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A real-time broadband radio frequency (RF) spectrum analyzer is proposed and experimentally demonstrated to rapidly measure the RF spectrum of broadband optical signal. Cross phase modulation in the highly-nonlinear fiber is used to convert the RF spectrum carried by the pump to the optical spectrum of the probe signal, then the optical spectrum is real-time analyzed with the parametric spectro-temporal analyzer (PASTA) technology. The system performances are investigated in detail, including bandwidth, resolution, frame rate, and dynamic range. It achieves large RF bandwidth of over 800 GHz, as well as 91-MHz frame rate without sacrificing the resolution. It is noted that 91-MHz frame rate is several orders of magnitude improvement over those previous reported all-optical RF spectrum analyzers. As a proof-of-concept demonstration, this real-time broadband RF spectrum analyzer successfully characterizes the ultra-short pulse trains with repetition rate of 160GHz, which is far beyond capability of the conventional electrical spectrum analyzer. It presents a new way to implement rapid and broadband RF spectrum measurement, and would be of great interests for some ultrafast scenarios, where the real-time RF spectrum analysis can be applied.
© 2017 Optical Society of America
1. Introduction
Radio frequency (RF) spectrum of an optical signal is defined as the power spectrum of the optical temporal envelop and has been applied in a wide range of applications, such as the radar and imaging system, the phase noise and dispersion measurement in optical communication systems [1–4]. The conventional scheme to measure the RF spectrum is based on the electrical spectrum analyzer (ESA), in which the optical envelop is first obtained by a fast square-law photo-detector, and then followed with an ESA to resolve the spectrum. However, the electronic components restrict the measurement bandwidth to be around 100 GHz [5], which hinders its applications for optical signals with ultra-large bandwidth.
Recently, the measurement schemes with broadband RF bandwidth (>100 GHz) are highly demanded due to the rapid development of the high-speed optical communication [6] and the ultrafast laser technology [7]. C. Dorrer et. al. introduced an all-optical RF spectrum analyzer with 800-GHz bandwidth [8], based on the cross-phase modulation (XPM) in highly-nonlinear fiber (HNLF) [9]. In this scheme, the XPM in HNLF plays an important role of transferring the RF spectrum of the pump signal under test to the optical spectrum of the probe signal, which can be directly analyzed by an optical spectrum analyzer (OSA) [10]. To further improve this scheme, M. Pelusi et. al. replaced the HNLF with a dispersion-engineered As2S3 waveguides and demonstrated a compact RF spectrum analyzer with over 2.5-THz bandwidth [11]. Moreover, B. Corcoran et. al. analyzed the impact of the free carrier effects and the two-photon absorption in silicon waveguide, and demonstrated a RF spectrum analyzer with 1.6-THz bandwidth [12]. More recently, M. Ferrera et. al. reported a CMOS compatible integrated RF spectrum analyzer based on the doped silica glass waveguide with the bandwidth larger than 2.5 THz [13]. Leveraging the advantage of the broadband bandwidth (>100 GHz), these all-optical RF spectrum analyzers have been applied in some areas, such as the dispersion monitoring for 640 Gb/s DPSK signals [14], the in-band optical signal-to-noise ratio monitoring of 320 Gb/s signals [15], and the ultrafast waveform analysis [16]. To improve the resolution of this analyzer, C. Heras et. al. has demonstrated a RF spectrum analyzer based on the Brillouin OSA with a resolution of 10 MHz [17].
However, these aforementioned all-optical RF spectrum analyzers are usually based on the low speed OSAs, the mechanical-scanning grating can only capture a few frames per second, and cannot be used to implement rapid RF spectrum measurement which required in the advanced optical communication [18] and the microwave communication systems [19]. Fortunately, some ultrafast OSAs, such as the parametric spectro-temporal analyzer (PASTA) and amplified dispersive Fourier transformation (ADFT), have achieved the frame rate up to tens of MHz [20,21]. In these ultrafast OSAs, the temporal dispersion is introduced and the spectrum of the signal is mapped into time domain. In terms of the input condition, the PASTA can capture arbitrary waveform within the time-window, while ADFT can only characterize the short pulse, therefore the PASTA is a better candidate to capture the continuous signal in our scheme. In this work, a real-time broadband radio frequency (RF) spectrum analyzer is proposed and experimentally demonstrated based on the XPM in HNLF and the PASTA technology. This RF spectrum analyzer not only has large observation bandwidth (over 800 GHz), but also achieves a frame rate as high as 91 MHz, which is several orders of magnitude improvement over the aforementioned RF spectrum analyzers. It provides a promising solution to implement the real-time RF spectrum analysis, such as the instantaneous frequency measurement [22] and real-time monitoring of the optoelectronic oscillator [23].
2. Principle and experimental setup
The spectrum analysis (optical spectrum and RF spectrum) is essential to characterize the optical signal. The optical spectrum F(ω) and the RF spectrum S(ω) are defined as,
where the optical spectrum F(ω) contains both amplitude and phase information, while the RF spectrum S(ω) only contains amplitude information. By using the aforementioned XPM effect, the amplitude information of the pump signal is converted into phase information of the probe signal, thus the RF spectrum of the pump signal can be directly obtained from the probe’s optical spectrum. As an assumption, the temporal intensity of the pump is given as I(t) = P[1 + cos(2πΩt)], where Ω is the radio frequency. It is noted that the intensity is assumed to be normalized such that P represents the pump average power [9]. Therefore, its RF spectrum can be expressed as S(ω) = P2[δ(ω) + δ(ω + 2πΩ)/4 + δ(ω–2πΩ)/4]. After the XPM process, the probe signal is phase-modulated by M[1 + cos(2πΩt)], where M = 2γLP is the average nonlinear phase shift, γ is the nonlinear coefficient and L is the length of the HNLF (neglecting the linear loss). Therefore, the probe signal can be expressed as the series of the Bessel function on Jacobi-Anger expansion [24]:where Jn is the n-th order Bessel function of the first kind. Equation (2) indicates that the optical spectrum of the modulated probe is consisted of the harmonic frequencies at ωprobe + 2nπΩ, whose amplitude corresponds to the Jn(M). In most cases, the optical spectrum of the probe signal cannot precisely reflect the RF spectrum of the pump signal. However, if M < 0.2 rad, J0(M) ≈1, the first order Bessel function J1(M) becomes dominant, and can be approximated as a linear function with slope k = 0.5, with less than –25-dB error, as shown in Fig. 1. Therefore, the modulated probe signal can be simplified as (neglecting constant phase components):
Fig. 1 The approximation of the XPM conversion process. (a) The ratio of the sum of other orders Bessel functions to the first order. (b) The first order Bessel function is fitted to a linear function with slope k = 0.5. (c) The error between first order Bessel function and the linear function.
After Fourier transform, the optical spectrum of the modulated probe signal can be expressed as:
which also reflects the RF spectrum of the pump signal. Moreover, the intensity of the RF spectrum is also reflected in Eq. (4), with the pump power P as a factor to the corresponding Dirac function.According to the space-time duality, the diffractive propagation of a beam in the spatial domain is analogous to the dispersive propagation of a pulse in the temporal domain. This analogy indicates that some spatial systems can be interpreted to the counterparts in the temporal domain [25,26]. For example, the time-lens, the counterpart of the spatial lens, introduces a temporal quadratic phase exp(–it2/2Φf) to the injected field, where Φf is the focal group delay dispersion (GDD). As shown in Fig. 2(a), at its temporal focal plane (output GDD Φo = Φf), the optical spectrum of the injected field will be mapped into the time axis, with the relation: Δt = ΦfΔω. This temporal focusing mechanism is the principle of the PASTA, and its output intensity can be simplified as:
where Ipulse(τ) represents the single wavelength point spread function (PSF) of the PASTA [27]. To make full use of the PASTA bandwidth and also avoid the temporal overlapping, only single side of the two probe sidebands generated after the XPM is filtered out and can be expressed as:Fig. 2 (a) Temporal ray diagram of temporal focusing mechanism. Φf: the focal GDD. (b) The schematic illustration of the real-time RF spectrum analyzer. Red-solid line: the temporal intensity; red-dashed line: the phase; black-solid line: the optical spectrum. (c) The detailed experimental setup of PASTA system. TLS: tunable laser source; WDMC: wavelength division multiplexing coupler; PD: photo-detector; BPF: band-pass filter.
Therefore, this PASTA based RF spectrum analyzer achieves the frequency-to-time mapping relation:
which reveals that the temporal position of the output pulse is proportional to the radio frequency Ω, with a factor of 2πΦf.The schematic illustration of the real-time RF spectrum analyzer is shown in Fig. 2(b). The pump signal under test is combined with a 4-dBm continuous-wave (CW) probe signal at 1544.1 nm, and injected into a HNLF (L = 300 m and γ = 10 w–1 km–1) for the XPM. Therefore, the RF spectrum carried by the pump is converted to the optical spectrum of the probe as the Fig. 2(b) shown. It is also noted that the power of pump signal should be appropriate to decrease the distortion taken by the conversion process. Since two generated sidebands of the probe are identical, a tunable rectangular filter with 10-nm bandwidth is adopted to filter out the short wavelength band in order to avoid the further temporal overlapping. Followed with the PASTA system, there are two-stage degenerated four-wave mixing (FWM) processes, as the Fig. 2(c) shown. The first stage FWM process acts as the time-lens, and adds the quadratic phase of the chirped pump to the filtered sideband. The chirped pump with a power of 18 dBm is generated from a short pulse (with 3.2-nm bandwidth) passing through sufficiently large dispersion (–1115 ps/nm) [28]. Here, the newly generated idler of the first FWM is filtered out by a band-pass filter (BPF1). The second stage FWM process with a 20-dBm CW pump acts as a phase conjugator or a spectral mirror [29], and it benefits the dispersion matching process. After the second stage of the FWM, the BPF2 is available to filter out the idler with conjugated phase. The focal dispersion of the PASTA system is –665 ps/nm, and achieves 3.57-ns temporal aperture. The compressed pulse at the temporal focal plane, namely the RF spectrum, is then captured in real-time by the acquisition system with 50-GHz bandwidth, including the photo-detector (PD) and oscilloscope. It is noticed that the bandwidth of the PASTA has been optimized to 10 nm by adopting a shorter HNLF (L = 100 m).
3. Results and discussion
3.1 Bandwidth
According to the aforementioned introduction, the observation bandwidth is essential for the RF spectrum analyzer. To explore its bandwidth, we can monitor the output pulse change in the time axis by sweeping the radio frequency Ω. Because the bandwidth of ordinary electro-optic modulator is limited under 60 GHz, we use the optical beating process to generate the ultrahigh frequency signals, in which the beating frequency equals to the difference frequency between two co-polarized CW sources. As shown in Fig. 3(a), one CW source (black solid line) is kept at 1557 nm, while the other (red solid line) is red-shift to generate the swept radio frequency. Combined with another CW probe signal (blue solid line) at 1544.1 nm, the XPM process in the HNLF generates two sidebands (red-dashed line) located besides the probe signal, with equal frequency spacing of Ω. Since these two sidebands carry the identical information, a tunable rectangular filter (green solid line) with 10-nm bandwidth is adopted to filter out the short wavelength band to avoid further temporal overlapping. The filtered spectrum is then measured by the PASTA, converted to the time axis, as shown in Fig. 3(b), where the temporal interval is proportional to the radio frequency Ω under test.
Fig. 3 Schematic of the bandwidth measurement. (a) The spectrum of the XPM process between the beating pump signals and the probe signal, and the generated sideband is filtered out by a rectangular filter (green line). (b) The filtered spectrum captured by the PASTA in the temporal domain. It is noted that, the blue line at zero point is part of the probe signal, which is located at the edge of the filter, and can be used as a temporal reference.
As a comparison, the 3-dB bandwidth (the frequency at half maximum) of the RF spectrum analyzer based on a conventional OSA is firstly measured as shown in Fig. 4(a). The 3-dB bandwidth is around 800 GHz (6.4 nm), and it is mainly limited by the walk-off effect between the pump and probe signal in the HNLF [8]. It is also noticed that, the measured RF intensity is almost linear decreasing as the radio frequency Ω is increasing. On the other hand, the bandwidth of the real-time RF spectrum analyzer based on the PASTA is shown in Fig. 4(b). Owning to the negative output dispersion (–665 ps/nm), the RF spectrum displays in the opposite direction, with the mapping relation of 5.2 ps/GHz. The 3-dB bandwidth of our scheme is also around 800 GHz, and not affected by the introduced PASTA system. In this configuration, the bandwidth of the PASTA is 1.25 THz (10 nm from 1534 nm to 1544 nm), which is beyond that of the XPM (800 GHz). In contrast to the conventional OSA configuration, the tendency of the RF intensity is different, which does not decrease until the radio frequency Ω increases beyond 500 GHz, which is affected by the observation window of the PASTA.
Fig. 4 The observation bandwidth of the RF spectrum analyzer. (a) Based on the conventional OSA. (b) Based on the PASTA.
3.2 Resolution
Besides the bandwidth, the resolution of the real-time RF spectrum analyzer is also critical for the applications, and it reflects the capability of distinguishing different radio frequencies. According to Eq. (7), the frequency resolution is proportional to the output pulsewidth. Therefore, the output pulse was first experimentally measured with the frequency Ω at 500 GHz, as the black solid line shown in Fig. 5(a), where the pulsewidth is around 15 ps, corresponding to the frequency resolution of 2.8 GHz (0.023 nm). In principle, without considering the bandwidth limitation, the resolution is determined by the output optical pulsewidth to. If the optical pulsewidth to can be fully captured, the resolution can be expressed as δf = to/2πΦf. In this experiment, 50-GHz acquisition bandwidth can fully resolve 8.8-ps pulsewidth, which is finer than the output optical pulsewidth. Therefore, the frequency resolution is fully determined by the output optical pulsewidth. Moreover, due to the higher order dispersion of the PASTA system, the pulse envelop also exhibits a long tail at its leading edge, and it further degrades the resolution. Furthermore, another RF frequency at 503.8 GHz was introduced to test its resolution, as the red-dashed line shown. The 3.8-GHz frequency difference can be distinguished by this real-time RF spectrum analyzer. In other words, it has demonstrated the resolution of 3.8 GHz. It is noted that compared with 3.8-GHz resolution, the two CW lasers with 100-kHz linewidth and 100-MHz frequency instability do not affect the experiment results.
Fig. 5 Performance of the real-time RF spectrum analyzer. (a) Resolution performance. Black-solid line: the output pulse envelop with single frequency at 500 GHz; red-dashed line: the output pulse envelop with two frequencies at 500 GHz and 503.8 GHz. (b) The two consecutive measured RF spectra with the frame rate of 91 MHz. (c) The dynamic range performance of the RF spectrum analyzer.
3.3 Frame rate
The frame rate, which reflects the temporal resolution of the RF spectrum analyzer to implement the dynamic spectrum analysis, is essential for some ultrafast observation and the major improvement of our scheme. The conventional OSA based on the mechanical-scanning or the charge-coupled device (CCD) sensor usually achieves the frame rate less than 1 kHz, thus can hardly be applied for some ultrafast scenarios. By comparison, the real-time RF spectrum analyzer based on PASTA provides a promising option for the ultrafast observation applications. As shown in Fig. 5(b), two consecutive RF spectra with the time spacing of 11 ns are captured by our scheme, which means that 91-MHz frame rate is achieved, and it is several orders of magnitude improvement over the aforementioned reported schemes. The frame rate is determined by the repetition rate of the pulse source, and it can be further improved to around the highest frame rate by time division multiplexing (TDM). However, to avoid the overlapping between the neighboring periods, the highest frame rate is also limited by the maximum frequency range, and 800-GHz bandwidth results in 235-MHz highest frame rate.
3.4 Dynamic range
In our scheme, the dynamic range is mainly limited by two factors. The first one (lower limit) is the minimum requirement for the XPM effects. The XPM induced phase shift range is proportional to the power of the pump signal, which determines the intensity of the newly generated sideband. The other factor (upper limit) is related with the RF spectrum conversion process. As discussed in the principle part, the average phase shift M should be smaller than 0.2 rad (corresponds to 15.2-dBm input power) to make sure the conversion accuracy. To measure the dynamic range of the real-time RF spectrum analyzer, the average input power was changed from 4 dBm to 16 dBm, and the corresponding output peak intensity versus the input power was plotted as the red dot in Fig. 5(c). The linear fitting (black solid line) shows the slope of 2, which matched well with the relation in Eq. (6). It is noted that, for the input power between 4 dBm to 14 dBm, the output peak intensity is linearly fitted. When the input power keeps increasing beyond 14 dBm, the output peak intensity is slightly deviated from the fitting (black line), owning to the harmonic sidebands generation introduced by some other nonlinear effects. This result is in accord with the aforementioned upper limit, and it exhibits the dynamic range from 4 dBm to 14 dBm. It is noted that, the lower limit can be enhanced by introducing an external booster amplifier, thus it can be applied in more applications with weak signal power under 4 dBm.
3.5 Characterization of ultrahigh repetition rate pulses
To investigate the performance of this real-time RF spectrum analyzer, a 10-GHz pulse train with 1.3-nm bandwidth was first introduced, with the RF 3-dB bandwidth around 110 GHz, as the red-dash-dotted line shown in Fig. 6(a). The RF spectrum is consisted by the harmonic frequencies, with the spacing of 10 GHz. This RF spectrum was firstly captured by the ESA with 40 GHz bandwidth, as the blue line shown. Due to the limited bandwidth, the frequency beyond 40 GHz cannot be observed. As a comparison, this pulse train was also measured by our scheme as the black solid line shown in Fig. 6(a), and the time axis is converted to the frequency according to the Eq. (7). It is obvious that the experiment matched well with the simulation with little deviation. The measured 3-dB bandwidth is also around 110 GHz, corresponding to the pulsewidth of 2.8 ps, which is matched well with the experiment value (2.78 ps) measured by an optical sampling oscilloscope (EYE-1100C). It should be emphasized that this measurement was performed with the frame rate as high as 91 MHz.
Fig. 6 Characterization of the pulses at ultrahigh repetition rate. (a) The RF spectrum of a 10-GHz pulse source. (b)&(c) The experimental measured & simulated RF spectrum of 160-GHz pulse trains.
To further demonstrate the system’s capability, another 10-GHz pulse source with 1.8-nm bandwidth was multiplexed to 160 GHz based on the optical time-division multiplexed (OTDM) technology, and its RF spectrum is far beyond the capability of the ESA. The RF spectrum of this ultrahigh-speed signal was then characterized by our real-time RF spectrum analyzer, as the black solid line shown in Fig. 6(b). Two harmonic tones at 160 GHz and 320 GHz were observed without other sub-harmonic tones, which manifests that the OTDM process is performed in good condition. By comparison, here some misalignment was introduced to the first multiplexed stage (10 GHz-20 GHz), with 3-dB intensity difference between two optical branches, and the results are shown as the red-dash-dotted line in Fig. 6(b). It is observed that, this misalignment makes some sub-harmonic tones at 10 GHz, 150 GHz, 170 GHz, 310 GHz and 330 GHz appear, and the origin two frequency tones are broadened. Similar effects are also observed in the simulation results as shown in Fig. 6(c). Therefore, our scheme is capable of monitoring the performance of the OTDM signal.
4. Conclusions
In conclusion, a real-time broadband RF spectrum analyzer has been proposed and experimentally demonstrated with over 800-GHz bandwidth and 91-MHz frame rate. This scheme is based on the XPM process and the PASTA spectroscopy, which helps to achieve large observation bandwidth and high frame rate, respectively. The detailed analysis of this RF spectrum analyzer is also explored, including bandwidth, resolution, frame rate and dynamic range. Firstly, the observation bandwidth is limited by the XPM conversion process in the HNLF, since the 10-nm PASTA bandwidth can fully cover this RF range. Leveraging some integrated nonlinear waveguides [30], the bandwidth is promising to be improved up to THz. Secondly, the 3.8-GHz RF resolution corresponds to 0.03-nm spectral resolution, and it is limited by the PASTA spectroscopy. In principle, the PASTA with 3.57-ns temporal aperture can achieve the finest resolution of 2.2 pm, while it is degraded by the higher-order dispersion and limited detection bandwidth. By introducing the temporal magnification [31], or better dispersive fiber matching, the RF resolution can be improved. Thirdly, the frame rate is as high as 91 MHz, which is several orders of magnitude improvement over the previous reported optical RF spectrum analyzers. Leveraging some temporal multiplexing methods, e.g. the OTDM or the temporal buffer [32], the frame rate can be further improved. Last but not the least, the dynamic range is measured to be 10 dB, with the average input power from 4 dBm to 14 dBm, limited by the average phase shift range of the XPM conversion. Furthermore, to demonstrate its capability of some dynamic signal measurement, the ultra-short pulse trains with ultrahigh repetition rates are characterized, and the measured RF spectrum of the 160-GHz pulse train are in good accordance with the simulation. Leveraging the nonlinear waveguides, the integrated all-optical RF spectrum analyzer with a frame rate of MHz and a bandwidth of THz can be realized in the future and it is promising as a key tool for numerous applications where the rapid RF spectrum acquisition is essential.
Funding
National Natural Science Foundation of China (NSFC) (Grants No. 61631166003, 61675081, 61505060, 61320106016, and 61125501), the Natural Science Foundation of Hubei Province (Grant No. 2015CFB173), and the Director Fund of WNLO.
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