A flexible ultra-wide frequency photonic-assisted method is proposed for microwave harmonic down-conversion based on re-circulating four-wave mixing (RFWM) in a semiconductor optical amplifier (SOA). The proposed down-converter consists of a RF-driven electro-optic modulator (EOM) and a RFWM-intensified optical local oscillator (LO) located in a ring-assisted Mach-Zehnder interferometer (R-MZI). In the optical LO, the optical carrier is first modulated by a low-frequency electrical LO through an EOM for triggering high-order harmonics sideband generation in the optical domain through the FWM effect in the SOA, and the generated harmonics sidebands are further intensified by re-circulating the FWM products back to the EOM and the SOA successively with an amplified ring loop. The RFWM-intensified optical LO enables accurate tunable and ultra-wide frequency operation of down-conversion by simply adjusting the low-frequency electrical LO. In the experiment, the RFWM-based optical LO is operated with wide spectrum of more than 0.8 nm (15-dB bandwidth) and 1.2 nm (20-dB bandwidth) and tunable frequency spacing from 4 GHz to 12 GHz. The microwave frequency conversion is successfully demonstrated in the RF range of 5-40 GHz down-converted to IF band below 2 GHz with a low-frequency electrical LO at about 4.8 GHz.
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Microwave frequency down-converter is one of the key modules in the electrical systems such as radio-frequency (RF) communication networks, phased-array antennas and electronic reconnaissance systems [1–3], which are evolving to meet the ever-increasing requirement of ultra-wideband applications. Photonic-assisted microwave down-conversion have been proposed and demonstrated with large bandwidth, frequency tunability, and immunity to electromagnetic interference over the conventional electronic methods [4,5].
In most photonics-assisted methods, the input RF signal is firstly converted to the optical domain through electro-optic modulator (EOM), and mixed with an electrical or optical local oscillator (LO) signal. The down-converted tones will then be generated in the electrical domain via photomixing with a photodiode (PD). The input RF signal and the LO signal can be interacted through serial or parallel modulation mixing, in which wideband tunable electrical LO sources are essential for wide frequency range operation [6–14]. The photonics-assisted methods based on harmonic down-conversion [15,16] and optoelectronic oscillation (OEO) [17–19] were also successfully implemented by replacing the high-frequency electrical LO with a low-frequency one or even without any extra LO. The OEO-based method is often limited by the narrow-band frequency range and the poor frequency tunability.
For the extended frequency range, the microwave harmonic down-conversion methods have been proposed by using a mode-locked laser diode (MLLD)  or an optical frequency comb (OFC) [15,21–24]. The evenly-spaced optical spectrum of MLLD provides ultra-wide frequency optical LO for microwave harmonic down-conversion, however, the fixed repetition frequency of MLLD leads to much difficulty for flexibly tunable down-converted IF tones . The EOM-based OFC can be used for reconﬁgurable harmonic down-conversion with tunable IF signals by adjusting the electrical LO frequency. Nevertheless, the major limitation of this method lies in the required heavy power driving [10–13] and/or precise phase control [12,13] of the electrical driving signals (typical at around 30 dBm) in the EOM-based OFCs. Therefore, the harmonic down-conversion methods that enable ultra-wide frequency range with low-frequency LO driver and at the same time allow precisely tunable operation, are of great attraction.
Recently, we proposed a tunable microwave harmonic down-conversion with a low-frequency electrical driver based on the four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) . In this paper, we propose an ultra-wide and tunable microwave harmonic down-conversion based on re-circulating four-wave mixing (RFWM) in a SOA. As shown in Fig. 1, the proposed down-converter consists of a RF-driven EOM and a RFWM-intensified optical LO located in a ring-assisted Mach-Zehnder Interferometer (R-MZI). In the RFWM-intensified optical LO, a low-frequency electrical LO is loaded onto the optical carrier through an EOM and injected into a SOA for triggering high-order harmonics sidebands generation in the optical domain through FWM effect in the SOA. Then, the harmonics sidebands are further enhanced by re-circulating the FWM products back to the input of EOM and SOA successively with an amplified ring loop, which is ready for accurately tunable ultra-wide and frequency operation of down-conversion. As compared with the open-loop FWM, the RFWM allows multiple interactions by recycling the FWM products and brings more power efficiency in the high-order harmonics generation in the optical domain. As a result, the RFWM-intensified optical LO harvests flatter and wider optical spectrum under the same driving condition of SOA, which helps to improve the power flatness of the down-converted tones in the interesting frequency range. Moreover, the RFWM-based down-conversion can be easily tuned by adjusting the low-frequency electrical LO. In this work, a proof-of concept experiment is demonstrated to elaborate our method and 5-40 GHz microwave signals are down-converted to IF signals below 2 GHz with a low-frequency electrical LO at around 4.8 GHz. The RFWM-based method is investigated and compared to the FWM-based one to check the performance.
2. Operation principle
As shown in Fig. 1(a), the proposed method is made up with an optical EOM (EOM-1) and an optical LO located in the upper and lower arm of R-MZI, respectively. In the upper arm of R-MZI, the polarization of the optical carrier is firstly aligned by a polarization controller (PC1) and the RF signal at fRF to be converted is modulated onto the optical carrier at f0 via EOM-1. In the lower arm of R-MZI, a low-frequency electrical LO at fLO is loaded onto the optical carrier by another EOM (EOM-2) and injected into a nonlinear SOA to trigger more high-order harmonic sidebands generation through the FWM effect, working as a basic FWM-based optical LO, as shown in Fig. 1(b). In our case, the FWM products are then amplified and coupled back to the EOM-2 and SOA through an erbium-doped optical fiber amplifier (EDFA) and optical delay line (ODL), respectively, which constructs a RFWM-intensified optical LO. Note that another PC (PC2) is used before EOM-2 to align the polarization between the electro-optic modulation and the RFWM intensification in the loop. The intensified optical harmonic sidebands and the RF-modulated optical signal are combined at the end of R-MZI and detected by a PD, in which the down-converted tones at the frequency of |fRF-NfLO| are generated by photo-mixing in the electrical domain and obtained with an electrical low-pass filter (LPF). The converted tones can be tuned at different frequencies by appropriately adjusting the frequency of electrical LO, enabling flexible and ultra-wide frequency microwave down-conversion.
The RF-modulated optical signal and the RFWM-intensified optical harmonics are combined at the end of R-MZI, and detected by a PD with responsivity R to generate a photocurrent. The desired IF signal at fIF=|fRF-nfLO| (i.e., p=±1) can be obtained after an electrical LPF as following
As is known, the red-shifted components towards longer wavelength receive higher efficiency than the blue-shifted ones towards shorter wavelength in the FWM effect of SOA [28,29], leading to asymmetrical harmonic generation around the optical carrier. So, it is necessary to discuss the impacts of asymmetry on the converted IF tones in our scheme. From Eq. (6), the magnitude coefficient α is related to the amplitude and phase of blue-shifted and red-shifted harmonic sidebands and the phase difference θ of R-MZI. For simple but without loss of generality, we normalize the amplitude F-n to1 and define the amplitude ratio as r = Fn/F-n (Fn<F-n, n>0), the magnitude coefficient α in Eq. (6) can be written as
As shown in Fig. 2, the magnitude coefficient α is calculated as a function of amplitude ratio r with different Δζ. The slope of magnitude coefficient α is flat in the case of r<0.1. When 0.1<r<1, the magnitude coefficient α has a certain fluctuation at different Δζ. However, the magnitude coefficient α can be optimized by changing Δζ, such as the bias phase of EOM-1 and/or EOM-2, in order to reduce the impacts of fluctuation on the down-converted IF tones, as shown by the purple curve in Fig. 2(a). From Eq. (4), the sidebands of electrical LO are extended up to the highest order Max(N1, N2) by the RFWM-intensified harmonics generation in the optical domain, and microwave down-conversion can be achieved in wide frequency range by using different harmonic sidebands of the RFWM-intensified optical LO. Moreover, the harmonics generation can be improved by tuning the bias voltage of EOM-2 and/or adjusting the delay of the ODL, for a better FWM efficiency or phase correlation of the generated harmonic sidebands . From Eq. (5), the converted IF signal can be tuned to different frequency by adjusting the frequency fLO of electrical LO. It is noteworthy that the RFWM-intensified optical LO avoids the requirement of complex phase control and heavy power driving of electrical LO.
3. Experiment and discussion
In the proof-of-concept experiment, an optical carrier with a wavelength of 1550.12 nm and an optical power of 12.5 dBm is injected into the R-MZI, which is originating from a distributed feedback laser diode (DFB-LD). The optical carrier in the upper arm of R-MZI is sent to a Sumitomo Mach-Zehnder modulator (MZM, EOM-1) via PC1, where it is modulated by the under converted RF signal at fRF. The optical carrier in the lower arm of R-MZI is sent to the RFWM-intensified optical LO consisting of an EOspace MZM (EOM-2), a nonlinear SOA (Kamelian SOA-NL) and an OBF (Santec OTF970). The feedback loop includes an EDFA (Amonics AEDFA-PKT) and a tunable optical delay line (ODL), which are used for optical amplification and phase optimization between the generated harmonic sidebands. The optical carrier is modulated by a low-frequency electrical LO at fLO in IM-2, in which several upper and lower sidebands are generated with respect to the optical carrier in the optical domain. Then, the LO-modulated optical signal from EOM-2 is sent to the SOA to trigger high-order optical harmonics generation based on FWM effect. The FWM products are filtered and amplified and treated as feedback to the input of EOM-2 and SOA successively to intensifying even higher-order optical harmonic sidebands, with which ultra-wide optical LO spectrally spaced by fLO are achieved for microwave harmonic down-conversion. The RF-modulated optical signals and the RFWM-intensified optical LO signals are combined by an optical coupler and detected by a PD (11982A, DC-16 GHz) and an electrical LPF (PE8725, DC-3 GHz) to extract the down-converted IF signals.
In order to demonstrate the RFWM-intensified optical LO generation, we set the electrical LO at the frequency of 4.88 GHz with the power of 10 dBm, and the SOA at the injection current of 100 mA. The RFWM-intensified optical LO is spectrally observed with an optical spectrum analyzer (OSA, AQ6370C). For a better spectrum performance, the OBF is set with the bandwidth of 1.6 nm around 1550.8 nm to reserve a spectral width of about 200 GHz of optical LO, and the OBF is set with 0.7-nm red-shifted with respect to the optical carrier to satisfy the stronger FWM in the red-shifted wavelength region. We think this setting is helpful to stimulate the red-shifted harmonic sidebands and to suppress the blue-shifted harmonic sidebands, meanwhile, it will also help to alleviate the impact of asymmetry of IF tones by decreasing the amplitude ratio r according to Eq. (8).
As shown in Fig. 3, the optical harmonic spectra are obtained in the cases of open-loop and closed-loop, which are corresponding to the results of FWM-based and RFWM-based intensification, respectively, when the SOA is biased at 100 mA. In the open-loop case, the optical harmonic sidebands are only nonlinearly intensified once in the SOA, in which the FWM-based optical LO shows narrowband optical spectrum with less harmonic sidebands. Comparatively, in the closed-loop case, the RFWM-intensified optical LO features wideband optical spectrum with more harmonic sidebands by recycling the FWM intensification through optical feedback.
As illustrated in Fig. 4(a), higher-order harmonic sidebands of LO are generated and the spectrum width is obviously extended by increasing the injection current of SOA from 50 mA, 100 mA to 150 mA. However, the spectrum width is growing less and less under deep saturation when the injection current is increased up to 200 mA and 250 mA. As shown in Fig. 4(b), the RFWM-intensified optical LO can be set with different frequency spacing by changing the electrical LO, such as 4 GHz, 6 GHz, 8 GHz, 10 GHz and 12 GHz. In every case, the optical LO can be kept with the spectrum width of at least 0.8 nm (100 GHz). Therefore, the RFWM harmonic intensification provides tunable and wideband optical LO for microwave down-conversion operation.
Figure 5(a) illustrates the optical spectra output from the R-MZI when the SOA is biased at 100 mA. In the open-loop case, the optical spectra include the RF-modulated optical sidebands and the LO-modulated optical sidebands, where the harmonic sidebands of LO are obviously degraded when extending to the first-order sideband of RF. In contrast, the degradation of the harmonic sideband of LO is largely compensated by introducing the RFWM effect in the closed-loop case. From Eq. (7), the power of IF tones will be affected by the amplitude ratio of the same nth-order sidebands. In our experiment, the red-shifted harmonic sidebands are intensified heavier than the blue-shifted ones with respect to the optical carrier, like single-sideband harmonic generation, in which the 8th-order upper sideband is typical 48.21 dB stronger than the lower one, corresponding to amplitude ratio r of less than 0.004, so as to make the best use of the asymmetry between the upper and lower sidebands of LO and to reduce the influence from the phase difference of R-MZI as much as possible.
After photodetection, the 40-GHz RF signal is down-converted through the 8th-order upper sideband of LO to the IF frequency at fIF=|40-4.88×8| GHz=0.96 GHz with the signal-to-noise ratio (SNR) of 38.36 dB, as shown in Fig. 5(b). It should be noted that the optical spectrum of the RFWM-intensified LO can be appropriately optimized by changing the bandwidth of OBF in order to achieve convincing SNR of the IF signal in the case of down-conversion within 40 GHz. The 40-GHz RF signal can be also flexibly down-converted to different IF signals below 2 GHz with the same 8th-order upper sideband of optical LO by tuning the frequency of electrical LO from 4.98 GHz to 4.76 GHz, as shown in Fig. 6. In the down-conversion, all the IF tones show extremely narrow spectrum lines due to the inherent coherence of the RF-modulated optical signal and the RFWM-intensified optical LO in the R-MZI originating from the same optical carrier. Moreover, in the traditional OFDM-ROF applications, the fiber dispersion will result in power fading problem, due to the use of double sideband modulation of RF subcarrier . In contrast, the RFWM-intensified LO enables harmonic sideband generation in the red-shifted wavelength region with respect to the optical carrier, similar to a single sideband (SSB) optical frequency comb. And the down-conversion can be selectively operated for the upper or the lower first-order sideband of RF subcarrier, which can be seen in Fig. 5(a). Therefore, our scheme easily overcomes the impairment of frequency-selective fading (FF) in the fiber transmission.
For the wide frequency operation, different frequency RF signals is down-converted to IF band with the same electrical LO by using different order harmonic down-conversion. As shown in Fig. 7, RF signals ranging from 5 to 40 GHz with a frequency step of 1 GHz are converted to IF signals within 2 GHz by using the harmonics down-conversion from the first-order to the eighth-order sidebands of fLO=4.88 GHz. The down-converted IF tones show gradually decreasing in power as a function of the RF frequency, which is determined by the amplitude of the RF-modulated sidebands and the intensified LO harmonics. For comparison, the down-conversion based on FWM in the open-loop case are also measured under the same operation conditions of R-MZI, as shown by the red square line in Fig. 7. In our experiment, the modulation index and half-wave voltages of EOM-1 are measured to be (0.53, 4.5 V) at 5 GHz, (0.31, 5.67 V) at 20 GHz and (0.21, 7.67 V) at 40 GHz, which is characterized by using the heterodyne spectrum mapping method proposed in Ref. . As we know, the increased half-wave voltages of EOM-1 show the degradation of modulation efficiency, when the modulation frequency goes up to tens of GHz. In order to investigate the intrinsic performance of the proposed optical LO, we normalize the power of the down-converted IF tones to the RF driving levels of the EOM-1, which means the difference of the comparison are mainly contributed by the performance of the RFWM- and FWM- based optical LO itself. In Fig. 7, both methods show similar variation tendency in the case of fRF <17 GHz, while the FWM-based IF tones in the open-loop case decrease rapidly in the case of fRF >17 GHz and cut off in the case of fRF>22 GHz, due to the degraded FWM effect for the high-order harmonic generation especially in the range away from the center wavelength, which can also be proved in Fig. 3. Nevertheless, the proposed RFWM-based down-conversion has been demonstrated with ultra-wide frequency range and relative flat conversion efficiency, which is driven and tuned with a low-frequency electrical LO. Moreover, the asymmetry nature between the red-shifted and blue-shifted sidebands of the RFWM-intensified harmonic generation helps to reduce the influence from the phase difference of R-MZI structure and to stabilize the microwave down-conversion in practical applications.
A flexible photonics-assisted method is proposed based on RFWM-intensified optical LO for ultra-wide frequency microwave down-conversion with a low-frequency electrical LO. In the demonstration, the RFWM-intensified optical LO driven by an electrical LO at 4.88-GHz enables ultra-wide frequency spectrum up to 100 GHz, and RF signals ranging from 5 to 40 GHz are down-converted to the IF signals below 2 GHz. Prior to the conventional serial or parallel EOM-based approach, the proposed method enables microwave down-conversion with a low-frequency electrical LO. Compared with the OFC-based method, ours achieves flexible down-conversion by tuning the frequency of electrical LO. In contrast to the FWM-based method, the RFWM method obviously extends the spectrum bandwidth of optical LO by recycling the FWM products back to the SOA with an amplified ring loop, which also helps to improve the power efficiency of microwave down-conversion.
National Natural Science Foundation of China (61927821, 61901069, 61421002); National Key Research and Development Program of China (2018YFE0201901, 2018YFB2200702); Joint Research Fund of Ministry of Education of the People's Republic of China (6141A02022436); Innovation Special Zone Funds of National Defense Science and Technology (18-163-00-TS-004-040-01).
The authors declare that there are no conflicts of interest related to this article.
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