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Abstract
On-chip optical group-velocity dispersion (GVD) is highly desired for a wide range of signal processing applications, including low-latency and low-power-consumption dispersion compensation of telecommunication data signals. However, present technologies, such as linearly chirped waveguide Bragg gratings (LCWBGs), employ spectral phase accumulation along the frequency spectrum. To achieve the needed specifications in most applications, this strategy requires device lengths that are not compatible with on-chip integration while incurring in relatively long processing latencies. Here, we demonstrate a novel design strategy that utilizes a discretized and bounded spectral phase filtering process to emulate the continuous spectral phase variation of a target GVD line. This leads to a significant reduction of the resulting device length, enabling on-chip integration and ultra-low latencies. In experiments, we show GVD compensation of both NRZ and PAM4 data signals with baud rates up to 24 GBd over a 31.12-km fibre-optic link using a 4.1-mm WBG-based on-chip phase filter in a silicon-on-insulator (SOI) platform, at least 5× shorter compared to an equivalent LCWBG, reducing the processing latency down to ∼ 100 ps. The bandwidth of the mm-long device can be further extended to the THz range by employing a simple and highly efficient phase-only sampling of the grating profile. The proposed solution provides a promising route toward a true on-chip realization of a host of GVD-based all-optical analog signal processing functionalities.
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1. Introduction
Rapid advancements in both ultra-wideband optical-amplifier technology and advanced modulation formats have expanded the capacity of standard single mode fibre (SMF)-based optical links beyond 150 Tb/s [1]. Additionally, proliferation of 5G networks [2] and adoption of low-latency hollow-core fibres [3] have ushered in a new era of ultra-reliable low latency communications addressing critical time-sensitive applications in the financial industry [4], edge-cloud computing [2], and augmented reality [5], among many others. Despite these improvements, chromatic or group-velocity dispersion (GVD)-induced broadening/distortion of the data signals still remains a key impairment in optical fibre links, especially over regional distances encountered in data centre interconnects (DCI), and in Passive Optical Networks (PONs). Typically, GVD-induced signal degradation in wavelength division multiplexing (WDM)-based optical links is compensated for by employing either receiver-side equalization techniques based on digital signal processing (DSP) [6,7], or through an optical (i.e., analog) linear dispersion management scheme consisting of dispersion compensating fibre (DCF) with an opposite GVD profile. DSP-based GVD compensation is a computationally expensive task (e.g., the required finite impulse response (FIR) filter order varies linearly with link length but quadratically with baud rate [8]), leading to undesired power consumption that scales dramatically with the total amount of GVD to be compensated for [9,10]. This solution also introduces a significant processing latency in the overall optical fibre link. On the other hand, DCFs generally require 10s of km of fibre length, leading to non-zero insertion loss and additional latency, up to 25% of the overall link length [11]. They can also introduce additional undesired nonlinear effects in the link [12]. Alternatively, linearly chirped fibre Bragg gratings (LCFBGs) can compensate for large amounts of GVD in significantly more compact forms [13] (e.g., 10s of cm device length over a single WDM channel), but they require the use of optical circulators for retrieving the reflected signal, ultimately resulting in bulky setups. Compared to DCFs, LCFBG-based dispersion compensation modules (DCMs) offer lower insertion losses and reduced latency (in the tens of nanosecond range), albeit over a relatively narrow operation bandwidth.
A highly desirable solution would be to realize a low-loss on-chip all-optical solution that provides GVD compensation of high-speed data signals over medium-reach optical links with ultra-low latency. Additionally, it is important to note that a plethora of analog signal processing functionalities are based upon chromatic or group-velocity dispersion, such as real-time Fourier transformation and gap-less spectogram analysis [14,15], temporal magnification/compression of ultrafast waveforms [16], photonic-based arbitrary waveform generation [17], passive amplification and recovery of (sub-noise) time and frequency-domain signals [18,19], etc. However, these functionalities require a large amount of GVD (typically > 1,000 ps$^2$/rad, equivalent to $\sim$ 50 km of SMF) over a broad bandwidth, eventually well into the THz range. Most of the aforementioned demonstrations employ DCFs to realize the required amount of GVD, leading to an overall bulky operation, with high insertion losses and large operational latency, thus hindering their utilization in real-world settings.
Therefore, it is imperative to realize a low-loss implementation of dispersive lines in a compact on-chip integrated platform. Towards this aim, linearly chirped waveguide Bragg gratings (LCWBGs) have been suggested as a potential solution for compact on-chip dispersive lines [20]. However, in an LCWBG or in an LCFBG, the spectral phase accumulation that is inherent to the design limits the net amount of GVD that can be compensated for over a prescribed operation bandwidth. This is so because a larger relative phase excursion translates into a longer device, thus increasing the overall device footprint. In particular, compensation of the GVD profile of a standard SMF with length just above 20 km over a 100-GHz WDM channel would require a LCWBG with a length well above 1 cm. This is a difficult target to realize in practice due to intrinsic waveguide losses and the inherent phase noise that is induced over longer device lengths due to random fluctuations in waveguide width. The latest is especially significant in a high refractive-index contrast platform, such as silicon-on-insulator (SOI) [21]. Alternatively, arrayed waveguide gratings [22], lattice filters based on multi-mode interference (MMI) couplers [23], single [24] or multistage-microring resonators [25] have been employed for residual dispersion compensation of data signals in WDM channels. Most of these techniques suffer from a severe intrinsic trade-off between useable bandwidth and the amount of GVD that can be compensated for. On the other hand, devices exploiting the dispersive properties of a coupled-defect waveguide in a photonic crystal can compensate for a large amount of GVD in an ultra-compact footprint [26]. However, such devices are severely affected from high scattering and coupling losses.
Discrete spectral phase filters based on integrated WBGs have been previously proposed and demonstrated for realization of the functionality of a chromatic dispersive line on broadband periodic temporal waveforms [27,28]. This strategy takes advantage of the inherent discrete frequency spectrum of a periodic signal. Further, the potential of the discrete phase filtering approach for processing isolated optical pulses has also been theoretically suggested [28].
In this article, we show that discrete phase filters can be designed and exploited to implement the functionality of a conventional GVD element on an arbitrary (generally, aperiodic and non-time-limited) optical signal. Specifically, to validate this proposal and the predicted performance, we demonstrate successful GVD compensation of data signals in fibre-optic telecommunication links using mm-long WBG phase filters in an SOI platform. We have chosen this platform for the implementation of on-chip phase filters owing to its excellent compatibility with the mature CMOS technology and the availability of high-speed modulators and photodiodes, which has enabled massive adoption of silicon photonics-based high-performance pluggable transceivers for data centre interconnects [29]. In experiments, we demonstrate GVD compensation of NRZ-OOK data signals with bit rates up to 24 Gbps after propagation through a 31.12 km long section of a standard SMF using SOI mm-long on-chip phase filters. In this demonstration, the phase filter provides the required performance while incurring a power penalty of $\sim$1.8 dB at a BER $\sim$ 1E-4 (below the pre-FEC threshold), with an estimated 100-ps latency. We further report additional experiments to showcase the potential of the on-chip phase filter approach for GVD compensation of multilevel modulation formats, in particular, pulse amplitude modulation 4-level (PAM4) with bit rates up to 32 Gbps. The reported designs provide a device length reduction by at least $5\times$ compared to an LCWBG. These results represent the first demonstration of GVD compensation of high-speed data signals (with tens of Gbaud rates) over a mid-range fibre-optic link using an SOI chip. Additionally, we show through numerical simulations that the operational bandwidth of the proposed WBG-based phase filter structure could be extended to the THz range by utilizing a highly efficient phase-only sampling technique. This would potentially enable GVD compensation of multiple WDM channels in a medium-reach fibre-optic link using a mm-long on-chip device, as well as on-chip realization of many other important GVD-based ultra-broadband analog processing techniques [14,16,19].
2. Design principle
We target GVD compensation in a fibre-optics link characterized by a second-order dispersion coefficient $\beta _2$ and of length $L$, over a full frequency bandwidth $\text {BW}_\text {30-dB}$. Towards this aim, we propose using a discrete and bounded spectral phase filter, with a frequency resolution $\omega _r=2\pi \nu _r$, see Fig. 1(a). The spectral discretization process involves evaluation of the continuous phase variation, $\phi (\omega )=-(\beta _2L/2)\omega ^2$, of the target dispersive line at discrete frequency locations $(\pm {k\omega }_r)$, $k=0,1,2,\ldots$ over the full operation bandwidth [28]. Here, $\omega$ is the baseband frequency variable. Next, a modulo-$2\pi$ operation of the discrete spectral phase values, $\Phi _k=\phi (k\omega _r)$, is conducted to ensure the resultant phase profile is bounded within the $[0, 2\pi )$ range, shown in Fig. 1(a) for the case of a 16-km fibre-optic link. We predict that the discrete phase filter will effectively emulate the continuous phase variation of the dispersive line, as long as this phase profile remains approximately constant over the filter’s frequency resolution. This condition can be expressed mathematically as
Equation (1) should be satisfied over the full operation bandwidth, which translates into the following condition
or, where $\Delta \tau _g=2\pi \cdot |\beta _2|\cdot L \cdot \text {BW}_\text {30-dB}$ is the net group-delay excursion of the target dispersive line. Equation (3) implies that the maximum group-delay excursion that can be emulated with the proposed discrete phase filtering approach is inversely proportional to the frequency resolution of the filter. To confirm this, we have carried out system-level simulations (i.e., Q-factor and BER estimates) of discrete phase filters designs with varying $\nu _r$, aimed at compensation of the GVD introduced by SMF sections with different lengths, $L_\text {SMF}$. Recall that the Q-factor is defined as the difference of the mean values of the two signal levels (a ’0’ and a ’1’ bit) divided by the sum of the noise standard deviations of the two levels. The BER is estimated from the Q-factor as BER=1/2$\cdot$erfc(Q/$\sqrt {2}$) [30]. We consider GVD compensation of a 50-Gbps NRZ-OOK signal consisting of $2^{15}-1$ pseudo-random bit sequence (PRBS). For these simulations, an ideal transmitter and receiver (i.e. with zero additional noise) is assumed. A root-raised cosine filter is used for spectral shaping of individual bits. For an output Q-factor of 6 (BER $\sim$ 1E-9), the corresponding $L_\text {SMF}$ values that can be compensated for are plotted against different $\nu _r$ in Fig. 1(b). As expected, phase filter designs with a narrower $\nu _r$ can compensate for a larger amount of GVD. For example, a 10-GHz phase filter can compensate for a 16 km long segment of a standard SMF, compared to at least 50 km, in the case of a 1-GHz phase filter. This analysis also shows that the aforementioned relation in Eq. (3) is far too restrictive, and can be significantly relaxed depending on the success criteria set at the receiver (e.g., in terms of BER). As observed in Fig. 1(c), the performance of a phase filter design, for a fixed $\nu _r$ (e.g., compared between 10-GHz and 2-GHz filter), improves proportionally with a reduction in the bit rate of the input (or the corresponding signal bandwidth).
Fig. 1. (a) Spectral discretization of the continuous quadratic spectral phase variation equivalent to 16 km of SMF using a discrete phase filter design with frequency resolution, $\nu _r=10$ GHz. Notice that the resultant discrete phase profile is bounded within a $2\pi$ range, which is the key to an overall compact device. The net group delay excursion, $\Delta \tau _g$ over the full bandwidth, $\text {BW}_\text {30-dB}=100$ GHz, is also shown with an orange trace. (b) Numerical simulations using discrete phase filter designs with different $\nu _r$ aimed at GVD compensation of a 50-Gbps NRZ-OOK $2^{15} - 1$ PRBS signal after propagation through different lengths of SMF, $L_\text {SMF}$. For an output Q-factor of 6 (BER $\sim$ 1E-9), the corresponding values of $L_\text {SMF}$ that can be compensated for is plotted against different $\nu _r$. The inverse relationship between $\nu _r$ and $L_\text {SMF}$ is clearly evident. (c) Performance of a phase filter design (in terms of compensated SMF length, $L_\text {SMF}$) for NRZ-OOK data signals with different bit rates show a proportional improvement for filters with narrower $\nu _r$ (compared here between 2-GHz and 10-GHz filters).
3. Results
3.1 Device fabrication and characterization
The resulting phase filters are implemented using a SOI WBG, scheme in Fig. 2. Specifically, we consider here a discrete phase filter design with $\nu _r=10$ GHz aimed at achieving GVD compensation of a 24-Gbps NRZ-OOK data signal after propagation through a 31.12 km long section of SMF. Toward this aim, we assume an $8^{th}$-order super Gaussian function with peak reflectivity of 0.9 and 3-dB bandwidth (BW) of 100 GHz as the target amplitude spectral response of the dispersive phase filter. The target filter’s spectral phase response is shown in Fig. 2(b). The optical spectrum of the input 24-Gbps NRZ-OOK signal with a $2^{15}-1$ PRBS is also depicted on the same plot. An inverse layer peeling algorithm is used to calculate the WBG’s coupling coefficient $(\kappa )$ profile (amplitude: $|\kappa (z)|$ and phase: $\phi _\kappa (z)$) that is required to achieve the target spectral response from the grating (operated in reflection), and it is shown in Fig. 2(c). The target apodization is achieved by incorporating a slowly varying sinusoidal phase component, $\phi _\text {AP}(z)$, in the phase function of the WBG, shown in Fig. 2(d). Specifically, the effective index profile of the WBG, $n(\lambda,z)$, as a function of wavelength $\lambda$ and device length $z$ can be expressed as:
Fig. 2. (a) Schematic of the on-chip layout utilized for coupling light in and out of the WBG-based phase filter. The zoomed-in view shows the SEM image of one of the fabricated WBGs. The cross-sectional schematic of the fully-etched silicon waveguide on top of the buried oxide is also shown; $H$ and $W$ is the waveguide height and width, respectively. $\Delta W$ is the corrugation width. $\Lambda$ is the nominal grating period. Subwavelength grating-based grating couplers (GCs) couple fundamental transverse-electric (TE)-like mode into the SOI chip with a device layer thickness of 220 nm. A Y-splitter collects the reflected signal from the WBG. A 20-$\mu$m linear adiabatic taper connects the input single mode waveguide ($W=0.5$ $\mu$m) with the 2-$\mu$m wide multimode waveguide, thus ensuring fundamental mode operation inside the WBG. The transmitted signal from the WBG is terminated using a taper. (b) Target reflectivity (left) and the spectral phase profile (right) of the discrete phase filter with $\nu _r=10$ GHz, superimposed with the spectrum of the input 24 Gbps NRZ-OOK $2^{15}-1$ PRBS signal (red). (c) Coupling coefficient $(\kappa )$ profile: magnitude $|\kappa (z)|$ on the left and phase $\phi _\kappa (z)$ on the right. (d) Variation of $\phi _\text {AP}$ along the WBG’s length. Inset shows a zoom of the sinusoidal variation. (e) Measured reflectivity of the WBG (top) and spectral phase response along the filter’s passband (bottom), centred at $\sim$ 1552 nm. The dashed trace shows the simulated response.
A schematic of the designed on-chip layout is shown in Fig. 2(a). The SOI chip was fabricated by Applied Nanotools using electron beam lithography and inductively-coupled reactive ion etching. The zoomed-in view in Fig. 2(a) shows the SEM image of one of the fabricated WBGs. The constant corrugation width ($\Delta W$) is clearly visible, along with the varying separation between adjacent corrugations — a distinct feature of the phase-modulation based apodization technique. A complex optical vector analyzer (OVA) [LUNA] is used to measure the full complex spectral response of the WBG (see Fig. 2(e)). The passband is centred at $\sim$ 1552 nm. The ripples in the amplitude response are mostly attributed to fabrication imperfections, such as small deviations in waveguide width and height resulting in phase errors that scale dramatically with device length, especially in a high refractive index contrast platform, such as SOI. Innovative designs involving coherence-breaking of Bragg filters could be utilized to overcome this limitation [31]. Yet, the spectral phase profile along the filter’s passband matches closely the simulated spectral phase response. To understand the fabrication process induced variability, a total of 56 devices were fabricated on the 1 cm $\times$ 1 cm chip. The measured standard deviation in the centre wavelength of the devices is $\sim$ 0.57 nm, well within the tolerance limits of the fabrication process [32]. Refer to Supplement 1 for a detailed description.
3.2 GVD compensation of NRZ-OOK data signals
We have conducted experiments related to GVD compensation of NRZ-OOK data signals with bit rates up to 24 Gbps using the WBG-based phase filter. The input signal consisting of a $2^{15}-1$ PRBS is generated using a 40-GHz intensity modulator [Optilab] driven by a 92-GSa/s arbitrary waveform generator (AWG) [Keysight] and an RF driver [Optilab]. The generated signal is subsequently dispersed through a 31.12 km spool of standard SMF. After amplification, the dispersed signal is coupled to the on-chip phase filter using grating couplers (GCs). The resultant signal is amplified and detected using a 50-GHz photodiode [Finisar] and an electrical sampling oscilloscope (ESO) [Tektronix]. A variable optical attenuator is used to ensure that the eye diagrams are recorded at a fixed average input power to the ESO. Optical amplification at the output stage is required due to the higher coupling loss of the GCs ($\sim$ 10 dB), which can be reduced to be less than 3 dB by utilizing inverse taper-based edge couplers. Figure 3(a.1,2,3) shows the measured eye diagrams of the input 16-Gbps signal, after dispersive propagation, and after reflection from the WBG phase filter, respectively. The bottom row shows the corresponding eye diagrams for the 24-Gbps signal. Eye diagrams are measured at a constant average power of $\sim$ 5 dBm. The phase filter provides the desired performance even when the data signal is completely distorted, especially for the 24-Gbps signal. Receiver sensitivity measurements of both the input and the output for the 16-Gbps and 24-Gbps NRZ-OOK signals are presented in Fig. 3(c, d), respectively.
Fig. 3. Measurements related to GVD compensation of NRZ-OOK data signals after propagation through 31.12 km of SMF using the WBG-based phase filter. Top row (a.1,2,3) corresponds to eye diagrams related to the input 16-Gbps NRZ signal, after dispersive propagation, and after reflection from the WBG, respectively. Bottom row (b.1,2,3) shows the respective eye diagrams for the 24-Gbps signal. (c, d) Receiver sensitivity measurements of both the input (dotted) and output (solid) for the 16-Gbps and 24-Gbps signals, respectively. The pre-FEC BER threshold of 1.4E-4 is also noted for reference. The respective power penalty at a BER of 1E-4 is $\sim$ 0.4 dB and 1.8 dB.
As observed, the receiver exhibits an error floor for the output signal, particularly for the 24-Gbps case. This is due to the ripples present in the amplitude response of the WBG. Nonetheless, a simple first generation low-power and low-latency FEC code, such as the RS (255,239) code can be employed for post-FEC error-free operation [33]. The incurred power penalty of the phase filter at a BER of 1E-4 (below the pre-FEC threshold), see Fig. 3(c, d) is measured to be $\sim$ 0.4 dB and 1.8 dB for the 16-Gbps and 24-Gbps signals, respectively. Further, the compact device footprint of the WBG-based phase filter device translates into an ultra-low latency operation of $\sim$ 100 ps (refer to Supplement 1 for the detailed calculation).
3.3 GVD compensation of PAM4 data signals
We have also carried out experiments related to GVD compensation of data signals encoded in the PAM4 modulation format after propagation through 31.12 km of SMF. The corresponding eye diagrams (measured at a constant average power of $\sim$ 8 dBm) for the input 16-GBd (32-Gbps) PAM4 signal are shown in Fig. 4(a.1,2,3). After dispersive propagation through the SMF, the induced inter-symbol interference leads to eye-closure, as shown in Fig. 4(a.2). Yet, as seen in Fig. 4(a.3), the phase filter recovers the dispersed signal, with well-defined lower and middle eyes. The distortions in the upper eye are mainly attributed to the ripples in the amplitude response of the phase filter. A comprehensive evaluation of the filter’s performance for dispersion compensation of PAM4 signals necessitates of a bit error rate analyzer. Nonetheless, we have characterized its performance by estimating the vertical eye closure (VEC) metric of both input and output signals from the measured eye diagrams. See related definitions in Supplement 1. The VEC of the output signal is calculated to be $\sim 12$ dB, compared to $\sim 8.5$ dB for the input, which is higher than the maximum limit of 5.5 dB, as recommended by the Optical Internetworking Forum (OIF) in [34]. This is mainly due to the broadband ASE noise of the input EDFA.
Fig. 4. Measurements related to GVD compensation of data signals encoded in the PAM4 modulation format after propagation through 31.12 km of SMF using the WBG-based phase filter. (a.1,2,3) Measured eye diagrams of the input 16-Gbd (32-Gbps) PAM4 signal, after dispersive propagation, and after reflection from the WBG, respectively.
3.4 Proposal for multichannel operation
The overall capacity of the proposed device can be increased by extending the range of operation to multiple WDM channels [35–39]. This can be achieved using a phase-only periodic sampling function in the grating equation (Eq. (4)) of the single-channel WBG [40]. For instance, in Fig. 5, we show through numerical simulations, a phase-sampled WBG-based phase filter design for dispersion compensation of nine WDM channels with a spacing of 200 GHz in a 31.12-km fibre-optic link. Notice the excellent uniformity and out-of-band rejection of the different WDM channels. The spectral phase response of the individual WDM channels is in excellent agreement with the single-channel WBG’s phase response (see insets of Fig. 5). Yet, the implementation complexity — in terms of device length and the required spatial resolution or the minimum feature size of the device remains unchanged. Refer to Supplement 1 for the detailed description of the phase-only sampling technique. Using this technique, the operational range of the proposed phase filter could be extended to the entire C&L telecommunication bands, thus potentially enabling GVD compensation with Tb/s-capacity in medium-reach fibre-optic links using a mm-long on-chip device. In a more general framework, this solution could be especially useful for the realization of various GVD-based signal processing functionalities with bandwidth requirements in the THz range.
3.5 Realization of a discrete phase filter-based dispersive line in an all-fibre platform
To highlight the excellent potential and versatility of the proposed phase filtering technique, we report results related to GVD compensation of NRZ-OOK data signals with bit rates up to 24 Gbps using a 6.9 cm long phase filter implemented in an all-fibre Bragg grating (BG) technology, with frequency resolution, $\nu _r=2$ GHz. This superior frequency resolution enables effective GVD compensation after signal propagation through 70.56 km of SMF, i.e., more than $2 \times$ improvement in the amount of GVD that can be compensated for compared to the demonstrated on-chip WBG device. Refer to Supplement 1 for the measured spectral response of the FBG-based phase filter and the related system-level measurements. We estimate that the demonstrated FBG-based phase filtering solution offers around $2 \times$ reduction in device length compared to an equivalent LCFBG device with similar specifications. This is especially important given the inherent challenges that hinder the fabrication of replicable ultra-long FBGs, such as devices with length $> 15$ cm [41]. The phase filter is designed according to the design framework discussed in the previous section. A femtosecond laser-based plane-by-plane direct writing scheme is employed to fabricate the designed FBG [42]. Compared to traditional UV-based interferometric writing schemes, phase modulation-based apodization coupled with the direct-writing technique provides the required precision and control of the target coupling coefficient profile (both in amplitude and phase). We anticipate that the direct-write scheme would further enable the realization of the proposed multichannel discrete phase filter design on an all-fibre platform, ensuring excellent performance across multiple WDM channels. The in-fibre implementation of the discrete phase filter designs provides a compact alternative to existing DCMs based on conventional LCFBGs [13] as such, they could be potentially used as stand-alone devices in the existing infrastructure in PONs for long-haul fibre-optic links.
Fig. 5. Design of a WBG-based phase filter for dispersion compensation of nine successive WDM channels, spaced 200 GHz apart in a 31.12-km fibre-optic link, using a multilevel phase-only sampling function. The phase-only function enables replication of the single-channel WBG’s response to consecutive channels. (Top) Amplitude response of the WBG. (Bottom) Phase response of the WBG. The insets show the phase response across the passband of the leftmost, central, and the rightmost channels, in excellent agreement with the simulated response of the single-channel WBG (dashed).
4. Conclusion
To summarize, we have proposed and experimentally demonstrated GVD compensation of high-speed data signals over distances exceeding 30 km using compact mm-long on-chip discrete phase filters in an SOI platform. Numerical analysis supported with system-level simulations confirm that the amount of GVD that can be compensated for using discrete phase filters depends on the frequency resolution of the filter. A WBG-based design framework was utilized for the implementation of the on-chip discrete phase filters. The design framework can be easily adapted to synthesize phase filters in a spiral geometry [43], thus enabling the realization of cm-long compact devices in a sub-mm$^2$ device footprint. In experiments, we report GVD compensation of NRZ and PAM4 data signals with baud rates up to 24 GBd after propagation through 31.12 km of standard SMF using a 4.1 mm long WBG-based discrete phase filter (at least 5$\times$ shorter compared to an LCWBG with similar specifications). The device provides the required GVD compensation functionality, incurring in a power penalty of 1.8 dB with an estimated latency of only $\sim$ 100 ps. The latest is critical for 5G-empowered applications in Industry 4.0, vehicle-to-anything communication, Internet of Things (IoT), algorithmic high-frequency stocks trading, etc [2]. End-to-end latency of these time-sensitive applications should be within 100 $\mu$s [44]. We envisage the possibility of the deployment of ultra-low latency on-chip discrete phase filters for GVD compensation over distances exceeding 10s of km in the fronthauls of 5G and edge-cloud networks, as well as in next generation PONs [45]. Moreover, the range of operation of the on-chip discrete phase filter can be extended to multiple WDM channels by employing a highly efficient phase-only sampling technique, thus enabling Tb/s-capacity in a medium-reach fibre-optic link using a mm-long on-chip device. We should note that the discrete phase filter based dispersive line is a passive analog signal processing element, which is designed to compensate the dispersion of a pre-defined optical fibre link length. We envision that a resistive heating scheme in conjunction with an optimization algorithm could be potentially developed to realize tunable operation for dispersion compensation over a range of link lengths.
The proposed phase filtering solution is independent of the material platform, as validated by the realization of discrete phase filters in an all-fibre BG technology. Specifically, we have realized an FBG-based discrete phase filter with a superior frequency resolution of 2 GHz, enabling GVD compensation of NRZ-OOK data signals with bit rates up to 24 Gbps in a 70.56-km fibre-optic link. Thus, we anticipate that discrete phase filters could be easily implemented in other low-loss on-chip platforms, such as silicon nitride [46] and thin-film Lithium niobate [47]. This would allow the realization of compact devices with frequency resolution narrower than 1 GHz, enabling GVD compensation of data signals with baud rates exceeding 50 GBaud over distances beyond 50 km — paving the path towards their direct integration in pluggable-transceivers. Additionally, in a more general framework, we anticipate that ultra-compact phase filters-based dispersive lines could be synthesized to provide the required spectral phase-filtering functionality for a true on-chip realization of a wide range of signal processing applications based on the use of group velocity dispersion.
Funding
Natural Sciences and Engineering Research Council of Canada; Fonds de recherche du Québec – Nature et technologies; FONEX Data Systems Inc.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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