1. Introduction

The use of photonics for analog-to-digital conversion [1] is attractive due to the possibility of eliminating the problem of timing jitter, which has been a major obstacle on the way to accurate digitization of wideband RF signals [2]. This can be achieved by performing sampling in optical domain using pulse trains generated by mode-locked lasers, which have timing jitter orders of magnitude lower than the jitter in the best electronic analog-to-digital converters (ADCs) [3, 4]. High sampling rates can be achieved by using a multi-channel ADC configuration, with each channel running at a relatively low rate [5]; the reduced analog bandwidth of each channel helps to solve the problem of the comparator ambiguity [2]. The implementation of a multi-channel photonic ADC system can be based on time [6] or wavelength [5, 7, 8] interleaving. In a time-interleaved ADC, a fast optical switch sends consecutive optical pulses into different outputs, so that an input pulse train with high repetition rate is converted into multiple lower-rate pulse trains. In a wavelength-interleaved system, which is the focus of this work, consecutive optical pulses have different center wavelengths, so that these pulses can be switched into different outputs using a passive wavelength demultiplexer. Results obtained with time- and wavelength-interleaved schemes include 7 effective bits for a 40 GHz input signal [9, 10].

For wavelength-interleaved systems, it is necessary to create a pulse train with wavelengths changing periodically from one pulse to another, i.e. a pulse train where mapping exists between the temporal position of the pulse and its wavelength. The continuous version of the time-to-wavelength mapping can be implemented using a dispersive element with linear chirp, such as a dispersive optical fiber, which delays different wavelengths by different amounts [5]. In the discrete version of the mapping considered in this work, the wavelength-interleaved pulse train is created by a block referred as a time-wavelength pulse interleaver. In this interleaver, a wavelength demultiplexer is used to split the pulse train generated by the laser into multiple wavelength components, with each of these components being a pulse train at its own center wavelength. These pulse trains are delayed with respect to each other with differential delay lines and then combined into a single pulse train with a wavelength multiplexer [7, 8], as described in more details in Section 2.

A time-to-wavelength pulse interleaver can be built with discrete commercially-available components, which has been the approach typically used in photonic ADC experiments [8, 10]. An 18-channel time-wavelength interleaver built with discrete commercially available components has been demonstrated in [11]. An interleaver can also be implemented as a filter with a staircase-shaped delay [12]. The wavelength-interleaved pulse train can be formed using the photonic spectral processor based on a liquid crystal spatial light modulator, as proposed in [13]. A special multi-wavelength interleaved pulse source suitable for optical sampling has been developed in [14].

This work presents a time-wavelength pulse interleaver integrated on a silicon chip using silicon-on-insulator (SOI) technology [15]. Integrated pulse interleavers have previously been demonstrated in silica waveguides [16] and SOI [17]. However, these interleavers have been increasing the pulse repetition rate, without interleaving the pulses in wavelength. The device presented in this work interleaves pulses in both time and wavelength, and consists of an array of microring resonators acting as a wavelength demultiplexer, long waveguide sections introducing differential delays into the demultiplexed pulse train, and a second array of microring resonators multiplexing the delayed pulses.

The time-wavelength pulse interleaver presented in this work is developed primarily for the wavelength-demultiplexed photonic ADC architecture described in [7, 8, 10]. However, the interleaver can also be relevant to other types of photonic ADCs, such as time-stretch ADCs [18, 19] and parametric processing-based ADCs [20–23]. In a time-stretch photonic ADC, a pulse train is linearly chirped, modulated with the RF signal to be sampled, then stretched again with a dispersive element; the stretched waveform can be sampled with a slower ADC. Some results obtained with this approach include 6.7 effective bits [18] and 8.2 effective bits [19] for a 10 GHz RF input. Continuous-time operation can be achieved by time-interleaving waveforms at different wavelengths [18], which can be done with a time-wavelength interleaver such as the one presented in this work. In ADCs based on parametric processing, sampling is done parametrically; recent demonstrations include 8 and 7 effective bits, for a 10 GHz and 40 GHz RF signal, respectively [21], as well as 5.4 effective bits for 74 GHz signals [22]. In [23], 7.1 effective bits have been demonstrated at 39.5 GHz, and 6.7 bits at 49.5 GHz, with 5 GHz analog bandwidth. These values increased to 8.0 and 7.4 bits, respectively, when the analog bandwidth is reduced to 1 GHz; to the best of our knowledge, this is the best result demonstrated with photonic ADCs so far. In these ADCs, multi-channel operation can be realized by creating copies of the input optical waveform at different wavelengths via parametric amplification, delaying these waveforms with respect to each other using a time-wavelength pulse interleaver, and parametrically sampling the resulting waveform [20].

The next section explains the principle of operation of wavelength-interleaved photonic ADCs, and describes the design of the time-wavelength interleaver for the SOI platform. Measurement results are presented in Section 3. Finally, the obtained results are analyzed in Section 4, where scaling to higher output pulse rates is also discussed.

2. Interleaver design

This section briefly reviews the principle of operation of the photonic ADC system based on the time-wavelength pulse interleaver, and describes the details of the proposed interleaver design.

The layout of the optically sampled wavelength-interleaved photonic ADC system under consideration is illustrated in Fig. 1 [7, 8, 10]. A mode-locked laser generates an optical pulse train with repetition period T and repetition rate f_R = 1/T. The pulse train has very low timing jitter, i.e. the time interval between the pulses of the pulse train is very stable. The generated pulse train is processed by the time-wavelength interleaver studied in this work. At the input of the interleaver, a wavelength demultiplexer slices the spectrum of the input pulse train into N parts, where each part constitutes a pulse train centered at a different wavelength. While the filtering process in the demultiplexer significantly reduces the optical bandwidth of the pulses (and therefore increases their time duration), the resulting pulses are still short enough for accurate sampling of high-speed signals. The demultiplexed pulse trains are delayed by T/N with respect to each other, with differential delay lines, and then multiplexed into a single path at the output of the interleaver using a wavelength multiplexer. As a result, the time-wavelength interleaver transforms the input pulse train with repetition rate f_R into an output pulse train with repetition rate N × f_R, with pulse center wavelengths changing from pulse to pulse with period N.

 

Fig. 1 Layout of a 4-channel wavelength-interleaved photonic ADC system. This work focuses on one component of this ADC – the time-wavelength pulse interleaver.

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The resulting time-wavelength interleaved pulse train is modulated in an electrooptic modulator driven by the RF signal which needs to be digitized. At the output of the modulator, the energies of the pulses represent the samples of the RF signal at the corresponding time moments. The aperture jitter of the sampling process is defined by the timing jitter of the optical pulses, and can be extremely low. The modulated train is then split into N channels with a wavelength demultiplexer. Each of the demultiplexed channels is processed separately: for each channel, the optical pulses are converted into the electrical domain with a photodetector, processed with post-detection electronics, and digitized with an electronic ADC. Finally, the digital outputs of the electronic ADCs are processed in the digital domain in order to compensate for errors, and then interleaved to obtain the digital representation of the input RF signal. By using N channels, the sampling rate of the photonic ADC is increased by a factor of N relative to the rate of each channel, so that high overall sampling rates can be achieved using relatively slow channels.

Strictly speaking, the term “photonic ADC” used in this work is not entirely accurate because electronics plays a major role in the ADC operation, and only the front-end of the ADC works in the optical domain. A more precise term would be an “electronic-photonic ADC”, or a “photonics-assisted ADC”. However, for simplicity, the term “photonic ADC” is used here.

An important advantage of the ADC architecture described above is that it can be implemented on a silicon chip using silicon photonics technology. In [10], a part of the integrated ADC system shown in Fig. 1 was implemented on a silicon chip with a silicon Mach-Zehnder modulator, an array of microring resonator filters acting as a wavelength demultiplexer, and integrated photodetectors. The time-wavelength pulse interleaver was created off-chip using discrete optical components. This work focuses on the implementation of the pulse interleaver on a silicon chip.

The schematic diagram of the integrated time-wavelength pulse interleaver realized in this work is shown in Fig. 2. The wavelength demultiplexer at the input of the interleaver is implemented as an array of single-ring resonator filters. To introduce differential delays between the demultiplexed pulse trains, waveguides of appropriate length are used. The delayed pulse trains are multiplexed into the output waveguide with another array of single-ring resonator filters, with center wavelengths matching the wavelengths of the input filters. The 4-channel interleaver is implemented on a silicon photonic chip with a 220 nm-thick Si layer and a 2μm BOX oxide. The layout of the interleaver is shown in Fig. 3, together with the relevant parameters of the design.

 

Fig. 2 Diagram of the 4-channel interleaver implemented on a silicon chip. The input wavelength demultiplexer and the output wavelength multiplexer are implemented as arrays of microring resonator filters, and the delay lines are realized as long sections of Si waveguides.

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Fig. 3 Layout of the 4-channel time-wavelength interleaver, extracted from the GDSII file. Waveguides belonging to different channels are shown in different colors.

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Long sections of Si waveguides are used as delay lines in the interleaver. To reduce the footprint of the interleaver, the waveguides are laid out in a space-efficient spiral shape, see Fig. 3. The interleaver is designed to work with a mode-locked laser with a 1.034 GHz repetition rate [24], which requires 241.8 ps differential delays between the channels, so that the pulses in the longest line are delayed by 725.4 ps with respect to the pulses in the shortest line. The required lengths of the delay lines are on the order of several centimeters, which means that the interleaver will be highly lossy if the delay lines are implemented using single-mode Si waveguides with typical propagation losses of 2-3 dB/cm. To reduce the overall loss, wide multi-mode waveguides, which are known to have lower propagation losses because of reduced scattering due to sidewall roughness [25], are used in the straight sections of the delay lines. The width of the multi-mode waveguides is 1200 nm. The multi-mode sections constitute more than 90% of the total length of the delay lines. The waveguide bends have 20 μm radius and are implemented using 500 nm-wide single-mode waveguides. The sections with 500 nm and 1200 nm core widths are connected with 50 μm-long linear tapers (see the inset in Fig. 3). The length of the delay lines required to produce the given delays are calculated taking into account the dependence of the group index on the core width, which is different in the single- and multi-mode sections, and changes along the tapers. The total lengths of the delay lines are 0.501, 2.498, 4.495, and 6.493 cm, for channels 1 to 4, respectively. The delay lines are designed for TE-polarized light at 1550 nm.

The microring resonator filters at the input and output of the delay lines are designed to operate in the Vernier mode [26] in order to increase the free spectral range (FSR) of the interleaver, which is necessary since the bandwidth of mode-locked lasers can exceed tens of nanometers. If the microrings at the input and output of each delay line have more than one resonance over this bandwidth, the undesired wavelength components will pass through that delay line, contaminating the output. This can be avoided by ensuring that the combination of the input and output filters of each delay line is resonant only at a single wavelength over the full bandwidth of the laser. This is achieved using a Vernier scheme, with the ratio of the radii of the input and output rings selected to be 3:4. The microring radii are 5 μm and 5 μm × (4/3) = 6.67 μm, and the FSR values are calculated to be 17.86 nm (2.229 THz) and 13.4 nm (1.672 THz) at 1550 nm. The effective FSR of the interleaver is expected to be 13.4 nm × 4 = 53.6 nm (6.688 THz). The ring radii are increased by a small step from channel to channel in order to space the resonances apart in wavelength. The core width of the microrings is 450 nm, and the core width of the input and output waveguides is narrowed down to 350 nm in the waveguide-microring coupling region in order to increase the coupling coefficient.

3. Measurement results

The interleaver was fabricated on a silicon photonic chip using 248 nm optical lithography. The size of the chip is 3 × 0.81 mm. In addition to silicon waveguides and microrings (shown in Fig. 3), metal heaters are fabricated on top of each microring resonator to enable thermal tuning of the resonant frequencies.

3.1 Bandwidth and insertion loss

The measured transmission spectrum of the interleaver is shown in Fig. 4. The microheaters have been used to align the resonant frequencies of the input and output filters in each of the 4 wavelength channels. From Fig. 4(a), the frequency response of the interleaver has an FSR of 51.98 nm (6.686 THz) if measured as the spacing from the central peak to the next shorter-wavelength peak, and 55.71 nm (6.687 THz) if measured as the spacing to next longer-wavelength peak. These FSR values are in excellent agreement with the design target of 6.688 THz.

 

Fig. 4 Transmission spectrum of the interleaver: (a) drop-port response, indicating the free spectral range; (b) central region of the spectrum, with transmission peaks of the 4 channels and the through-port response of the filter bank at the input of the interleaver (“input through” curve) and the output of the interleaver (“output through” curve); (c) zoom-ins of the 4 peaks.

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Figure 4(b) zooms in on the region of the spectrum with the passbands of the 4 channels, and Fig. 4(c) shows these passbands individually. For reference, the through-port transmission of the filter banks at the input and the output of the interleaver is also plotted. The FWHM bandwidths of the channels vary from 17.1 to 19.9 GHz. The achieved channel bandwidths are rather narrow, which limits the energy efficiency of the photonic ADC because only the part of the laser spectrum inside the channel passbands is utilized. Moreover, low channel bandwidth can limit the analog bandwidth of the photonic ADC because the channel bandwidth determines the temporal duration of the sampling pulses; for 17 GHz channel bandwidth, the 3dB analog bandwidth will be limited to 17 GHz. For these reasons, it is desirable to increase the bandwidth of the channels while making sure the cross-talk remains low. The channel bandwidth can be increased by using wider-bandwidth single-ring filter designs; even wider bandwidths with low cross-talk can be achieved using double-ring filter designs.

The insertion losses in channels 1-4 are 1.6, 2.1, 2.8, and 5.8 dB, respectively. The propagation loss ${\alpha }_i$ in the delay line of channel $i$can be estimated by using the first channel as the reference:

3.2 Group delay

The group delay response of the interleaver is measured using an optical vector analyzer (see Fig. 5). The spectral regions corresponding to the passbands of the interleaver channels are highlighted in color, while the spectral regions outside the passbands (which are not relevant) are shaded with gray. The measured group delays of channels 2-4 relative to channel 1 are 254.2, 506.6, and 759.6 ps, respectively. The average measured differential delay is 253.2 ps, which is 4.7% higher than the design target of 241.8 ps. Most of the error resulted from neglecting the impact of the material dispersion of Si and SiO₂ on the group index at the design stage. If the delays in the fabricated delay lines are re-calculated taking into account material dispersion [27], a 253.8 ps differential delay is predicted, which is within 0.24% of the measured value. In the discussion that follows, the 253.8 ps differential delay is assumed to be the design value. This is justified by the fact that the comparison of the measured delays with the properly calculated delays gives a measure of how well the interleaver is implemented, while the comparison with the improperly calculated delays does not allow to draw any conclusions apart from the fact that taking the material dispersion into account is essential.

 

Figure 5 Group delay of the interleaver measured with an optical vector analyzer. The spectral regions outside the passbands of the filters are shaded in gray; these regions carry almost no optical power and the output of the optical vector analyzer is very noisy. The relevant spectral regions within the passbands of the filters are highlighted in color.

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When using the pulse train produced by the interleaver for optical sampling, the important value is the deviation of the pulse timings from the uniform sampling grid. This is illustrated in Fig. 6, where the green pulses indicate the ideal uniform sampling grid, and the red pulses indicate the obtained timings, as derived from the group delay measurements. The constant shift of the measured sampling times with respect to the ideal sampling grid is not relevant for the accuracy of the sampling, and was removed in Fig. 6. The errors in the sampling times of channels 1-4 relative to the ideal sampling grid are 0.6 ps (0.23%), 1.03 ps (0.40%), −0.41 ps (−0.08%), and −1.22 ps (−0.16%), corresponding to an RMS timing error of 0.88 ps (0.35% of the sampling interval).

 

Fig. 6 Timings of the sampling pulses at the output of the interleaver, derived from the group delay measurements (shown in red), relative to the uniform timing grid (shown in green). Not to scale.

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It should be noted that some oscillations in the measured group delay over the channel bandwidth can be observed in Fig. 5, most likely due to limitations of the measurement setup. Even if these oscillations are real, they will lead to some distortion of the pulse waveform, which is not expected to affect the performance of the photonic ADC since the values of the samples are found from the total energies of the pulses and do not depend on the details of the pulse shape.

3.3 Crosstalk

The crosstalk in the interleaver can be defined as the fraction of the pulse power that passes through a wrong delay line, and therefore gets delayed by a wrong amount. For example, referring to Fig. 2, consider the “blue” light at λ₁ and the “green” light at λ₂. In the ideal case, all green light should go through the green delay line. However, because the drop-port transmission of the blue rings for green light is not exactly zero, some fraction of the green light will pass through the blue delay line, getting delayed by a wrong amount. In this case, the crosstalk can be defined by the fraction of power of the output green light that traveled through the blue delay line.

The magnitude of the crosstalk cannot be seen directly from the transmission spectrum in Fig. 4(a), since it shows the total power collected from all delay lines. To determine the crosstalk, the measured transmission spectrum is fitted to the analytical model, which calculates the interleaver frequency response by combining the frequency responses of all four channels, with the response of each channel determined by the responses of its input and output microring resonator filters and its delay line. The fit to the measured transmission spectrum is shown in Fig. 7(a), and the frequency responses of the individual channels are shown in Fig. 7(b), with different colors representing the power delayed by different delay lines. The largest crosstalk occurs in channel 4, where the power of the pulse delayed by delay line 1 (blue peak around λ₄) is 24 dB below the power of the pulse delayed by delay line 4 (red peak at λ₄). The crosstalk in other channels is below −32 dB. It is expected that the observed −24 dB crosstalk can be reduced by optimizing the frequencies of the microring resonators using thermal tuning.

 

Fig. 7 Interleaver crosstalk analysis: (a) measured frequency response of the interleaver (blue line) fitted with the theoretical model (grey line) that calculates the interleaver response by combining the responses of the input and output arrays of single-ring resonator filters and the respective delay lines; (b) frequency responses of the individual channels acquired from the model. The blue, green, yellow, and red colors represent the power delayed by the delay lines 1, 2, 3, and 4, respectively. The crosstalk of the interleaver is determined by the blue peak that can be seen under the red peak at λ₄; this blue peak represents the signal that should travel through the delay line 4, but travels through the delay line 1 instead.

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The peaks outside the passbands of the channels are not considered in the crosstalk calculation for two reasons. First, the peaks that are located far away from the center wavelength (e.g. the peak at 1584 nm) are less important because the spectral density of the laser at these wavelengths is low. Second, in the wavelength-interleaved photonic ADC system shown in Fig. 1, the pulse train produced by the interleaver is additionally filtered by the demultiplexer that follows the modulator. This filtering suppresses the wavelength components outside the channel passbands. For this reason, the peaks outside the channel passbands, such as the peak at ~1544 nm, are not counted towards the interleaver crosstalk. In fact, the additional filtering will also significantly reduce the −24 dB crosstalk mentioned above, since the peak of the crosstalk signal is shifted away from the main peak at λ₄ (see Fig. 7(b)) and will therefore be further suppressed by the filter centered at λ₄. In this respect, the −24 dB crosstalk of the interleaver reported in this work is too conservative in the context of the full photonic ADC.

4. Conclusions

This work shows that an important component of a high-speed wavelength-interleaved photonic ADC, the time-wavelength pulse interleaver, can be implemented on a silicon photonic chip. The demonstrated 4-channel interleaver converts a pulse train with 1 GHz repetition rate into a 4 GHz pulse train, with pulse wavelength changing periodically every 4 pulses. The interleaver is suitable for photonic ADCs with 4 GSa/s sampling rates.

The insertion loss of the interleaver is relatively low, despite the fact that the delay lines are long – the length of the longest line is about 6.5 cm. The losses are reduced by using wide multi-mode waveguides over more than 90% of the length of the delay lines. The measured losses for channels 1 to 4 is 1.6, 2.1, 2.8, and 5.8 dB, respectively, and the delay line lengths are approximately 0.5, 2.5, 4.5, and 6.5 cm. Channel 4 is more lossy than expected, possibly due to fabrication errors. Note that if the photonic ADC is scaled to higher sampling rates by increasing the repetition rate of the laser, the length of the delay lines will be reduced, which has a favorable effect on the interleaver loss and on-chip footprint.

The measured delay values have 0.88 ps (0.35%) RMS timing error with respect to the uniform timing grid predicted through simulations. In perspective, such a timing error would limit the ADC resolution to 6.5 effective bits for a 2 GHz input signal, which is lower than desired. The question on what causes these timing errors and how to reduce them remains open. Using microheaters to compensate for the timing errors is not very practical, since the dependence of the delay on temperature is weak and the required heating power is large. It should be noted, however, that the timing error of the interleaver is different from the timing error associated with jitter – the former is static, while the latter is random. Static timing errors can be removed at post-processing stage, using one of the many well-developed timing skew compensation algorithms used in multi-channel electronic ADCs.

The crosstalk of the interleaver is estimated to be −24 dB. However, as described in Section 3, the crosstalk in the photonic ADC will better than −24 dB because the pulses are additionally filtered by the demultiplexer which follows the modulator (see Fig. 1). Furthermore, the crosstalk can be reduced with additional tuning of the microring filter frequencies. These considerations indicate that the achieved crosstalk level is sufficient for a photonic ADC with more than 10 effective bits without any post-processing. However, the crosstalk issue is expected to become more significant when the number of channels is increased. For a large number of channels, it is difficult to ensure that none of the undesired peaks in Fig. 7(b) falls within the channel passbands. The crosstalk will also increase if the channel bandwidth is increased, which would be needed to capture a larger fraction of the laser spectrum and improve the power efficiency. In these cases, it is expected that second-order microring resonator filters will need to be used at the input or output of the delay lines.

The free spectral range of the interleaver obtained using the Vernier effect is about 52 nm, sufficient to accommodate spectra of common mode-locked lasers. If necessary, the FSR can be further increased by reducing the radius of the microring resonators. For example, the FSR can be doubled if the microring radius is reduced from the 5.0 μm used in this work to 2.5 μm.