1. Introduction

In comparison with the single-band radar systems, multi-band radar systems provide many prominent advantages, including the multi-function detection, reducing the false probability in detection under strong interference condition, the jamming mitigation, and the eliminating of Doppler blind speed in the moving target detection [1–4]. For conventional electronic radar transmitters, additional hardware is necessary to generate additional microwave signal in additional band, which inevitably increases the complexity and power-consumption of the multi-band radar systems [5]. Owning to the ultra-wideband characteristic of photonic technique, photonics-assisted microwave signal generation is a promising candidate to obtain multi-band microwave signals with reduced implementation complexity and excellent reconfigurability [6,7].

In the past few years, numerous schemes of multi-band microwave signals generation based on the microwave photonic technique have been demonstrated [8–13]. The main idea of those schemes is to utilize optical frequency comb to up-convert the baseband or the intermediate-frequency (IF) signals to the desired radio-frequency (RF) signals. Mode-locked fiber laser (MLL) is the first one to be considered as the candidate to act as the optical frequency comb for sampling, in order to generate multi-band phase-coded RF signals [8,9]. However, the repetition rate of the passively MLL is restricted by its fixed resonant cavity length, leading to the limitation of the RF frequency tunability. For the actively MLL, although its repetition rate can be easily tuned by varying the driven signal frequency, its mode locking performance is sensitive to the environment disturbance. Hence, the stability of the multi-band microwave signals generation cannot be guaranteed. Electro-optic modulation is an alternative solution to generate the stable optical frequency comb with flexible frequency tunability [14,15]. Based on a Mach-Zender modulator (MZM) biased near its minimum transmission point, an optical frequency comb with three optical tones has been generated by the carrier-suppressed double sideband modulation (CS-DSB), where the repetition rate of the used optical frequency comb is determined by the frequency of the driven local oscillator (LO) signal [10]. After the electrical coding signal is loaded onto the optical frequency comb via a polarization modulator (PolM) or a dual-output MZM, two phase-coded microwave signals at different frequencies are generated with the help of balanced photodetector (BPD) [10,11]. Meanwhile, high-order modulation sidebands induced by the MZM nonlinearity can be utilized to enlarge the number of the generated frequency bands. In [12], the multi-frequency phase-coded microwave signals at six different microwave carrier frequencies has been realized by the assistance of a dual-polarization dual-drive MZM (DP-DDMZM). The power fluctuation of six microwave signals is less than 2 dB over the range of 1.5 GHz to 6 GHz after the optimization of the amplitude of the LO signal and the bias voltages of the DP-DDMZM. Nevertheless, the power fluctuation becomes worsen, as both the microwave frequency range and the number of microwave carriers are increased. To further extend the coverage of microwave frequency, intermodulation products of two LO signals induced by the modulation nonlinearity of a single DDMZM has been used to realize the multi-band microwave up-conversion. In [13], twelve phase-coded microwave signals have been generated over the frequency range of 1 GHz to 16 GHz. Nevertheless, the power fluctuation over the microwave frequency range is more than 11.5 dB. In summary, the performance of multi-band microwave signals generation based on an optical frequency comb generated by the electro-optic modulation is limited by narrow operation frequency range, small amount of carriers, and severe power fluctuation among the generated multi-band microwave signals. Only when those issues are well addressed, can the microwave photonic technique play a powerful role in the multi-band radar systems.

In current work, we propose and experimentally generate multi-band microwave signals over a wide frequency range with an excellent mitigation of power fluctuation. As a result, the IF signal is up-converted to high frequency output signals in multiple microwave frequency bands after being optically sampled by an ultra-short optical pulse via a MZM and being detected by the use of a broadband photodetector (PD). Thereinto, the ultra-short optical pulse source is generated by an electro-optical phase modulation-based time lens with the chirp compensation, where its parameters can be flexibly reconfigured to optimize the performance of frequency up-conversion. In our proof-of-concept experiment, ten phase-coded microwave signals are generated over the frequency range of 7 GHz to 41 GHz, where the power fluctuation is less than 5.9 dB.

2. Operation principle

Figure 1 shows the schematic of the proposed multi-band microwave signals generation method based on photonic sampling. The ultra-short optical pulse source, for the purpose of photonic sampling, is realized by a cavity-less optical pulse source-based time lens and the chirp compensation. The corresponding waveforms and the frequency spectra at different points in the cavity-less optical pulse source are presented in Fig. 1(a)-(d). Firstly, the continuous-wave (CW) light from a distributed feedback laser diode (DFB-LD) is carved into an optical pulse train with a repetition rate of f_LO via the MZM1, which is driven by a microwave frequency synthesizer at f_LO under the push-pull mode. Meanwhile, an electro-optic phase modulator (PM) driven by the same output of microwave frequency synthesizer, introduces an approximate quadratic phase to the optical pulse. Through properly adjusting the phase of the microwave signal via an electrical phase shifter (EPS), the temporal profile of the single-tone microwave signal aligns with that of the optical pulse in the time domain, leading to the occurrence of linear chirp at the middle of optical pulse [16]. Finally, the chirped optical pulse train propagates over a dispersion compensation module (DCM) with a proper value of group velocity dispersion (GVD), leading to the final generation of an ultra-short optical pulse train. Next, the ultra-short optical pulse train with a repetition rate of f_LO from the cavity-less optical pulse source acts as the optical input of the MZM2 biased at its quadrature point, where the input IF signal centered at f_IF is optically sampled through the linear electro-optic modulation. After the photonic sampling, the IF signal is frequency up-converted to different frequency bands centered at f₀± nf_LO±f_IF (n = 0, 1, 2…), as shown in Fig. 1(e). Then, the sampled optical pulse train is detected by the use of broadband PD, where the IF signal is up-converted to multiple microwave frequency bands centered at (n-1)f_LO+f_IF and nf_LO-f_IF (n = 1, 2, 3…), due to the mutual beating of the optical spectral components, as shown in Fig. 1(f). The distinct advantages of the proposed scheme can be summarized as follows. Firstly, the repetition rate of the generated ultra-short optical pulse train can be adjusted by varying the frequency of the microwave signal applied to the MZM1 and the PM, which guarantees the frequency flexibility of the generated multi-band microwave signal. Secondly, the power fluctuation of the up-converted microwave signal can be mitigated, after tuning the bias voltage and the modulation index of MZM1. Thirdly, the stability of the cavity-less optical pulse source is substantially improved, in comparison with that of the MLL, leading to a performance enhancement of the multi-band microwave signals generation.

 

Fig. 1. Schematic of the proposed multi-band microwave signals generation based on photonic sampling. DFB-LD: distributed-feedback laser diode, MZM: Mach-Zehnder modulator, PM: phase modulator, DCM: dispersion compensation medium, PD: photodetector, EPS: electrical phase shifter, EA: electrical amplifier, PC: polarization controller, LO: local oscillator, and IF: intermediate frequency.

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Mathematically, the MZM1 within the cavity-less optical pulse source is driven by a single-tone microwave signal ${V_{\textrm{LO}1}}(t )= {V_{\textrm{LO}1}}\cos ({{\omega_{\textrm{LO}}}t} )$, where ${V_{\textrm{LO}1}}$ and ${\omega _{\textrm{LO}}}$ are the voltage magnitude and the angular frequency of the microwave signal, respectively. Hence, the optical field at the MZM1 output can be described as

It can be seen from Eq. (3) that, the optical field at the DCM output is an optical frequency comb with a frequency interval of f_LO, where the power of each frequency component is determined by the bias phase shift of MZM1 [15], together with the modulation indices of the MZM1 and the PM. Meanwhile, those frequency components can be tuned to be in-phase with each other by choosing a proper GVD value to compensate the frequency-dependent phase shift introduced by the cascaded amplitude and phase modulation. The explicit analytical expression of the generated ultra-short optical pulse train is challenging to derive. Therefore, for the ease of discussion, the optical field of the ultra-short optical pulse train in the frequency domain is simplified as

As shown in Eq. (7), the IF signal centered at ω_IF is simultaneously up-converted to multiple frequency bands centered at Nω_LO±ω_IF. In addition, multiple frequency components from the LO signal are generated at Nω_LO accordingly. Both the up-converted microwave signal and the frequency-multiplied components of the LO signal are with an identical amplitude ${Q_N}$. It can be seen from Eqs. (3)-(7) that, the amplitudes ${Q_N}$ are dependent on the parameters of the ultra-short optical pulse source, including the modulation index and the bias phase shift of MZM1 (i.e., ${m_1}$ and ${\varphi _1}$), the modulation index of the PM (i.e., ${m_{\textrm{PM}}}$), the length and the GVD coefficient of the DCM (i.e., L and ${\beta _2}$), and the frequency of the applied microwave signal (i.e., ${\omega _{\textrm{LO}}}$). In practice, ${m_{\textrm{PM}}}$ is set to a specific value, which is generally large enough to enhance the number of optical frequency tones. In addition, a proper GVD value (i.e., ${\beta _2}L$) is optimized for a specific repetition rate of f_LO, in order to compensate the linear chirp completely. Hence, the power fluctuation of the multi-band up-converted microwave signal can be mitigated by finely tuning the modulation index ${m_1}$ and the bias phase shift ${\varphi _1}$ of MZM1.

3. Parameter optimization

Numerical simulation is carried out to optimize the parameters of the ultra-short optical pulse source, for the ease of realizing a broadband frequency up-conversion. The ultra-short optical pulse source is developed by the use of a DFB-LD at 1550 nm, a LO signal source at 8 GHz, a MZM and a PM with 3-dB bandwidth of more than 30 GHz, and a spool of SMF with a GVD value of 41.4 ps/nm. Thereinto, the modulation index of the PM is set to be $3\mathrm{\pi }$, which corresponds to the GVD value of the SMF for achieving optimal pulse compression. To eliminate the device-induced performance penalty at the high frequency band, a PD with a bandwidth of 100 GHz is used to emulate the optical-to-electrical conversion. Additionally, the insertion loss of all devices is not taken into account during the simulation, which has no impact on the parameter optimization of the ultra-short optical pulse source in realizing the broadband frequency up-conversion, except for the power of the generated microwave signal.

During the simulation, the power of the multiplied-frequency components is evaluated under the condition of various modulation indices and bias phase shifts of MZM1. Figure 2(a) and 2(b) show the contour maps of the normalized power for the 1^st-order multiplied-frequency component at 8 GHz and the 5^th-order multiplied-frequency component at 40 GHz, respectively, where the maximum power of the 1^st-order multiplied-frequency component at 8 GHz is used as the reference value for the normalization. Figure 2(c) shows the contour map of the power fluctuation over the frequency range of 8 GHz to 40 GHz, where the area of a power fluctuation below 3 dB is denoted with the blue slash. It can be seen from Fig. 2(a) and (b) that, the parameter set of MZM1 to obtain a high normalized power of -5 dB at 40 GHz can simultaneously guarantee a high normalized power more than -4 dB at 8 GHz, which is denoted by the red slash in Fig. 2(c). Therefore, the optimal parameter set to achieve efficient broadband frequency up-conversion are located at the overlapped area of the blue slashed area and the red slashed area in Fig. 2(c). For example, the modulation index of 0.7π and the bias phase shift of 0.6π, as shown by the red dot in Fig. 2(c), are one optimal parameter set.

 

Fig. 2. Contour maps presenting (a) the normalized power in decibel of the 1^st-order multiplied-frequency component at 8 GHz, (b) the normalized power in dB of the 5^th-order multiplied-frequency component at 40 GHz and (c) the power fluctuation over the frequency range of 8 GHz to 40 GHz, under various modulation indices and bias phase shifts of MZM1.

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4. Experimental results and discussion

In this section, a proof-of-concept experiment is carried out to verify the feasibility of the proposed scheme. The ultra-short optical pulse source includes a 1550 nm DFB-LD with an output power of 6 dBm (Pure Photonics, PPCL200), a 40-Gb/s LiNbO₃-based MZM (Photline, MXAN-LN-40-00-P-P-FA-FA) with a half-wave voltage of 6 V at 8 GHz, a 20-Gb/s PM (EOSpace, PM-SSES-20-PFA-PFA-UV) with a maximum RF input power of 33dBm, a spool of SMF (YOFC, G652D) with a GVD value of 41.4 ps/nm, and a self-developed two-channel LO signal source. Thereinto, the two-channel LO signal source consists of a microwave frequency synthesizer with a tunable frequency range of 5 GHz to 8 GHz, an electrical power splitter, a tunable electrical phase shifter with a controlled phase shift from 0° to 360° over the frequency range from 5 GHz to 8 GHz, and two pairs of electrical attenuators and RF power amplifiers. Specifically, the power tuning step is 1 dB, and the phase tuning step is smaller than 1.6°. Therefore, the power and the phase difference of two LO signals applied to the MZM and the PM can be finely tuned to optimize the up-conversion performance. In the experiment, the frequency of the LO signal is set to be 8 GHz, and the power of the LO signal applied to the PM is adjusted to guarantee the modulation index of the PM at 3π. In addition, the phase difference between two LO signals applied to the MZM and the PM is finely optimized to guarantee the occurrence of time lens. The input IF signal is sampled by the generated ultra-short optical pulse train via a 20-Gb/s LiNbO₃-based MZM (EOSpace, AX-0MSS-20-PFA-PFA) with a half-wave voltage of 5 V at 1 GHz. The MZM is biased at its quadrature point by using a modulator bias controller (iXblue, MBC-AN-LAB). A broadband PD (Waveopt, WOP46-OC-FA-M) with a 3 dB bandwidth of 40 GHz and a responsivity of 0.65A/W is used to detect the multi-band frequency up-conversion signals. The optical spectrum of the generated ultra-short optical pulse train, the temporal waveforms of the up-conversion signals, and their electrical spectra are characterized by an optical spectrum analyzer (OSA, Yokogawa AQ6370D), a high-speed real-time oscilloscope (OSC, LeCroy 816Zi-B), and an electrical spectrum analyzer (ESA, R&S FSW50), respectively.

Firstly, the generated ultra-short optical pulse train is directly introduced to the PD, in order to verify the optimized parameters with numerical simulation results. Figure 3 presents the power of the 5^th-order multiplied-frequency component at 40 GHz and the power flatness of the multi-band microwave signal within the frequency range of 8 GHz to 40 GHz under various DC bias voltages of MZM1, where the modulation index of MZM1 is set to be $0.5\mathrm{\pi }$ and $0.7\mathrm{\pi }$ in Fig. 3(a) and 3(b), respectively. Thereinto, the DC bias voltage of MZM1 is tuned from -3 V to 3 V, which corresponds to a bias phase shift within the range of 0 to π. It can be seen from Fig. 3 that, the optimal power flatness and the maximum power of the 5^th-order multiplied-frequency component at 40 GHz are 5.5 dB and -30 dBm, respectively, when the modulation index and the DC bias voltage of MZM1 are set to be 0.7π (i.e., ${m_1} = 0.7\mathrm{\pi }$) and 0.5 V, respectively. Based on the characteristic of MZM1 used in the experiment, the DC bias voltage of 0.5 V corresponds to a bias phase shift of 0.6π. Hence, the optimal parameter set in the experiment agrees well with the numerical simulation results.

 

Fig. 3. The power of the 5^th-order multiplied-frequency component at 40 GHz and the power flatness of the multi-band microwave signals within the frequency range of 8 GHz to 40 GHz under various DC bias voltages of MZM1, where the modulation index of MZM1 is set to be (a) 0.5π and (b) 0.7π, respectively.

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Then, a phase-coded microwave signal centered at 1 GHz is generated by using an arbitrary waveform generator (AWG, Keysight M8195A), which acts as the input IF signal. Thereinto, the phase-coded microwave signal is generated with a 13-bit Barker code pattern of “1111100110101” and a coding rate of 13 Mb/s. The peak-to-peak voltage of the phase-coding signal is 1 V, which corresponds to a modulation index of 0.1π for the MZM2. In addition, an erbium-doped fiber amplifier (EDFA) (Amonics, AEDFA-PA-35-B-FA) and an optical tunable filter (OTF, SANTEC OTF-350-W-SMF-FC-A) are employed, for the purpose of compensating the insertion loss and eliminating the amplified spontaneous emission (ASE) noise, respectively. Figure 4(a) and 4(b) present the optical spectrum of the generated ultra-short optical pulse train and the electrical spectrum of the generated multi-band microwave signals. It can be seen from Fig. 4(a) that, an optical frequency comb with a frequency interval of 8 GHz is obtained. Based on the ultra-short optical pulse train, phase-coded microwave signals centered at ten different frequencies within the range of 7 GHz to 41 GHz is generated as shown in Fig. 4(b), where the power flatness within the frequency range is measured to be 5.9 dB. The measurement results indicate that, the proposed scheme can achieve efficient and flat multi-band frequency up-conversion. It should be noted that the power flatness in the experiment is not as good as that in the simulation, which is attributed to the following reasons. Firstly, the PD used in the experiment is with a narrower bandwidth, which results in an extra power degradation at the high-frequency band. Secondly, the deviation of the parameter settings from the optimal values induced by the relatively rough power tuning step of the LO signals, the DC bias drift of the MZM and the residual chirp of the optical sampling pulse train also leads to the power variation of the frequency-converted signals.

 

Fig. 4. (a) Optical spectrum of the generated ultra-short optical pulse train and (b) electrical spectrum of the generated multi-band phase-coded microwave signals.

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The generated multi-band phase-coded microwave signals are recorded by the high-speed real-time OSC with a 3-dB bandwidth of 16 GHz and a sampling rate of 80 GS/s. Based on the recorded waveform data, the phase-coded microwave signals centered at 7 GHz and 17 GHz are selected by the implementation of digital bandpass filtering. Figure 5(a) and 5(b) show the waveforms centered at 7 GHz and 17 GHz, respectively, where the phase is retrieved by implementing Hilbert transform of the corresponding signal. The insets in Fig. 5 exhibit the temporal waveform of the corresponding RF signals with a duration of 0.4 ns. It can be seen from Fig. 5 that, the original phase-coded signal centered at 1 GHz is simultaneously up-converted to 7 GHz and 17 GHz, and the phase coding information can be maintained. respectively. Figure 6(a) and 6(b) present the autocorrelation results of two up-converted signals centered at 7 GHz and 17 GHz, respectively, where the insets exhibit the theoretical autocorrelation result of the input IF signal at 1 GHz. It can be seen from Fig. 6 that, the peak-to-side lobe ratios (PSRs) after the autocorrelation are 9.22 dB and 8.57 dB for the up-converted signal centered at 7 GHz and 17 GHz, respectively. In addition, the full-width at half-maximums (FWHMs) after the autocorrelation for the up-converted signal centered at 7 GHz and 17 GHz are 0.092 µs and 0.094 µs, respectively, which correspond to pulse compression ratios (PCRs) of 10.87 and 10.64. As a comparison, the theoretical PSR and FWHM are 11.1 dB and 0.076 µs, respectively. Those results indicate that, the proposed scheme can achieve a broadband frequency up-conversion with a high fidelity. Additionally, it can be seen from Fig. 1(f) that the IF signal centered at f_IF is up-converted to different frequency bands centered at (n-1)f_LO+f_IF and nf_LO-f_IF (n = 1, 2, 3…). Hence, the bandwidth of the IF signal must be smaller than twice the minimum value of f_IF and f_LO/2-f_IF (supposing f_IF< f_LO/2). The maximum IF signal bandwidth is equal to f_LO/2 in theory, which can be obtained by setting f_IF= f_LO/4. Therefore, the maximum IF signal bandwidth is calculated to be 4 GHz under the repetition frequency of 8 GHz, indicating that the proposed multi-band up-conversion scheme can support a phase coding rate up to Gb/s level.

 

Fig. 5. Waveforms of the up-converted phase-coded microwave signals centered at (a) 7 GHz and (b) 17 GHz, and their retrieved phase.

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Fig. 6. Autocorrelation results of the up-converted phase-coded microwave signals centered at (a) 7 GHz and (b) 17 GHz. Insets: the autocorrelation results of the input IF signal at 1 GHz.

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Finally, it should be pointed out that the repetition frequency of the ultra-short optical pulse train can be tuned to achieve flexible up-conversion. For a certain repetition frequency, the up-conversion performance can be optimized by simply varying the bias phase shift of the MZM and the modulation indices of the MZM and the PM. In addition, the operation bandwidth of the proposed up-conversion scheme can be further enhanced by increasing the spectral width of the ultra-short optical pulse train and the PD bandwidth. To enhance the spectral width of the ultra-short optical pulse train, the chirp introduced into the optical pulses from the MZM should be enlarged by applying a higher power LO signal to the PM, or cascading two or more PMs in the cavity-less optical source.

5. Conclusion

In summary, we have proposed and experimentally demonstrated a photonic sampling-based multi-band microwave signals generation scheme with a mitigation of severe power fluctuation over a wide microwave frequency range. The ultra-short optical pulse train used to achieve the photonic sampling is generated by the use of a time lens and the chirp compensation, and its characteristics can be flexibly varied for various frequency up-conversion scenarios. During numerical simulation, the optimal parameter set of the MZM in the optical pulse source with a repetition rate of 8 GHz has been obtained, which agrees well with the experimental verification. Based on the optimal optical pulse source, ten phase-coded microwave signals with a 13-bit Barker code have been successfully generated within the frequency range of 7 GHz to 41 GHz by employing a PD with a 3-dB bandwidth of 40 GHz in the experiment. The power fluctuation among the generated multi-band microwave signals has been mitigated to be less than 5.9 dB. The pulse compression results of the generated microwave signals centered at 7 GHz and 17 GHz indicate that, the proposed scheme can achieve a broadband frequency up-conversion with a high fidelity. Hence, the proposed scheme is a promising candidate to realize multi-band microwave signals generation in agile radar systems, due to its simple architecture and broadband operation.