Real-time electrical spectrum analysis is of great significance for applications involving radio astronomy and electronic warfare, e.g. the dynamic spectrum monitoring of outer space signal, and the instantaneous capture of frequency from other electronic systems. However, conventional electrical spectrum analyzer (ESA) has limited operation speed and observation bandwidth due to the electronic bottleneck. Therefore, a variety of photonics-assisted methods have been extensively explored due to the bandwidth advantage of the optical domain. Alternatively, we proposed and experimentally demonstrated an ultrafast ESA based on all-optical Fourier transform and temporal magnification in this paper. The radio-frequency (RF) signal under test is temporally multiplexed to the spectrum of an ultrashort pulse, thus the frequency information is converted to the time axis. Moreover, since the bandwidth of this ultrashort pulse is far beyond that of the state-of-the-art photo-detector, a temporal magnification system is applied to stretch the time axis, and capture the RF spectrum with 1-GHz resolution. The observation bandwidth of this ultrafast ESA is over 20 GHz, limited by that of the electro-optic modulator. Since all the signal processing is in the optical domain, the acquisition frame rate can be as high as 50 MHz. This ultrafast ESA scheme can be further improved with better dispersive engineering, and is promising for some ultrafast spectral information acquisition applications.
© 2017 Optical Society of America
Electrical spectrum analyzer (ESA) is a fundamental instrument widely applied in a verity of fields including the wireless communication, the radar system, and the radio astronomy [1–3]. Conventional super-heterodyne spectrum analyzer can achieve hyperfine resolution and large observation bandwidth, but the operation speed is mainly restricted by the sweep time of the local oscillator. As an improvement, the fast Fourier transform (FFT) based ESA greatly enhanced the measurement speed while maintaining a finer resolution. However, the observation bandwidth of this ESA system is inherently limited by that of the analog-to-digital converter (ADC) which is essential for the FFT process . Therefore, the conventional ESA based on electronic technology is hard to further extend the observation bandwidth and the acquisition frame rate, which is undesirable in many applications where ultrafast analysis or large bandwidth measurement is required. Fortunately, photonics-assisted spectrum analysis approaches have arisen with the advanced microwave photonics, which leverages the large bandwidth in the optical domain, and multiplexes the radio-frequency (RF) to the optical field by an electro-optic modulator (EOM) . These RF measurement approaches are able to achieve large bandwidth or fast acquisition frame rate, based on different mechanisms, such as optical power monitoring [6–9], optical channelizing [10–13], time-domain optical processing like time stretch [14,15] and all-optical Fourier transform [16,17], and compressed sensing (CS) [18–20]. The optical power monitoring maps the RF frequency to the output power, thus the frequency can be identified by measuring the optical power. Although a fine resolution and wide bandwidth can be achieved, this kind of method can only characterize a single frequency component. Alternatively, the optical channelizer approach is usually implemented with the RF source multiplexed to an optical carrier that its spectrum is up converted to the optical band, thus, can be resolved by an optical spectrum analyzer, namely the optical channelizer, which maybe a Fabry-Perot etalon , a array waveguide gratings (AWG) , or a diffraction grating . Owing to the limited resolving power of the optical channelizer, the resolution of this approach is always exceed 1-GHz. To improve the resolution, another scheme is proposed with the RF waveform multiplexed to a dispersive stretched optical pulse, and then sampled in the spectral domain by an optical channelizer with 25-GHz channel spacing. According to the Nyquist’s law and the RF spectrum can be precisely retrieved from the sampling data through an FFT manipulation . The resolution is improved to hundreds of megahertz or even tens of megahertz, while sacrificing the acquisition frame rate due to the post processing based on digital signal processor. Time stretch attracted wide attention recently for its unique of fast continuous single-shot measurement . For the application of the analog-to-digital conversion , the electrical signal is intensity modulated on a chirped pulse, and followed with another spool of dispersive fiber, the envelope of the electrical signal is temporally stretched and can be captured with lower bandwidth. However, the time-bandwidth product is degraded as well, since its temporal magnification process do not improve the resolution while greatly enlarge the temporal window. Moreover, an FFT manipulation is required for the spectral analysis, which further hinder the operation speed. This concept combined with compressed sensing technology can further reduce the acquisition bandwidth, e.g. using <1% of the Nyquist sampling rate , which is of great importance for ultra-wideband signal. However, this scheme is not suitable for the observation of some fast chirped frequency components, and the complex reconstruction algorithm also hindered its wide application.
Moreover, the all-optical Fourier transform approach multiplexes the RF source to the Fourier domain of an optical pulse by an EOM, followed by a dispersive Fourier transform, its frequency information will be converted to the time domain, proportional to the convolution of the pulse and the scaled RF spectrum. It is noted that 1-GHz frequency only corresponds to 8-pm optical spectral width, in order to obtain finer resolution, a picosecond or even femtosecond pulse source as well as large volume of dispersion are employed here. However, another problem brought by the ultrashort pulse source is that the output field is far beyond the observation bandwidth of the state-of-the-art photo-detector (PD) and oscilloscope, so that the spectral resolution is greatly degraded . Otherwise, some nonlinear gating methods like the autocorrelation detection technique is required, which would greatly hinder the operation speed . To overcome this limitation, a temporal magnification system is introduced in this paper to further stretch the time axis and relax the bandwidth requirement. With suitable dispersion relation, the temporal magnification system is capable of scaling the time axis by hundreds of times [21,22]. Therefore, the aforementioned ultrafast output field can be directly measured in real-time, and this ESA system can easily achieve over MHz acquisition frame rate, leveraging the dispersive frequency-to-time mapping and the time-resolved detection . The ultrafast spectrum analyzer proposed here provide an alternative solution for some applications where ultrafast acquisition frame rate and large observation bandwidth are demanded simultaneous, such as the observation of dynamic frequency evolutions, the capture of instantaneous frequency, etc.
2. Principle of operation
Figure 1(a) shows the temporal ray diagram of the proposed scheme for RF frequency measurement. A point light source is first transformed to the Fourier domain by propagating a certain distance before periodically modulated by a sinusoidal grating in the Fourier plane. After opposite propagation (opposite direction with identical distance), namely an inverse Fourier transform, the modulated field will be focused into two spots, and the departure of them is proportional to the density of the grating, according to the convolution theorem of Fourier transform. To further separate the two spots, a converging lens is employed here to construct a magnification system. According to the space-time duality , the temporal counterpart of this system is proposed as shown in Fig. 1(b). Firstly, an ultrashort optical pulse A0(τ) (U0(ω) in frequency domain) is stretched by a spool of dispersion-compensating fiber (DCF), and the output field A1(τ) (U1(ω) in frequency domain) can be expressed in frequency domain as U1(ω) = U0(ω)G1(ω), where G1(ω) = exp(iβ2(1)L1ω2/2) is the frequency-domain transfer function of the DCF, with β2(1) and L1 being the group velocity dispersion (GVD) parameter and the fiber length, respectively. Followed by an EOM, the RF source f(τ) (F(ω) in frequency domain) to be measured is uploaded to the optical band. In order to ensure the linear modulation, the bias should be set around Vπ (switching voltage of the EOM) and the voltage of the RF source should be smaller enough. Assuming that Vbias = Vπ and |f(τ)| is sufficiently small (small signal approximation), the modulated field can be approximated as:
After passing through another spool of single-mode fiber (SMF) (frequency-domain transfer function is G2(ω)), the modulated field is focused to be:16], or some complex methods like the autocorrelation detection were employed to measure the output pulses , but greatly degraded the acquisition frame rate. Leveraging the space-time duality, a temporal magnification system is introduced here to stretch the temporal axis, so that the ultrashort pulse will be enlarged to be detectable for the conventional oscilloscope. As show in Fig. 1(b), the temporal magnification system is consist of a spool of SMF, a time-lens and a spool of DCF, where Φin = β2(2)Lin and Φout = β2(1)Lout correspond to the input and the output GDDs, respectively. Similar to the space-lens, the time-lens introduces a quadratic phase modulation in the time axis, and it can be implemented by a variety of methods . Considering the four-wave mixing (FWM) based time-lens, an ultrashort pulse first passes through a dispersive fiber to generate the swept-pump. When the bandwidth is wide enough, the amplitude envelop can be neglected, and the swept-pump can be expressed as Ap(τ) = exp(–iτ2/2Φp) , where Φp is the GDD of the dispersive fiber. On the other hand, the focused A3(τ) (U3(ω) in frequency domain) is the input field of the temporal magnification system, it is first diverged by the input GDD (Gin(ω) as the transfer function) and becomes A4(τ). The parametric mixing process happens between the signal A4(τ) and the swept pump Ap(τ) in a high nonlinear dispersion-shifted fiber (HNL-DSF), the quadratic phase of the pump will be multiplied to the newly generated idler. The idler can be simply written as A5(τ) = A4*(τ) Ap2(τ) = A4*(τ)h(τ) , where h(τ) = exp(–iτ2/Φf) is the transfer function of the time-lens, with Φf = Φp/2 being its focal GDD. Therefore, the scaled output field of the magnification system can be derived as:Equation (4) can be further simplified as:
It is indicated that the output field is scaled by a factor of M. By adjusting the dispersive parameters of the temporal magnification system, the time axis can be stretched by tens of times, and the conventional PD and oscilloscope are able to capture the output field. Thus an ultrafast RF spectrum analysis approach is realized without degrading the resolution. According to the derived spectral resolution expression, 1-ps pulsewidth (δτ) and 1ns/nm dispersion (Φ0) indicated a resolution of about 200 MHz. The simulation results of this ultrafast ESA is shown as Fig. 2(a), with the ideal temporal magnification system, it can resolve frequencies with 200-MHz separation (red line). If consider the limited temporal window of the magnification time-lens, the resolution will be a little bit degraded (blue line). While the high-order dispersion will further degraded as the black line, which can only resolve 500-MHz frequency spacing. Another important feature of this ultrafast ESA is its ability to resolve some fast chirped frequencies, and its simulation performance is manifested in Fig. 2(b). As the frequency sweeping increasing, the resolving spectral width is broadened, and this scheme can capture the maximum chirp rate of 40 MHz/ns, with the peak power degraded by a factor of 2.
3. Experimental results and discussions
The experimental setup of the ultrafast and large bandwidth ESA is illustrated in Fig. 3, and it consists of the optical Fourier transform part and the temporal magnification part. To make sure the repetition rates are synchronized, the pulse sources of these two parts are filtered from the same mode-locked fiber laser (MLFL), with 1-ps pulsewidth and 50-MHz repetition rate. The spectrum and the normalized waveform (seriously broadened due to the limited observation bandwidth) of the MLFL are shown in Fig. 4. To generate a swept pump of the time-lens, part of the pulse source (the lower branch, filtered from 1555 nm to 1565 nm) passes through a spool of 5-km SMF. While the upper branch of the pulse source (filtered from 1532 nm to 1544 nm) is applied for the optical Fourier transform part, which is first stretched by a spool of DCF with ~1-ns/nm dispersion (compensating 60-km SMF). Then the RF signal under test was multiplexed onto the wavelength-to-time mapped stretched source through an amplitude modulator, with 20-GHz bandwidth and 3.5-V switching voltage. The small signal approximation requires the drive voltage under 1 V. This modulator is followed with 63-km SMF, 60-km of which is matched with the dispersion of the first DCF, and compresses the stretched source to realize the optical Fourier transform part. Another 3-km SMF is acted as the input dispersion of the temporal magnification system. Subsequently, the signal is coupled into a 100-m HNL-DSF with the lower branch swept-source as the time-lens. The generated idler is filtered out, and passing through a spool of DCF as the output dispersion. Finally, it is boosted up by a pre-amplifier and captured by a 40-GHz PD and a 16-GHz real-time oscilloscope. It is emphasized that the fiber length of the time-lens system is optimized to satisfy the temporal imaging condition, while ensuring a large magnification factor to stretch the pulse to be directly captured by the conventional temporal oscilloscope.
A 10-GHz sinusoidal signal under test is first applied to the modulator with 2.5-V bias voltage. The waveform before (average power of 8.5 dBm) and after (average power of –3.5 dBm) the amplitude modulator is exhibited in Fig. 5, with ~12-dBm insertion loss. As shown in Fig. 5(a), the ultrashort pulse source is temporally stretched to around 13 ns, which represents the time window of this ultrafast ESA system. Considering the limited time window, this ESA is incapable of measuring a frequency below 70 MHz, though it can be further improved by increasing the dispersion (> 1 ns/nm) of the optical Fourier transform part or providing larger spectral width. Figure 5(b) certified that the RF frequency is successfully multiplexed to the time axis of the stretched field.
After the 63-km SMF, the signal is coupled together with the lower branch swept pump into the HNL-DSF, where the FWM process took place. With 15-dBm pump power and 5-dBm signal power, the FWM process achieves –20-dB conversion efficiency, as shown in Fig. 6(a). The idler was filtered out and passed through the output dispersion (DCF), and the output trace was captured as shown in Fig. 6(b), where 50-MHz acquisition frame rate is realized. Within a single observation period, as shown in Fig. 6(c), the central pulse represents the DC component, which can be adjusted by controlling the bias voltage, and it is set as the reference frequency. Besides the DC pulse, the other two neighboring pulses represent the frequency of the RF signal, also characterized by a conventional ESA (inset of Fig. 6(c)). Some harmonic frequency components appear due to the large drive voltage (2.2 V in this configuration) breaking the small signal approximation, as well as the FWM process. It is also noted that, the harmonic can be suppressed as the drive voltage decrease, and by adjusting the Vbias, the DC component can be controlled accordingly, as shown in Fig. 6(d).
Scanning the frequency of the RF signal from 2 GHz to 20 GHz with an equal spacing of 2 GHz, the results recorded by the oscilloscope is exhibited in Fig. 7(a), where different colors represent different response frequencies. The amplitude roll-off curve mainly comes from the limited EOM bandwidth, the pump pulse shape, and FWM conversion bandwidth. Also the temperature fluctuation will introduce some misalignment between the pump and signal pulse in the FWM processing, thus lead to a time-dependent amplitude fluctuation. Owing to the third-order dispersion in the fibers, there is a notable asymmetry between the two neighboring pulses under the same RF frequency. Since the right hand side part is much sharper than the left part, only the right hand side is considered to achieve finer resolution. Considering the frequency-to-time mapping ratio is 4 GHz/ns, 250-ps pulsewidth corresponds to 1-GHz RF spectral resolution. According to the time-bandwidth product limit, the idea resolution of the proposed ultrafast ESA will be 50 MHz, by making full use of the 20-ns temporal window (with ideal dispersion). However, in practical, the resolution will be seriously degraded by the higher-order dispersion and the dispersion mismatch in the temporal magnification system, as well as the partially occupied temporal window [28,29].
Finally, the dynamic range performance of the ultrafast ESA system is investigated by successively increasing the amplitude of the RF signal before the drive amplifier, and the normalized response power (the maximum peak power as the reference) of the output pulse is depicted in Fig. 7(b). It is evident that the modulator has an optimum operating range, namely the small signal approximation, where the output power of the ultrafast ESA is quasi-linear increasing, as the Eq. (3). In fact, a low driving voltage would result in poor signal-to-noise ratio, while the higher driving voltage exceeds the small signal approximation range of the EOM, and both cases will confine the dynamic range. Therefore, suitable pre-amplification is necessary before measuring an RF signal using the ultrafast ESA proposed here.
In conclusion, we have experimentally demonstrated an ultrafast and large bandwidth ESA. Under the condition of the experimental parameters, the spectral resolution can theoretically achieve hundreds of megahertz, furthermore, it will be enhanced if a shorter pulse source or larger dispersion is employed. But actually, the experimental result shows that the minimum resolvable frequency spacing of the analyzer is about 1-GHz, which can be greatly improved when a more accurate dispersion matching is implemented. Additionally, a larger pupil size of the time-lens, or equally a longer duration of the swept pump here, brings a finer resolution. Moreover, the demonstration confirmed an observation bandwidth over 20 GHz. Due to the limitations of the equipments, a higher frequency is not tested in the experiment. In fact, the measurement range of the analyzer can be increased by using a time-lens with a larger aperture, but finally limited by the bandwidth of the modulator. Specially, an acquisition frame rate of 50 MHz is demonstrated here, which can be further raised up if necessary. Such an ultrafast operation speed of the RF spectrum analyzer is of great significance for various applications such as dynamic spectrum monitoring and instantaneous frequency capturing.
The work was partially supported by grants from the National Natural Science Foundation of China (Grants No. 61631166003, 61675081, 61505060, 61320106016, and 61125501), the Natural Science Foundation of Hubei Province (Grant No. 2015CFB173), and the Director Fund of WNLO.
References and links
1. T. S. Rapport, Wireless Communications: Principles & Practice (Prentice Hall, 1996).
2. A. W. Rihaczek, Principles of High-Resolution Radar (Artech House, 1996).
3. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]
4. A. A. Adnani, J. Duplicy, and L. Philips, “Spectrum analyzers today and tomorrow: part 1 towards filter banks-enabled real-time spectrum analysis,” IEEE Instrum. Meas. Mag. 16(5), 6–11 (2013). [CrossRef]
5. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
6. L. A. Bui, M. D. Pelusi, T. D. Vo, N. Sarkhosh, H. Emami, B. J. Eggleton, and A. Mitchell, “Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber,” Opt. Express 17(25), 22983–22991 (2009). [CrossRef] [PubMed]
7. J. Zhou, S. Fu, P. P. Shum, S. Aditya, L. Xia, J. Li, X. Sun, and K. Xu, “Photonic measurement of microwave frequency based on phase modulation,” Opt. Express 17(9), 7217–7221 (2009). [CrossRef] [PubMed]
8. H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008). [CrossRef]
9. D. Marpaung, “On-chip photonic-assisted instantaneous microwave frequency measurement system,” IEEE Photonics Technol. Lett. 25(9), 837–840 (2013). [CrossRef]
10. S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006). [CrossRef]
11. J. M. Heaton, C. D. Watson, S. B. Jones, M. M. Bourke, C. M. Boyne, G. W. Smith, and D. R. Wight, “Sixteen channel (1 to 16 GHz) microwave spectrum analyzer device based on phased-array of GaAs-AlGaAs electrooptic waveguide delay lines,” Proc. SPIE 3278, 245–251 (1998). [CrossRef]
12. W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001). [CrossRef]
13. C. Wang and J. P. Yao, “Ultrahigh-resolution photonic-assisted microwave frequency identification based on temporal channelization,” IEEE Trans. Microw. Theory Tech. 61(12), 4275–4282 (2013). [CrossRef]
14. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013). [CrossRef]
15. F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory 47(7), 1309–1314 (1999). [CrossRef]
16. M. Li and J. P. Yao, “All-optical short-time Fourier transform based on a temporal pulse shaping system incorporating an array of cascaded linearly chirped fiber Bragg gratings,” IEEE Photonics Technol. Lett. 23(20), 1439–1441 (2011). [CrossRef]
17. R. E. Saperstein, D. Panasenko, and Y. Fainman, “Demonstration of a microwave spectrum analyzer based on time-domain optical processing in fiber,” Opt. Lett. 29(5), 501–503 (2004). [CrossRef] [PubMed]
18. H. Chi, Y. Chen, Y. Mei, X. Jin, S. Zheng, and X. Zhang, “Microwave spectrum sensing based on photonic time stretch and compressive sampling,” Opt. Lett. 38(2), 136–138 (2013). [CrossRef] [PubMed]
20. B. T. Bosworth, J. R. Stroud, D. N. Tran, T. D. Tran, S. Chin, and M. A. Foster, “Ultrawideband compressed sensing of arbitrary multi-tone sparse radio frequencies using spectrally encoded ultrafast laser pulses,” Opt. Lett. 40(13), 3045–3048 (2015). [CrossRef] [PubMed]
22. C. V. Bennett, R. P. Scott, and B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65(20), 2513–2515 (1994). [CrossRef]
23. C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric spectro-temporal analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep. 3, 2064 (2013). [PubMed]
24. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994). [CrossRef]
25. R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013). [CrossRef]
26. E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012). [CrossRef]
27. C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000). [CrossRef]
28. Y. Duan, H. Zhou, L. Chen, C. Zhang, and X. Zhang, “Ultrafast and large bandwidth spectrum analyzer based on microwave photonics and temporal magnification, ” in Asia Communications and Photonics Conference 2016, OSA Technical Digest (online) (Optical Society of America, 2016), paper AF2A.15. [CrossRef]
29. C. Zhang, P. C. Chui, and K. K. Y. Wong, “Comparison of state-of-art phase modulators and parametric mixers in time-lens applications under different repetition rates,” Appl. Opt. 52(36), 8817–8826 (2013). [CrossRef] [PubMed]