A 60 Gb/s Mdm-wdm Si Photonic Link with < 0.7 Db Power Penalty per Channel References and Links

Mode-division-multiplexing (MDM) and wavelength-division-multiplexing (WDM) are employed simultaneously in a multimode silicon waveguide to realize on-chip MDM and MDM-WDM transmission. Asymmetric Y-junction MDM multiplexers and demultiplexers are utilized for low coherently suppressed demultiplexed crosstalk at the receiver. We demonstrate aggregate bandwidths of 20 Gb/s and 60 Gb/s for MDM and MDM-WDM on-chip links, respectively, with measured 10 −9 BER power penalties between 0.1 dB and 0.7 dB per channel. Photonic networks-on-chip for future generations of chip multi-processors, " IEEE Trans. " On-chip optical interconnect roadmap: Challenges and critical directions, " IEEE J. Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks, " IEEE Photon. On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer, " Opt. 1.28-Tb/s demultiplex-ing of an OTDM DPSK data signal using a silicon waveguide, " IEEE Photon. Silicon multimode photonic integrated devices for on-chip mode-division-multiplexed optical interconnects, " Prog. On-chip transformation optics for multimode waveguide bends, " Nat. Two-mode division multiplexing in a silicon-on-insulator ring resonator, " Opt. On-chip silicon 8-channel hybrid (de) multiplexer enabling simultaneous mode-and polarization-division-multiplexing, " Laser Photon. Design of a compact two-mode multi/demultiplexer consisting of multimode interference waveguides and a wavelength-insensitive phase shifter for mode-division multiplexing transmission, " J. On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing–mode division multiplex-ing, " Opt.junctions in silicon waveguides for on-chip mode-division-multiplexing, " Opt. Mode multi/demultiplexer based on cascaded asymmetric Y-junctions, " Opt.modulation of Si photonic wires for quasi-phase-matching of four-wave-mixing: experimental and theoretical demonstration, " Opt.


Introduction
Computational performance gains are currently driven by an increased number of processing cores as opposed to clock-frequency-scaling [1][2][3].This shift towards parallel computing has placed a considerable emphasis on efficient and high-capacity on-chip communication networks to manage information exchange between multiple cores.One approach towards meeting such demands is photonic on-chip networks enabled by Si-waveguide interconnects.Si waveguides can support substantial aggregate bandwidths since the optical states supported by waveguide structures have many degrees of orthogonality, and thus, possible potential orthogonal data channels.The most ubiquitous example is wavelength, where wavelength-divisionmultiplexing (WDM) has already been used to demonstrate 1.28 Tb/s transmission through a single Si waveguide [4].However, other orthogonalities can be used alongside WDM to either extend bandwidth scaling, or to diminish system-level cost and complexity by reducing the number of required lasers for a given aggregate bandwidth, which in turn results in a favorable reduction in electrical power consumption.
Fiber-optic networks are similarly facing enormous demands on communication bandwidth due to rapidly-increasing network traffic.To keep pace researchers have turned to additional orthogonalities to use alongside or in place of WDM.One promising direction is to use multimode fiber and mode-division-multiplexing (MDM) in order to transmit multiple data channels per wavelength, carried by separate guided modes.MDM has been demonstrated in fiber using a number of approaches, including the utilization of only a few modes in few-mode-fiber, or using multiple-input-multiple-output (MIMO) signal processing techniques to deconvolve crosstalk from mode-mixing between the separate channels.
Only recently has MDM started to find application in on-chip Si photonics interconnects.In particular, MDM has been demonstrated in Si waveguides using a directional-coupler-based coupling scheme to selectively excite individual modes with bit-error-rate (BER) receiver sensitivity penalties between 1.6 dB -1.8 dB [5].MDM-WDM has also been demonstrated using  a unique ring-resonator-based solution, however the solution required active tuning of the rings while resulting in BER penalties between 0.6 dB -1.4 dB [6].In this work, on-chip MDM and MDM-WDM transmission through a multimode Si waveguide (MM-SiWG) is enabled by completely passive and compact asymmetric Y-junction mode multiplexers (muxes) and demultiplexers (demuxes).As will be described, using asymmetric Y-junction muxes/demuxes, an aggregate bandwidth of 60 Gb/s using 2 × 3 × 10 Gb/s MDM-WDM over a 1.2 mm link with power penalties < 1 dB per channel at the receiver was obtainable.

Advantages of multimode waveguides for on-chip interconnects
The link capacity of on-chip optical interconnects can be increased using a number of techniques, including WDM [4], polarization-division-multiplexing (PDM) [7], and time-divisionmultiplexing (TDM) [8]; recently, however, spatial-division-multiplexing (SDM) has been targeted as a means to ameliorate the future communication-capacity gap by using multiple spatial modes to carry multiple information channels.Two examples of SDM realized in fiber-optic links include the following: 1. Using multiple waveguides, such as multi-core fibers (MCF), where each channel occupies the fundamental mode of a spatially separate waveguide core.
2. Using MDM in a few-mode-fiber (FMF), where all modes are spatially overlapped in the same waveguide core, but are described by separate orthogonal states.
In applying these ideas to Si-waveguide-interconnects, SDM can be realized by either of the following: 1. Increasing the number of waveguides, N W G , in an approach similar to using MCFs.
2. Using N MM separate orthogonal modes of an multimode waveguide (MM-SiWG) in an approach similar to using MDM in FMFs.
There are significant system-level differences between using M waveguides or M modes of a MM-SiWG to scale the link aggregate bandwidth, especially in terms of inter-channel crosstalk, and network complexity.Using N W Gs = M waveguides to carry M separate spatial modes is advantageous because each spatial mode is separated spatially and therefore can be designed such that the crosstalk is almost entirely eliminated.However this approach also requires M times as many modulators, switches, and routers, and potentially as many as M 2 waveguide crossings, quickly leading to significant system complexity.
On the other hand, if integrated devices like switches/routers and waveguide crossings can be designed to be compatible over multiple guided modes, a single MM-SiWG supporting N MM = M modes might not need significant scaling in the number of switches, routers, or crossings compared to a single-mode system.The challenge of using a single MM-SiWG is that the guided modes overlap in the same waveguide core and can potentially couple to one another through waveguide perturbations or waveguide nonlinear processes, resulting in crosstalk.Therefore this approach requires an emphasis on devices which are carefully designed to suppress crosstalk from mode-coupling.Already, MM components are being developed [9], including MM waveguide bends designed with conformal mapping [10], such that the coupling between modes along the bend is almost entirely eliminated, and ring resonators supporting multiple modes [11] which could be used as the foundation for future multimode switches and routers.
We have recently demonstrated a simple passive Si asymmetric Y-junction, which can serve as both the MDM mux and demux with demultiplexed crosstalk as low as −30 dB [18].Asymmetric Y-junctions are Y-junctions where each arm exhibits a different geometry and therefore supports a fundamental mode with a different wave-vector.If the angle, θ , between the arms is sufficiently small, then the mode supported by one arm adiabatically evolves into the mode in the multimode stem with the closest corresponding wave-vector, allowing an asymmetric Yjunction to be designed such that each arm excites a different mode in a multimode waveguide (Fig. 2).A parameter called the "mode-conversion-factor," (MCF), is commonly used to define the transition between a Y-junction acting as a mode-sorter instead of a standard power-splitter, and is defined as where is θ the angle between the Y-junction arms, β A (β B ) is the wavevector of the fundamental mode supported by Arm A (Arm B), γ AB = 0.5 (β A + β B ) 2 − (2kn) 2 is related to the evanescent decay constant of the two modes, k is the free-space wavevector, and n is the cladding index of refraction [16][17][18].The MCF can be used in a well known mode-sorting criterion, where for MCF > 0.43, an asymmetric Y-junction acts as a mode sorter allowing each individual mode of the MM-SiWG to be individually excited and demuxed [16,17].
A natural trade-off exists between mux/demux footprint and device operation since MCF is inversely proportional to θ [Eq.(1)].However, the Y-junction does not necessarily have to be designed to operate in the mode-sorting regime to function as a mux/demux for MDM.Instead, each arm of the Y-junction in the mux can excite a unique ensemble of modes in the MM-SiWG which then evolve into a single output arm of the demux.This behavior is demanded by time-reversal symmetry and the fact that the mux and demux are geometrically identical devices.
Each mode excited by the mux has a different wave-vector and thus the modes accumulate a relative phase difference after they propagate along the MM-SiWG link.At points where the relative phase difference between the modes (∆φ ) is equal to an integer multiple of 2π, an identical demux can be used to extract an individual data channel, even in cases where each data channel is spread over multiple guided modes of the interconnect.This manifests itself as periodic spectral regions of low demuxed crosstalk, centered at wavelengths where ∆φ = m2π with m an integer.Therefore, larger values of θ can be used in order to decrease the overall mux/demux footprint, while still achieving low crosstalk at the receiver.This process of low demultiplexed crosstalk is a result of destructive interference in each crossport, and can be rigorously described by investigating the system transfer matrix.For our system, we use a two-arm asymmetric Y-junction and a two-mode MM-SiWG.Assuming negligible reflection and scattering to radiation modes, we can describe the mux in this system using a device matrix, D mux , [20] with matrix elements κ i j that converts a set of orthonormal input modes, | ψ i , to orthonormal output modes, | ψ o : In this case, the input vector-space consists of the fundamental mode of each arm (ψ A and ψ B ), and the output vector-space consists of the even and odd QTM mode of the MM-SiWG (ψ T M,e , ψ T M,o ).Once the modes from the input arms couple to the modes of the multimodes waveguide, the even and odd modes experience different phase shifts, which can be described by a propagation matrix, P: where L MM is the length of the MM-SiWG and β e (β o ) is the propagation constant of the even (odd) mode of the MM-SiWG.The demux then couples the MM-SiWG modes to the fundamental modes of the output Y-junction arms with a corresponding device matrix, D demux , related to D mux by D demux = D −1 mux .The full mode-coupling system can then be described in the following way: For the case where ∆φ e,o = (β o − β e )L MM = m2π, the full system matrix simplifies to i.e., the matrix describing the whole system simplifies to the identity matrix with a phase prefactor.This shows that the output modes of the demux equal the input modes of the mux, and represents the successful multiplexing, transmission, and demultiplexing of two MDM channels.
What this analysis describes is a Mach-Zehnder interferometer (MZI) where, instead of the phase differential coming from arms with different path lengths, the phase differential arises from two modes in the same MM-SiWG with different wave-vector.Consequently, for ∆φ e,o = 2πm, the crosstalk channel in the demux experience destructive interference for both channels and the main channels experience constructive interference.
Note that this result is independent of the values of κ i j , therefore any device that can be described by a unitary device operator that maps the fundamental mode of each Y-junction arm to an ensemble of modes of the MM-SiWG can be used as the mux and demux for MDM with the appropriate design of the interconnect geometry.

Properties and fabrication of mux/demux
We use the general result from Sec. 3.1 in the asymmetric Y-junction MDM coupler designed for our experiments.The cross-sectional dimensions for the Y-junction arms are 250 nm × 450 nm (height × width) for Arm A, 250 nm × 550 nm for Arm B, and 250 nm × 1 µm for the MM-SiWG link.At λ = 1550 nm, this choice of geometry results in MCF = 4.4/θ (where here θ is in degrees) and therefore acts as a mode sorter for θ < 9°.We choose an angle of θ = 3°c orresponding to MCF of 1.3.The length of the MM-SiWG is chosen to be L MM = 1.2 mm.More details on the Y-junction design can be found in [18].We subsequently fabricate the device using the same method as in [18,21], which includes 100 keV e-beam lithography with hydrogen silsesquioxane resist and HBr/Cl inductively coupled plasma etching to isolate the Si devices.The chip is completely covered with SiO 2 cladding deposited by plasma-enhanced chemical vapor deposition.For this design, the first even (odd) QTM mode of the MM-SiWG has an effective index of n e f f ,e = 2.20 (n e f f ,o = 1.90) and a group index of n g,e = 4.44 (n g,o = 4.70) at λ = 1550 nm.Therefore, we expect to see reduced demultiplexed crosstalk in the demux for wavelengths that satisfy with a free spectral range of Figure 3 shows spectral scans of the demultiplexed crosstalk, ε, found by coupling a tunable laser into either Arm A or Arm B of the mux, and measuring the ratio of the power exiting the cross-port (P x ) to the power exiting the through-port (P t ) of the demux as the wavelength is varied between λ = 1520 nm and 1620 nm.For the asymmetric Y-junction used in this work, and for Arm A (Arm B) excitation, Arm C (Arm D) is the through-port and  Arm D (Arm C) is the cross-port as described in Fig. 2. The results reveal spectral regions where the crosstalk is as low as −30 dB, consistent with wavelengths that satisfy Eq. ( 6).The ∆λ FSR near λ = 1550 nm matches well with Eq. ( 7).Nearly identical spectral responses for excitation of either arm of the mux are also observed, demonstrating equal effectiveness muxing/demuxing the even mode and odd mode.For the remainder of this work, the wavelengths associated with low ε are utilized for demonstrating both MDM and MDM-WDM with minimal BER power penalties.
For one wavelength (λ = 1561 nm), the scattered light from the top of the device was imaged using an IR camera (Fig. 4).Different launch conditions were used, including only illuminating the top arm, only illuminating the bottom arm, and illuminating both arms of the MDM mux.The scattered light shows the general mux, multimode propagation, and demux behavior using the Y-junction devices, including the low demultiplexed crosstalk in the demux.

MDM and MDM-WDM experimental setups
The experimental setup used to demonstrate both 2 × 10-Gb/s MDM (20 Gb/s aggregate bandwidth) and 2 × 3 × 10-Gb/s MDM-WDM (60 Gb/s aggregate bandwidth) is shown in Fig. 5.For MDM, light from a tunable laser is passed through a polarization controller (PC), modulated using a LiNbO 3 modulator, and encoded with a 2 15 -1 pseudorandom binary sequence generated by a pulsed-pattern generator (PPG).The signal is amplified with an erbium-doped fiber amplifier (EDFA), passed through an optical isolator (ISO), and then split via a 50%/50% fiber splitter into two tributaries.The tributaries are decorrelated from one another with a 5.5 km spool of standard single-mode fiber (SMF-28) placed in one arm, which supplies > 15 bit-slots of delay between neighboring wavelength channels.The state-of-polarization (SOP) of each path is controlled with a PC, inline polarization splitter (PS), and another PC before being connected to separate input channels of a pitch-reducing optical fiber array (PROFA).The power in each arm can be adjusted for the purpose of balancing the demultiplexed crosstalk by using the PC to rotate the SOP with respect to the PS within each tributary.The power in each tributary is monitored with a 1% tap.Each input of the PROFA produces a 10 µm (1/e 2 ) mode-fielddiameter output, where each channel is spatially separated by 38 µm.The pitch of the PROFA matches the pitch of the on-chip inverse-taper mode converters fabricated at the input facet of each arm of the Y-junction MDM mux.A lensed-tapered fiber (LTF) is used at the output facet to select one of the two arms of the MDM demux for characterization, which are also fabricated with inverse-taper mode converters.The outcoupled power is monitored with a 10% tap, and the remaining signal is passed through a tunable band-pass-filter (BPF) to suppress amplified spontaneous emission (ASE) noise from the EDFA, then a low noise figure EDFA, and followed by another tunable BPF used to suppress ASE noise.A 90%/10% tap is used to send the optical signal to a digital communications analyzer (DCA) and variable optical attenuator (VOA) respectively.The DCA is used to produce eye diagrams, and the VOA controls the detected power for bit-error-rate (BER) measurements.A 10% tap monitors the power output from the VOA and the remaining signal is detected with a commercial avalanche PIN photodiode.The electrical data signal is sent to a transimpedence amplifier (TIA) followed by a limiting amplifier (LA), and the signal from the LA is sent to a BER tester (BERT).The other MDM channel is then characterized by moving the LTF to the other port of the demux while keeping the rest of the experimental setup unaltered, including PCs and PROFA fiber alignment.
The differences between the MDM and MDM-WDM setups are illustrated in Fig. 5 by the two switches (S1 and S2), where if both S1 and S2 are in position 2, the experimental setup is configured for MDM.If both S1 and S2 are set to position 1, the setup is configured for MDM-WDM.The experimental setup for the MDM-WDM is the same as the MDM setup, with the exception that instead of using a single tunable laser, the source is generated with three lasers tuned to three different wavelengths and combined into a single fiber with a fiberoptic wavelength-division-multiplexer.All the wavelengths are then patterned simultaneously in the LiNbO 3 modulator.An additional 5.5 km spool of SMF is inserted between the ISO and 50%/50% fiber splitter in order to decorrelate each wavelength channel by ∼ 90 ps/nm.The remaining experimental setup remains the same, and the two BPF are tuned to isolate one wavelength channel at a time for optical eye and BER analysis.

2 × 10-Gb/s MDM transmission
The experimental setup shown in Fig. 5 (in the single-laser configuration) was used to explore on-chip MDM transmission in a MM-SiWG.A single CW laser source is first coupled into one of the arms of the mux by using one input channel of the PROFA.In this configuration, when light is launched into Arm A (Arm B) with power P A (P B ), the signal is optimally dropped through Arm C (Arm D) (through-port) with power P AC (P BD ); power dropped through Arm D (Arm C) (cross-port) with power P AD (P BC ) represent a source of crosstalk and a consequential BER receiver sensitivity penalty.The expected crosstalk, ε, for the MDM channel in Arm C and Arm D of the demux can then be found from the measured out-coupled powers by ε C = P AD /P AC and ε D = P BC /P BD respectively.From the measured crosstalk ε, the expected BER power penalty (PP) from coherent crosstalk can be calculated directly by [22].
In order to ensure that each MDM channel incurs the same PP at the receiver, the input powers P A and P B must be adjusted such that ε C = ε D .This in effect equalizes crosstalk such that any insertion loss or propagation loss imbalance does not lead to an imbalance the the power-penalty at the receiver.This equalization procedure can be accomplished by finding a power offset, ∆P: and then setting P A → P A + ∆P or P B → P B − ∆P, which successfully results in a balanced PP for both channels.Note that in the case of equal total insertion loss between both throughports and both cross-ports, the system is balanced for P A = P B and ∆P = 0; however fabrication variations in the inverse-taper mode-converter, differences in propagation loss between the different arms of the Y-junctions, and mode-dependent propagation loss in the MM-SiWG all contribute to variations in the insertion loss.Therefore applying Eq. 10 allows for the equalization of the crosstalk-induced PP.
Five different wavelengths are targeted to demonstrate MDM transmission, corresponding to wavelengths denoted by λ 1 through λ 5 in Fig. 3, which correspond to the measured lowcrosstalk dips.For each wavelength, the out-coupled powers are first measured in order to calculate ∆P, as listed in Table 1.Then, the launched power is adjusted by altering the laser power and through slight adjustments of the PC before the PS in each tributary.
Once the ∆P equalization factor is found, then the power launched into Arm A is altered by P A → P A + ∆P.After balancing the power in each arm using this method, BER measurements and eye diagrams can be obtained as detailed in Section 4.
At each wavelength, five BER curves are obtained corresponding to the following cases: 1.The baseline back-to-back (B2B) found by bypassing the PROFA and Si chip.
2. The MDM channel dropped into Arm C of the demux for the case of P B = 0 and P A ON.
3. The MDM channel dropped into Arm D of the demux for the case of P A = 0 and P B ON.
Table 1.MDM: Measured demuxed power levels for each wavelength channel, through each of the two arms of the MDM demux: P AC , P AD , P BD , P BC , P AD , and P BC represent demultiplexed crosstalk power at the receiver.Crosstalk imbalance resulting from insertion loss imbalance is equalized by finding ∆P and using Eq.(10).The balanced crosstalk after equalization is given by the ε column.
λ 5.The MDM channel dropped into Arm D of the demux when data is launched into both arms of the mux, both P A and P B ON.
Figure 6 shows the BER measurement results.The BER curves for case 1, 2, and 3 all overlap, which is expected since no crosstalk channel exists in these configurations, verifying that no additional BER PP is introduced by the Si chip itself.A PP is observed, however, when both channels of the mux are ON simultaneously.This is a direct result of coherent crosstalk in the demux between the two MDM channels.
Clear and open eye diagrams are also observed for each MDM channel at each wavelength (Fig. 6), and, in the case of crosstalk, a slight spread in the one-rail can be observed as expected.
length, corresponding to an aggregate bandwidth of 20 Gb/s for the on-chip MM-SiWG link, with 10 −9 BER PP as low as 0.1 dB -0.2 dB for λ = 1561 nm, associated with a MDM mux/demux pair with demultiplexed crosstalk of ∼ −34.2 dB.All 5 wavelengths exhibited 10 −9 BER PP < 0.7 dB/channel and levels of crosstalk < −21.8 dB.

2 × 3 × 10-Gb/s MDM-WDM transmission
Using the same MDM mux/demux pair, as used for the MDM demonstration in Sec.5.1, MDM-WDM could be realized by using multiple low-crosstalk wavelengths found in the transmission experiment shown in Fig. 3.In this way, 2 × 10 Gb/s MDM could be utilized at each of M wavelengths simultaneously multiplexed in each arm of the PROFA, to achieve 2×M ×10 Gb/s MDM-WDM link with an aggregate bandwidth of 20M Gb/s.In principle, all 5 wavelengths used to characterize MDM with low PP could be used for 2 × 5 × 10 Gb/s MDM-WDM with an aggregate bandwidth of 100 Gb/s, however the relatively large insertion loss experienced in practice using the PROFA, which was not well mode-matched to the on-chip inverse-taper mode-converters, lead to a power-limited system and competition for the gain of the pre-chip EDFA.Therefore, 3 of the wavelengths were used instead, for a demonstration of a 2 × 3 × 10 Gb/s MDM-WDM on-chip link, with an aggregate bandwidth of 60 Gb/s.Experimentally, the experimental setup had to be adapted according to Fig. 5 with S 1 → P 1 and S 2 → P 1 .This change added three laser sources which were multiplexed with a fiber wavelength-division-multiplexer, and a 5.5 km spool of SMF-28 in one tributary in order to decorrelate the different WDM channels; the additional 5.5 km spool was necessary since the all wavelength channels were modulated with the same modulator.The two MDM channels were further decorrelated with the 500 m spool of SMF-28 inserted into one of the tributaries in the same way as the MDM experiment.The combination of 5.5 km spool and 500 m spool of SMF-28 allow for all 6 data channels to be decorrelated from one another.Table 3. MDM-WDM: Measured demuxed power levels for each wavelength channel, through each of the two arms of the MDM demux: P AC , P AD , P BD , P BC , P AD , and P BC represent demultiplexed crosstalk power at the receiver.Crosstalk imbalance resulting from insertion loss imbalance is equalized by finding ∆P and using Eq.(10).The balanced crosstalk after equalization is given by the ε column.For each wavelength, the two MDM channels had to be equalized from the perspective of demultiplexed crosstalk, in the same way as described in Sec.5.1 and through Eq. ( 10).This was done by again finding ∆P, as shown in Table 3, and adjusting the PC in each tributary before the PS.Since independent control of the power levels of all 6 channels was not available due to the fact the two MDM channels at each wavelength were derived from the same source, and all 6 channels were modulated by the same modulator, slight adjustments of the PC before the PS was performed to balance each wavelength channel before the corresponding BER measurement.This mimicked a true MDM-WDM system where each channel would be derived from a separate modulator.Figure 7 shows the resulting BER measurements.For each of the three wavelengths, 5 curves are again shown, as similarly defined in Sec.5.1.The bit difference between the BER curves in Fig. 7 and the BER curves in Fig. 6, is that for the MDM demonstration, only one laser was used at a time, while for MDM-WDM, all three laser sources were muxed simultaneously into the MM-SiWG, and post-chip filters were used for WDM demuxing before each BER curve was obtained.
Table 4 shows the resulting PP measured for each of the 6 channels muxed simultaneously, which were found to be (MDM CH1 PP/MDM CH2 PP) 0.70 dB/0.60 dB, 0.70 dB/0.70 dB, and 0.10 dB/0.10 dB at WDM channels of 1543 nm, 1551 nm, and 1561 nm, respectively.These BER results demonstrate successful 2 × 3 × 10-Gb/s MDM-WDM multiplexing, corresponding to an aggregate bandwidth of 60 Gb/s for the on-chip MM-SiWG link, with 10 −9 BER PP as low as 0.1 dB.All 6 demultiplexed data channels exhibited PP < 0.7 dB/channel.

Conclusion
We have demonstrated the utility of asymmetric Y-junctions for compact on-chip interconnects supporting MDM multiplexing schemes.Devices were fabricated, showing crosstalk at the receiver as low as −30 dB, which was realized by taking advantage of coherently suppressed crosstalk at specific target wavelengths.This suppression was found to be due to destructive interference in the crossport, in an equivalent fashion to the destructive port in an MZI.The Y-junctions were thus suitable for MDM multiplexers and demultiplexers, and a full systems-level demonstration with a 2 × 10−Gb/s MDM link (20 Gb/s aggregate bandwidth), and 2 × 3 × 10−Gb/s MDM-WDM link (60 Gb/s aggregate bandwidth) was shown, each with 10 −9 BER penalties < 0.7 dB for all channels, and as low as 0.1 dB.
Thus, when coupled with other multimode devices such waveguide bends designed for MDM, asymmetric Y-junctions can serve as a simple means towards building robust Si muxes and demuxes for MDM to enable further optical aggregate bandwidth scaling at the chip level.

Fig. 1 .
Fig. 1.Illustration showing simultaneous multiplexing of M wavelengths and N modes at bandwidth B for MDM-WDM with a total N × M × B aggregate bandwidth.

Fig. 2 .
Fig. 2. (a) Illustration of mode mux/demux using asymmetric Y-junctions.For a 1 µm wide waveguide at λ = 1550 nm, E y component of: (b) fundamental QTM mode of Arm A and Arm C, (c) fundamental QTM mode of Arm B and Arm D (d) first even QTM mode of multimode interconnect (e) first odd mode of multimode interconnect.

5 Fig. 3 .
Fig. 3. (a) Spectral response of the crosstalk port, Arm D (Arm C) in the demux for launching into Arm A (Arm B) of the mux.Low crosstalk dips are observed at specific wavelengths, which are chosen for MDM and MDM-WDM demonstrations with low crosstalk.

Fig. 4 .
Fig. 4. (a) Schematic showing muxing and demuxing of different MDM channels.Top view of IR camera for (b) CH1 ON CH2 OFF, (c) CH1 OFF CH2 ON, and (d) both MDM channels ON.
(9) P AC (dBm) P AD (dBm) P BD (dBm) P BC (dBm) ∆P (dBm) ε Table2. 2 × 10 Gb/s MDM (20 Gb/s aggregate bandwidth) PP: Measured 10 −9 BER PP for both MDM channels at 5 different wavelengths.Expected PP column shows the expected penalty from using the crosstalk numbers from Table1in conjunction with Eq.(9).Measured PP values are extracted from complementary error-function fitting of experimental data points as shown in Fig.6.The MDM channel dropped into Arm C of the demux when data is launched into both arms of the mux, both P A and P B ON.

Table 4 .
(9)sured 10 −9BER PP for all 6 MDM-WDM channels.Expected PP column shows the expected penalty from using the crosstalk numbers from Table3in conjunction with Eq.(9).Measured PP values are extracted from complementary errorfunction fitting of experimental data points as shown in Fig.7.