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Abstract
In this paper, we propose a microwave frequency measurement system that simultaneously achieves a large measurement range, high resolution, and linear frequency mapping in a compact configuration with a single laser and photodetector. The system is based on a novel dynamic microwave amplitude comparison function (ACF), which performs the power comparison in cascaded time intervals. The continuous movement of the dynamic ACF generates a series of steep and linear frequency-to-power mapping intervals, which can be seamlessly pieced together without sacrificing the frequency measurement range, thus breaking the trade-off between measurement resolution, linearity, and range. The proposed frequency measurement system is experimentally demonstrated by using an integrated silicon-on-insulator (SOI) microring resonator with an optical bandwidth of 1.8 GHz and outperforms current solutions by achieving a measurement resolution of over 80 dB/GHz throughout a frequency measurement range up to 20 GHz. Meanwhile, the highly linear system shows excellent accuracy where the average measurement error throughout the range is only 47.2 MHz, which is around 0.31% of the total measurement range.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave photonic (MWP) signal processing is a vibrant interdisciplinary field that bridges the realms of microwave and optical engineering [1–6]. Since the inception of radio-over-fiber links, the field of MWP signal processing has revolutionized the way signals are generated, transmitted, and received, pushing the speed and bandwidth boundaries of traditional telecommunications. Once regarded as a niche technology, MWP signal processing has now spurred substantial industrial interest as it evolves dramatically to drive numerous applications such as radar and electronic warfare [7–10], wireless communication [11], and cognitive radio systems [12]. In this context, photonic-assisted frequency measurement systems, which is one of the essential building blocks in microwave communication and sensing networks for identifying incoming microwave and millimeter-wave signals, have been widely explored as they demonstrate inherent advantages over conventional electronic techniques such as abundant frequency coverage and immunity against electromagnetic interference [13–17]. In particular, microwave photonic frequency measurement systems with measurement accuracy ranging from MHz to sub-GHz are actively pursued for broadband frequency sensing by a host of applications such as cognitive radio [12] and radar systems [17,18], due to their superior performance in high frequency bands ranging from tens of gigahertz to hundreds of gigahertz, which can hardly be achievable by its electronic counterparts. For example, direct frequency measurement via microwave channelization has been immensely investigated with the aid of photonic technologies such as optical filter banks [19–21] and frequency combs [21–25]. However, such configurations either require precise frequency positioning of a large number of optical filters or a comb source with highly stabilized optical power and wavelength, thus increasing the complexity of the system. Alternatively, frequency information can also be extracted indirectly from other measurable quantities such as time and power [26–36]. For example, in [36], frequency-to-time mapping has been demonstrated by a photonic-assisted Fourier transform system based on a frequency-shifted feedback loop. However, the usage of an Erbium-doped fiber amplifier (EDFA) and an acousto-optics frequency shifter increases the system's complexity for future chip-scale integration. In the schemes involving frequency-to-power mapping, the input frequency can be derived easily from an amplitude comparison function (ACF), which is constructed based on the microwave power ratio between two frequency-dependent power fading functions [7]. The ACF slope, which is typically defined in terms of dB/GHz for the frequency-to-power mapping system, stipulates the minimum input frequency variation that can be resolved. To acquire a high measurement resolution, it is desirable to have a steeper ACF slope. Commonly adopted structures for achieving this is to implement two complementary fading functions, which include the use of a dispersive delay element in conjunction with a variety of discrete devices such as polarization modulators [37–39], non-sliced broadband optical sources [40], polarizers [41,42], and dual-parallel or dual-drive Mach–Zehnder modulators [43,44]. However, the long dispersive delay lines employed in conventional structures render the system bulky and hard to be integrated. In [33,45,46], steep ACF slopes have been presented by constructing microwave photonic filters based on the stimulated Brillouin scattering (SBS) effect, which typically requires high optical power to initiate the nonlinear process and non-reciprocal devices to route counterpropagating signals, thus increasing the integration complexity. These configurations also require a frequency-scanning RF signal generator for generating reference signals, which limits the real-time bandwidth and frequency coverage of the system. Recently, optical filters fabricated on silicon photonic platforms such as microring resonators (MRRs), microdisk resonators (MDRs), and waveguide Bragg gratings have drawn great interest to provide a compact and CMOS-compatible approach [32,47–50], where the conventional microwave power fading functions are replaced with microwave notch filters based on the optical-to-microwave mapping. In [32], the microwave ACF is constructed by comparing the transmission and reflection RF outputs of a waveguide Bragg grating. However, the obtained ACF has limited linearity and steepness, which leads to a measurement error around hundreds of MHz. Approaches using a pair of optical resonators or optical carriers to create two microwave notch filters with different center frequencies based on direct optical-to-microwave mapping have also been proposed, where the microwave ACF is achieved by comparing the output electrical powers of the two filters with offset frequencies [48–50]. To acquire a substantial amount of ACF variation, an optical response with a high extinction ratio is required to produce a proportionately high rejection ratio in the microwave domain. Although current development in nano-fabrication allows the realization of optical resonators with high quality factors in the order of 106 [51], precise control of the coupling strength is still essential for the devices, which imposes stringent fabrication requirements. Furthermore, as the formation of the microwave ACF relies on the power difference and relative location of the two microwave photonic notch filters, a fundamental trade-off between measurement range and resolution is always present. In [48], a measurement range of 10 GHz produces a flat ACF transition of around 8 dB/GHz resulting in a measurement accuracy of only ±200 MHz. On the other hand, a steeper transition of the ACF slope of 65 dB/GHz produces a maximum error lower than 31 MHz but imposes constraints on the measurement range to within 1 GHz [49]. Additionally, due to the intrinsic resonance property of the resonators, signals approaching the resonance dips of the notch filters tend to experience an increasingly fast ACF variation. This compromises the linearity of the ACF obtained. Whilst the ACF slope dictates the resolution, the linearity of the ACF addresses the accuracy of the estimated frequency, a parameter that is rarely considered. In fact, current approaches rely on tuning the relative frequency difference between the two notches in order to extend the measurement range [48–50], which worsens the ACF linearity and renders a nonuniform accuracy throughout the measurement range.
In this paper, we present a novel concept for implementing a compact microwave frequency measurement system with a single laser and photodetector. The proposed method is based on a novel dynamic frequency-to-power mapping concept, where an ACF with a consistently high steepness and linearity is swept over time, hence successfully widening the frequency measurement range without compromising either the ACF frequency resolution or the linearity. This is performed by continuously tuning the relative frequency difference between the optical carrier and optical resonance with a sweeping laser source, where microwave notch filters at different center frequencies can be obtained at successive time intervals. By performing the power comparison in cascaded time intervals, the continuous movement of the dynamic ACF curve centered at distinct RF frequency bands can be seamlessly pieced together without sacrificing the frequency measurement range, thus breaking the trade-off between measurement resolution, linearity, and range. We demonstrate experimentally a frequency measurement system based on an integrated silicon-on-insulator (SOI) microring resonator with an optical bandwidth of 1.8 GHz. The system outperforms state-of-the-art resonator-based demonstrations by exhibiting an ACF frequency slope of over 80 dB/GHz throughout a frequency measurement range from 5 GHz to 20 GHz while the average measurement error is about 47.2 MHz, which is only around 0.31% of the total measurement range.
2. Operational principle
The main concept for frequency-to-power mapping is to construct a unique ACF as a function of input frequency for frequency estimation, which is independent of the input optical and microwave powers. Conventionally, this is done by subtracting the output electrical powers of two parallel microwave notch filters with different center frequencies [13]. In our work, a simplified implementation is realized by utilizing a frequency-swept microwave photonic notch filter to mimic a large number of frequency-to-power processing subsystems occurring in parallel along the time axis. Figure 1 illustrates the schematic diagram and the operational principle of our proposed photonic-assisted microwave frequency measurement system, which consists of a wavelength-swept laser, a dual-drive Mach-Zehnder modulator (DDMZM), an optical notch filter based on an MRR, a photodetector, and a radiofrequency (RF) sensor.
Fig. 1. Schematic and principle of the proposed microwave frequency measurement system. DDMZM: dual-drive Mach-Zehnder modulator; PD:photodetector; RF PS:RF power sensor; DSP:digital signal processing. Point A: Modulated signal swept in the optical domain; Point B: Microwave notch filters at different time intervals; Point C: Time-varying microwave power variance recorded by an RF power sensor; Point D: Parallel ACFs centered at distinct RF frequencies.
The DDMZM modulates the unknown input RF signal onto the optical carrier, hence generating two sidebands where the RF spectral information is directly mapped onto the optical domain. When the optical carrier frequency changes with a constant sweeping rate, the modulated RF signal is also shifted at the same sweeping rate. Hence, additional synchronization between the sweeping rates of the optical carrier and the RF signal is not needed. Assuming the laser emits a lightwave at an angular frequency ${w_0}(\tau )$ which varies along with time, and the DDMZM is driven by the input microwave signal at ${w_{RF}}$, via an electrical hybrid coupler under small signal condition, the field at the output of DDMZM can be described as
The modulated signal is then sent to an optical notch filter based on an SOI MRR with its resonance fixed at ${w_{MRR}}$. In our proposed scheme, the carrier is swept at a fixed sweeping speed and maintains a sweeping range within the left-hand side of the optical notch, as depicted in Fig. 1 (Point A). Here, given a fixed sweeping speed, the sweeping point for a laser source can be denoted as an integer n, where $n = 1,2,3\ldots N$, and N is the total sweeping number in a sweeping cycle. Meanwhile, $f$ and T represent the constant frequency and time intervals between two successive sweeping points, respectively. The unsuppressed USB, which falls within the stopband of the filter, is then attenuated according to the optical notch spectrum. At time instance $nT$, this produces a mapped microwave notch response centered at ${w_{MRR}} - {w_0}(nT)$ at the output of the photodetector. Hence, simply by tuning the relative frequency difference between the optical carrier and optical resonance of the MRR, microwave notch filters at different center frequencies can be obtained at different time intervals. For example, as shown in Fig. 1 (Point B), at instances $nT$ and $(n + 1)T$, the scanning laser source produces a microwave notch filter centered at $nf$ and $(n + 1)f$, respectively.
Depending on the relative frequency difference between the notch dip and the input RF frequency, the signal will experience a specific amount of attenuation at each time instance. This time-varying microwave power variance can be recorded by an RF power sensor as shown in Fig. 1 (Point C). Given ${w_0}(nT) = {w_{MRR}} - nf$, the instantaneous output microwave power at time $nT$ after beating at the photodetector, is proportional to the square of the photocurrent and can be approximated as
$P(nT)$ describes the RF power sensor readout at time $nT$, which represents the remaining power of the input signal after being attenuated by the frequency-swept microwave notch filter. If the unknown microwave frequency is in the vicinity of $nf$, it experiences the largest attenuation at time $nT$. Therefore, by examining the power minimum in the time domain, we can conduct an estimation of the frequency of the input signals. More importantly, the RF power sensor readout at time $nT$ and $(n + 1)T$ are exactly equal to the output electrical powers of the microwave filters centered at $nf$ and $(n + 1)f$. Therefore, by comparing the detected power at time $nT$ and $(n + 1)T$, the ACF can be expressed as
The final ACF, as shown in Fig. 1 (Point D) is thus a function which only depends on the frequency of the input RF signal. By comparing the detected power at two successive time intervals, the effect of the unexpected input laser power fluctuations on the frequency measurement is eliminated. Hence, an accurate measurement estimation can be achieved by utilizing this ACF for frequency-to-power mapping. There are three parameters influencing the construction of the ACF. The first factor contributing to the ACF is the parameter a, which represents the sideband suppression ratio achieved by the DDMZM, and the second is governed by the transmission and phase characteristics of the MRR employed in the system, denoted as ${H_f}$ and ${\varphi _f}$, respectively. Those two parameters jointly determine the spectrum of the frequency-swept microwave photonic notch filter. Thanks to the introduction of the DDMZM, the amplitudes of the two sidebands can be equally matched at the transmission dip of the microring notch filter, which ensures a frequency-swept microwave notch filter with an extremely high rejection ratio throughout the laser sweeping range [52]. This allows us to alleviate the dependence on the optical filter response and achieve a large ACF variation even with poor rejection optical notches. The third parameter affecting the construction of the ACF is the location of the wavelength-swept optical carrier, as determined by $nf$ and $(n + 1)f$. First, this parameter defines the linearity of the monotonic region of the ACF where the frequency-to-power mapping can be implemented. Specifically, ACF based on the power ratio between time $nT$ and $(n + 1)T$ corresponds to a mapping region between $nf$ and $(n + 1)f$ in the microwave domain. By eliminating the nonlinear transition region and enhancing the complementary parts of the two notch responses, the sweeping step allows us to engineer each ACF curve within the corresponding frequency window. Note that while the sweeping step dictates the slope as well as the linearity of the ACF curve in a narrowband, the overall measurement range is much wider than that of the conventional system as it can be continuously extended by piecing together segments of individually derived ACF curves which are obtained along with the sweeping range of the optical carrier wavelength, as shown in Fig. 1 (Point D). For example, if the laser frequency is swept over $N$ points, then there will be $N - 1$ parallel ACFs centered at distinct RF frequencies up to $Nf$. As opposed to conventional frequency-to-power mapping systems, which require $N$ parallel subsystems to perform the same functionality, the proposed system with a single wavelength-swept laser, a photodetector, and an RF power sensor allows us to establish a high-order ACF which is equivalent to a bank of microwave ACFs without the need for complicated and bulky setups with multiple laser sources and photodetectors. Furthermore, the proposed method establishes a dynamic frequency-to-power mapping system that always guarantees a steep and linear ACF to maintain a high measurement accuracy and linearity without sacrificing the measurement range.
3. Simulation and discussion
To investigate the aforementioned influencing parameters on the formation of our dynamic ACF, the microwave notch filter is first simulated based on a fabricated all-pass MRR, which was patterned using electron beam lithography technology on an SOI wafer, consisting of a 220 nm top silicon layer and a 2 µm buried oxide layer. The scanning electron microscope (SEM) image of the fabricated MRR is shown in the inset of Fig. 2(a), which is composed of a straight bus waveguide and a racetrack waveguide with a fixed width of 450 nm. Figure 2(a) shows the simulated and measured amplitude responses of the MRR-based optical notch filter, where the measurement was conducted by a high-resolution optical vector network analyzer (Lunar 5000). It can be seen that the resonance at 1559.84 nm exhibits a moderate extinction ratio of 14 dB and a 3dB-bandwidth of 1.8 GHz. The corresponding quality factor, which is defined as the ratio of the resonance frequency to filter bandwidth, is around 0.1×106.
Fig. 2. (a) Measured (solid line) and simulated (dashed line) spectral responses of the MRR. Inset: SEM image of the fabricated device. (b) Optical LSB suppression ratio (blue line) and rejection ratio (red line) for the MRR-based microwave notch filter at different bias voltages. Inset: RF filter response with unequal sideband suppression. (c) Rejection ratio and bandwidth deviation percentage for an MRR-based microwave notch filter at different bias voltages.
The LSB suppression ratio ($10\log a$) of the DDMZM modulated signal and the corresponding attainable rejection ratio for the MRR-based microwave photonic notch filter are plotted in Fig. 2(b). It is seen that when the bias voltage, ${V_{DC}}$, is between the half-wave voltage of the modulator ${V_\pi }$ and $1.5{V_\pi }$, LSB is suppressed with respect to the USB. When the bias voltage is equal to the half-wave voltage, the DDMZM operates optimally as an optical single sideband (OSSB) modulator ($a = 0$). Hence, the optical spectrum of the MRR is perfectly mapped to the microwave domain, leading to a microwave photonic notch filter with the same rejection ratio of 14 dB. Evidently, given a fixed measurement range, the obtained ACF frequency resolution is limited by the extinction ratio of the MRR. Whilst improving the extinction ratio in the optical domain requires an extremely precise fabricated MRR under critically coupling, an RF notch with a much higher extinction ratio can be easily generated with the flexible control of the sideband suppression ratio by adopting the DDMZM [52]. By increasing the bias voltage from ${V_\pi }$ to $1.5{V_\pi }$, the LSB suppression ratio gradually reduces where zero suppression occurs at $1.5{V_\pi }$. As depicted in Fig. 2(b), when ${V_{DC}}$ is chosen between $1.11{V_\pi }$ and $1.16{V_\pi }$, it leads to a high rejection ratio of over 30 dB for the microwave filter based on the MRR. To investigate the effect of DC bias drift on the frequency measurement performance, Fig. 2(c) illustrates the relative rejection ratio and 3dB bandwidth variance at different DC bias drifts. Here, the relative deviation is defined as the deviation percentage per 1‰ bias drift. The blue dashed region shows the target range for a relative rejection ratio deviation of less than ±1%. By properly selecting the bias voltage point to operate within this region, the impact of the bias drift on the response of the microwave filter can be minimized. In our experiment, the bias voltage, as denoted by the green dashed line in Fig. 2(c), is chosen as $1.16{V_\pi }$, where a small relative deviation to bias drift and a high rejection ratio of around 30 dB can be obtained, simultaneously. Additionally, the stability of the modulator is expected to be further improved by introducing an additional feedback control circuit, thus locking the device at the desired voltage point [53,54]. The inset of Fig. 2(b) shows the frequency response of the generated microwave filter at ${V_{DC}} = 1.16{V_\pi }$. The corresponding ACF is also simulated and shown in Fig. 3. The solid blue lines in Fig. 3(a) and (b) show a vast improvement as compared to the ACF curves obtained without sideband manipulation, as drawn in black dashed lines.
Fig. 3. Simulated microwave ACFs based on RF filter with rejection ratio of 30 dB (solid lines) and 14 dB (dashed lines) when the sweeping step is (a) 1 GHz (b) 5 GHz. (c) ACF frequency resolution (blue lines) and linearity (red lines) based on RF filter with rejection ratios of 30 dB (solid lines) and 14 dB (dashed lines).
Another critical parameter affecting the construction of the ACF is the sweeping interval of the optical carrier, as determined by the parameter f. Figure 3(a) and (b) show the simulated microwave ACFs with different sweeping step of 1 GHz and 5 GHz while $nf$ is fixed at 10 GHz. As can be seen in Fig. 3(a) and (b), the mapping relationship between the microwave frequency and the ACF is unique and monotonically increasing within the sweeping step. When a large sweeping step is chosen, the ACF shows poor linearity where the middle region is relatively flat compared to the edges of the frequency band due to the sharp transition at the resonant frequency of the MRR. This results in a deformation of the ACF curve, which restricts the resolution of the microwave measurement system considerably. Conversely, a narrow sweeping step enhances the slow transition region of the two microwave notch filters, thus yielding a more linear and steeper ACF, which are both beneficial for achieving high measurement resolution and accuracy. Figure 3(c) illustrates the ACF frequency resolution and linearity as a function of the laser sweeping step in the proposed system with the sideband suppression ratio tuned to achieve an RF rejection ratio of 30 dB. As a comparison, the ACF resolution and linearity for a microwave notch filter using an MRR with an identical optical rejection ratio of 14 dB but in a conventional OSSB configuration, are also plotted in dashed lines. As can be seen, the manipulation of the sideband suppression ratio in the DDMZM configuration offers a significant enhancement in the ACF frequency resolution of up to 6-fold higher than that in the OSSB configuration. In both configurations, the ACF frequency resolution, as well as the linearity, degrade significantly with the increase in sweeping step.
In our proposed scheme, the scanning laser produces a series of adjacent microwave notch filters and generates a sequence of narrowband ACFs at different frequency bands which is swept along with time. Given that commercially available wavelength-sweeping laser sources can easily achieve a tunable range of about hundreds of gigahertz, the novel system allows us to independently manipulate the ACF curve while the measurement range is not affected by the sweeping step. Hence, the trade-off between measurement range and ACF resolution can be eliminated simply by reducing the sweeping step of the laser, thus accomplishing a frequency measurement system with high resolution, high linearity and wide range, simultaneously. As an example, a sweeping step of 0.5 GHz ensures a linearity over 99% and ACF frequency resolution of over 85 dB/GHz. Moreover, the measurement range of the proposed system is not constrained by the RF filter response and is only determined by the operating bandwidth of the devices employed in the system, which includes a modulator, photodetector, and RF power sensor. Currently, all of these devices with an operating bandwidth of a hundred gigahertz and beyond are commercially available, which provides greater capacity to further broaden the overall frequency measurement range of the proposed system [55,56].
To investigate the effects of different MRR spectral characteristics, the quality factor of the optical resonator is varied from 0.1×106 to 0.8×106 by altering the propagation loss of the SOI waveguides. With the geometric parameters of the device unchanged, the sideband suppression ratio was adjusted to maintain an RF notch filter with a rejection ratio of 30 dB. Figure 4(a) and (b) illustrate the simulated ACF frequency resolution and linearity for the different quality factors, when the laser sweeping step is varied up to 1 GHz. As predicted in Eq. (3), the characteristics of the ACF curve are dependent on the transmission response of the MRR. It can be seen that increasing the quality factor by 8 times only result in an increase in the peak ACF resolution by a factor of around 1.7, while the linearity is still maintained over 90%. This demonstrates the proposed technique eases the quality factor requirement of MRR, and can tailor the ACF curve according to the desired characteristics for various quality factors via proper manipulation of the laser and DDMZM.
Fig. 4. (a) ACF frequency resolution and (b) linearity when an MRR with different quality factors is used.
4. Experiment results
A proof-of-concept experiment for the proposed microwave frequency measurement system has been performed according to the schematics in Fig. 1. To obtain the microwave ACF for frequency-to-power mapping, a frequency-swept RF signal generated by a vector network analyzer (Keysight N5230A) is first applied to the DDMZM (Sumitomo). The RF signal from the vector network analyzer (VNA) is set to have a constant power of 5 dBm. The DDMZM with a half-wave voltage of 5 V is used to generate an unequal optical double-sideband signal. The bias voltage is set to be 5.3 V to achieve a rejection ratio of 30 dB. The modulated signal is then launched into the MRR, whose resonance is centered at 1559.84 nm as presented in the previous section, and finally sent to the photodetector. Upon photodetection, the output signal is transmitted back to the VNA to capture the spectrum of the microwave notch filters.
Figure 5(a) illustrate the measured RF spectra obtained by sweeping the tunable laser (Keysight 81960) at a constant frequency step of 0.5 GHz where the curves of different colors show the progression of the microwave notch filter locations as the relative frequency spacing between the optical carrier frequency and the center of the optical notch is varied. By increasing the laser wavelength with respect to a fixed optical notch filter, the center frequency of the microwave notch filter increases accordingly. As compared to the optical notch depth with an extinction ratio of 14 dB, the RF notch rejection is enhanced expectedly with a simple adjustment of the DC bias voltage. Noticeably, the RF notch rejection ratio shows an increasing trend with the increase of notch filter frequency. This discrepancy mainly arises from the frequency-dependent roll-offs of the modulator and photodetector, where the additional magnitude and phase of the modulation/demodulation affects the power and phase matching between the two modulation sidebands, thus affecting the cancellation of the RF beatings. Meanwhile, by comparing the two successive microwave spectra occurring at neighboring time intervals, we are able to obtain a dynamic ACF swept along with time. The curves of different colors plotted in Fig. 5(b) represent the obtained ACF at a different time interval, where each of them covers an effective mapping frequency band of 0.5 GHz. As can be seen, the mapping relationship between the microwave frequency and the ACF within each sweeping step is quite linear and monotonically increasing. The drift effects of the microwave notch center frequency is found to be negligible throughout the experiment. This is because the movement of the ACF across the frequencies is achieved by continuously sweeping the laser wavelength while stabilizing the resonance frequency of the MRR via an external thermoelectric temperature controller (Newport 325) with thermal stability of ±0.005° [57]. Since the MRR resonance variations due to environmental perturbations is a relatively slow process as compared to the laser scanning speed, measurement ambiguity induced by overlapping in the successive ACF frequency sub-bands is negligible. For longer periods of measurement, the temperature drift can be further reduced via employing commercial temperature controllers with higher thermal stability [57]. Meanwhile, calibration via an auxiliary frequency feedback system can be utilised to lock the measurement range [58]. The ACF frequency resolution and the linearity of the ACFs are also plotted in Fig. 5(c) and Fig. 5(d), respectively. Here, the ACF resolution is calculated in dB/GHz to evaluate the measurement resolution of the proposed frequency-to-power mapping system, where a higher ACF resolution is desired for distinguishing small input frequency variation. The measured ACF frequency resolutions for frequency bands between 5 GHz and 8.5 GHz are seen to be around 80 dB/GHz, which agrees well with the simulation. Given the specification of the employed RF power sensor, the measured ACF resolution in dB/GHz can be converted to frequency resolution in MHz. Considering that an RF power sensor with a power measurement resolution of 0.15 dB used in the experiment, the frequency resolution can be as high as 1.875 MHz [59]. At the same time, the R-squared (R2) linear coefficients within the frequency bands are almost unity, showing a highly linear ACF curve. For RF frequency bands over 8.5 GHz, although there is a slight decrease in the linearity of the ACF due to the corresponding increase in rejection ratio of the microwave notch filters, the measured ACF curve remains highly linear, showing an R2 value well kept above 0.95. It should be mentioned that the small discrepancy between the measured and simulated spectra of the microwave notch filter has a negligible effect on the frequency estimation since the frequency-to-power mapping is conducted based on the measured ACF, which includes the characteristics of all components in the system. Additionally, the proposed system exhibits an ACF frequency resolution over 80 dB/GHz and an R2 linear coefficient over 95% throughout the 15 GHz frequency range investigated, which supersedes the performance of previous works based on optical resonators.
Fig. 5. (a) Measured microwave responses and (b) ACF when the laser wavelength is tuned away from the optical notch filter. (c) Frequency resolution and (d) linearity for ACF centered at different microwave frequencies.
Next, to verify the accuracy of the proposed frequency measurement system, a microwave signal at 10.1 GHz is generated by a VNA and is applied to the DDMZM while an RF power sensor (Rohde & Schwarz, Z81) with a measurement range from -60 dBm to +20 dBm is used to record the instantaneous microwave power at the output of the photodetector [59]. To ensure a one-to-one mapping between the sweeping time and frequency, the laser wavelength is swept at a fixed sweeping speed of 0.5 nm/s and a synchronization trigger signal is sent from the laser source to the RF power sensor. Meanwhile, the optical power coupled into the vertical fiber-to-chip grating coupler is set at 6 dBm to minimize the optical nonlinear effect such as the two photons absorption and Kerr effect, thus ensuring a consistent filter response throughout the measurement. The time-varying RF powers of the photodetector output are recorded by the RF power sensor as illustrated in Fig. 6(a). The overall time span shown in the figure represents a single sweeping cycle, which covers a measurement frequency range from 5 GHz to 20 GHz. As can be seen from the shaded region which covers the time span between 72 ms and 80 ms where the lowest and second-lowest attenuations occur, respectively, for the input signal at 10.1 GHz, indicating that the signal is located within the frequency band between 10 GHz and 10.5 GHz, considering the sweeping speed is 0.5 nm/s. To perform frequency-to-power mapping, the power difference at these two points which corresponds to the bounded region, ΔP, is calculated. The blue dashed line in Fig. 6(b) shows the pre-calculated ACF measurement, which displays a linear and monotonically increasing ACF within the specified frequency range. Based on this relationship, the frequency of the input signal is successfully derived.
Fig. 6. (a) Output waveform of the RF power sensor when input signal is at 10.1 GHz. (b) Estimated frequency versus measured power ratios. (c) Histogram of the measurement error.
Changes in operating conditions over time such as modulator bias voltage drifts, fluctuations in the laser wavelength, and environmental induced filter variations are typical factors that could affect the accuracy and stability of the frequency measurement system performance. In the experiment, an optimum bias point was selected to minimise the deviation to bias drift while optimizing the rejection ratio to ensure small deviations of the ACF from its ideal curve notwithstanding changes in bias voltage. Alternatively, additional feedback control circuit could be introduced to stabilize the modulator. Meanwhile, the fast-scanning nature of the dynamic ACF allows the proposed system to negate the relatively slow effects of environmental perturbations, thus making the scheme intrinsically insensitive to filter resonance variations and modulator bias drift. To evaluate the repeatability of the proposed system, the frequency of the input signal from VNA is increased from 10 GHz to 10.4 GHz with a constant step of 0.1 GHz, where each frequency is measured 50 times repeatedly over a period of less than 2 minutes. The 250 measurement results exhibit excellent repeatability with a mean absolute error of 24.2 MHz and a standard deviation of 12.4 MHz. The measurement error distribution detuned from the mean absolute error is shown in Fig. 6(c). It can be clearly seen that the proposed system demonstrates a highly accurate frequency measurement where over 90% of the measurement errors stay within ±40 MHz.
The measurement range is then extended by enlarging the laser sweeping range. In the experiment, the laser is swept from 1559.8 nm to 1559.68 nm, which corresponds to a frequency range from 5 GHz to 20 GHz. It should be mentioned that the frequency range in the experiment is mainly limited by the operating bandwidth of the RF power sensor and can be easily extended as commercial power sensors can achieve a broad operating range up to 120 GHz [56]. Moreover, electro-optic modulators and photodetectors with a bandwidth over a hundred GHz are also presently available, which can further enhance the capability of the proposed system to cover a wide range of frequencies [60,61]. In the experiment, the measurement speed of the presented prototype is mainly determined by the scanning speed of the wavelength-swept laser. The response speed of the proposed system can be further improved via adopting a high-speed modulator and photodetector in conjunction with a laser or an MRR with fast wavelength tunability, thus enabling the detection of frequency-agile signals. Integrated lasers with fast wavelength sweeping speed [62], and detector logarithmic video amplifiers with nanosecond response time for RF power sensing [63,64] have been reported, which makes the proposed system a potential solution to rapidly detect fast-changing incoming signals. Meanwhile, current developments in integrated photonics have demonstrated devices displaying fast response time based on various tuning mechanisms such as Pockels effect and carrier injection effects, which can significantly reduce the time required to scan the entire frequency range to nanosecond scale [65–67]. It is noted that the proposed system is capable of detecting multi-tone frequency signals. The use of the dynamic ACF allows the measured microwave power at the RF power sensor to contain both time and power information. Hence, each individual frequency component can be mapped to the minima of the RF power sensor readout at specific time intervals when the center frequency of the generated RF notch filters is swept in the time domain. Similar to the frequency-to-power mapping of a single-tone signal as depicted in Fig. 6, the time and power information of the measured microwave power at the RF power sensor can be used to extract multi-tone frequency signals over a wide frequency range with a well-calibrated ACF curve.
Figure 7 shows the comparison between the input and the measured frequency. The inset of Fig. 7 shows the frequency difference between measurement and the theoretical result while the average frequency difference is plotted by a dashed line. As can be seen, the proposed system exhibits a highly precise frequency estimation. The relative measurement error remains less than 1% throughout the frequency range while the average measurement error is about 47.2 MHz. The errors are mainly attributed to the relatively high RF loss caused by high fiber-to-chip coupling loss of the employed MRR filter, which arises from its fiber-to-chip coupling interface. In our experiment, a pair of vertical grating couplers are utilized for coupling light between the standard single-mode fibers and the MRR, which results in a total coupling loss of around 15 dB. This relatively high optical loss reduces the signal-to-noise ratio and leads to a negative RF gain of around -20 dB after optoelectronic conversion. The key aspect of the proposed frequency measurement system is to set up a dynamic microwave ACF for frequency-to-power mapping by creating a frequency-swept microwave photonic notch filter using one optical notch filter based on a compact MRR. The dynamic range and minimum detectable RF power are determined by the RF gain of the microwave photonic system, which is defined as the ratio of the output and input powers of the RF signal, and the power measurement range of the RF power sensor employed in the system. Under this limit, the minimum detectable RF power is predicted to be around -40 dBm. However, the RF gain of the proposed system can be improved by increasing the signal strength in both optical and RF domains, thus facilitating a substantial improvement in the measurement accuracy while extending the dynamic range of the system to enable the identification of signals at lower levels of received power. In the optical domain, the signal can be improved by combating the dominant optical loss source in the experiment, which is the fiber-to-chip coupling of the employed microring filter. This coupling loss can be reduced to less than 1 dB by adopting state-of-the-art coupler designs [68]. Additionally, the optical signal level can also be boosted by using high-power laser sources and optical amplifiers with low noise figures. In the RF domain, RF amplification can be realized with the aid of low-noise RF amplifiers to increase the strength of weak incoming RF signals. Recently, on-chip modulators with built-in CMOS driver circuits have been used for high-efficiency, low-power electro-optic conversion, offering an integrated solution to further reduce the RF loss [65].
Fig. 7. Estimated frequency over a frequency range from 5 GHz to 20 GHz. Inset: Frequency difference between measurement and theoretical result as a function of input RF frequency, where the average frequency difference of 47.2 MHz is plotted by a dashed line.
To put this paper in context with the prior work on frequency measurement systems based on microwave ACF, Table 1 compares several key performance parameters of the systems such as ACF frequency resolution, measurement range, and measurement error. Considering that other methods, including techniques based on dispersive element and optical nonlinearity [37–46], have been reviewed in the introduction section, the table is limited to the silicon-based approaches where optical filters are employed for constructing microwave ACF to align with the main focus of the paper. With the use of a dynamic ACF, the proposed system exhibits an outperforming ACF frequency slope over 80dB/GHz throughout a frequency measurement range up to 20GHz while the average measurement error is only about 47.2MHz, which offers a viable solution to achieve on-chip frequency measurement system with improved measurement range, resolution, and linearity at the same time.
Table 1. Performance comparison of microwave measurement systems based on RF ACF ratio
5. Conclusion
In conclusion, we have presented a novel dynamic frequency-to-power mapping based on a frequency-swept microwave notch filter. By creating a unique and dynamic ACF which compares the microwave power between the detected power at different time intervals, the proposed frequency measurement system effectively creates a bank of parallel and independent ACFs in a simple and compact configuration system using only a single laser source and photodetector. By engineering a steep and linear dynamic ACF curve via the laser sweeping step, the proposed system features a high ACF frequency resolution and a high measurement accuracy without sacrificing the frequency measurement range. The system experimentally demonstrated exceptional performances with a measured ACF frequency resolution of over 80 dB/GHz throughout a frequency measurement range up to 20 GHz. Whilst an off-chip wavelength-sweeping laser was used in this work to demonstrate the proof-of-concept experiment, the prospect of using an on-chip scanning laser source or a fast tunable MRR together with a fixed laser source opens up a new avenue of possibilities for implementing an all-integrated frequency measurement system. Current developments in nano-fabrication have already demonstrated CMOS-compatible and fast tunable MRRs as well as laser sources [63]. It is believed the reported novel technology will find wide applications in civilian as well as defense systems.
Funding
Department of Defence, Australian Government (Research Contract); Australian Research Council (Discovery Project).
Acknowledgments
The authors would like to acknowledge valuable discussions with Xiaoyi Tian from the University of Sydney.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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