Abstract

The ability to achieve low phase noise single-mode oscillation within an optoelectronic oscillator (OEO) is of fundamental importance. In the frequency-tunable OEO, the wide microwave photonic filter (MPF) bandwidth is detrimental to select single-mode among the large number of cavity modes, thus leading to low signal quality and spectral purity. Stable single–mode oscillation can be achieved in a large time delay OEO system by harnessing the mechanism from parity-time (PT) symmetry. Here, a PT-symmetric tunable OEO based on dual-wavelength and cascaded phase-shifted fiber gratings (PS-FBGs) in a single-loop is proposed and experimentally demonstrated. Combining the merits of wide frequency tuning of PS-FBG-based MPF and single mode selection completed by the PT-symmetric architecture of the OEO, where the gain and loss modes carried by dual-wavelengths to form two mutually coupled resonators in a single-loop, signals range from 1 GHz to 22 GHz with the low phase noise distributed in −122∼ −130 dBc/Hz at 10 kHz offset frequency are obtained in the experiment.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since proposed by Yao X S and Maleki L, OEO has been used in related fields such as communications, data processing and radar [1,2]. Advanced radar and communication systems place requirements on radio frequency (RF) signals with high spectral purity and wide frequency tuning range [2]. So, many tunable OEO schemes based on tunable MPFs constructed by fiber components have been proposed and verified in experiments. In [3,4], tunable MPFs based on PS-FBG were introduced to realize frequency-tunable OEOs, whose frequency tuning ranges are 8.4∼11.8 GHz [3] and 3∼28 GHz [4], respectively. In terms of spectral purity, by adopting the loop lengths of 25m [3] and 500m [4], the obtained phase noises are −65 dBc/Hz [3] and −102 dBc/Hz [4] at 10 kHz offset frequency, respectively. In [5], a tunable OEO based on an MPF constructed by using a subtraction operation of transmission responses between two high-pass filters and fiber loop lengths of 150 m was proposed. A frequency tuning range of 7.8∼14.2 GHz with phase noises of −85 dBc/Hz at 10 kHz offset frequency was obtained. Furthermore, some tunable OEO schemes based on tunable MPFs using integrated photonic chips were also proposed, such as stimulated Brillouin scattering (SBS) of the chalcogenide waveguide [6], silicon-based micro-ring resonator (MRR) [7], and silicon-based micro-disk resonator (MDR) [8]. Among them, only Ref. 6] mentioned that the OEO’s loop length is 25m. In terms of spectral purity, the phase noises of the schemes are −80 dBc/Hz [6], −95 dBc/Hz [7] and −78 dBc/Hz [8] at 10 kHz offset frequency, respectively. Although frequency tuning of OEOs were achieved by using above schemes, the phase noise of the generated signal is relatively poor, which is limited by the short OEO’s loop length. Under certain conditions, the OEO’s phase noise can be reduced as the length of the fiber increases according to the Yao–Maleki model [1]. As known, a long optical fiber delay line in OEO’s loops will make the mode spacing of the potential oscillation modes very small (∼ kHz for km fiber), which needs very narrow electronic filter to realize single mode operation. However, the frequency tuning range of electronic filter is very limited, which cannot support wide-band tunable OEO. So typical tunable MPFs based on optical filters are introduced into the OEO loop to realize wideband frequency tuning. However, comparing with electronic filter, optical filter usually has a relatively larger bandwidth (typically ∼ GHz or hundreds of MHz) [9,10,11], which prohibited single-mode selection in OEO. Therefore, in order to obtain single-mode oscillation, usually short optical fiber delay must be used, which limits the phase noise of the generated signal.

Recently, the mode selection mechanism of PT-Symmetric breaking has been put forward as a viable solution for achieving single mode operation in photonic [12,13] and electronic cavities [14]. Relatively early, Ref. [15] and Ref. [16] respectively conduct theoretical and experimental researches on PT-symmetry in optics. In [17], the PT-symmetry was introduced in microwave photonics to construct a PT-symmetric OEO system with fiber loop length of 3.216 km, in which a 4.07 GHz RF signal with a phase noise of −139 dBc/Hz at 10 kHz offset frequency was obtained. In [18], by introducing a longer optical delay of 9.1 km in PT-symmetric OEO’s loop, a 9 GHz RF signal with even lower phase noise of −142.5 dBc/Hz at 10 kHz offset frequency was realized. However, narrow bandwidth electronic filters were introduced in the above PT-symmetric OEOs and the signal frequencies are fixed. Comparing with electronic filter, MPF has the merits of wide frequency tunability, which can be introduced into the PT-symmetric OEOs to achieve frequency tuning. Various frequency tunable PT-symmetric OEOs based on the dual-loop structure with tunable MPFs have been proposed, such as using the reconfigurable dispersion-induced power fading [19], silicon-based MDR [20], and silicon nitride MDR [21]. These solutions have achieved a large frequency tuning range and good spectral purity. However, in the PT-symmetric system of the dual-loop scheme, the lengths of the two loops are required to be the same. So variable optical delay lines (VODL) are introduced to balance the loop length and will cause power loss and system instability. In [22], a non-tunable PT-symmetric OEO was built in a single physical loop with fiber loop length of 10 km through the dispersion adjustment in the wavelength space. A 10 GHz RF signal with a phase noise of −129.3 dBc/Hz at 10 kHz offset frequency was obtained. In [23], the phase modulator (PM) without internal polarizer and a PS-FBG were applied to construct tunable PT-symmetric OEO in a single dual-polarization loop with fiber loop length of 5 km. A frequency tuning range of 2∼12 GHz with phase noises of −124 dBc/Hz at 10 kHz offset frequency was obtained. However, the different modulation efficiencies of the ordinary and extraordinary modes in the PM make it difficult to balance the loop’s gain and loss.

Here, we propose a tunable PT-symmetric OEO based on dual-wavelength and cascaded PS-FBGs in a single-loop, which can balance the loop’s gain and loss much easier. In order to optimize the phase noise of OEO, a longer fiber of 3.7 km is introduced. The OEO achieves wide frequency tunability and single-mode operation by using the dual mode selection mechanism of the PS-FBG based MPF and PT-symmetry. The frequency tuning of the proposed OEO can be achieved by changing the two laser wavelengths simultaneously. The experiment results show that RF signals range from 1 GHz to 22 GHz with a phase noise about −130 dBc/Hz at 10 kHz offset frequency are obtained and the side-mode suppression ratio (SMSR) is about 37 dB.

2. Principle

Figure 1 shows the system scheme and working principle in different locations of the proposed PT-Symmetric tunable OEO based on dual-wavelength and cascaded PS-FBGs. Two continuous optical carriers emitted by the two TLSs are injected into PC3 (polarization controller) through the polarization beam combiner (PBC). The PC1 and PC2 are respectively used to modify the polarization states of the optical carriers to align with the two orthogonal polarization axes of the PBC to obtain the maximum coupling efficiency. Two continuous optical carriers with the frequency of fc1 and fc2 co-propagate along the PC3 and then are sent to the PM which has a built-in polarizer (Location A). By adjusting the PC3, the polarization alignment between the carriers’ polarization direction and the PM’s principal axis can be changed continuously. Since the total power injected into the PM is constant, this means that the power ratio of the two orthogonal optical carriers injection into the OEO loops can be continuously tuned by adjusting the PC3. In this case, the condition of synchronous changing the net gain and loss required by the PT-symmetric system is satisfied [16]. The phase-modulated optical double sideband (ODSB) signals are sent into cascaded PS-FBGs through the optical circulator (Location B). Then, the cascaded PS-FBGs will tailor one of the optical sidebands to form optical single sideband (OSSB) signals (Location C). The two OSSB signals travel via a 3 km single mode fiber (SMF) and 700 m dispersion compensation fiber (DCF) and then detected at the photodetector (PD). Here, the DCF is used to balance the power fading caused by the dispersion induced by the two different optical carriers. At this point, the TLSs, PM, cascaded PS-FBGs, and PD are connected to form two tunable MPFs. The frequency of the MPF is determined by the frequency difference (fRF1 or fRF2) between the optical carrier's wavelength and the notch wavelength of the PS-FBG. By keeping the frequency difference fRF1 and fRF2 to be consistent, a single passband MPF with a frequency of fRF can be obtained. At location D, the demodulated RF signals are divided into two parts after being amplified. One part is fed back into PM to close the OEO loop, and the other part is fed into electronic spectrum analyzer (ESA) for testing. In the proposed OEO, the gain and loss modes are carried by dual-wavelengths to form two mutually coupled resonators in a single-loop and the power ratio is tunable as mentioned above. Thus, the proposed OEO system fits the characteristics of PT-symmetry.

 figure: Fig. 1.

Fig. 1. (a) Scheme of the proposed tunable PT-symmetric OEO based on dual-wavelength and cascaded PS-FBGs. (b) Principle analysis in different locations. TLS, tunable laser source; PC, polarization controller; PBC, polarization beam combiner; PM, phase modulator; OC, optical circulator; PS-FBG, phase-shifted fiber grating; SMF, single mode fiber; DCF, dispersion compensation fiber; PD, photodetector; Amp, amplifier; ATT, attenuator; EC, electronic coupler; ESA, electronic spectrum analyzer.

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According to [21], the coupling relationship of the OEO’s gain and loss loops in the proposed system can be expressed as:

$$i\frac{d}{{dt}}(\frac{{{a_n}}}{{{b_n}}}) = (\begin{array}{{cc}} {\omega _{^n}^{(a)} + i\gamma _{^n}^{(a)}}&{ - {\kappa _n}}\\ { - {\kappa _n}}&{\omega _{^n}^{(b)} + i\gamma _{^n}^{(b)}} \end{array})(\frac{{{a_n}}}{{{b_n}}})$$
where the ${a_n}$, ${b_n}$ are the amplitudes and the $\omega _{^n}^{(a)}$, $\omega _{^n}^{(b)}$ are the eigen angular frequencies of the n-order localized eigenmodes in the gain and loss loops, respectively, ${\kappa _n}$ is the n-order mode coupling coefficient between the gain and loss loops, $\gamma _{^n}^{(a)}$, $\gamma _{^n}^{(b)}$ are the gain coefficients of the gain and loss loops. From Eq. (1), the $\omega _{^n}^{(a)}$, $\omega _{^n}^{(b)}$ can be expressed as:
$$\omega _{^n}^{(a),(b)} = {\omega _n} + i\frac{{\gamma _{^n}^{(a)} + \gamma _{^n}^{(b)}}}{2} \pm \sqrt {\kappa _n^2 - {{(\frac{{\gamma _{^n}^{(a)} - \gamma _{^n}^{(b)}}}{2})}^2}}$$

When the PT-symmetric condition is satisfied, it is required that $\gamma _{^n}^{(a)} ={-} \gamma _{^n}^{(b)} = {\gamma _n}$. At this point, Eq. (2) can be simplified as:

$$\omega _{^n}^{(a),(b)} = {\omega _n} \pm \sqrt {\kappa _n^2 - \gamma _n^2}$$

The Fig. 2 is created to interpret mode selection mechanism of the PT symmetry breaking involved in Eq. (3). The solid and dashed lines denote with and without PT symmetry breaking, respectively. According to the Eq. (3), in the case of $\gamma < \kappa$, $\omega _{^n}^{(a),(b)}$ split into two real frequencies as shown in Fig. 2. In the case of $\gamma > \kappa$, the value of $\omega _{^n}^{(a),(b)}$ is an imaginary number, meaning that only one frequency is generated. Notice that the OEO system is in the PT-symmetry breaking state in such a situation. The point where $\gamma = \kappa$ is called a broken transition point.

 figure: Fig. 2.

Fig. 2. OEO mode selection mechanism based on PT-symmetric structure.

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According to [11,12], the coupling coefficient (${\kappa _n}$) of low-order modes is usually smaller than that of high-order modes. This means that during the tuning process of the gain coefficient (${\gamma _n}$), the PT-symmetry breaking occurs first in the 0th-order mode, as show in Fig. 2. Here, we take n=0 to further study the effect of PT-symmetry breaking on single mode selection. The maximum gain difference $\Delta {g_{\max }}$ (see Fig. 2) between the 0th-order and 1st-order modes in the system without PT-symmetry breaking can be expressed as:

$$\Delta {g_{\max }} = {\gamma _0} - {\gamma _1}$$

According to Eq. (3), The maximum gain difference $\Delta {g_{\textrm{PT} - \max }}$ (see Fig. 2) between the 0th-order mode and 1st-order in the system with PT-symmetry breaking can be expressed as:

$$\Delta {g_{\textrm{PT} - \max }} = \sqrt {\gamma _0^2 - \gamma _1^2}$$

Since the value of Eq. (5) is significantly greater than the value of Eq. (4) ($\sqrt {\gamma _0^2 - \gamma _1^2} > {\gamma _0} - {\gamma _1}$), the PT-symmetry breaking can achieve single mode selection extremely effective. As shown in Fig. 2, we can use the MPF for coarse mode selection and tuning of the oscillation frequency, and further strengthen the single mode selection ability through PT-symmetric breaking.

3. Experimental results and discussion

To verify the proposed scheme, an experimental link was built according to the structure shown in Fig. 1. Two continuous optical carriers emitted by two tunable lasers (IDphotonics, CoBriteMX) were combined by a PBC, and then injected into the PM (Eospace, PM-0S5-20-PFA-PFA, DC∼20 GHz) to achieve phase modulation. In this process, the PC1 and PC2 are separately adjusted to maximize the output power of PBC. The cascaded PS-FBG (PYOE-Multi-PSFBG) is the key component to realize the PM-to-IM conversion in the system. The reflection spectrum of the cascaded PS-FBG was measured by the Swept Test System (Santec, MPM210, TSL710) with the measuring accuracy of 0.1pm, as shown in Fig. 3(a). In order to achieve higher measuring accuracy to characterize the PS-FBGs, the optical vector network analysis (OVNA) method was introduced to map the optical domain response of the PS-FBG into the RF domain response one by one [24]. The detailed reflection magnitude response of PS-FBG1 and PS-FBG2 in the cascaded PS-FBG were measured by a vector network analyzer (Keysight, N5242A). The sharp notch with full width at half maximum (FWHM) of 2.43 GHz (PS-FBG1) and 2.65 GHz (PS-FBG2), and the extinction ratio (ER) both about of 18 dB can be found in Fig. 3(b-c). About a 3dB fluctuation exists in the measurement results of Fig. 3(b-c). This fluctuation is attributed to the residual sideband caused by limited out-of-band suppression ratio at the edge of the tunable optical filter in the OVNA system.

 figure: Fig. 3.

Fig. 3. (a) Reflection spectra of the cascaded PS-FBGs. (b)-(c) Detailed reflection spectra of the PS-FBG.

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At the PD (Optilab, 0∼40 GHz), the OSSB signals convert into the RF signal. The recovered RF signal was amplified through two cascaded electronic amplifiers (MWLA-1966, 20 kHz∼20 GHz), and an electronic variable attenuator (RBS-69-26.5-7) was introduced to protect the link components. Finally, the amplified RF signal passed through a 3dB electric coupler (RS2W04260-S, 0.4∼ 26.5 GHz) and divided into two parts, where one part was sent back to the PM to close the OEO loop, and the other part was fed into the ESA (Keysight, N9040B) for measuring the RF spectrum and the phase noise.

Importantly, the open-loop response curve was measured by the vector network analyzer (VNA) at the gain probing point in Fig. 1. As shown in Fig. 4, the center frequency of the measured open-loop response (red) is at 10.1 GHz with a smooth profile, and the full width at half maximum (FWHM) is about 3 GHz. On the other hand, as a 3km SMF and a 700m DCF were employed in the OEO, which induces a mode spacing about 54 kHz. This means that there are about ten thousands of potential oscillation modes within the FWHM range. Without PT-symmetry, it is very impossible to achieve single-mode oscillation. According to the Eq. (4), open-loop response curve was calculated and a spike like curve with smaller FWHM is obtained as shown in Fig. 4, which extremely enhances the single-mode selection capability.

 figure: Fig. 4.

Fig. 4. (a) The open-loop response curve at 10.1 GHz (red) and the calculated response curve with PT-symmetry (green), (b) Detailed spectra in the black dot box.

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After closing the OEO loop, the PT-symmetric states can be changed from the non-breaking state ($\gamma < \kappa$) to breaking state ($\gamma > \kappa$) by modifying the PC3. Figure 5 shows the RF spectra of the generated RF signals in different PT-symmetric states at the frequency of 10.1 GHz. In the state of the PT-symmetric non-breaking, multi-mode oscillation can be seen within the frequency bandwidth (BW) of 100 MHz as shown in Fig. 5(a). By adjusting PC3 until the PT-symmetric breaking is satisfied, at which time the oscillating signal becomes single-mode, as shown in Fig. 5(b). In order to further explore the mode-selection capability of PT-symmetric breaking, we have compared the generated RF spectra with and without PT-symmetric breaking in a smaller BW of 300 kHz. As we can see from the Fig. 5(c), with PT-symmetric breaking, the main oscillation mode and the side oscillation modes are enhanced and suppressed, respectively. And a side mode suppression ratio (SMSR) about 37 dB is obtained. This indicates single mode selection capability of the OEO’s loop can be greatly enhanced by introducing PT-symmetric breaking mechanism. Moreover, as shown in Fig. 5(c), the mode spacing of the OEO is 54 kHz, which is consistent with the above-mentioned mode spacing of the OEO’s cavity. By synchronously tuning the wavelength difference between the TLSs and the PS-FBGs, the oscillation frequency can be easily tuned in the frequency range of 1 to 22 GHz, as shown in Fig. 5(d). Significant amplitude decreases and fluctuation are found for the OEO output signals shown in Fig. 5(d). The reasons are the performance degradations of the phase modulator, the electrical amplifier and the electronic coupler at higher frequencies. Meanwhile, the uneven frequency responses of these devices cause the amplitude fluctuations of the OEO output signals. In future, using devices with the larger bandwidth and flatter spectral responses could reduce the amplitude fluctuations of the OEO output signals.

 figure: Fig. 5.

Fig. 5. The RF spectra of the OEO at the frequency of 10.1 GHz. (a) Multimode oscillation measured with the resolution bandwidth (RBW) of 910 kHz, (b) Single-mode oscillation measured with the RBW of 910 kHz, (c) Single-mode oscillation (red) and multimode oscillation measured (blue) with the RBW of 2.7 kHz, (d) Frequency tunability of the proposed OEO.

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As an important parameter of the OEO, the phase noise was also measured by the phase noise measurement modules of ESA. The measured phase noise is about −130 dBc/Hz at 10 kHz offset frequency with the carrier frequency of 1.26 GHz. The slight deterioration of phase noise at high frequencies of 10.1 and 21.9 GHz are mainly blamed on the deterioration of the RF device performances and the noise floor increase of the ESA at high frequencies. The sharp parasitic noise peaks within the 1/f region arise from the residual phase noises induced by the electrical amplifiers [25]. In addition, since the 1/f noise of the amplifier increases linearly in series, for the cascaded two amplifiers in the proposed OEO chain, the series 1/f phase noise further increases. The parasitic noises of the proposed OEO can be improved by introducing a single low-noise amplifier (LNA) with larger gain and better noise performance. In Fig. 6, the side modes are lower than −50 dBc/Hz, which is consistent with the result obtained in Fig. 5(c). Due to the small mode spacing (54 kHz) of the OEO and the large optical filter’s bandwidth, the gain differences among the main mode and the side modes are small, which cause the oscillations of the side modes. By adopting an optical filter with steeper slope and narrower bandwidth, the phase noises of the side modes can be further reduced.

 figure: Fig. 6.

Fig. 6. Phase noise spectrum with the carrier frequency of 1.26 GHz, 10.1 GHz, and 21.9 GHz.

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The proposed OEO is compared with the reported OEOs on some critical parameters, and the results are shown in Table 1. As seen in Table 1, the phase noise has been greatly optimized after introducing a longer fiber into the OEO loop. Meanwhile, a larger tuning range is also achieved in the scheme.

Tables Icon

Table 1. The performance comparison between our tunable OEO and other reported tunable OEO

4. Conclusion

A broadband tunable PT-symmetric OEO based on dual-wavelength and cascaded PS-FBGs in a single-loop is proposed. The single physical loop would be benefit to the stability of OEO. The single-mode oscillation and frequency tuning of the OEO are realized through the PS-FBG based MPF and the mode-selection mechanism of PT-symmetric breaking. RF signals with frequency tuning range of 1∼22 GHz and phase noise about −130 dBc/Hz at 10 kHz offset frequency were obtained. Furthermore, by using PS-FBG with narrower bandwidth, the phase noise can be further improved through longer SMF in OEO’s loop.

Funding

National Key Research and Development Program of China (2018YFB2201800); National Natural Science Foundation of China (6217010526).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. X. Steve Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]  

2. L. Maleki, “The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011). [CrossRef]  

3. B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012). [CrossRef]  

4. 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. Microwave Theory Tech. 60(6), 1735–1742 (2012). [CrossRef]  

5. Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015). [CrossRef]  

6. Moritz Merklein, Birgit Stiller, Irina V. Kabakova, Udara S. Mutugala, Khu Vu, Stephen J. Madden, Benjamin J. Eggleton, and Radan Slavík, “Widely tunable, low phase noise microwave source based on a photonic chip,” Opt. Lett. 41(20), 4633–4636 (2016). [CrossRef]  

7. Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020). [CrossRef]  

8. W. Zhang and J. Yao, “Silicon photonic integrated optoelectronic oscillator for frequency-tunable microwave generation,” J. Lightwave Technol. 36(19), 4655–4663 (2018). [CrossRef]  

9. F. Jiang, Y. Yu, T. Cao, H. Tang, J. Dong, and X. Zhang, “Flat-top bandpass microwave photonic filter with tunable bandwidth and center frequency based on a Fabry–Pérot semiconductor optical amplifier,” Opt. Lett. 41(14), 3301–3304 (2016). [CrossRef]  

10. N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018). [CrossRef]  

11. J. Li, P. Zheng, G. Hu, R. Zhang, B. Yun, and Y. Cui, “Performance improvements of a tunable bandpass microwave photonic filter based on a notch ring resonator using phase modulation with dual optical carriers,” Opt. Express 27(7), 9705–9715 (2019). [CrossRef]  

12. Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014). [CrossRef]  

13. H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016). [CrossRef]  

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16. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010). [CrossRef]  

17. Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018). [CrossRef]  

18. J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018). [CrossRef]  

19. C. Teng, X. Zou, P. Li, W. Pan, and L. Yan, “Wideband frequency-tunable parity-time symmetric optoelectronic oscillator based on hybrid phase and intensity modulations,” J. Lightwave Technol. 38(19), 5406–5411 (2020). [CrossRef]  

20. Z. Fan, W. Zhang, Q. Qiu, and J. Yao, “Hybrid frequency-tunable parity-time symmetric optoelectronic oscillator,” J. Lightwave Technol. 38(8), 2127–2133 (2020). [CrossRef]  

21. P. Liu, P. Zheng, H. Yang, D. Lin, G. Hu, B. Yun, and Y. Cui, “Parity-time symmetric frequency-tunable optoelectronic oscillator based on a Si3N4 microdisk resonator,” Appl. Opt. 60(7), 1930–1936 (2021). [CrossRef]  

22. J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020). [CrossRef]  

23. P. Li, Z. Dai, Z. Fan, L. Yan, and J. Yao, “Parity–time-symmetric frequency-tunable optoelectronic oscillator with a single dual-polarization optical loop,” Opt. Lett. 45(11), 3139–3142 (2020). [CrossRef]  

24. Shilong Pan and Min Xue, “Optical vector network analyzer based on optical single-sideband modulation,” 2013 12th International Conference on Optical Communications and Networks (ICOCN), 1–3, (2013).

25. A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

References

  • View by:

  1. X. Steve Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
    [Crossref]
  2. L. Maleki, “The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
    [Crossref]
  3. B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
    [Crossref]
  4. 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. Microwave Theory Tech. 60(6), 1735–1742 (2012).
    [Crossref]
  5. Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
    [Crossref]
  6. Moritz Merklein, Birgit Stiller, Irina V. Kabakova, Udara S. Mutugala, Khu Vu, Stephen J. Madden, Benjamin J. Eggleton, and Radan Slavík, “Widely tunable, low phase noise microwave source based on a photonic chip,” Opt. Lett. 41(20), 4633–4636 (2016).
    [Crossref]
  7. Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
    [Crossref]
  8. W. Zhang and J. Yao, “Silicon photonic integrated optoelectronic oscillator for frequency-tunable microwave generation,” J. Lightwave Technol. 36(19), 4655–4663 (2018).
    [Crossref]
  9. F. Jiang, Y. Yu, T. Cao, H. Tang, J. Dong, and X. Zhang, “Flat-top bandpass microwave photonic filter with tunable bandwidth and center frequency based on a Fabry–Pérot semiconductor optical amplifier,” Opt. Lett. 41(14), 3301–3304 (2016).
    [Crossref]
  10. N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
    [Crossref]
  11. J. Li, P. Zheng, G. Hu, R. Zhang, B. Yun, and Y. Cui, “Performance improvements of a tunable bandpass microwave photonic filter based on a notch ring resonator using phase modulation with dual optical carriers,” Opt. Express 27(7), 9705–9715 (2019).
    [Crossref]
  12. Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
    [Crossref]
  13. H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
    [Crossref]
  14. J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
    [Crossref]
  15. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
    [Crossref]
  16. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
    [Crossref]
  17. Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
    [Crossref]
  18. J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018).
    [Crossref]
  19. C. Teng, X. Zou, P. Li, W. Pan, and L. Yan, “Wideband frequency-tunable parity-time symmetric optoelectronic oscillator based on hybrid phase and intensity modulations,” J. Lightwave Technol. 38(19), 5406–5411 (2020).
    [Crossref]
  20. Z. Fan, W. Zhang, Q. Qiu, and J. Yao, “Hybrid frequency-tunable parity-time symmetric optoelectronic oscillator,” J. Lightwave Technol. 38(8), 2127–2133 (2020).
    [Crossref]
  21. P. Liu, P. Zheng, H. Yang, D. Lin, G. Hu, B. Yun, and Y. Cui, “Parity-time symmetric frequency-tunable optoelectronic oscillator based on a Si3N4 microdisk resonator,” Appl. Opt. 60(7), 1930–1936 (2021).
    [Crossref]
  22. J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
    [Crossref]
  23. P. Li, Z. Dai, Z. Fan, L. Yan, and J. Yao, “Parity–time-symmetric frequency-tunable optoelectronic oscillator with a single dual-polarization optical loop,” Opt. Lett. 45(11), 3139–3142 (2020).
    [Crossref]
  24. Shilong Pan and Min Xue, “Optical vector network analyzer based on optical single-sideband modulation,” 2013 12th International Conference on Optical Communications and Networks (ICOCN), 1–3, (2013).
  25. A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

2021 (1)

2020 (5)

2019 (1)

2018 (4)

N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
[Crossref]

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018).
[Crossref]

W. Zhang and J. Yao, “Silicon photonic integrated optoelectronic oscillator for frequency-tunable microwave generation,” J. Lightwave Technol. 36(19), 4655–4663 (2018).
[Crossref]

2016 (3)

2015 (1)

Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
[Crossref]

2014 (1)

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

2012 (2)

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

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. Microwave Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

2011 (2)

L. Maleki, “The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
[Crossref]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

2010 (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

2007 (1)

1996 (1)

Bouchier, A.

A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

Cao, T.

Capmany, J.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

Chi, H.

Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
[Crossref]

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

Christodoulides, D. N.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref]

Christodoulides, Demetrios N.

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

Cibiel, G.

A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

Cui, Y.

Dai, Z.

Dong, J.

Eggleton, Benjamin J.

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref]

Ellis, F. M.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

Fan, Z.

Feng, X.

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

Guan, B.-O.

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

Hao, T.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
[Crossref]

Hassan, A. U.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Hayenga, W. E.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Heinrich, M.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Heinrich, Matthias

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

Hodaei, H.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Hodaei, Hossein

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

Hu, G.

Hu, X.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

Jiang, F.

Jin, X.

Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
[Crossref]

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

Kabakova, Irina V.

Khajavikhan, M.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Khajavikhan, Mercedeh

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Kottos, T.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

Li, A.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

Li, J.

Li, L.

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

Li, M.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
[Crossref]

Li, P.

Li, W.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
[Crossref]

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. Microwave Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

Lin, D.

Liu, P.

Liu, W.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

Liu, Y.

Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, and M. Li, “Observation of parity-time symmetry in microwave photonics,” Light: Sci. Appl. 7(1), 1–9 (2018).
[Crossref]

Llopis, O.

A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

Madden, Stephen J.

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref]

Maleki, L.

Merklein, Moritz

Merrer, P.-H.

A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

Miri, M.-A.

H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-mode PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

Miri, Mohammad-Ali

Hossein Hodaei, Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides, and Mercedeh Khajavikhan, “Parity-time–symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref]

Musslimani, Z. H.

Mutugala, Udara S.

Pan, Shilong

Shilong Pan and Min Xue, “Optical vector network analyzer based on optical single-sideband modulation,” 2013 12th International Conference on Optical Communications and Networks (ICOCN), 1–3, (2013).

Pan, W.

Qiu, Q.

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Saleh, K.

A. Bouchier, K. Saleh, P.-H. Merrer, O. Llopis, and G. Cibiel, “Theoretical and experimental study of the phase noise of opto-electronic oscillators based on high quality factor optical resonators,” 2010 IEEE International Frequency Control Symposium, 544–548, (2010).

Schindler, J.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Shi, N.

N. Shi, T. Hao, W. Li, N. Zhu, and M. Li, “A reconfigurable microwave photonic filter with flexible tunability using a multi-wavelength laser and a multi-channel phase-shifted fiber Bragg grating,” Opt. Commun. 407, 27–32 (2018).
[Crossref]

Slavík, Radan

Steve Yao, X.

Stiller, Birgit

Tang, H.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

F. Jiang, Y. Yu, T. Cao, H. Tang, J. Dong, and X. Zhang, “Flat-top bandpass microwave photonic filter with tunable bandwidth and center frequency based on a Fabry–Pérot semiconductor optical amplifier,” Opt. Lett. 41(14), 3301–3304 (2016).
[Crossref]

Teng, C.

Vu, Khu

Wang, G.

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

Wang, Y.

Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
[Crossref]

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

Xiao, X.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

Xue, Min

Shilong Pan and Min Xue, “Optical vector network analyzer based on optical single-sideband modulation,” 2013 12th International Conference on Optical Communications and Networks (ICOCN), 1–3, (2013).

Yan, L.

Yang, B.

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

Yang, H.

Yao, J.

Z. Fan, W. Zhang, Q. Qiu, and J. Yao, “Hybrid frequency-tunable parity-time symmetric optoelectronic oscillator,” J. Lightwave Technol. 38(8), 2127–2133 (2020).
[Crossref]

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

P. Li, Z. Dai, Z. Fan, L. Yan, and J. Yao, “Parity–time-symmetric frequency-tunable optoelectronic oscillator with a single dual-polarization optical loop,” Opt. Lett. 45(11), 3139–3142 (2020).
[Crossref]

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018).
[Crossref]

W. Zhang and J. Yao, “Silicon photonic integrated optoelectronic oscillator for frequency-tunable microwave generation,” J. Lightwave Technol. 36(19), 4655–4663 (2018).
[Crossref]

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. Microwave Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

Yu, Y.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

F. Jiang, Y. Yu, T. Cao, H. Tang, J. Dong, and X. Zhang, “Flat-top bandpass microwave photonic filter with tunable bandwidth and center frequency based on a Fabry–Pérot semiconductor optical amplifier,” Opt. Lett. 41(14), 3301–3304 (2016).
[Crossref]

Yun, B.

Zhang, J.

J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, and J. Yao, “Parity-time symmetry in wavelength space within a single spatial resonator,” Nat. Commun. 11(1), 1–7 (2020).
[Crossref]

J. Zhang and J. Yao, “Parity-time–symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018).
[Crossref]

Zhang, R.

Zhang, W.

Zhang, X.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

F. Jiang, Y. Yu, T. Cao, H. Tang, J. Dong, and X. Zhang, “Flat-top bandpass microwave photonic filter with tunable bandwidth and center frequency based on a Fabry–Pérot semiconductor optical amplifier,” Opt. Lett. 41(14), 3301–3304 (2016).
[Crossref]

Y. Wang, X. Jin, Y. Zhu, X. Zhang, S. Zheng, and H. Chi, “A wideband tunable optoelectronic oscillator based on a spectral-subtraction-induced MPF,” IEEE Photonics Technol. Lett. 27(9), 947–950 (2015).
[Crossref]

B. Yang, X. Jin, X. Zhang, S. Zheng, H. Chi, and Y. Wang, “A wideband frequency-tunable optoelectronic oscillator based on a narrowband phase-shifted FBG and wavelength tuning of laser,” IEEE Photonics Technol. Lett. 24(1), 73–75 (2012).
[Crossref]

Zhang, Y.

Y. Yu, H. Tang, W. Liu, X. Hu, Y. Zhang, X. Xiao, Y. Yu, and X. Zhang, “Frequency Stabilization of the Tunable Optoelectronic Oscillator Based on an Ultra-High-Q Microring Resonator,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–9 (2020).
[Crossref]

Zheng, M. C.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84(4), 040101 (2011).
[Crossref]

Zheng, P.

Zheng, S.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. (a) Scheme of the proposed tunable PT-symmetric OEO based on dual-wavelength and cascaded PS-FBGs. (b) Principle analysis in different locations. TLS, tunable laser source; PC, polarization controller; PBC, polarization beam combiner; PM, phase modulator; OC, optical circulator; PS-FBG, phase-shifted fiber grating; SMF, single mode fiber; DCF, dispersion compensation fiber; PD, photodetector; Amp, amplifier; ATT, attenuator; EC, electronic coupler; ESA, electronic spectrum analyzer.
Fig. 2.
Fig. 2. OEO mode selection mechanism based on PT-symmetric structure.
Fig. 3.
Fig. 3. (a) Reflection spectra of the cascaded PS-FBGs. (b)-(c) Detailed reflection spectra of the PS-FBG.
Fig. 4.
Fig. 4. (a) The open-loop response curve at 10.1 GHz (red) and the calculated response curve with PT-symmetry (green), (b) Detailed spectra in the black dot box.
Fig. 5.
Fig. 5. The RF spectra of the OEO at the frequency of 10.1 GHz. (a) Multimode oscillation measured with the resolution bandwidth (RBW) of 910 kHz, (b) Single-mode oscillation measured with the RBW of 910 kHz, (c) Single-mode oscillation (red) and multimode oscillation measured (blue) with the RBW of 2.7 kHz, (d) Frequency tunability of the proposed OEO.
Fig. 6.
Fig. 6. Phase noise spectrum with the carrier frequency of 1.26 GHz, 10.1 GHz, and 21.9 GHz.

Tables (1)

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Table 1. The performance comparison between our tunable OEO and other reported tunable OEO

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

i d d t ( a n b n ) = ( ω n ( a ) + i γ n ( a ) κ n κ n ω n ( b ) + i γ n ( b ) ) ( a n b n )
ω n ( a ) , ( b ) = ω n + i γ n ( a ) + γ n ( b ) 2 ± κ n 2 ( γ n ( a ) γ n ( b ) 2 ) 2
ω n ( a ) , ( b ) = ω n ± κ n 2 γ n 2
Δ g max = γ 0 γ 1
Δ g PT max = γ 0 2 γ 1 2