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Abstract
We demonstrate an optical time-gate isolator entirely fabricated on the silicon-on-insulator (SOI) platform based on a conventional traveling-wave Mach-Zehnder modulator (TW-MZM) design. The device achieves 18.2 dB (22.7 dB) time-averaged isolation when driven with 2.0-Vpp (7.1-Vpp) differential clock signals at 6.8 GHz and biased at null. Under these conditions, the isolator blocks backward light at all time regardless of driver amplitude, but produces periodic modulation in the forward direction. Moreover, we embed our isolator in a digital communication link and measure a signal-to-noise ratio (SNR) penalty of only 0.5 dB due to the isolator at 13.6 Gbaud PAM-4 data rate. Our device can be integrated in larger circuits to protect laser sources or mitigate interference.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical isolators are used to protect lasers, prevent oscillations in optical amplifiers and mitigate multi-path interference in communications systems, to name a few applications [1]. In commercial silicon photonics (SiP), the isolator is typically an external micro-optic component based on Faraday rotation, requiring precise alignment and generating additional packaging costs [2]. As efforts are made to develop silicon sources and as the complexity of photonic integrated circuits (PICs) increases, integrated silicon isolators have become highly desirable. However, due to the absence of magneto-optic materials in standard CMOS processes, their development is not straightforward. Furthermore, integrated isolators for telecom bands should achieve 30-35 dB of broadband isolation (>100nm) with <0.5 dB insertion loss to rival with micro-optic products [3].
Numerous approaches to integrate non-reciprocal devices on the silicon-on-insulator (SOI) platform have been demonstrated. Photonic crystal designs have shown asymmetrical power transmission [4–6], but their symmetric scattering matrix does not break Lorentz reciprocity, which is a strict requirement of optical isolators [1]. The three most common mechanisms to break Lorentz reciprocity are the Faraday effect, non-linear effects and the time modulation of permittivity. In the first category, bonding or deposition of a magneto-optic layer on top of SOI rings or interferometers enables up to 30 dB isolation [7–11], but requires post-processing at present. SOI isolators based on non-linearity are CMOS-compatible, but require significant pump power [12–14], or isolate only above a certain signal power threshold [15,16]. Isolators based on index modulation have also been demonstrated, in the III-V [17], $\textrm {LiNbO}_{3}$ [18], heterogeneous SiP [19], and SOI platforms [20]. In [20], a design based on tandem SiP phase modulators was proposed, but the measured isolation was only 3 dB. In [21–23], a similar design involving directional couplers has been simulated with SiP physics, but demonstrated using $\textrm {LiNbO}_{3}$ modulators. In both implementations, the optical path lengths between the modulators and their relative driving phase have to be carefully controlled. A simpler modulation-based approach is to use a conventional traveling-wave Mach-Zehnder modulator (TW-MZM) as a ‘time-gate’ isolator [24], which can block counter-propagating light completely, at the expense of periodic modulation of the co-propagating light.
In this work, we demonstrate to the best of our knowledge the first optical time-gate isolator leveraging a conventional TW-MZM architecture fully fabricated on the SOI platform. We achieve 18.2 dB and 22.7 dB average isolation in the C-band with differential clock signals at 2.0 V$_{\textrm {pp}}$ and 7.1 V$_{\textrm {pp}}$ per arm as the driver, respectively. Our device does not require post-processing and works in the linear regime. This paper is divided as follows. In Section 2, we review the time-gate isolator theory and its inherent bias point trade-off, and present specific theoretical and operational considerations for the SiP platform. In Section 3, we detail the design and fabrication of our SiP time-gate isolator. We present its experimental characterization in Section 4, and in Section 5 we integrate it in a complete digital communication link to assess its system-level penalty. Finally, we discuss practical implications in Section 6.
2. Theory and simulations
2.1 Linear-phase time-gate isolator
A general schematic of a time-gate isolator based on a TW-MZM is shown in Fig. 1(a). The total phase accumulated over the electrode length $L$ by a short light pulse co-propagating with a time-varying RF signal in the arm $i\in \lbrace 1,2\rbrace$ of the Mach-Zehnder will be labeled $\Delta \phi _{i,+}(t)$. Similarly, if the short pulse is counter-propagating, its total phase is $\Delta \phi _{i,-}(t)$. For a linear phase-shifter, i.e. $\Delta \phi _i(V_i) \propto V_i$, the phase shifts $\Delta \phi _{i,+}(t)$, $\Delta \phi _{i,-}(t)$ are [18,24,25]:
Fig. 1. (a) Schematic of an optical time-gate isolator based on a TW-MZM. (b) Effective voltage seen by two arbitrary-phase optical pulses counter-propagating with the RF signal. The top (bottom) horizontal red line is the propagation start (end) time for the 1$^{\textrm {st}}$ light pulse in the isolator, same in blue for the 2$^{\textrm {nd}}$ pulse. The net voltage seen by the 2 pulses is the integral of the RF signal over $\tau _o$ + $\tau _e$. The condition (3) is met: the net voltage seen is 0 regardless of the pulse phase. (c) Simulated isolator 2$V_\pi$ (total) differential drive signal, before an after the low-pass filter shown in blue. (d) Relative optical power transmission in both directions for various driver frequencies $f$ for a linear-phase time-gate isolator biased at min (top) and at max (bottom).
From (1b), the accumulated phase in counter-propagation is proportional to the net voltage “seen” by the optical pulse during its propagation through the device. To make a time-gate isolator, one first needs to choose a periodic $V(t)$ pattern having symmetrical positive and negative sections within one period, such as a sinusoidal or square wave. Then, the period $T$ of $V(t)$ needs to be set such that an optical pulse counter-propagating with the RF signal sees an integer multiple of periods $nT$ during its course. In this case, the net voltage affecting the light pulse is 0. Mathematically, this condition is:
where $\mu _o$ and $\mu _e$ are the optical and electrical group velocities, and $n$ is a positive integer. Using $\mu _o=L/\tau _o$ and $\mu _e=L/\tau _e$, (2) is equivalent to the condition derived in [18]: In the case where $\mu _o\approx \mu _e$, (2) and (3) simply reduce to $nT=2\tau _o$. The condition (3) is met for $n=1$ in Fig. 1(b). For both optical pulses of arbitrary phase shown, the total duration of the positive and negative RF signal sections seen are equal during their propagation through the isolator. Note that in counter-propagation, the only impact of velocity mismatch is to shift the values of $T$ satisfying (3). This is also illustrated in Fig. 1(b), where arbitrarily $\mu _e=2\mu _o$.At the output of a balanced Mach-Zehnder, assuming no voltage-dependent optical attenuation, the normalized optical power $P_{\textrm {opt.},\pm }(t)$ is:
Fig. 2. Impact of isolator E-O bandwidth at $f=7.5$ GHz, shown for $\Delta \phi _0=\pi$ (left) and $\Delta \phi _0=0$ (right).
The “forward” direction of light in the isolator, i.e., for which optical power transmission must be maximized, depends on the isolator bias point in the schematic of Fig. 1(a). If the isolator is biased at maximum transmission ($\Delta \phi _0=0$), the forward light is the light counter-propagating with the RF signal. If however $\Delta \phi _0=\pi$, the forward light is the light co-propagating with the RF signals. Moreover, from Fig. 1(d), if the driver frequency $f$ approximately satisfies Eq. (3), the bias point brings a trade-off. If $\Delta \phi _0=0$, there is almost no residual forward modulation, but also limited isolation due to periodic backwards transmission spikes [18]. If $\Delta \phi _0=\pi$, there is inherent forward modulation, but light is almost completely blocked in the backwards direction at all time [17,24]. Also note from Fig. 1(d) that a significant practical tolerance exists around the value of $f_0$, i.e., residual modulation in counter-propagation at $f=7.5$ GHz ($\sim$0.35 GHz away from the theoretical $f_0$) is almost imperceptible at either bias point. Finally, note that the amplitude of this residual modulation decreases with increasing $f$ [24].
The BPG rise time and isolator bandwidth have a significant impact on the co-propagating light and the overall time-gate isolator performance. This is illustrated in Fig. 2, where the rise time is fixed to 12 ps and $f=7.5$ GHz. If $\Delta \phi _0=\pi$, higher isolator bandwidths lead to narrower transmission dips in the forward light, and thus to higher average transmitted power in the useful direction. If alternatively $\Delta \phi _0=0$, setting the isolator bandwidth to 15 GHz, 35 GHz and infinity respectively lead to the time-averaged transmission of 0.29, 0.16 and 0.11 of the normalized power in the backwards direction, translating to average isolation levels of 5.4 dB, 8.0 dB and 9.6 dB, respectively.
2.2 SiP time-gate isolator
SiP MZMs typically use waveguide pn junctions and the plasma dispersion effect for modulation [28]. The free-carrier-induced change to the real and imaginary parts of the complex refractive index is non-linear with respect to the applied voltage. In Fig. 3(a), we simulate the DC optical phase change $\Delta \phi (V)$ and attenuation $\alpha (V)$ for a 5.0 mm-long silicon phase-shifter at 1550 nm. To do so, we first retrieve the specific doping profile for our modulator cross-section (from foundry data), and then follow the method described in [29]. Negative voltage (carrier depletion) is chosen to limit optical attenuation and improve the MZM bandwidth [26]. The simulated DC $V_\pi$ is 3.2 V.
Fig. 3. (a) Simulated optical phase and attenuation of a 5.0 mm-long silicon phase-shifter at $\lambda _0=$1550 nm, normalized to 0 V and −9 V respectively. (b) Corresponding optical power transmission when $\Delta \phi _0=\pi$ and $f=7.5$ GHz, for various RF signal amplitudes. $V_\pi =$ 3.2 V, so dynamic voltages are V$_{\textrm {pp},i}=V_\pi =3.2$ V in each arm, V$_{\textrm {pp},i}=V_\pi /2=1.6$ V in each arm, and V$_{\textrm {pp},i}=V_\pi /4=0.8$ V in each arm.
Because of $\alpha (V)$ and the non-linearity of $\Delta \phi (V)$, (1) and (4) do not hold for a SiP time-gate isolator. Again assuming velocity-matching, impedance-matching between the TW and termination and perfect 50/50 splitters, we can reformulate these equations more generally as:
In Fig. 3(b), we simulate a SiP time-gate isolator at $\Delta \phi _0=\pi$ and $f=7.5$ GHz using Eqs. (5)–(7) and the DC characteristics shown in Fig. 3(a). The isolator is differentially driven around a bias point of −2 V to ensure constant reverse bias. Other parameters (driver rise time, isolator length and bandwidth) are unchanged versus simulations of Section 2.1. Comparing Fig. 1(d) for the $\Delta \phi _0=\pi$ case with Fig. 3(b), the SiP time-gate isolator shows a forward (co-propagation) transmission penalty versus its linear-phase counterpart even if a full $V_\pi$ swing is applied on each arm, due to the static loss component and the loss imbalance arising from $\alpha (V)$. Optical transmission with a reduced driver swing is also shown in Fig. 3(b).
3. Design and fabrication
A SiP time-gate isolator should have phase-shifters efficient enough to allow for $2V_\pi$ amplitude modulation with a reasonable drive voltage budget. As importantly, the optical and electrical path lengths in the device must be long enough to allow for a $f_0$ value below the transmitter bandwidth, as was shown in Fig. 2. For these reasons, our design is dual-drive and has long (5-mm) electrodes. The chosen length should keep $f_0$ below $\sim$7.2 GHz, as simulated in Section 2. The differential RF signals are applied with a 50 GHz GSSG probe, and the isolator has 50-$\Omega$ on-chip terminations. The RF electrodes are defined on both available metal layers to limit RF attenuation. We used the strongest pn junction doping available, improving $V_\pi$ but increasing optical loss. To reduce this attenuation and prevent current flow along the waveguide, a longitudinal waveguide pn junction loading fraction of 2/3 is chosen, yielding an effective phase-shifting length of 3.3 mm in each arm. Finally, thermal phase-tuners are used to set the MZM bias point, and TE grating couplers (GCs) are used to couple light in and out of the chip. The overall dimensions of the isolator are 5.7 mm x 0.7 mm. The device layout and phase-shifter detail are shown in Fig. 4. Fabrication on a 220 nm silicon wafer was done through the IMEC commercial open-access SOI process.
Fig. 4. (a) Layout of the fabricated SiP time-gate isolator. (b) Phase-shifter detail. Left: cross-section. M1 and M2 are metal layers, Si wg. is the optical waveguide layer, and BOX is the buried oxide layer. Drawing is not to scale. Right: top view showing the waveguide pn junction loading factor of 2/3 (optical waveguide is in pale purple).
4. Experimental characterization
The fabricated SiP time-gate isolator has a measured optical propagation loss of 8 dB when biased at maximum transmission, and no pn junction reverse bias is applied. Throughout experiments, we choose not to apply such a bias to limit the device V$_\pi$ as much as possible [26]. Propagation loss is partly caused by the exaggerated proximity of high-doping regions with the optical waveguide. This distance will be increased in future designs and should reduce loss by 3-3.5 dB for a 3.3-mm effective phase-shifter length, based on foundry data. The measured max-min extinction ratio of the Mach-Zehnder (within the same direction) is 28 dB, setting the theoretical isolation limit for this device [24]. The E-O bandwidth cannot be measured directly, but is estimated to be 25-30 GHz at 0 V bias based on measurements of similar devices on the same chip. Using a digital communication analyzer (DCA), the RF V$_\pi$ at 0 V and 7.5 GHz is $\sim$7.5 V.
We use a synthesized signal generator (clock source), a splitter, two RF amplifiers and two RF delay lines to generate the differential sinusoidal drive signals for the time-gate isolator. The experimental setup is shown in Fig. 5(a). To study the isolator bi-directional behavior, the input and output optical fibers are swapped. The drive signals reaching the isolator are shown in Fig. 5(b). Using the DCA, we find empirically $f_0\approx 6.8$ GHz. A first assessment of the time-gate isolator performance at $f=f_0$ is shown in Fig. 5(c). Throughout the paper, green labels on DCA captures mean light is propagating in the forward (useful) direction, and red labels mean light is propagating in the backward direction (to be blocked). The bias point trade-off simulated in Section 2.1 is well reproduced experimentally in Fig. 5(c): $\Delta \phi _0=0$ leads to a poor average contra-directional isolation of 3 dB, but also to forward light with very small residual modulation. Alternatively, $\Delta \phi _0=\pi$ leads to a substantial time-averaged isolation of 22 dB, but also to large forward modulation. For $\Delta \phi _0=0$, the small residual ripples in the forward direction at twice the driver frequency (barely distinguishable) can be attributed to the tolerance around the empirically determined $f_0$ and to RF attenuation along the electrode.
Fig. 5. (a) Experimental setup for time-gate isolator characterization. RF amp: RF amplifier; 50%: 3-dB RF splitter. (b) Differential clock signals at $f_0=6.8$ GHz and 5.4 V$_{\textrm {pp}}$ each just before the isolator. (c) Corresponding optical signals on the DCA after the isolator, for both bias points and both propagation directions. The isolation reported is the ratio of the time-averaged optical power transmitted in both directions.
We now quantify more precisely the value of $f_0$. We sweep the driver frequency and use an electrical spectrum analyzer (ESA) to measure the residual RF modulation power in the contra-directional light after the isolator. Results are shown in Fig. 6(a). Corresponding time-domain traces are also shown for 4 GHz, 6.8 GHz and 8 GHz driver frequencies. The first two transmission dips in the Power vs. Frequency plot allow to identify directly $f_0=6.8$ GHz and $f_1=13.6$ GHz. Note that when $f=8$ GHz (1.2 GHz away from $f_0$), the residual RF power in counter-propagation is 15 dB higher than at $f_0$, but the corresponding time-domain residual modulation is of modest amplitude: the average optical power at the DCA is only 0.2 dB lower than at $f_0=6.8$ GHz. This means that there is a practical tolerance around the driver frequencies satisfying (3), i.e., small driver frequency deviations from $f_0$ lead to time-domain ripples in counter-propagation of minimal amplitude. This corroborates simulations of Fig. 1(d), where a 350 MHz driver frequency deviation from the theoretical $f_0$ led to barely perceivable residual modulation in counter-propagation.
Fig. 6. (a) Top: Measured residual RF power in the contra-directional light after the isolator versus driver frequency ($\Delta \phi _0=0$). 500-MHz ESA sweeps are performed around each clock frequencies (red circles). Bottom: corresponding time-domain traces from the DCA at selected clock frequencies. (b) Average isolation (difference between purple and red traces) from 1500 nm–1580 nm at $\Delta \phi _0=\pi$ and drive signals at $f_0$, V$_{\textrm {pp},i}=5.4$ V. Input optical power is 0 dBm, and grating coupler response is de-embedded. The vertical arrow is located at the wavelength used for Fig. 5(c) measurements. (c) Impact of drive signal amplitude on forward light ($\Delta \phi _0=\pi$, $f_0$).
Next, the measured spectral response of the isolator is shown in Fig. 6(b) for $\Delta \phi _0=\pi$, again at $f=6.8$ GHz. Since the isolation level is rather constant across the C-band, the condition (3) derived in Section 2.1 is satisfactorily met across a very large optical bandwidth. This is explained by the modest impact of optical dispersion on the value of $f_0$.
Finally, the impact of the isolator drive voltage on the average power of the co-propagating light is shown qualitatively in Fig. 6(c) for $\Delta \phi _0=\pi$. The pattern matches well simulations of Fig. 3(b). Table 1 quantifies the impact of drive voltage for $\Delta \phi _0=\pi$. Although the average isolation achieved with the different swings are relatively close (18.2 dB–22.7 dB), the forward optical power penalty is much lower with larger RF swings. The total forward optical loss of the isolator biased at $\Delta \phi _0=\pi$ is the sum of its intrinsic loss (8 dB), and the modulation penalty listed in Table 1 (dependent on driver swing). This can be verified in Fig. 6(b), where the overall loss in co-propagation is $\sim$ 8 dB + 2.1 dB = 10.1 dB close to 1550 nm.
Table 1. Driver V$_{\textrm {pp}}$ impact on isolator performance ($\Delta \phi _0=\pi$, $f_0$).
5. Transmission experiment
In this section, we integrate the isolator in a direct-detection back-to-back digital data transmission link, just after the laser. The isolator is only biased at $\Delta \phi _0=\pi$, because of the much higher isolation achievable (see Fig. 5(c)). Furthermore, modulating the forward light out of the isolator when $\Delta \phi _0=0$ is already known to generate a very small penalty, due to the quasi-absence of residual modulation [18]. In our setup, an external Avanex 7910507-A 40 Gbit/s intensity modulator (MZM) follows the isolator. Importantly, a tunable optical delay line is inserted between the isolator and the external MZM to phase-align the periodic transmission minima after the isolator with the symbol transitions of the external MZM. We use an 88 GSa/s arbitrary waveform generator (AWG) to drive both the isolator (with differential sinusoidal signals) and the external MZM (with random data). At the receiver, a 80 GSa/s real-time oscilloscope (RTO) collects the two differential outputs of the 33 GHz photo-detector (PD) + transimpedance amplifier (TIA). Basic digital signal processing (DSP) is applied at the transmitter (Tx) and receiver (Rx) sides. The complete experimental setup and DSP are shown in Fig. 7(a).
Fig. 7. (a) Experimental transmission setup. Two AWG channels drive the isolator differentially with sinusoidal signals, and a third channel modulates an external MZM with random PAM-4 data. Pol. cont.: polarization controller; EDFA: Erbium-doped fiber amplifier; Ext. MZM: external MZM; VOA: variable optical attenuator. (b) External modulation of the forward isolator light at 13.6 Gbaud PAM-4. The DCA captures (pink) show the optical trace after the external MZM, and the eye diagrams (blue) are the corresponding received symbols after DSP at −6 dBm ROP. Left: data from external MZM only, when the isolator is inactive (transparent). Right: the isolator is biased at $\Delta \phi _0=\pi$ and driven at $f_0=6.8$ GHz, 6 V$_{\textrm {pp},i}$. The dashed blue lines on the DCA captures represent the phase alignment of isolator transmission minima with symbol transitions using the optical delay line.
In Fig. 7(b), we show on the right-hand side DCA capture the phase-matched superposition of the forward light out of the isolator ($\Delta \phi _0=\pi$, $f=6.8$ GHz, 6 V$_{\textrm {pp}}$/arm) with random 13.6 Gbaud PAM-4 data generated by the downstream external MZM. The superposed signals can qualitatively be compared to a return-to-zero (RZ) stream. Its peak-to-average power ratio (PAPR) reaches 4.8 dB, compared to 2.7 dB for the standard (reference) PAM-4 eye when the isolator is inactive (left DCA capture). At −6 dBm received optical power (ROP) at the PD, the SNR penalty due to the isolator is only 0.5 dB, compared to when it is turned off. The corresponding BERs, using error function-based computation since the actual BER is below RTO storage capacity, is shown for both cases on processed eye diagrams in 7(b). Note that symbol rates are constrained to 2$f_n$, i.e. twice any isolator driver frequency satisfying (3), but the isolator design (length) can easily be scaled to shift the $f_n$ values for a specific target symbol rate.
6. Discussion
The differential isolator dynamic electrical power consumption can be estimated with $P_{tot.}=2\times \left (V^2_{RMS}/R\right )$, where $V_{RMS}$ is the driver output root-mean-square voltage, and $R$ is the 50-$\Omega$ RF termination (load) in each arm [30]. With 2-V$_{\textrm {pp}}$ sinusoidal drive signals, we find $P_{tot.}=20$ mW, which (to give perspective) is comparable to the switching power of thermo-optic phase-shifters in commercial SiP processes [31]. Since no DC offset is applied to the RF signals, there is no static component to the isolator electrical power consumption.
Globally, our optical time-gate isolator design has advantages and limitations versus competing isolator approaches. A list of state-of-the-art SiP isolator designs based on magnetic material deposition/bonding can be found in [32]. Most achieve 20-30 dB isolation and have time-independent behavior, and involve better or comparable insertion loss (4-22 dB) as a result of the significant optical attenuation of magnetic materials, up to 60 dB/cm [9]. However, as stated in Introduction, none of these designs is entirely compatible witch commercial SOI foundries at present. Compared to other modulation-based isolator designs demonstrated in SiP, such as [20], our device (at $\Delta \phi _0=\pi$) features much higher time-averaged isolation ratios and strong time-independent backward light blocking, but also higher propagation loss (>8 dB vs 4.1 dB).
Finally, few additional comments are necessary about the time-gate isolator bias point. The $\Delta \phi _0=0$ operation can be useful if, for example, the backward light contains modulation having a rise time much smaller than the laser it protects. To this end, square drive signals with short rise/fall times and high-bandwidth isolators are desirable, as simulated in Fig. 2. In addition, for $\Delta \phi _0=0$ operation there is no (or very little) residual modulation in the forward light, leading to negligible BER penalties if there is subsequent data modulation, as demonstrated in [18]. However, the achievable isolation ratio is rather low (3 dB experimentally here). On the other hand, $\Delta \phi _0=\pi$ operation enables much higher time-averaged isolation ratios (>22 dB here), while the forward transmission dips still allow for subsequent data modulation with limited BER and SNR penalties (Fig. 7). Moreover, and most importantly, for the SiP applications where only the average optical power matters in the forward direction and a low-speed detector can be used, such as for sensing, $\Delta \phi _0=\pi$ operation of the isolator enables both excellent isolation and no functional disruption, since the forward GHz-range ripples get integrated by the detector. Other examples of compatible applications include LIDAR, spectroscopy and optical clock distribution [24].
7. Conclusion
We reviewed the theory and simulated the operation of optical time-gate isolators based on conventional TW-MZMs, and further characterized the specifics of the SiP platform. We designed, fabricated and demonstrated such a time-gate isolator in an open-access SOI process. We experimentally characterized its performance against various parameters: bias point, driver frequency, optical wavelength and drive voltage, and explained operational trade-offs.
When biased at minimum transmission, our design achieves 22.7 dB (18.2 dB) time-averaged isolation with 6.8 GHz, 7.1-V$_{\textrm {pp}}$ per arm (2-V$_{\textrm {pp}}$ per arm) differential sinusoidal drive signals from a commercial clock generator. The isolator propagation loss is 8 dB. The additional penalty due to intrinsic periodic modulation in the forward direction is only 0.5 dB with 7.1-V$_{\textrm {pp}}$ drivers. Because our isolator design is optically broadband, requires simple drivers at a relatively low RF frequency (vs. its bandwidth), can operate with limited drive voltage and is fully compatible with commercial SOI fabrication, it can be implemented in several circuits for source protection or other applications. As an example, we embedded our isolator in a back-to-back digital link after the laser, and measured a SNR penalty due to the isolator of only 0.5 dB at 13.6 Gbaud PAM-4, versus when the isolator is inactive.
Disclosures
The authors declare no conflicts of interest.
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