Rapidly and continuously frequency-scanning opto-electronic oscillator

Qizhuang Cen; Yitang Dai; Feifei Yin; Yue Zhou; Jianqiang Li; Jian Dai; Lan Yu; Kun Xu

doi:10.1364/OE.25.000635

1. Introduction

Exceptionally pure microwaves are required in radar systems, navigations and precise scientific measurements, since microwave purity is directly attached to performance in these applications. Direct generation rather than frequency multiplication is always required because of phase noise deterioration of $20 \log_{10} (N)$ during the frequency multiplication process, where N is the multiplication factor. Since electronic high quality factor (Q-factor) resonators [1] are usually limited by the bulky and lack of tunability, significant efforts, which are based on photonics technology, have been focused on developing new low-phase-noise microwave sources with high frequency and wideband tunability. Ultra-stable lasers and optical frequency comb based optical-to-radio frequency division scheme is a promising approach to produce microwave signals with both extremely high stability and low noise. The state-of-the-art photonic microwave source with ultra-low phase noise (< −173 dBc/Hz @ 10 kHz) has been reported [2]. Opto-electronic oscillator (OEO) is another scheme utilizing the optical transmission, which, with advantages of low loss and high bandwidth, enables the generation of high-frequency carrier with low and frequency-independent phase noise, as well as the broadband tunability [3–9]. In a basic OEO, coherent light from a laser is launched into an electro-optic modulator (EOM). The output passes through an optical delay line, which is usually hundreds of meters or a few kilometers optical fiber, and then detected by a photodiode (PD). The recovered microwave is amplified, filtered, and finally fed back to the EOM. Desired microwave is then generated in this opto-electronic hybrid cavity. With a long, filtering-free fiber, the OEO cavity supports thousands of oscillation modes, so that a narrow bandpass microwave filter or microwave-photonic filter is required to select one out.

Besides fixed microwave oscillation, frequency-modulated microwave with low phase noise also plays an important role in modern scientific system [10–12]. Though broadband frequency-agile radio, e.g. frequency-modulated continuous wave (FMCW), can be generated by voltage controlled oscillator (VCO) [13] and digital electronic circuits [14, 15], as well as frequency multiplication, further improved phase noise performance is always expected for modern systems, especially in radar system. Frequency-variable OEOs have been widely studied, where a wideband-tunable microwave or microwave-photonic filter is always employed. Schemes which are based on yttrium iron garnet (YIG) filter [6], electro-optic crystalline whispering gallery mode (WGM) resonator [7], phase-shifted fiber Bragg grating (PS-FBG) [8], and stimulated Brillouin scattering (SBS) [9], etc., have been reported. Even though wideband frequency tunable OEOs covering dozens of GHz have been achieved, rapid frequency tuning and continuous frequency scanning are fundamentally impeded. In all of the previous efforts, to our knowledge, the tunable OEOs are still believed to operate statically: when the bandpass filter (BPF) is aligned to one of OEO potential modes, an oscillation will build up from thermal noise. Since the modes are always isolated in frequency by 1/τ_C, where τ_C is the total cavity delay, the traditional tuning, from one mode to its neighbors, results in a series of new oscillations which are connected by noisy states. Such operation results in discontinuous microwave both in amplitude and in phase, while the tuning speed is quite limited since every new oscillation building up time is long for a long cavity.

In this paper, we propose an OEO scheme which operates at “chirp oscillation” mode, i.e. rather than a sinusoidal wave with fixed frequency, a continuous frequency-modulated microwave is running roundly in the OEO cavity, which is also the output. We show theoretically that as long as the in-cavity BPF is continuously and periodically tuned and the period is exactly the same as the cavity round-trip time, stable FMCW oscillation can be obtained. The FMCW bandwidth is the same as scanning spectral range of the filter and the duration is the cavity delay, resulting in a significantly improved OEO tuning speed. Low phase noise can also be preserved due to the long optical delay. Our scheme is experimentally demonstrated, where the scanning filter is equivalently obtained by a delay-matched frequency conversion pair, an intermediate frequency (IF) filter, and a local electronic frequency-swept oscillation with large phase noise. The in-cavity oscillation to be scanning-filtered is firstly up-converted by the local oscillation (LO), then narrow-band filtered with fixed center frequency, and finally down-converted by the same but delay-matched LO to recover the oscillation. Our generated FMCW centers at 7 GHz with 1-GHz bandwidth and the instantaneous frequency scans linearly with a chirp rate of about 156 MHz/μs. Single-side-band (SSB) noise improvement as large as 23 dB is observed, compared with the electronic LO.

2. Principle and simulation

In order to obtain a stable oscillation, the OEO has to recover any microwave running inside after each round trip, both in amplitude and in phase. In the traditional OEO, as shown in Fig. 1(a), the BPF works statically or quasi-statically, which forces any stable microwave fixed at discrete frequencies given by $n / τ_{C}$ (n is an integer). Since no oscillation stands long in between, the OEO is actually OFF or outputs noise during the transition from one frequency to another.

Fig. 1 A comparison between (a) single-frequency OEO and (b) the proposed frequency-scanning OEO.

Download Full Size | PDF

We here do not stimulate the isolated frequencies one by one, but propose to force a frequency-rapidly-modulated microwave oscillation directly in the cavity, as shown in Fig. 1(b), where the usual fixed filter or any tunable one is replaced by a frequency-rapidly-scanning narrow BPF. Given a specific frequency-time route map (i.e. spectrogram), the scanning filter works as a dynamic spectral window: a specific frequency component passes through the scanning filter only if the filter, at the exact time, is at the same spectral position. Obviously, as long as the dynamic filter repeats its spectrogram and the period is the same as the cavity delay, the cavity will operate in a chirp and stable mode. As shown in Fig. 1(b), the frequency-modulated microwave with exactly the same spectrogram synchronizes with the scanning filter, and passes through after each round trip to recover itself, while others cannot get reproductive and finally get extinguishing. Note that the stable oscillation requires a continuous frequency-time route map. The total output bandwidth is the same as the scanning range of BPF, while its instantaneous frequency can vary with time either linearly or nonlinearly.

We study the above theory numerically. The OEO model follows [16], and is run in MATLAB. Different from fixed filter in traditional OEO, the rapidly-scanning BPF, which is the key component in our scheme, can be expressed mathematically as following [17]:

a_{OUT} (t) = {[a_{IN} (t) \cdot e^{i Φ (t)}] \otimes h_{fix} (t)} \cdot e^{- i Φ (t)}

a_{IN} (t) e^{- i ω_{0} t}

and

a_{OUT} (t) e^{- i ω_{0} t}

are the input and output frequency-modulated microwave, respectively, in their corresponding analytic representations, and ω₀ is the center carrier frequency.

e^{i Φ (t)}

and

e^{- i Φ (t)}

are a time-varying frequency-shift operator and its reverse, respectively. The expression

e^{- i Φ (t)}

represents a sinusoid with a time-varying carrier. Its instantaneous frequency, defined as

d Φ / 2 π d t

, varies with time, which is also the instantaneous center frequency of the scanning filter. In simulation, we assume a linearly-changed frequency, i.e. it changes linearly from ω₀/2π-B_scan/2 to ω₀/2π + B_scan/2 during half scanning period, while back to ω₀/2π-B_scan/2 after the other half, where B_scan = 10 GHz is the scanning bandwidth. As a result, instantaneous center frequency of the scanning filter is expressed as:

\begin{matrix} \frac{1}{2 π} \frac{d Φ}{d t} = \frac{B_{scan}}{2} - \frac{2 | t |}{τ_{C}} B_{scan} & - \frac{τ_{C}}{2} \leq t < \frac{τ_{C}}{2} \end{matrix}

where τ_C = 1 μs is the scanning period, and is also the cavity delay according to above theory. h_fix(t) in Eq. (1) is impulse response of a time-invariant low-pass filter, and

\otimes

is convolution. h_fix(t) indicates an unchanged window width, which is assumed to have a Gaussian profile with 3-dB bandwidth of B_fix = 10 MHz. Note that if Φ(t)≡0 then one gets the traditional static OEO. The microwave-photonic link plus the following low-noise amplifier (LNA) is modeled by [16]:

a_{OUT} (t) = \sqrt{G_{LNA}} R_{P D} I_{P D} Z_{P D} J_{1} (\frac{π | a_{IN} (t) |}{V_{π}}) e^{i \arg [a_{IN} (t)]}

where G_LNA = 13 dB is the power gain of linear LNA, R_PD = 1 A/W is the PD responsivity, I_PD = 10 dBm is the average optical power hitting on the PD, Z_PD = 50 Ω is the output impedance of PD, J₁(⋅) is the 1st-order Bessel function of the first kind, and V_π = 5 V is half-wave voltage of the ideal quadrature-biased Mach–Zehnder modulator (MZM). The corresponding link noise figure (NF) is 16 dB. Numerically, an initial random field passes through the noisy microwave-photonic link and the scanning filter, alternately and iteratively, until the field becomes constant after a finite number of cavity traversals. The in-cavity oscillation after LNA is analyzed.

Stable output is presented in Fig. 2, both in time and in frequency domain. In Fig. 2(b), the temporal output in two waveform periods is shown, and Fig. 2(a) and (c) show that the temporal waveform is continuous both in phase and in amplitude even when the frequency has a sharp turn. This chirp oscillation covers the same bandwidth as B_scan = 10 GHz, and its instantaneous frequency follows Eq. (2), as shown in Fig. 2(c). The traditional OEO (Φ(t)≡0) is also simulated for a comparison. Figure 2(d) shows the power spectrums of the single-frequency OEO and frequency-scanning OEO. About ten thousands (10⁴) of discrete frequency components, with the same power and strictly spaced by 1 MHz, are found in the proposed OEO. As a result, the power of each frequency component is ~40 dB less than the single one from traditional OEO.

Fig. 2 A numerical example of the proposed frequency-scanning OEO. As a comparison, traditional OEO is also simulated. (a) and (c) Parts of temporal waveform of frequency-scanning OEO. (b) Instantaneous frequencies of the frequency-scanning OEO (in pink) and traditional OEO (in blue) and temporal waveform of the frequency-scanning OEO in two periods (in red). (d) Power spectrums. (e) Single-frequency-tone SSB noises of frequency-scanning OEO under different B_scan.

Download Full Size | PDF

The SSB noise performance of discrete tone is evaluated and results are shown in Fig. 2(e). SSB noise curves under different B_scan, from 0 (corresponding to the traditional OEO) to the largest 10 GHz, are plotted together for comparison. In the low frequency offset range, all of the SSB noise curves share almost the same value and tendency as the traditional OEO. However, the frequency-scanning OEO touches a higher SSB noise floor at high frequency offset, and the floor gets increased as the scanning range is enlarged. Such noise floor can be explained by Fig. 2(d). As large bandwidth is implemented in chirp OEO, the discrete lines gets lower power so that the additive noise after the LNA will play the major contributor to the SSB noise. As a result, high-frequency-offset SSB noise increases correspondingly as the scanning bandwidth increases. It should be noted that the absolute noise floor is kept unchanged, as shown in Fig. 2(d) as well as its inset, so as to the total signal-to-noise ratio (SNR) under the same bandwidth. One can then conclude that the frequency-scanning OEO preserves the low-noise feature as the traditional one.

3. Experiment and results

The proposed frequency-scanning OEO is experimentally demonstrated, as shows in Fig. 3(a). The setup contains a laser centered at 1550 nm, a quadrature-biased MZM which has a 3-dB bandwidth of 10 GHz and half-wave voltage of ~5 volts, a 2.5-km dispersion-shifted fiber (DSF), a PD with 3-dB bandwidth of 10 GHz and responsibility of 0.8 A/W which receives average optical power of 2 dBm, a microwave LNA with about 30 dB gain, a frequency-scanning filter, and an electrical power splitter (E-PS).

Fig. 3 (a) The experiment setup; (b) Equivalent frequency-scanning BPF.

Download Full Size | PDF

The scanning filter is achieved equivalently, which essentially follows Eq. (1). It contains a delay-matched frequency conversion pair, an intermediate frequency (IF) bandpass filter, an external frequency-modulated microwave (noted as LO-FMCW) and a wideband BPF. The LO-FMCW is generated by an E-AWG (Tektronix, AWG7122B). Its instantaneous frequency varies linearly from 2.5 GHz to 3.5 GHz, back and forth. The LO-FMCW is divided into two parts, which drives the up- and down-conversion, respectively. The oscillating FMCW (noted as sig-FMCW) is firstly spectral compressed and frequency shifted by LO-FMCW, filtered by the IF filter which centers at 10 GHz with 3-dB bandwidth of 10 MHz, and then recovered, both in bandwidth and in frequency, by the common LO-FMCW. The wideband filter, where microwaves from 6.5 GHz to 7.5 GHz can pass through, is used to suppress the mirror spectrum after the second conversion, and an IF LNA with 20-dB gain is used to compensate the loss of the equivalent filter. In a static OEO, we have used the above equivalent filter for perfect side-mode suppression, and phase noise of 120 dBc/Hz at 10-kHz offset from 10-GHz carrier frequency was achieved in a 1-μs loop cavity [18]. Similarly, here the IF bandpass filter is also mapped to a scanning filter from 6.5 GHz to 7.5 GHz by the LO-FMCW (note the other window from 12.5 GHz to 13.5 GHz is blocked by the wideband filter). Different from the ideal mapping in Eq. (1), LO-FMCW from E-AWG is quite noisy, and additional phase noise may show significant impact on the oscillation during the frequency conversions. We in [18] and [19] have demonstrated theoretically and experimentally that as long as the time delay of the second LO-FMCW matches that of the IF filter, the phase noise of the input microwave after the above equivalent filtering can be precisely preserved, so that the phase noise of the final oscillation is independent from that of the noisy LO-FMCW. For the equivalent filtering, the phase noise of LO-FMCW can be suppressed as much as |2πΔfΔτ|², where Δf is the frequency offset and Δτ is the delay mismatch. <10-ns delay mismatch results in more than 64 dB noise suppression at 10-kHz offset, which is easy to obtain in experiment. In out setup, the IF filter path has delay ~50 ns, which is well matched by an electronic cable. The total cavity delay is around 12.8 μs, and the scanning period of the LO-FMCW is set accordingly, based on our theory.

When the loop gain exceeds the loss and the dynamic spectral window synchronizes with cavity round trip, stable sig-FMCW is generated. The oscillation is characterized both in time and in frequency domain. Firstly, a high-speed oscilloscope (Tektronix, MSO/DPO72004C), which has 20-GHz analog bandwidth and 100-GHz sampling rate, is used to record the real-time temporal output without average. The output waveform in two waveform periods is shown in Fig. 4(b) and detail is shown in Fig. 4(a), illustrating continuous amplitude and phase. One may find that the temporal envelope shown in Fig. 4(b) is uneven. This ripple results from the poor flatness of LO-FMCW and the frequency-dependent loss of electric parts. The instantaneous frequency is calculated by mature Hilbert transform and numerical differentiator [14], shown in Fig. 4(b). The corresponding characteristics of LO-FMCW are also plotted. One can find the sig-FMCW shares the same scanning spectral width as the LO-FMCW. However, their instantaneous frequency slopes along with time is opposite, because the lower sideband after the second frequency conversion is selected. According to our design, the sig-FMCW has central frequency of 7 GHz and covers 1-GHz bandwidth. The frequency scanning speed is as high as 156 MHz/μs, while both phase and amplitude are continuous, as shown in Fig. 4(a).

Fig. 4 Experiment results of proposed frequency-scanning OEO. (a) Parts of temporal waveforms. (b) Instantaneous frequencies (sig-FMCW in pink and LO-FMCW in green) and temporal waveforms in two periods (sig-FMCW in red and LO-FMCW in blue). (c) Power spectrums in 500-kHz span. (d) Power spectrums in 2-GHz span. The inserted graphic is the power spectrums of the sig-FMCWs with 500-MHz bandwidth in different center frequencies (e) SSB noises.

Download Full Size | PDF

The power spectrum of sig-FMCW is measured by an electrical signal analyzer (Keysight N9030A). The flatness of 1-GHz band is within 2.5 dB, as shown in Fig. 4(d). The power As the instantaneous frequency varies periodically, the Fourier frequency is discrete and spaced by $1 / τ_{C}$ . Discrete power spectrum is shown in Fig. 4(c). One may conclude that a frequency-scanning OEO is actually a multi-mode one which supports thousands of frequencies to oscillate at the same time. Distinguished from the traditional single-loop OEO where an excessive BPF is employed in a long cavity and multiple modes oscillates independently, the rapidly frequency-scanning filter makes sure that all frequencies have specific phase relationship so that stable and broadband FMCW can be generated. Similar to the same concept in laser, all the neighboring frequencies are “mode-locked”.

Noise characteristic is implemented by measuring absolute SSB noise of one discrete frequency line. We use a narrow-band filter to select a few discrete frequency lines from those thousands of lines, and the selected lines are then amplified before measurement (dashed box in Fig. 3(a)). The result is shown in Fig. 4(e). As a comparison, SSB noise of one LO-FMCW tone is also plotted. We can find that the two noise spectrums are actually independent, which has been predicted by our previous theory [18]. SSB noise is well suppressed by delay-matched frequency conversion pair. Compared to the E-AWG-generated one, more than 23-dB improvement at offset frequency around 3 kHz can be observed in the sig-FMCW. The absolute SSB noise is −104 dBc/Hz at 10 kHz offset frequency.

By adjusting center frequency and bandwidth of the local-FMCW, the scanning range of the equivalent BPF is changed accordingly [19], so is the output swept frequency. When the LO-FMCW is tuned at center frequency of 2.675/3.65 GHz with 500-MHz bandwidth, sig-FMCW at 7.325/6.35 GHz with same bandwidth is generated accordingly. The results are shown in the inserted graphic of Fig. 4(d). Currently, output with wider bandwidth is limited by the electric parts in our setup, e.g. the wideband BPF. Wideband scanning filter could be employed pure optically, for example, the WGM resonator made of electro-optic crystalline material, which has ~MHz bandwidth and sub-μs tuning speed [7]. Even though the equivalent filtering is driven electrically and bandwidth of sig-FMCW is not extended, our design in Fig. 3 is still rewarding. Currently octave-span FMCW can be easily obtained by off-the-shelf VCO. With the help of frequency multiplication, larger bandwidth can be achieved, with however serious phase noise. Our theory and experiment show that phase noise can be greatly suppressed while the bandwidth and continuous scanning are preserved. Such unique feature distinguishes our proposal far from those based on simple frequency mixing or frequency conversion [20–22], where the high phase noise is always preserved or even boosted. In our measurement, we use a low-noise microwave (generated by Keysight E8257D), centered at 4 GHz (SSB noise is over 10 dB less than the LO-FMCW in the full measurement span), to up-convert the LO-FMCW, and then an FMCW centered at 7 GHz with 1 GHz bandwidth is generated. We use the same setup to measure its SSB noise. High SSB noise is preserved and plotted in the Fig. 4(e). In our scheme, the period of the generated signal is restricted by the cavity round-trip time, which shows less tunability than the direct up-conversion method.

4. Conclusion

We have proposed a frequency-scanning OEO where a frequency-modulated microwave is oscillating inside. Experimentally, the output frequency scanning rate was as high as ~156 MHz/μs, and both the temporal amplitude and the phase were continuous, which significantly distinguishes our proposal from traditional tunable OEO. The chirp operation occurs when a frequency rapidly scanning filter is inserted and the tuning synchronizes with the cavity round trip. We achieved the scanning filter equivalently, and the generated phase noise was much lower than the driving electronic waveform, which, together with our simulation, shows that the low-noise feature of traditional OEO is well preserved. It is the first time to our knowledge to demonstrate an OEO where multiple frequencies, spaced by 1/τ_C, oscillate simultaneously with fixed and stable phase relationship.

Funding

Natural National Science Foundation of China (NSFC) (61671071, 61625104, 61675031).

References and links

1. C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301 (2008). [CrossRef] [PubMed]

2. X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11(1), 44–47; advance online publication (2016). [CrossRef]

3. X. S. Yao, “Opto-electronic oscillators” in RF Photonic Technology in Optical Fiber Links, W. S. C. Chang, ed. (Cambridge University Press, 2002).

4. D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra-low noise floor cross-correlation microwave photonic homodyne system,” in Proceedings of IEEE Conference on Frequency Control Symposium (IEEE, 2008), pp. 811–814. [CrossRef]

5. W. Zhou and G. Blasche, “Injection-locked dual opto-electronic oscillator with ultra-low phase noise and ultra-low spurious level,” IEEE Trans. Microw. Theory Tech. 53(3), 929–933 (2005). [CrossRef]

6. D. Eliyahu and L. Maleki, “Tunable, ultra-low phase noise YIG based opto-electronic oscillator,” in Proceedings of IEEE Conference on Microwave Symposium Digest (IEEE, 2003), pp. 2185–2187. [CrossRef]

7. A. A. Savchenkov, V. S. Ilchenko, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Voltage-controlled photonic oscillator,” Opt. Lett. 35(10), 1572–1574 (2010). [CrossRef] [PubMed]

8. W. Li and J. Yao, “A wideband frequency tunable optoelectronic oscillator incorporating a tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(6), 1735–1742 (2012). [CrossRef]

9. H. Peng, C. Zhang, X. Xie, T. Sun, P. Guo, X. Zhu, L. Zhu, W. Hu, and Z. Chen, “Tunable DC-60 GHz RF generation utilizing a dual-loop optoelectronic oscillator based on stimulated Brillouin scattering,” J. Lightwave Technol. 33(13), 2707–2715 (2015). [CrossRef]

10. A. W. Rihaczek, Principles of High-Resolution Radar (Artech House, 1996).

11. M. Bertero, M. Miyakawa, P. Boccacci, F. Conte, K. Orikasa, and M. Furutani, “Image restoration in chirp-pulse microwave CT (CP-MCT),” IEEE Trans. Biomed. Eng. 47(5), 690–699 (2000). [CrossRef] [PubMed]

12. R. L. Peterson, R. E. Ziemer, and D. E. Borth, Introduction to Spread-spectrum Communications (Prentice Hall, 1995).

13. H. Kwon and B. Kang, “Linear frequency modulation of voltage-controlled oscillator using delay-line feedback,” IEEE Microw. Wirel. Compon. Lett. 15(6), 431–433 (2005). [CrossRef]

14. D. Gomez-Garcia, C. Leuschen, F. Rodriguez-Morales, J.-B. Yan, and P. Gogineni, “Linear chirp generator based on direct digital synthesis and frequency multiplication for airborne FMCW snow probing radar,” in Proceedings of IEEE Conference on Microwave Symposium (IEEE, 2014), pp. 1–4. [CrossRef]

15. Tektronix arbitrary waveform generators AWG7000 series datasheet, http://www.tek.com/datasheet/arbitrary- waveform-generators-7.

16. E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B 26(1), 148–159 (2009). [CrossRef]

17. K. Pann and Y. Shin, “A class of convolutional time-varying filters,” Geophysics 41(1), 28–43 (1976). [CrossRef]

18. Y. Dai, R. Wang, F. Yin, J. Dai, Y. Zhou, J. Li, and K. Xu, “Hybrid radio-intermediate-frequency oscillator with photonic-delay-matched frequency conversion pair,” Opt. Lett. 40(12), 2894–2897 (2015). [CrossRef] [PubMed]

19. Y. Dai, Q. Cen, L. Wang, Y. Zhou, F. Yin, J. Dai, J. Li, and K. Xu, “Low phase noise microwave extraction from femtosecond laser by frequency conversion pair and IF-domain processing,” Opt. Express 23(25), 31936–31944 (2015). [CrossRef] [PubMed]

20. A. Kanno and T. Kawanishi, “Broadband frequency-modulated continuous-wave signal generation by optical modulation technique,” J. Lightwave Technol. 32(20), 3566–3572 (2014). [CrossRef]

21. W. Xie, Z. Xia, Q. Zhou, H. Shi, Y. Dong, W. Hu, and W. Hu, “Photonic generation of low phase noise arbitrary chirped microwave waveforms with large time-bandwidth product,” Opt. Express 23(14), 18070–18079 (2015). [CrossRef] [PubMed]

22. D. Zhu and J. Yao, “Dual-chirp microwave waveform generation using a dual-parallel Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 27(13), 1410–1413 (2015). [CrossRef]

Rapidly and continuously frequency-scanning opto-electronic oscillator

Abstract

1. Introduction

2. Principle and simulation

3. Experiment and results

4. Conclusion

Funding

References and links

Cited By

Figures (4)

Equations (3)

Optics Express