Gigahertz optical tuning of an on-chip radio frequency photonic delay line

YANG LIU,* AMOL CHOUDHARY, DAVID MARPAUNG, AND BENJAMIN J. EGGLETON Centre for Ultrahigh Bandwidth Devices for Optical System (CUDOS), Institute of Photonics and Optical Sciences (IPOS), School of Physics, University of Sydney, NSW 2006, Australia Australian Institute for Nanoscale Science and Technology, University of Sydney, Sydney, NSW 2006, Australia *Corresponding author: yang.liu@sydney.edu.au


INTRODUCTION
Microwave photonic (MWP) delay lines are key components in signal filtering, signal synchronization, and radar target simulators in advanced defense and radio frequency (RF) communication systems [1][2][3][4].In these applications, fast delay tunability is necessary to provide a fast signal-pointing speed to microwave radar phased array systems [4] and the fast reconfigurability required in dynamic cognitive RF systems [5].To avoid suffering from large footprints, MWP delay lines are preferably implemented in compact photonic devices based on optical resonances where the dispersive properties determine the signal group delay responses [6][7][8]-for instance, fiber Bragg gratings (FBGs) [9] and stimulated Brillouin scattering (SBS) [10] in fiber.However, these schemes require long-length waveguides and high pump power.
Recent progress on photonic integrated circuits (PICs) has included an impressive demonstration of on-chip MWP delay lines [11], but they lack the required tuning speed.The fast tunability based on the complementary phase-shifted spectra technique shows the integration potential, but its on-chip implementation is constrained by the difficulty of realizing a triangular-shaped spectral filter for spectrum tailoring [12].Compact tunable time-delay lines were achieved by employing the optical resonances of integrated silicon [13][14][15] and silicon nitride [16,17] ring resonators, but the tuning speed is constrained by the slow thermal-optic effect.An on-chip photonic delay line was demonstrated using subwavelength grating waveguides in silicon-on-insulator (SOI), but it only offered discrete tuning of time delays [18].A continuously tunable time-delay realization was reported based on SBS in an integrated photonic chip, but the intrinsic response time of the SBS process limits the tuning speed to ∼10 ns, governed by the lifetime of acoustic waves [19].A controllable delay line based on a highly dispersive photonic crystal waveguide was demonstrated to be a potential candidate for a fully integrated MWP system; however, the tuning speed of several microseconds was limited by the frequency tunability of the optical source [20].Although these efforts towards miniaturization are crucial for fully integrated MWP processors, they bring complexity to the tuning mechanism of the dispersive properties, increasing the requirements for device fabrication and power consumption.Hence, an entirely new approach to creating dynamically tunable MWP delay lines from an otherwise passive optical device is desired to facilitate the widespread implementation of this technology in real-world applications.
In this work, a principle for realizing gigahertz (GHz) tunable MWP delay lines in an integrated Si 3 N 4 device is introduced and experimentally demonstrated.The technique relies on the interference between a data signal and a reference signal [21,22] to synthesize larger phase shifts in the microwave domain, which results in RF signal group delay enhancement.Through experiments, we demonstrate that this technique enables flexible switching between advancement and delay of RF signals and allows for fast tunability up to a GHz tuning speed solely by controlling the optical power.The results presented in this work imply the feasibility of wideband operation and compatibility with existing schemes based on dispersive photonic devices.

PRINCIPLE OF PHASE AMPLIFICATION
The schematic configuration of a conventional tunable MWP delay line is shown in Fig. 1(a).An RF signal is modulated onto an optical carrier via electronic-to-optical (E-O) conversion, and then processed by a photonic device which imparts dispersioninduced signal group delay, i.e., τ g ∂φ OR ω∕∂ω, where φ OR ω is the imposed phase response over the signal frequency ω.In contrast to the conventional MWP delay line, where the group delay is consistently determined by the optical dispersion of photonic devices, in the tunable delay line based on phase simplification shown in Fig. 1(b), an optically controlled unit of phase amplification is added to enhance the dispersion-induced group delay.By changing the optical power, a larger phase slope is synthesized, resulting in an enhanced group delay of the RF signal through optical-to-electronic (O-E) conversion.
This method that allows for the phase-response amplification is based on a vector-sum operation [22], as shown by a phasor diagram in Fig. 2(a).The vector in solid black represents a data signal A 1 cosωt Δφ at a frequency of ω, with an initial phase shift Δφ obtained from an optical resonance.Through a vector summation with a reference signal A 2 cosωt π illustrated by a vector in solid blue, a synthesized signal depicted by a vector in solid red can be obtained.It is clear to see that the phase shift φ 0 of the synthesized signal is magnified with respect to the initial phase response Δφ of the data signal.The resultant phase shift φ 0 can be controlled by varying the strength of the reference signal amplitude A 2 .This amplified phase response imparted on the synthesized RF signal results in an magnified signal group delay τ 0 g , written as τ 0 g G • τ g , where G is the amplification factor expressed by G 1 − A 2 ∕A 1 −1 (for derivations, see Supplement 1).
In Fig. 2(b), the black line shows the phase response induced by an optical ring resonator operated in the under-coupled (UC) regime where the coupling losses are less than the internal losses of the resonator, with an intrinsic quality factor (Q) of 1 × 10 6 , which approximates the performance of the optical resonator we used in the experiments.In the UC region, the optical resonator has dispersive phase shifts over the resonance frequency range.The phase shift depicted by the black dot is enhanced by the phase-amplification method to a larger phase denoted by the red dot.By extending this principle across the frequency range around the resonance, the dispersion will be enhanced to achieve a larger phase slope, as shown by the red curve, resulting in an improvement in the signal group delay according to τ 0 g G • τ g .

DISPERSION CONTROL
With this scheme, we demonstrated the activation of tuning the signal group delay by solely varying the strength of the reference signal.We implemented the technique with a dual-sideband modulation where two signals were generated for vector summing by the mixing of sidebands and the optical carrier.As shown in Fig. 3(a), an optical carrier is modulated by RF signals, generating two intrinsically out-of-phase (π difference) optical sidebands for the data signal and reference, respectively.The optical upper sideband acquires a phase shift Δφ imparted by the optical resonance over the signal spectrum, while the lower sideband serves as the reference signal with a constant π-phase offset.The amplitude of the lower sideband is tuned by an optical filter so as to implement different amplitude ratios A 2 ∕A 1 .After signal mixing of the optical carrier and dual-sideband-based RF interferometry via photodetection, a resultant RF signal is synthesized with an enhanced dispersion across the signal spectrum.The tuning of the amplitude ratio A 2 ∕A 1 results in a tunable phase-amplification factor G.
Simulation results for investigating the feasibility of this technique are shown in Fig. 3(b).In the simulations, a cascade of three under-coupled ring resonators, representing the experiment described later in this paper, is utilized to broaden the operation bandwidth for the phase amplification.The black trace shows the initial phase response on the upper sideband induced by the optical resonance and the red and blue curves represent the enhancement of the synthesized dispersion, with operations under the condition of the amplitude ratio A 2 ∕A 1 < 1. Importantly, when operating in the regime of A 2 ∕A 1 > 1, the phase slope of the synthesized dispersion flips to the opposite sign, indicating the switching between negative and positive signal group delay.Note that the RF signal delay is manipulated by solely controlling the lower sideband power, without tuning the actual optical resonators.
Figure 4(a) depicts the experimental setup to demonstrate the phase-amplification technique for dispersion control.An optical carrier from a distributed feedback laser (Teraxion Pure Spectrum, λ 1550 nm) was modulated by RF signals driven by a vector network analyzer (VNA, Agilent PNA 5224A) via a phase modulator (PM).The PM is used to generate the π phase difference for dual sidebands, while the unbalanced sideband amplitudes controlled by post processing will result in the intensity modulation.The modulated light was then fed to three cascaded UC rings fabricated using low-loss TriPleX (Si 3 N 4 ∕SiO 2 ) technology [23].Each ring has a free spectral range of 26 GHz and an intrinsic Q of ∼1 × 10 6 (a 3 dB linewidth of ∼200 MHz ), and exhibited a low propagation loss of ∼0.1 dB∕cm.The chip was equipped with on-chip tapers, leading to 7.5 dB fiber-to-fiber insertion loss.The amount of coupling, and hence the Q-factor and rejection of the ring resonator, can be tailored through thermooptic tuning implemented using on-chip chromium heaters.For the demonstration, we set the rings to the UC state around 10 GHz away from the optical carrier frequency and arranged the resonance frequencies with an equal interval of ∼100 MHz to broaden the 3 dB bandwidth up to ∼400 MHz with a rejection of 5 dB.Subsequently, the upper sideband was processed by these optical resonances.A programmable optical filter (Finisar 4000s) was utilized to control the amplitude of the lower sideband.This can also be done by utilizing an IQ modulator that enables independent control of the amplitude and the phase.The processed optical signal came out of the photonic chip, and was detected by a high-speed photodetector (u2t XPDV2120).Through mixing of the processed sidebands along with the optical carrier via photodetection, the synthesized phase response in the RF spectral domain was acquired by the VNA, as shown in Fig. 4(b).An amplification factor G of 3 was obtained with A 2 ∕A 1 < 1, while the slope flipped to the opposite sign when A 2 ∕A 1 > 1, as expected from the simulation results shown in Fig. 3(b).These changes in measured phase slope indicate a flexible tunability of the signal group delay, which needs to be experimentally verified with real RF signal delay.

OPTICAL TUNING OF SIGNAL DELAY
Based on the dispersion control, here we performed a demonstration of MWP signal delay with flexible tunability, using the setup shown in Fig. 5.In the experiment, we emulate a scenario where a tunable MWP delay line works at 10 GHz within the x band (8-12 GHz), which is a frequency range for extensive microwave applications such as satellite communications, radars, and space communications.RF pulse trains (a baseband RF signal with a width of ∼3 ns and 20 MHz repetition rate) were generated from an RF signal source (Tabor, WS8352) and then were up-shifted to 10 GHz by mixing with an RF carrier at 10 GHz from a local oscillator via a frequency mixer.The up-converted RF signals centered at 10 GHz were modulated onto an optical carrier via a PM, generating two out-of-phase sidebands.The modulated optical signal was then processed by the optical filter and the photonic chip, as described previously in Fig. 4(a).After the photonic delay line, the detected RF signal was down-shifted from 10 GHz to the baseband and monitored on an oscilloscope.One can note that the frequency bandwidth of the ∼3 ns signal pulse is ∼340 MHz, which can fit within the bandwidth of ∼400 MHz provided  by the cascade of three optical ring resonators.Potentially, this scheme can also operate over a wide range of RF carrier frequencies.
When operated in the region A 2 ∕A 1 < 1, as shown in Fig. 6(a), the RF pulse in purple trace using phase amplification shows an evident enhancement in time delay, in contrast to the delay signal in red trace with time-delay magnification.The dispersion enhancement allows for a group-delay magnification from −440 to −1110 ps with an amplification factor G of ∼3, as indicated by the corresponding measured phase responses.For the comparison of the group delay, an RF pulse without time delay is shown by the black trace.
We achieved flexible switching between negative group delay (signal advancement) and positive group delay by changing the amplitude ratio to the region A 2 ∕A 1 > 1.As shown in Fig. 6(b), the pulse indicated by the blue trace switches to positive group delay (1570 ps) from signal advancement (−400 ps), which results from the change in the sign of the synthesized phase slope imparted on the RF signal spectrum.From the phase response diagram in Fig. 6(b), the positive group delay can be tunable when the RF signal undergoes a different positive phase slope in yellow trace.The switching of delay can be explained by the change in the sign of amplification factor G, when the amplitude ratio varies from A 2 ∕A 1 < 1 to A 2 ∕A 1 > 1.We note that the symmetry of the phase responses originates from the dispersive response imparted by optical resonances, and the phase amplification is transparent to the chirp of modulated RF signals as the relative phase offset of two sidebands is fixed.

GHZ TUNABILITY
We proceed to demonstrate that the phase-amplification technique enables rapid tunability, which is a striking performance for MWP systems, such as cognitive RF systems, where rapidly adjustable MWP components are required.
We evaluated the tuning speed by measuring the change of the synthesized phase shift at a single frequency, using the method based on a phase detector [24] that can convert the phase change into voltage signal (for details in methods and experiments, see Supplement 1).A gate signal with a duty circle of 50% and repetition rate of 100 MHz was used to achieve the switching between two discrete synthesized phase responses, leading to a time-variable voltage signal that results from the phase difference.From Fig. 7, the converted voltage signal denoted by the blue dotted line can dynamically follow the variations of the gate signal depicted by the solid red curve, which indicates that the tuning speed of the synthesized phase response is dominated by the dynamic power control via the high-speed IM.Since the rise and fall times of the gate signal are below 1 ns, the dynamic tuning speed experimentally achieved beyond 1 GHz.It is potentially expected to be as high as tens of GHz using a faster driven RF signal and high-speed IM.We compared the tuning speed of this work to other stateof-the-art tuning schemes for RF and MWP applications, as summarized in Table 1.The scheme we proposed shows a distinct advantage over other works based on electric switches [25], micro-electro-mechanical system (MEMS) devices [26], laser frequency tuning [27], thermal tuning [28], and spatial light modulators (SLMs) [29], with a much faster speed by 4-5 orders of magnitude.The tuning speed can be further improved to be comparable with the report work based on PM [30][31][32].For this reason, there is a potential to develop rapidly tunable MWP delay lines.

DISCUSSION
Here we discuss the time-delay performance of this tunable MWP delay line based on phase amplification.From the complex plane    [30] <1 ns Filter Plasmonic modulator [31] <1 ns Phased array feeder PM [32] ∼40 ns Filter Electric switches [25] ∼100 ns Delay line MEMS RF devices [26] 1 ∼ 300 μs Phase shifter et al.Laser frequency tuning [27] ∼100 μs Filter Thermal tuning [28] ∼170 μs Filter SLM [29] 5 ∼ 30 ms Delay line in Fig. 2(a), the maximum amplified phase shift is constrained to π by the principle of vector-sum operation.This limit implies a larger group delay of half the signal pulse length according to τ g φ max ∕Bω, where Bω is the bandwidth of a transform-limited signal, in comparison with the maximal time delay offered by a maximum phase shift of 1 2 π in Ref. [12].For the tunability, the performance can be flexibly tuned through varying the amplitude ratio, achieving desirable amplification factor G. From the numerical analysis shown in Fig. 8(a), overall, the output phase responses are obviously enhanced compared with the response when A 2 ∕A 1 0, which indicates no phase amplification.Small phase shifts can be significantly amplified with a good response linearity.The increase in the amplitude ratio results in a magnified phase output, while the linearity of the phase amplification begins to degrade at a ratio of 0.6.For amplitude ratio above 0.6, although the phase response shows a saturation behavior when the input phase shift increases, it keeps a good linearity with an input less than 10°.From Fig. 8(b), the smaller phase input can obtain a larger G when applying the same amplitude ratio.
It is worth noting that this scheme also introduces inevitable signal loss for the synthesized RF signal, as partially destructive RF interference always occurs.As shown in Fig. 9, the absolute group delay increases to peak values when the amplitude ratio approaches 1, while the amplitude of the delayed RF pulse decreases to a minimum.This can be explained by considering that stronger destructive RF interference occurs when the amplitude ratio is close to 1.However, this signal cancellation can be avoided by operating in the region away from this critical point, and the reduced signal is easily compensated by using a conventional RF amplifier.Considering an attenuation of 10 dB in the peak power of the signal pulses for practical applications, the bounds of the operation region are A 2 ∕A 1 0.75 for negative signal delay and A 2 ∕A 1 1.25 for positive signal delay, respectively.
Due to the radical functionality separation of power control from the dispersion, this phase-amplification method provides a general method to manipulate MWP signal group delay, which is compatible with other types of delay lines based on dispersive optical resonances such as integrated Bragg gratings [18] or onchip SBS [33].Furthermore, this scheme has the potential to achieve separate carrier tuning [34] for true time delay [35] through additional control of the phase shifts of the two optical carriers.

CONCLUSION
In conclusion, this simple and versatile scheme paves the way to the realization of on-chip dynamically tunable photonic delay lines and the achievement of both MWP signal delay and advancement in a passive platform.This technique is promising for enhancing conventional microwave photonic delay lines with flexibility and rapid tunability (GHz) and radically relaxing the requirements of complex designs and power consumption for integrated MWP tunable delay lines.These features are beneficial for applications in RF signal processors, multi-tap RF filters, and phased array antennas.

Fig. 1 .
Fig. 1.Basic block diagrams of (a) a conventional MWP delay line and (b) a MWP delay line with phase amplification.O-E, optical-toelectronic conversion; E-O, electronic-to-optical conversion.

Fig. 2 .
Fig. 2. Schematic illustrations of the operational principle of (a) phase-amplification technique and (b) dispersion enhancement from an initial dispersion induced by an optical resonance.

Fig. 3 .
Fig. 3. (a) Schematic implementation of dispersion control based on the phase-response amplification, using dual-sideband phase modulation.(b) Simulation results of synthesized phase response with various amplitudes of the reference signal.The phase slope flips when the amplitude ratio changes from A 2 ∕A 1 < 1 to A 2 ∕A 1 > 1.

Fig. 4 .
Fig. 4. (a) Schematic of the experimental setup to confirm the working principle of the phase-amplification technique.PM, phase modulator; PD, photodetector; VNA, network analyzer.Qualitative optical spectra denoted by red points are shown above the setup diagram.(b) Experimental results of synthesized phase response with various amplitude ratios.Notably, the phase slope flips when the amplitude ratio changes from A 2 ∕A 1 < 1 to A 2 ∕A 1 > 1.

Fig. 5 .
Fig. 5. Schematic of the experimental setup to demonstrate tunable RF signal delay based on the phase-amplification technique.PM, phase modulator; PD, photodetector; LO, local oscillator.Qualitative optical spectra denoted by red points are shown above the setup diagram.

Fig. 6 .
Fig. 6.Experimental results of (a) pulse delay enhancement and (b) switching from negative delay to positive delay, along with corresponding spectra.

Fig. 7 .
Fig. 7. Measured oscilloscope signals for demonstration of rapid tuning.The gate signal drives the phase switching that is reflected by the converted voltage indicated by the synthesized signal.

Fig. 8 .
Fig. 8. Simulation results for the analysis of the phase-amplification capacity based on the schematic phasor representation in Fig. 2(a).(a) Synthesized phase response as a function of the phase input under different amplitude ratios A 2 ∕A 1 .(b) Amplification factor as a function of the amplitude ratio A 2 ∕A 1 under different phase inputs.

Fig. 9 .
Fig. 9. Simulation results for analysis of the RF signal loss and synthesized group delay as a function of amplitude ratio.Parameters used in the simulation are based on those used in experiments.

Table 1 .
Tuning Speed Comparison of Reported MWP Tuning Schemes