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Abstract
A photonic-assisted microwave frequency measurement (MFM) method based on optical heterodyne detection is proposed and experimentally demonstrated. In the proposed MFM system, a linearly chirped optical waveform (LCOW) from a three-electrode distributed Bragg reflector laser diode (DBR-LD) and a multi-wavelength signal from a Mach-Zehnder modulator (MZM), where the signal under test (SUT) is modulated on an optical carrier from a distributed feedback laser diode (DFB-LD), are heterodyne detected by the photodetector (PD). A bandpass filter then filters the detected signal, and the envelope is detected by an oscilloscope. Then, frequency-to-time mapping is realized, and the signal frequency is measured. Thanks to the fast tuning rate and large tuning range of the DBR-LD, the proposed MFM system has a high measurement speed and a broad instantaneous measurement bandwidth. In the experimental demonstration, a measurement error below 39.1 MHz is achieved at an instantaneous bandwidth of 20 GHz and a measurement speed of 1.12 GHz/µs. The MFM of a frequency-hopping signal is also experimentally demonstrated. The successful demonstration of the MFM system with a simple structure provides a new optical solution for realizing broadband and fast microwave frequency measurements.
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1. Introduction
Microwave frequency measurement (MFM) technology is crucial in numerous fields, such as communications and radars [1,2]. With the growing complexity of the electronic environment, MFM technologies with broad bandwidth, high precision, high measurement speed, and small size are becoming increasingly important. However, traditional electrical MFM schemes are still challenged regarding measurement bandwidth, precision, and speed due to bottleneck restrictions in analog-to-digital conversion rates and instantaneous electronic bandwidth [3]. One solution that has been proven to be effective is the introduction of photonics with the advantages of broad bandwidth, fast response, and resistance to electromagnetic interference in the MFM system. Several photonic-assisted MFM methods have been proposed and verified in the past decade [4–32].In general, photonic-assisted MFM approaches can be categorized into three types: frequency-to-power mapping (FTPM) [4–14], frequency-to-space mapping (FTSM) [15–19], and frequency-to-time mapping (FTTM) [20–33].
The FTPM technique obtains a specific response relationship between the frequency of the signal under test (SUT) and the output power through a dispersive element [4–6], an optical mixing unit [7–9], or an optical filter [10–14]. Generally, an amplitude comparison function (ACF) is used to relate the SUT frequency and the output power. The FTPM method has an impressive measurement speed but faces difficulties and challenges in measuring multi-frequency signals. It should also be noted that the limited power range and slope of the ACF curve create a trade-off between measurement range and accuracy in the FTPM method. The measurement accuracy of this method is usually only in the order of a hundred megahertz.
The FTSM technique is usually realized using optical channelizers, such as Fabry-Perot etalon [15,16], arrayed waveguide grating [17], and diffraction grating [18,19]. Critical components, such as optical filter banks with continuous passbands, optical frequency combs, Fabry-Perot filters with different free spectral ranges, and photodetector (PD) arrays, required in FTSM-based systems need to be specially designed. Consequently, implementing an FTSM-based system is normally more complicated than implementing an FTPM-based one. Meanwhile, the sizeable optical channel spacing results in undesirable frequency measurement accuracy and resolution.
The FTTM method has received widespread attention in recent years because of its relatively simple system structure and capability of multi-frequency measurement. Usually, the FTTM can be performed by dispersion effect [20,21], frequency shifting recirculating delay line [22,23], optical filter passband scanning [24–27], and optical-domain frequency scanning [28–33]. The FTTM based on the dispersion effect provides improved measurement speed but suffers from insufficient frequency measurement resolution, typically on the order of gigahertz [21]. The frequency-shifting recirculating delay line approach can achieve 250-MHz frequency resolution at the expense of real-time performance and the necessity for a complicated system architecture [22,23]. The FTTM based on optical filter passband scanning typically utilizes high-Q micro-ring resonators (MRR) [24,25] or the Stimulated Brillouin Scattering (SBS) effect [26,27] to obtain a narrowband filter response. This approach offers a low measurement error but comes at the cost of increased system complexity and expense. For FTTM based on optical-domain frequency scanning, the frequency under test at which the light source or optical sideband sweeps across correlates to the temporal position of the output electrical signal. FTTM solutions based on Fourier domain mode-locked lasers can deliver a frequency range of 20 GHz, yet the accuracy is in the order of a hundred megahertz [28]. The FTTM scheme based on optical sideband scanning exhibits superior resolution and accuracy compared to previous methods [29–33]. Still, it faces a limited instantaneous measurement bandwidth due to the small laser continuing scanning range.
In this work, we propose and experimentally demonstrate an MFM approach with a simple structure and an extensive instantaneous measurement bandwidth based on optical heterodyne detection. In the proposed MFM system, the optical carrier from a distributed feedback laser diode (DFB-LD) is modulated by the SUT at an intensity modulator, generating an optical carrier and ±1st-order sidebands. Then, a linearly chirped optical waveform (LCOW) generated from a three-electrode distributed Bragg reflector laser diode (DBR-LD) sweeping through the optical carrier, and the +1st- or -1st-order optical sideband is combined with the modulated signal and sent to a PD for optical heterodyne detection. The detected electrical signal from the PD is then selected by an electrical bandpass filter (BPF) for intermediate-frequency (IF) filtering. Along with subsequent time-domain signal acquisition and envelope detection, the FTTM relationship is established based on optical heterodyne detection, and MFM is realized. Thanks to the rapid sweeping speed and large bandwidth of the DBR-LD [34–37], the proposed optical heterodyne detection-based MFM has a high measurement speed and large instantaneous measurement bandwidth. An instantaneous bandwidth of 20 GHz with a measurement root-mean-square (RMS) error of 39.1 MHz at a 1.12-GHz/µs measurement speed is experimentally demonstrated. Higher instantaneous bandwidth can be achieved using optoelectronic devices with large bandwidths, such as intensity modulators and PDs.
2. Principle
The schematic diagram illustrating the proposed MFM scheme is presented in Fig. 1(a). A control current is injected into the phase section of the three-electrode DBR-LD to generate the LCOW at point A, whose frequency sweeps from fstart to fend, shown in Fig. 1(b). The DBR-LD output light field can be written as,
where Es is the amplitude of the LCOW, T is the duration of positive chirp, and γ=(fend-fstart)/T is the chirp rate. The DFB-LD supplies the optical signal with a stabilized frequency fc, slightly lower than fend, ensuring it remains within the scanning range of LCOW. The optical signal from the DFB-LD is expressed as, where Ec is the amplitude of the optical carrier. The Mach-Zehnder modulator (MZM) is driven by the SUT with a frequency of fRF. The direct-current (DC) bias voltage of the MZM is adjusted so that the amplitude of the optical carrier is equal to the ±1st-order optical modulation sidebands. Neglecting the higher-order sidebands, the multi-wavelength optical signal generated at point B, shown in Fig. 1(c), can be expressed as,
Fig. 1. (a) Schematic diagram of the proposed photonic-assisted MFM scheme. The signals at (b) Point A, (c) Point B, (d) Point C, and (e) Point D in the time-frequency domain, and the signals after envelope detection (f) in the time domain. DBR-LD: distributed Bragg reflector laser diode; Distributed feedback laser diode (DFB-LD); MZM: Mach-Zehnder modulator; DC: direct current; OC: optical coupler; PD: photodetector; BPF: band-pass filter; OSC: oscilloscope; PC: personal computer.
The LCOW and the modulated signal are combined into one path via an optical coupler (OC) and detected by the PD, where the optical heterodyne detection is implemented. Figures 1(d) and 1(e) depict the time-frequency distribution of the optical signals at point C and the microwave signals at point D, respectively. The detected electrical signal at the output of the PD is given by,
As illustrated in Fig. 1(f), a pair of pulses is obtained at t0 and t0’ when the instantaneous frequency |fstart+γt-fc|=fIF. Similarly, another pair of pulses is obtained at t-1 and t-1’ when the instantaneous frequency |fstart+γt-fc + fRF|=fIF. The pulse signal generated at tm during the ultrafast negative chirp of the sawtooth wave serves as a reference pulse to distinguish the pulse pair corresponding to the carrier from that corresponding to the -1st-order sideband. According to Eq. (5), t0, t0’, t-1, and t-1’ can be expressed respectively as,
At the midpoint of each pulse pair, the instantaneous frequency of the LCMW becomes zero, signifying that the instantaneous frequency of the LCOW at that time location is equal to the frequency of the -1st order optical sideband or the optical carrier. Therefore, the mapping relationship between fRF and the time interval of pulse pair midpoints can be expressed as,
The MFM is achieved by calculating the time interval between the midpoints of specific pulse pairs. Noting that the long-term wavelength interval fluctuation between the DBR-LD and the DFB-LD will not affect the MFM results, but short-term (less than the measurement period) wavelength interval fluctuation will introduce extra frequency measurement errors.
3. Experiment
To demonstrate the performance of the proposed photonic-assisted MFM scheme, a proof-of-concept experiment based on the setup of Fig. 1(a) is conducted. The key device used in the proposed system is a three-electrode DBR-LD (CETC), which has three distinct sections covering electrically isolated electrodes [34,36]. The LCOW is generated by injecting a pre-distortion sawtooth wave current into the phase section of the DBR-LD. A DFB-LD (CETC) generates the optical carrier with a power of 13 dBm. The SUT from a microwave source (Ceyear 1466 H) drives an MZM (CETC AM-25) with a 3-dB bandwidth of 25 GHz and an insertion loss of about 4.5 dB to modulate the optical carrier. The LCOW and the multi-wavelength optical signal are combined into one optical fiber via a 3-dB OC and then detected by a PD (Huasheng RM-A132401) with a responsivity of 0.75 A/W and a bandwidth of 2 GHz. The BPF (Zhiqu-bpf500) has a center frequency of 515 MHz and a 3-dB bandwidth of 10 MHz. The IF-filtered signal is monitored and captured by an oscilloscope (Tektronix MSO54) with a 3-dB bandwidth of 1 GHz, followed by envelope detection and calculation of the SUT frequency value via a PC.
The LCOW performance is experimentally demonstrated in Figs. 2 and 3. Figure 2 shows the sweeping bandwidth of the LCOW in the optical and electrical domains, analyzed using an optical spectrum analyzer (Yokogawa AQ6317C) and an electrical spectrum analyzer (Ceyear 4052 H), respectively. In particular, a PD (KangGuan KG-PD-20 GHz) is used to detect the optical heterodyne signal for analyzing the LCOW in the electrical domain. It is seen that the LCOW has a bandwidth of 0.204 nm in Fig. 2(a) in the optical domain, equaling the measured 25.4-GHz bandwidth in the electrical domain in Fig. 2(b). Setting the period and the positive-chirp duration of the sawtooth wave to be 23.04 µs and 22.68 µs, respectively, the LCOW is recorded in the time domain by an oscilloscope (Teledyne Lecroy SDA 820Zi-B) with a sampling rate of 80 GS/s and a bandwidth of 20 GHz in Fig. 3(a). The zoom-in-views of the temporal waveform at various time instances are shown in Fig. 3(b), indicating that the generated signals have different periods at different time locations. According to the data acquired in Fig. 3(a), the spectrogram of the generated LCMW is plotted in Fig. 3(c) using a short-time Fourier transform (STFT). Limited by the bandwidth of the device, the LCMW comprises a negative chirp of 19.4 GHz and a positive chirp of 6.0 GHz. By extracting the time and frequency components from the spectrogram and utilizing the linear fitting method, the chirp rate is calculated as 1.12 GHz/µs.
Fig. 2. Measured (a) optical spectrum of LCOW from DBR-LD and (b) electrical spectrum of the corresponding LCMW based on heterodyne frequency-beating.
A single-frequency SUT with a 10-GHz frequency is measured first to demonstrate the measurement process of the proposed photonic-assisted MFM system. As discussed in Fig. 1(c), a multi-wavelength signal should be generated at the output of the intensity modulator. Adjusting the DC bias voltage of the intensity modulator to be 7.82 V, the generated multi-wavelength signal, which consists of the optical carrier and the ±1st-order sidebands exhibiting identical amplitudes, is shown in Fig. 4(a) when the SUT has a frequency of 10 GHz. Then, the multi-wavelength optical signal is combined with the LCOW via the 3-dB OC, and the optical spectrum at the output of the OC is depicted in Fig. 4(b), where the frequency of the optical carrier is 1.19-GHz lower than the high-termination frequency of the LCOW. After optical-to-electrical conversion and IF filtering, the OSC records five microwave pulses during a measurement period. Their envelope signals through envelope detection are shown in Fig. 5. As discussed in Fig. 1(f), a pair of pulses is obtained at t0 and t0’ when the LCOW sweeps through the optical carrier, and the instantaneous frequency of the PD output signal equals the center frequency of the BPF. Another pair of pulses is obtained at t-1 and t-1’ when the LCOW sweeps through the +1st-order sideband, and the instantaneous frequency of the PD output signal equals the center frequency of the BPF. A reference pulse is obtained at tm during the ultrafast negative chirp of the sawtooth wave that sweeps through the multi-wavelength signal. However, a lower amplitude of the pulse at tm compared to others is observed due to the rapid scanning speed that exceeds the response time of the BPF [39]. It is seen that the time interval between the midpoints of these two pulse pairs is 8.92 µs. According to Eq. (10), the frequency of the SUT can be calculated as 9.994 GHz, with only a 6-MHz error from the input 10-GHz frequency. The frequency measurement resolution can be calculated as ΔR = max{0.7γ/Δf, Δf} [31], where Δf represents the bandwidth of the BPF. It is seen that the measurement resolution could be improved by using a lower chirp rate DBR-LD and a smaller bandwidth BPF. The best measurement resolution equaling the bandwidth of the BPF could be achieved when the chirp rate of the DBR-LD is lower than (Δf)2/0.7. With the10-MHz bandwidth BPF in the experimental demonstration, the measurement resolution could be 78 MHz when the chirp rate is 1.12 GHz/µs, and a best measurement resolution of 10 MHz could be achieved when the chirp rate is lower than 0.14 GHz/µs.
Fig. 4. (a) Optical spectrum of the multi-wavelength optical signal at the output of the MZM and (b) the combined optical signal at the output of the optical coupler.
To evaluate the bandwidth performance of the proposed photonic-assisted MFM system, SUTs with different frequencies ranging from 2 to 22 GHz with a 2-GHz step are measured by the proposed MFM system in Fig. 6. Figure 6(a) shows the optical spectrums of modulated multi-wavelength signals when the SUTs have different frequencies. The resulting temporal waveforms are illustrated in 6(b). It is seen that the time intervals between the midpoints of the generated pulse pairs are 1.79, 3.58, 5.36, 7.14, 8.93, 10.70, 12.50, 14.28, 16.05, 17.85, and 19.64 µs, corresponding to measured frequencies of 2.009, 4.013, 5.998, 7.990, 9.990, 11.978, 13.991, 15.982, 17.979, 19.995, and 21.981 GHz, respectively. Measurement errors at different frequencies are 9, 13, 2, 10, 22, 9, 18, 21, 5, and 19 MHz, respectively. The linearly fitted frequency-time relationship of the sampled data is demonstrated in Fig. 6(c), affirming the successful establishment of FTTM. Then, one hundred measurements are conducted at different frequencies in Fig. 6(d), where the data histogram and normal fit curve are plotted. As can be seen, the measurement results at different frequencies follow a normal distribution. According to the results shown in Fig. 6(d), the RMS errors for different input frequencies are calculated and shown in Fig. 6(e). The measurement RMS errors remain below 28 MHz across the entire measurement range. The measurement error is mainly caused by the frequency instability and nonlinearity of the LCMW. Enhancing the coherence between the DBR-LD and DFB-LD through a phase-locking technique presents a promising solution to this challenge [38].
Fig. 6. (a) Optical spectrum of the multi-wavelength optical signal, (b) measured temporal waveform, (c) measured data and the linear fitting of the FTTM relationship, (d) normal fitting of one hundred measured data at each frequency, and (e) RMS error at each frequency when the SUT ranging from 2 GHz to 22 GHz with a step of 2 GHz.
The frequency-hopping signal measurement is demonstrated in three experiments to further validate the performance of the proposed photonic-assisted MFM method. In the first experiment, the hopping frequencies are set to 2, 11, and 20 GHz to cover the measurement range from 2 to 20 GHz. In the second experiment, the hopping frequencies are 2, 8, 14, and 20 GHz. In the third experiment, the hopping frequencies are set to 2, 6, 10, 14, and 18 GHz. The duration of each frequency is approximately tens of milliseconds, including over one thousand MFM periods. The recorded temporal waveforms with a 200-ms duration for the three experiments are shown in Figs. 7(a1), (b1), and (c1), respectively. In the first experiment, the zoom-in temporal waveforms at different frequencies of 2, 11, and 20 GHz are plotted in Figs. 7(a2) to 7(a4). In the second and third experiments, the zoom-in temporal waveforms at different frequencies are shown in Figs. 7(b2) to (b5) and Figs. 7(c2) to (c6), respectively. According to the recorded temporal waveforms in Fig. 7, the data histogram and normal fit curve of one hundred measurements at each frequency are plotted in Fig. 8(a) to (c). Similar to the results shown in Fig. 6, the measurement results at each frequency follow a normal distribution. According to the results in Figs. 8(a) to (c), the RMS measurement errors are calculated and shown in Fig. 8(d), which shows that the measurement errors for the frequency-hopping microwave signals are below 39.1 MHz. The measurement error for the frequency-hopping microwave signals is larger than that for single-frequency microwave signals due to the power or frequency fluctuation introduced by the frequency-hopping operation.
Fig. 7. Measurement temporal waveforms of frequency-hopping signals stepped by (a1) 9 GHz, (b1) 6 GHz and (c1) 4 GHz. The zoom-in temporal waveforms at (a2) ∼ (a4) 2 GHz, 11 GHz and 20 GHz, (b2) ∼ (b5) at 2 GHz, 8 GHz, 14 GHz and 20 GHz, (c2) ∼ (c6) at 2 GHz, 6 GHz, 10 GHz, 14 GHz and 18 GHz.
Fig. 8. Normal fitting of one hundred measured data (a) at 2 GHz, 11 GHz and 20 GHz, (b) at 2 GHz, 8 GHz, 14 GHz and 20 GHz, (c) at 2 GHz, 6 GHz, 10 GHz, 14 GHz and 18 GHz, respectively. (d) RMS error of frequency-hopping signals.
The performance comparison of the proposed optical heterodyne detection-based MFM scheme with the other FTTM-based MFM works is given in Table 1, where the key figures of measurement instantaneous bandwidth, speed, error, and resolution for MFM systems are listed. Among these works, the proposed optical heterodyne detection-based MFM scheme simplifies the system architecture by using only one modulator, two semiconductor lasers, one low-speed PD, and one BPF. Thanks to the substantial chirp bandwidth and fast tuning capability of the DBR-LD, the proposed method has advantages in instantaneous measurement bandwidth and measurement speed. An instantaneous bandwidth of 20 GHz with a measurement RMS error below 39.1 MHz at a 1.12-GHz/µs measurement speed and 10-MHz resolution is realized. Note that the instantaneous bandwidth could be improved to over 40 GHz by using a modulator with a larger bandwidth and a laser with a broader chirp range [28]. The resolution performance can be enhanced using a BPF with a narrower bandwidth.
Table 1. Performance comparison of FTTM-based MFM schemes
4. Conclusion
In summary, we proposed and experimentally demonstrated a photonic-assisted MFM method based on optical heterodyne detection. In the proposed MFM system, a SUT-modulated optical signal and an LCOW were optical heterodyne detected at a PD. Then, the FTTM was achieved after bandpass filtering and envelope detecting the optical heterodyne detected signal from the PD. The LCOW was generated from a three-electrode DBR-LD. Thanks to the fast-sweeping speed and large tuning bandwidth of the DBR-LD [34–37], the proposed MFM has a high measurement speed and broad instantaneous measurement bandwidth. In the experiment, an instantaneous bandwidth of 20 GHz with a measurement RMS error below 39.1 MHz at a 1.12-GHz/µs measurement speed was demonstrated. Note that a higher instantaneous bandwidth can be achieved using optoelectronic devices with large bandwidths. The successful demonstration of the MFM system with a simple structure provides a new optical solution for realizing broadband and fast microwave frequency measurements, indicating broad applications in modern radar and electronic systems.
Funding
National Natural Science Foundation of China (62201120, 61971110); Natural Science Foundation of Sichuan Province (2023NSFSC1379, 2023NSFSC0448).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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