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Abstract
We investigate modal crosstalk in silicon photonic MDM-based interconnects using tapered multiplexers. Crosstalk from coherent optical interference originates from variation in the physical structure and alters the transmission link performance. Through simulations and experimental work, optical crosstalk as a function of wavelength is analyzed to understand its impact in MDM and MDM-WDM dual-multiplexing applications. The detrimental effects are validated in the frequency and time domains through fabricated MDM interconnects of various lengths. Results indicate modal crosstalk must be < −22 dB to maintain a BER of 10−12. The experimental methodology assesses the optical modal crosstalk’s impact on the data, towards a mitigation approach to improve the payload signal integrity and enable system-level optimization such as channel wavelength allocation.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical multiplexing significantly increases the aggregated throughput of interconnects in transmission lengths ranging from inter- and intra-data center down to intra-chip communication. Techniques such as wavelength-division multiplexing (WDM) using silicon photonic (SiP) waveguides have been studied [1,2]. Silicon-on-insulator (SOI) based waveguides take advantage of the large refractive index difference between the core and cladding. This index contrast allows for high confinement of light and relatively low loss in the integrated waveguides [3]. The use of SOI also brings about the possibility of photonic/electronic co-design, allowing for the creation of large and complex systems [4,5].
An interesting multiplexing dimension is mode-division multiplexing (MDM) which uses orthogonal optical modes as transmission channels [6,7]. This method has the advantage of using a single wavelength to modulate all channels, which could lead to lower complexity and power dissipation than WDM [8]. MDM has already shown promise, for example, with eight data channels transmitted simultaneously in [9].
One of the challenges in optically multiplexed links is crosstalk. In MDM-based interconnects, since all modes are transmitted using the same wavelength, crosstalk between channels is coherent in nature and cannot simply be filtered out [10]. In [11], we explored the implications of low and high crosstalk for an integrated SiP MDM waveguide on the bit-error rate (BER) performance of a clock-forwarded (source-synchronous) interconnect. We observed that crosstalk levels varied considerably across wavelengths and between modes of a given interconnect, as well as from die to die, even for identically drawn interconnects. Through experimentation, it was shown that the BER exponentially deteriorated as crosstalk onto the clock-carrying channel increased above −19 dB. In this case, to minimize crosstalk, we found we needed to limit transmission to modes and wavelengths where the crosstalk was below a −19 dB threshold to maintain a BER of 10−12 [11]. In practice, however, it is not always possible to select the wavelength corresponding to the lowest crosstalk of a given interconnect. One of the methods that has been explored to increase the throughput of a link is the use of MDM in conjunction with WDM [7,12]. Based on our experimental observations, mode crosstalk across wavelengths of an MDM interconnect would be one of the determining factors in the quality of the link when using this dual-multiplexing technique. It is thus crucial to understand the crosstalk spectrum in MDM links to bring their benefits from the laboratory setting to the consumer market.
In this paper we focus on tapered couplers and look at some causes of crosstalk spectrum variation of an integrated SiP MDM interconnect. We show how crosstalk will vary from an expected spectrum in the design stages to that of a fabricated device, along with the consequences of such changes on the eye diagram obtained using an experimental setup at 8 Gb/s. We consider the eye as the standard by which an interconnect’s transmission should be verified, since it is ultimately this metric which will determine if the electronics in the receiver will successfully recover the data. Findings demonstrate how modal crosstalk between −29 dB and −19 dB in a two data channel MDM link correspond to calculated bit-error rates from < 10−12 to 10−6. The analysis and results of this work will have implications on system level design aspects, such as channel allocation in MDM-WDM links. In Section II, we will first discuss such topics as leakage and interferometric interference which manifest themselves as crosstalk. We then show how these elements in the crosstalk’s spectrum change due to variation caused by fabrication. In Section III and IV, experimental measurements in the frequency and time domain are used to validate the simulation findings.
2. Modal leakage in MDM interconnects
As the crosstalk power between one signal channel (aggressor) and another (victim) increases, it can become detrimental to the latter’s transmission. This crosstalk comes from different sources, one of which is modal crosstalk [13]. In an ideal straight waveguide, it is nonexistent since modes are mathematically orthogonal and theoretically do not interfere with other modes in the interconnect [14,15]. However, crosstalk involving one mode coupling into another can occur when perturbations or surface roughness in a fabricated waveguide structure are present. These perturbations cause a redistribution of energy in the modes, a phenomenon previously investigated [13,14]. Another source of crosstalk is mode leakage, where a mode is incorrectly coupled to or from a mode in a bus waveguide. Although mode crosstalk occurs within the interconnect waveguides [12–15], leakage as a form of crosstalk, specifically in tapered multiplexers, is the focus of this paper.
Mode multiplexers (MUX), used for coupling signals in and out an optical multimode bus waveguide, have been implemented in numerous ways using passive components [7]. One approach, illustrated in Fig. 1(a), is an asymmetric directional coupler (ADC) used to excite supermodes between the waveguide that adds and drops a specific mode and an appropriately designed bus waveguide supporting multiple modes [3]. In the image, port 1 handles mode 1 (M1) transmission and port 2 handles mode 2 (M2) transmission. The coupling between the ADD/DROP waveguide (WG) and the BUS waveguide in the ADC is sensitive to fabrication variations in the waveguides’ physical dimensions. To find the most effective dimensions to vary, simulations similar to those in [16] were carried out to evaluate the sensitivity of the ADD WG and BUS WG to variation. It was observed that the ADD WG effective index changes twice as much as that of the BUS WG effective index over a given span. It was thus chosen to use the ADD WG width as the dimension to demonstrate fabrication sensitivity.
Fig. 1. (a) Directional coupler illustrating the input signal coupling from the add port WG to the bus WG, with incorrectly coupled signal from ADD WG shown as leakage; (b) transmission characteristics of M2 from add WG at the MUX output, with a subplot of transmission across width variation at 1570 nm as an example; (c) crosstalk characteristics of M2 to M1 from add WG at the MUX output, with a subplot of crosstalk across width variation at 1545 nm as an example. Both (b) and (c) are for ADD WG width variations between −10 nm and 10 nm.
These sensitivity simulations are explored for a MUX ADC using FDTD simulation in which a directional coupler (length 34 µm; gap 150 nm) adds the mode through a waveguide (ADD WG) with its width varying +/- 10 nm from its designed width of 430 nm to account for fabrication variation within a die [3,16]. Figure 1(b) illustrates the transmission spectrum of the first fundamental mode M1 (TE0) which is sent through the add waveguide input port 1 (ADD WG) coupling to the second mode M2 (TE1) in the bus waveguide. This is done while the add waveguide is subject to width variations. The width variations result in a spread of transmission for a given wavelength, for example > 6 dB at 1570 nm as plotted in the subfigure of Fig. 1(b). This suggests that within even the same die the multiplexer design may fail to couple modes between the add and the bus waveguides, resulting in poor transmission or failure of the multiplexed link.
Coupling of energy between the multiplexer waveguide and bus waveguide is determined by the phase-matching condition, related to the propagation constants of both modes [13]. As shown in [12], coupled mode theory indicates that the closer the two propagation constants are, the higher the coupling strength between the two modes. The coupling strength between the bus and add waveguides is thus highest for the modes intended to couple (i.e., input port 2 to mode 1, TE0, in the bus waveguide), indicating most of the energy transfers to this mode. However, weak coupling may still occur unintentionally amongst any other guided modes or an infinite number of radiative (lossy) modes of the bus waveguide. Since radiative modes do not guide light well and the energy coupled to them dissipates quickly [3], we will assume any light at the output ports were transmitted on guided modes. It is thus the strength of the mode coupling to a given guided mode that will determine the leakage and ultimately measured crosstalk. The signal that is coupled to the incorrect mode (i.e., coupled to M1 instead of M2) in the bus waveguide is presented in Fig. 1(c). The inset image shows how the crosstalk spectrum also changes in the presence of parameter variation, for example with a spread of 8 dB at 1545 nm. Crosstalk will be considered as the ratio of the sum of optical power, P, leaked from all other modes over the expected signal power of the given output port, an example of which is given in (1). That is, the ratio of power at a given wavelength in Fig. 1(c) to that in Fig. 1(b). In Eq. (1), the crosstalk at port 1, XTalkOut_Port1, is the ratio of the optical power leaked from port 2 to the output port 1, Pin_Port2→Out_Port1, over the optical power transmitted from port 1 to that waveguide output (Output Port 1), PIn_Port1→Out_Port1.
A tapered multiplexer (length 103 µm; gap 150 nm) as in [17] and [18] is simulated and subjected to the same +/- 10 nm variation conditions as the ADC in Fig. 1. On the MUX side, as with the ADC, the input port 2 is excited but not the input port 1. The simulated transmitted output of the MUX inside the BUS waveguide for both M2 and M1 is illustrated in Fig. 3(a) and 3(b), respectively. The transmitted signal in Fig. 3(a) shows much smaller variation in signal transmission across wavelength and width variations than its equivalent signal in the ADC. Crosstalk in Fig. 3(b), however, still shows a large variation both across wavelengths for a given waveguide width and across widths for a given wavelength (e.g., subfigure in Fig. 3(b) at 1575 nm). The crosstalk is thus wavelength dependent and caused by incorrect coupling, where the crosstalk mode is excited (M1) instead of the transmission mode (M2) due to effective index mismatch. The plots in Fig. 3 demonstrate the optical spectrum profile of the crosstalk where only the MUX is subjected to width variation. However, the couplers on both sides of the interconnect suffer from these variations. This leads to complex wavelength dependencies in the transmission spectrum.
Fig. 3. Simulated tapered MDM MUX transmission for (a) input port 2 to M2 mode in the bus interconnect and (b) input port 2 to M1 mode in the bus interconnect while varying the drop WG width from −10 nm to 10 nm. Subplot in (b) shows crosstalk across width variation at 1575 nm as an example.
As discussed briefly in [19], it was observed that the length of the MDM interconnect impacted the crosstalk spectrum. To investigate, simulations are conducted on the structure in Fig. 2 using an ideal multiplexer, interconnect, and demultiplexer. The multiplexer and demultiplexer are identical and without parameter variation, with the only change being in the length of the interconnect between the two. Interconnect lengths of 100 µm, 250 µm, 750 µm, and 1 mm are simulated and plotted in Fig. 4, with the through mode transmission (i.e., M1 to M1 through input port 1 to output port 1) used to normalize the crosstalk mode (i.e., M2 to M1 from input port 2 to output port 1). The spectrum of the crosstalk shows an interferometer-like shape. This originates from the interference between the multiplexer and demultiplexer leakage signals. The free-spectral range (FSR) is indicated for each length.
Fig. 4. Simulated crosstalk using ideal structures (MUX, interconnect, and DEMUX) for interconnect lengths of (a) 100 µm and 250 µm; (b) 750 µm and 1000 µm. FSR is indicated for each interconnect length.
The MUX can be divided into two parts, the bend and the taper. For the taper, the crosstalk can be derived using coupled-mode theory (CMT) as previously demonstrated by Lipson [12]. However, for the bend, since the gap and width vary together, the coupling coefficient between add and bus waveguide vary as well. Making an analytical expression of the coupling coefficient for CMT becomes challenging. For practical purposes, a commercially available and widely used simulation software Lumerical FDTD is thus employed to get the crosstalk amplitude instead of using the CMT method.
When the input is given through input port 2, two crosstalk components are derived as having the following form
The 1 mm long interconnect structure in Fig. 2 is simulated for width variations in the multiplexer and demultiplexer. First, in Fig. 5(a), the width of the add waveguide is varied +/−10 nm from the designed width while keeping the nominal dimensions for the demultiplexer. One can see how the null, for example found at 1572 nm for the ideally sized waveguide (black dotted curve), changes to a peak for a width variation of only 5 nm. Secondly, in Fig. 5(b), the width of the demultiplexer taper in the bus waveguide is reduced by 5 nm in addition to the add waveguide width variation of 5 nm and 10 nm in the multiplexer. Here, a peak is suppressed around 1574 nm for a 5 nm change to the input port 2 waveguide width (blue curve). Two peaks are also merging when the width change is increased to 10 nm (red curve). These changes alter the effective index (neff) and coupling strength to a given mode, thus changing the spectrum.
Fig. 5. 1 mm interconnect with (a) +/- 10 nm width variation at input port 2 (add WG); (b) Combined effects of 5 nm and 10 nm width variation at input port 2 (add WG) along with 5 nm reduction in the width of the DEMUX taper in the bus WG.
Varying the width of the ADD and DROP waveguides, and therefore the gap adjacent to the waveguide as well simultaneously, results in a wavelength shift of approximately 1 nm in the nulls of the spectrum without affecting the FSR. This is the reason that two different aspects of the structure were varied (e.g. the ADD WG in the MUX and taper in the DEMUX), highlighting how the combined effects of interferometric patterns and random structure variation can change the crosstalk spectrum across chips and cause complex crosstalk patterns.
3. Mode crosstalk measurements in the frequency domain
The experimental setup in Fig. 6 is used to characterize interconnect lengths of 100 µm, 250 µm, 750 µm, and 1 mm. Each interconnect is designed using the same multiplexer structure illustrated in Fig. 2. In presenting the results, the input mode, X, corresponds to where the continuous wave (CW) light is injected and the output mode, Y, is the mode which is measured at the output of the interconnect. The graphs in this section are then labeled as a mode input to mode output labeling scheme (MxMy). For example in Fig. 6, the injected light from the source is added to input port 2 (mode 2 input, M2) at the input while crosstalk is measured by monitoring output port 1 (mode 1 output, M1). This situation leads to a label of M2M1.
Fig. 6. Experimental setup for crosstalk measurement of Mode 2 to Mode 1 (M2M1) using a wideband ASE source as input and an optical spectrum analyzer (OSA) at the output.
Experimental results for M1M2 and M2M1 are presented in Fig. 7. These results were obtained using a broadband ASE source (erbium-doped fiber amplifier) as input (total output power 0 dBm), and the output is recorded using an optical spectrum analyzer (OSA) (sensitivity: −80 dBm; resolution: 0.06 nm). The results are normalized to the input mode straight-through case (i.e., M1M1) as a reference to show crosstalk power across the spectrum. The wavelength range was chosen due to the useable region of the ASE source. For the 100 µm interconnect length the indicated FSR is approximated to where the lobe abruptly ends, however, the actual range appears to be larger.
Fig. 7. Experimental results of wavelength sweeps for (a) 100 µm, (b) 250 µm, (c) 750 µm and (d) 1000 µm MDM interconnects.
In Fig. 7(c) at 1550 nm and Fig. 7(d) at 1557 nm, a merging of peaks in the crosstalk spectrum is observed. This is similar to the simulation results in Fig. 5(b), indicating multiple variations from the design parameters of the interconnect. Qualitatively, as expected, the FSR is shown to decrease as the interconnect increases in length.
Figure 8 plots the FSR from the model in (5) (blue curve), the results from the simulated structure in Fig. 4 (red curve) and the experimentally measured interconnects in Fig. 7 (dotted black curve). It shows the measured FSR matches the calculated and simulated values well. Since the full derivation is hard to evaluate without simulation, the approximation is also plotted in Fig. 8 (green dotted curve). The approximation of (5), however, only begins to match the others as the interconnect length increases. This is expected as the model approximation given in Eq. (5) is only valid for lengths which satisfy the stated requirement. The FSR of the interconnect is determined by both the first and second terms of the denominator in the full form of (5). The contribution of the first denominator term in (5) comes from the wavelength dependence of the phase term which is fixed and does not change for any of the different interconnect lengths. The second term comes from the phase difference of the different modes. This term increases as the length of the interconnect length increases and will become the dominant term. It is instructive for the reader to note that practically, for this particular device, the approximation closely resembles the full solution after the interconnect length of 600µm, with higher accuracy as the interconnect length increases. This is because the first denominator term of the full form in (5) becomes less than one-quarter the value of the second denominator term at the length value of 600 µm.
Fig. 8. Comparison between simulated (red trace), calculated model from (5) (blue trace), model approximation from (5) (green trace) and experimentally measured FSR values (black trace).
By knowing what shapes the crosstalk spectrum, designers can use the nulls to their advantage and place channels in these low crosstalk windows. Control on the spectrum will lead to better performance for multichannel (MDM-WDM) applications by exploiting FSR nulls to minimize crosstalk.
To show the combined effect of deterministic (such as interferometric interference) and random crosstalk effects (such as variation due to fabrication), two identical 1 mm interconnect devices were fabricated on the same SiP chip, Interconnect – A and Interconnect - B. The measurements are presented in Fig. 9(a) and (b) and normalized to the straight through case. As predicted by simulation in Fig. 5(a), the two devices show similar FSR, however, have a shifted spectrum due to variation of waveguide parameters. These results highlight the difficulty in predicting crosstalk in MDM links, where fabricated devices will differ, even within a die making mitigation of crosstalk difficult. This will lead to potentially requiring optimized optical or electronic solutions to mitigate crosstalk in large volume consumer applications [20].
Another way of understanding the differences in crosstalk spectra due to variation is the accumulation of phase of one signal with respect to the other. Assuming the undesired phase introduced by fabrication imperfections is constant over the entire range of wavelengths, the phase offset is calculated by fitting the experimental results following Eq. (4) for 100 µm, 250 µm, 750 µm and 1 mm, resulting in 1.8, 3.5, 5 and 4 radians, respectively. The phase offset will vary from die to die, impacting the spectrum differently for the same interconnect length (e.g., 4 and 4.7 rad., respectively, for Figs. 9(a) and 9(b)).
4. Experimental mode crosstalk in the time domain
This section ties the previously discussed theoretical topics together, showing why the MDM crosstalk spectrum is an important metric in the quality of transmission in MDM and WDM-MDM multiplexed links. It explores the crosstalk effects in the time domain using an experimental setup, shown in Fig. 10, similar to the one used in [11]. To that setup an optical attenuator is added to vary crosstalk coupling strength. The 1 mm MDM interconnect device under test (DUT) on a SiP chip receives modulated optical input from a PRBS31 data sequence generator at 8 Gb/s. It has been observed that the data rate applied to the interconnect does not affect the crosstalk signature on the spectrum. The data rate in this experimental setup was chosen based on equipment availability. The DATA and DATABAR are fed to two electro-optic modulators (MOD), where the DATABAR is electrically delayed with significant RF cable differential path delay (45 cm) for approximately 14 bits of decorrelation between the two PRBS NRZ data streams. To make the effects of crosstalk more prominent from the 1 mm interconnect, the wavelength is set to 1545.2 nm to obtain a high amount of crosstalk for interconnect B for the M2M1 scenario (−17.4 dB), as shown in Fig. 9(b). A variable optical attenuator (VOA) is used at the M2 input port to vary the input signal strength on this mode. This is done to create a variable crosstalk mechanism, whereby the maximum crosstalk is set by the physical attributes of the interconnect when the optical attenuator is set to 0 dB. This mimics sweeping wavelengths with different peak crosstalk values. As the attenuation is increased, the optical power into M2 input port is reduced and thus the crosstalk coupling strength is effectively lowered. The output is then taken from M1 output port, amplified using an EDFA and filtered before being measured on the oscilloscope. Due to the VOA, there is a 1.8 dB difference in input power between the input grating couplers of the two modes. This is taken into account in the following section by adding the 1.8 dB loss to the intentional attenuation of the VOA.
Fig. 10. Experimental setup for crosstalk data measurements in the time domain with one PRBS aggressor signal at M2 input port 2.
Figure 11 shows time domain recorded eye diagrams using a sampling oscilloscope (Agilent DCA X 86100D) of M1 input signal receiving optical crosstalk from M2 input (aggressor) as M2 input strength is increased (attenuation reduced). The image is labeled using an effective crosstalk value, which takes into account the inherent crosstalk value of the interconnect (−17.4 dB plus VOA loss) and the optical attenuator value. The VOA is adjusted to give an effective crosstalk of −29.2 dB, −24.2 dB, −22.2 dB and −19.2 dB in Figs. 11(a) to 11(d), corresponding to VOA attenuation values of −10 dB, −5 dB, −3 dB and 0 dB respectively. The inset text indicates the optical input to the grating couplers (GC) as the aggressor signal is increased. As the crosstalk from M2 increases, the received eye at M1 output port closes and the timing jitter worsens. Our experimental setup is limited to a crosstalk coupling strength of −19.2 dB, although it is expected that the eye will continue to worsen as crosstalk increases. On the lower end, the experimental setup can reduce the crosstalk as low as −39.2 dB (not shown), although insignificant changes occur for crosstalk below −29.2 dB.
Fig. 11. Eye diagram showing impact of modal crosstalk in the time domain for an aggressor signal from M2 onto a decorrelated signal on M1 for effective crosstalk of (a) −29.2 dB, (b) −24.2 dB, (c) −22.2 dB and (d) −19.2 dB. Inset text indicates input optical power to the grating couplers for each mode.
To understand what is happening in the images of Fig. 11, let us consider two electromagnetic fields of propagating signal, ESig and EXT, of equal carrier frequency in a waveguide. Similar to Eq. (4), Eq. (6) describes the resulting output intensity of a port (optical power), IOUT, due to the interaction between the two fields at the input to a photodetector.
Fig. 12. Illustration in MATLAB of the resulting eye diagrams for both extremes of the beat term signs, (a) positive and (b) negative.
The amount of peak-to-peak increase or reduction in the eye opening is determined by both the amount of crosstalk from the aggressor to the victim channel and the argument of the cosine term. The sign of the cosine term (positive or negative) cannot be predicted in an actual system [21]. The beat term results in the uneven growth of the “1” logic level of the eye diagram compared to the “0” level as crosstalk increases. This can be clearly seen in Fig. 11 from the examples with higher amounts of crosstalk in Fig. 11(d) compared to the lower amounts of crosstalk in Fig. 11(a).
Using the oscilloscope measurements obtained, a few examples of which are shown in Fig. 11, the vertical and horizontal eye openings are recorded. The vertical eye opening is normalized to the widest point, found at the effective crosstalk value of −29.2 dB. The horizontal eye opening is plotted on a secondary axis in unit intervals (UI) with respect to the ideal 8 Gb/s bit period. It is observed that both traces worsen above a crosstalk value of approximately −27 dB in Fig. 13(a).
Fig. 13. (a) Graph showing effective crosstalk versus the vertical eye opening (normalized to the opening at −29.2 dB crosstalk) and the horizontal eye opening (with respect to the UI of an ideal 8 Gb/s bit period); (b) effective crosstalk versus calculated BER from oscilloscope measurements.
Using oscilloscope measurements of the eye, the bit error rate (BER) is estimated and plotted in Fig. 13(b) [22]. The slice point is assumed to be in the center of the eye, anticipating instances where the jitter or timing error might be higher towards the edges. Also, as the crosstalk is increased, the decision threshold (vth) is varied so as to always be in the middle of the two logic bands (“1” and “0”). This is assumed since many optical receivers have the functionality to do these adjustments using eye monitoring circuitry. When dealing with crosstalk, it is important to understand that the dominant impact on the BER is due to closure of the eye, caused by the “1” logic level approaching the “0” logic level, and not an increase in the noise. This is analogous to how increased ISI increases BER [23]. Based on these calculations, the crosstalk must be less than −21 dB to maintain a BER better than 10−12. The plot in Fig. 13(b) focuses only on data points which give a BER worse than 10−12, highlighting the crosstalk values that become problematic.
Referring to Fig. 7, the FSR lobes have maxima and minima corresponding to −19 dB and −30 dB, respectively. Referring back to the BER estimation in Fig. 13(b), this corresponds to a BER ranging from 10−6 to 10−12, respectively. The inset image in Fig. 13(b) shows an example of degradation due to crosstalk in eye diagrams, illustrating the difference between modal crosstalk at −19 dB and −29 dB.
Using the information found in Fig. 13(b), a theoretical BER response across wavelengths for interconnect lengths of 250 µm and 1 mm are plotted in Fig. 14(a) and 14(b) respectively. A BER floor of 10−12 is used in to simplify the image. The estimated BER plot provides insight into the system-level planning of channel wavelength allocation. Inset eye diagrams are added to locations corresponding to crosstalk values as a visual aid.
Fig. 14. Crosstalk spectrum overlaid onto calculated BER bar graph (approximated and with BER floor of 10−12) for interconnect lengths of (a) 250 µm and (b) 1 mm.
One observation made from Fig. 14 is that channels across the spectrum will inherently experience a wide range of BER outcomes, based solely on the interconnect itself without other system-level considerations taken into account. Depending on the wavelengths used, this will limit the ability to reduce laser power in the link since it will be the poorer-performing channels imposing these limits. One can also see how larger FSR, as in Fig. 14(a), will lead to both an increased window of poor BER performance (i.e., 1540 nm to 1550 nm) as well as a window of improved performance (i.e., 1550 nm to 1560 nm). On the other hand, at longer interconnect lengths as in Fig. 14(b), there still exists opportunities to intelligently place channels at wavelengths corresponding to low BER. This indicates that MDM can be used efficiently for a variety of interconnect lengths with some trade-offs and considerations of the channel placement and spacing. These trade-offs may also require further investigation since interconnects with distances greater than 250 µm will most likely be of interest for the foreseeable future. Also, variation of device parameters due to fabrication will cause the spectrum to change, possibly requiring post processing of data or the use of optical tuning mechanisms.
5. Conclusion
This paper discusses the impact of modal crosstalk in silicon photonic MDM-based interconnects. Using simulations and experimental measurements of tapered couplers, fabrication variation and its effects on the crosstalk spectrum have been investigated. Next, interconnect length influence on the crosstalk spectrum was investigated and shown that the FSR, caused by the interconnect length dependence, is correctly captured by presented equations and simulations. Following this, time-domain experimental results highlighted the effects of low and high crosstalk strength from an aggressor to victim signal and gave rationale to the importance crosstalk coupling strength has on transmission quality. The optical crosstalk-shaping topics presented in this paper are thus essential for enabling high throughput WDM-MDM dual multiplexed links of the future.
Funding
Canada Research Chairs; Concordia University;.
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