VI. CONCLUSION
In summary, we have demonstrated an ultra-compact ADC/SWG-based MDM with a high-performance and broadband operation covering the entire S-, C-, and L-bands. The SWG-based waveguide is introduced in the access waveguide, with dimensions carefully chosen to phase-match the higherorder mode of the bus waveguide. The ability of engineering the refractive index leads to a higher interaction of the mode evanescent fields with the cladding and thus enhances the coupling between the waveguides on a faster mode coupling over shorter lengths, making the device compact. The bus waveguide is a conventional strip single mode waveguide, which is combined to a multimode waveguide utilizing cascaded tapers, easing the fabrication sensitivity in such a way that a phase match condition can always be found along the taper. These characteristics allow a constant strong conversion efficiency and efficient implementation of high-order modes multiplexing, additionally broadening the operational wavelength range.
Our device has a very compact size with a coupling region of 8.5 µm while the entire MDM (mux and demux) link is only 55 µm long. The device was fabricated on a standard SOI platform, using e-beam lithography technology and butt-coupling was used to experimentally validate its performance. The MDM link exhibits measured IL and CT at 1550 nm wavelengths better than 0.9 dB and −18.7 dB, respectively. Covering the 200 nm wavelength range, it reached a maximum IL and crosstalk of 2.3 dB and −18.6 dB, respectively. A system demonstration was carried out using NRZ-modulated signals at 40 Gbps and 64 Gbps. Open and clear eye diagrams were obtained validating the use of the device for on-chip demultiplexing.

ACKNOWLEDGMENT
The experimental characterization was conducted in the NYUAD Photonics Lab and simulations were performed on the NYU IT High-Performance Computing resources given its services and staff expertise. We are very thankful to Nikolas Giakoumidis and the Core Technology Platform Facility (CTP) for all the technical and instrumentation support.