Open Access
Add to BibSonomyAbstract
We propose and experimentally demonstrate a novel and practical microwave photonic system that is capable of executing cascaded signal processing functions comprising a microwave photonic bandpass filter and a phase shifter, while providing separate and independent control for each function. The experimental results demonstrate a single bandpass microwave photonic filter with a 3-dB bandwidth of 15 MHz and an out-of-band ratio of over 40 dB, together with a simultaneous RF phase tuning control of 0-215° with less than ± 3 dB filter shape variance.
© 2016 Optical Society of America
1. Introduction
The heart of microwave photonic (MWP) signal processing lies in its ability to capture the exceptional qualities of photonics technology to seamlessly replace the traditional method of radio frequency (RF) signal processing that is quickly approaching an electronic bottleneck [1]. The alluring features of MWP signal processing with its inherently larger bandwidth, low loss, wide tunability, and natural immunity to electromagnetic interference (EMI) have promised an attractive approach to overcome the major impairments existing in electronic signal processing [2–4]. Growing interest in this field of research has since accomplished unprecedented photonic signal processing techniques such as high-resolution and adaptive filtering, wideband phase shifting, tunable true time delay, and frequency conversion, which have been proposed in numerous works but which have almost invariably been implemented as single units of signal processing functions [5–12]. Whilst many have demonstrated superior performance over their electronic counterparts, having individually defined functions however, limits the full capability of MWP signal processing. Without intentionally investigating the realization of compound functions that can be implemented together to form an MWP subsystem, the individual single-unit functional merits will be of little practical use. Hence, a crucial push in a new direction which focuses on MWP systems that looks beyond providing single signal processing function, but instead establishes the means to realize a distributed variety of functionalities within the signal processing subsystem, is essential.
There is considerable interest in implementing photonic signal processors in the fields of defense and radioastronomy, which enables the processing of wideband fiber-fed distributed antenna signals in addition to providing for essential EMI immunity, which is otherwise not an easy task for electronic approaches [13]. In radar applications such as RF phased array antennas, optical RF phase shifters are used to impose optically-mapped microwave phases on each antenna element in order to steer the signal in a specified direction [14]. At the same time, highly selective frequency filtering in multioctave radar systems is also needed to suppress the unwanted out-of-band interference, and tunable RF filters in particular are mandatory to adapt to the constant changes in the front-end operational requirements. In microwave fiber-optic systems where the signal is already in the optical domain, it is thus attractive to continuously process the signal directly in the optical domain itself. Thus, it is required that future photonic approaches are able to provide cascaded functions such as frequency filtering and phase shifting in the same photonic link in order to eliminate the need for unnecessary optoelectronic conversions between the individual functions.
The need for multiple signal processing functions has been indirectly recognized in [15] by demonstrating a switchable dual-function system that could switch between implementing an optical single-sideband modulation with tunable optical carrier-to-sideband ratio, or alternatively a MWP phase shifter. However, it could not achieve both functions simultaneously. More in-depth research is imperative to investigate the practicality of scaling the functionalities in a photonic subsystem by cascading multiple signal processors. Moreover, it is important to note that in order to expand distributed optical signal processing in a MWP subsystem, isolated tuning is required for each of the signal processors located within the subsystem without interfering with the other processing functions. Recently, a simultaneous implementation of a filter and a phase shifter, using broadband optical source and phase modulator, was presented [14]. Whilst this method shows an approach for integrating two functions into one, the lack of a clear distinction between the two functions makes it difficult to perform isolated control and independent tuning of the filter and of the phase.
In this paper, we present a novel and practical MWP signal processing system that combines the cascaded usage of different optical signal processors into one MWP subsystem. The proposed system configuration is capable of performing individually controlled, cascaded MWP bandpass filter and phase shifter functions within one MWP subsystem. The concept is validated by cascading a stimulated Brillouin scattering (SBS) based MWP bandpass filter and an on-chip phase shifter based on single all-pass microring resonator [16,17]. Unlike previous implementations of the SBS-based filtering function [18,19] where a pure optical carrier derived directly from the source laser was used as the pump signal, we have obtained a new SBS configuration in order to support the cascaded signal processing function, which is otherwise not achievable using conventional structures. This involves reusing the modulated optical carrier, which can be continuously frequency shifted and filtered to act as a tunable pump signal. The individual signal processing functions of the MWP bandpass filter and MWP phase shifter were first investigated to demonstrate their functionalities as independent subunits. The tunability of the MWP filter passband is realized by tuning the optical pump driven by an external RF source generator. This performs the channel selection for different RF frequencies and provides the suppression of unwanted signals, thus allowing the desired signal to be directed to the next stage of phase shifting, which can be used typically for selective channel beamforming applications. The tunability of the MWP phase shifter is performed by tuning the wavelength of the optical carrier. The wideband operation of the phase shifter allows the same phase shifts to be achieved for different RF frequencies selected by the tunable MWP bandpass filter. Finally, the two functions are cascaded into one MWP subsystem to investigate the capability of the proposed system in executing the two functions simultaneously. We show that the system is able to achieve the cascaded multiple functions of a tunable single passband filter over a span of up to 20GHz and also a phase shifter with continuous phase tunability of 0-215°, while simultaneously demonstrating the concept of separate control between the two functions.
2. Principle of operation
The structure and operational principle of the proposed MWP subsystem configuration with two cascaded photonic RF signal processing functions is shown in Fig. 1.
Fig. 1 Schematic diagram of the distributed optical signal processing MWP subsystem with cascaded functionalities.
The first signal processor presents the configuration of a SBS-based microwave photonic bandpass filter (MPBF) while the second processor implements the tunable microwave photonic phase shifter (MPPS). An optical carrier from a tunable laser source (LD) is modulated by a frequency-swept RF signal via an optical phase modulator (PM). For small signal modulation, only the first-order sidebands are considered and the optical signal from the phase modulated laser source can be written as [20,21]
where E0 is the electrical field amplitude of the laser, Jn(.) is the nth-order Bessel function of the first kind, m1 is the phase modulation index, fc is the frequency of the laser, and fRF is the frequency of the injected RF signal. The modulated light, after transmission through a fibre link, is then passed through to the first stage of RF signal processing. Here, we present a new SBS-based MPBF scheme which is the essence of enabling a cascaded signal processing system. We have adopted the concept of re-modulating the transmitted phase modulated light in the lower arm of the first signal processor via an intensity modulator (IM). The corresponding electrical field at the output of the IM can be expressed aswhere m2 is the intensity modulation index and fm is the frequency of the function generator driving the IM. The modulated signal is subsequently sent into an optical bandpass filter (OBPF) which effectively selects just the frequency shifted carrier signal located at frequency fc + fm of the modulated signal. Note that alternatively, a phase modulator can also be used in place of the IM where the pump signal is obtained via an OBPF positioned after the modulator which also allows reusing the modulated optical carrier. The filtered signal acts as a pump signal to initiate the SBS process and an optical amplification e.g. the usage of an erbium-doped fiber amplifier (EDFA) may also be necessary in order to raise the optical power above Brillouin threshold before injecting it into a nonlinear medium in a counter-propagating direction by means of an optical circulator, and any residual light is ultimately eliminated by the optical isolator. Meanwhile, the upper branch carries the initial phase modulated signal which is launched in the forward direction into the same nonlinear medium. Only the RF signal with the frequency of fRF = fm-fB undergoes the SBS gain effect, where is the Brillouin frequency shift. Considering the case where fm > fB, the upper sideband undergoes amplification to become significantly larger than the lower band as shown in Fig. 1, and Eq. (1) can thus be expressed as [22]where G(fc + fRF) is the Brillouin gain which is given by [23]where g0 is the peak value of Brillouin gain coefficient, Ip is the intensity of the Brillouin pump, ГB is the linewidth of the SBS, and f represents the frequency offset from the SBS frequency shift relative to the RF frequency. It can be seen that only the RF signals within the bandwidth of the Brillouin gain will experience amplification giving rise to ultra-narrow bandwidth single sideband of RF signals to selectively emerge at the output of the circulator.The RF signals within the SBS amplification profile is then transmitted together with the optical carrier along the MWP subsystem to the next stage of signal processing, which comprises the MPPS. Due to the selective amplification of the RF signals from the previous stage, the optical signals at this stage can be viewed as a narrow array of single sideband RF frequencies. Therefore, a phase shifter based on an OSSB modulation format can conveniently provide a one-to-one mapping of optical to RF phase shifts. The carrier wavelength is aligned with the resonance of the phase change induced by the MPPS so that an optical phase change, ϕc is induced at the optical carrier. After beating at the photodetector, the resulting output photocurrent for frequency fRF can be expressed as
where is the magnitude response of the phase shifter and where Pp is the input Brillouin pump power, L is the effective fiber length, and Aeff is the effective area. Assuming the SBS induced phase shift imparted on the sideband is constant for a fixed RF filter response, the effective phase of the output RF signal is therefore dependent on the phase difference between the optical carrier and its sideband. By tuning the carrier wavelength with respect to the resonance of the MPPS, the phase difference can be varied to realize different RF phase shifts. On the other hand, the RF magnitude response of the filter determined by the RF output power after the PD is given bywhere ℜ is the photodetector responsivity and R is the load resistance.From Eq. (8), it shows that the phase introduced at the carrier will generate some phase dependencies on the magnitude response of the RF filter. However, as the SBS gain is typically sufficiently large (GB>>1) [24], the term with carrier phase dependency contributes to a negligible variation in the RF magnitude response. Thus the RF response is just predominantly proportional to the SBS gain response GB2 determined by the peak gain of the SBS gain spectrum. A reasonable assumption that the bandpass filter is virtually independent of the phase introduced at the carrier can then be deduced, thus achieving separate control of the two cascaded functions.
3. Experimental setup and result
3.1 Bandpass Filter Operation
An experiment based on the setup shown in Fig. 2 was carried out to verify the proof of principle where the inset shows the scanning electron microscope (SEM) image of the fabricated silicon-on-insulator (SOI) ring resonator. We first investigated the individual stages of the signal processing functions. The laser source operating with an output power of 9.5dBm was modulated by an optical phase modulator and was sent to photonic RF processor 1 to implement the MPBF. The modulated input signal was split into two arms using an optical coupler. The smaller portion of light was launched into the top arm where it encounters a nonlinear medium consisting of 6km length of single mode fiber (SMF). Meanwhile, the majority of the light enters the lower branch comprised of an IM to remodulate the input phase modulated signal. This was driven by an RF generator with 20dBm input power to provide the pump signal fm which is tunable within a 20GHz frequency span. As a proof of concept, the IM was biased for double-sideband suppressed carrier. A PC2 was used to align the polarization state into the IM. After amplification (EDFA1), an OBPF (Finisar Waveshaper) with a bandwidth of 10GHz was used to filter out just a pure pump signal from the modulated signal, which was then further amplified (EDFA2) to initiate the SBS process in the SMF optical fiber. The Brillouin frequency shift of the fiber was 10.838GHz. The SBS effect was optimized using PC3, yielding a highly selective SBS-based RF bandpass filter with more than 45dB out-of-band rejection ratio and a 3-dB bandwidth of around 15MHz. The resulting bandpass filter response generated by the photonic RF processor 1 was detected by the PD. The independent control for this first photonic RF processor was executed by varying the frequency of the RF generator that determined the frequency of the pump signal, thus allowing the center passband of the bandpass filter to be tuned. Figure 3 illustrates the continuously tunable bandpass filter from 10.838GHz to 30.838GHz that was achieved successfully with this new topology.
Fig. 2 Experimental setup of the proposed system. Inset: Top-view scanning electron microscope (SEM) image of the fabricated on-chip microring resonator
Capitalizing on the megahertz spectrum selectivity of the SBS effect, the proposed system provides an ultra-narrowband single bandpass filter with continuous tuning capability where the tunability of the SBS-based filter is only limited by the frequency range of the optical pump. Moreover, as the RF filter bandwidth is characterized by the SBS gain effects in the fiber, it is therefore also possible to extend the bandwidth of single bandpass filter if required, as demonstrated in [25,26], by shaping the modulation pattern of the pump spectrum to tailor the Brillouin gain profile.
3.2 Phase Shifter Operation
Due to the promising trends in silicon-based photonics components [27–29], the second stage of signal processing, which involves the implementation of a MPPS, was provided by an on-chip RF processor fabricated on a SOI wafer via ePIXfab. It consists of a straight waveguide coupled to a single microring resonator as shown in the inset of Fig. 2. The amplitude coupling coefficient between the straight waveguide and racetrack waveguide is designed to be around 0.1. The height of the silicon core waveguide is 220nm and the waveguide width is 450nm for both the bus and racetrack waveguide. The phase response of the single ring all-pass filter was measured using a vector network analyzer (Keysight) by sweeping a single sideband frequency spectrum about its resonance location with maximum sweeping frequency of 40GHz. The wavelength of the laser was then aligned with the resonance of the microring and swept from 1554.30nm to 1554.55nm to generate continuous phase tuning from 0 to 270°, as shown in Fig. 4(a). It can be noted that the phase shifter operation suffers from frequency dependent phase shifts at lower frequencies, but performs better at higher frequencies starting from around 20 GHz where the phase shift is almost RF frequency independent. We also measured the amplitude response of the MPPS during phase tuning from 0 to 270°. The results are shown in Fig. 4(b). The optical response of the phase shifter is illustrated in the inset of Fig. 4(b) as well, measured by using an optical analyzer (Finisar Wave Analyzer), showing a notch depth of approximately 7dB at the resonance location. Due to the attenuation of the optical carrier as it passes through resonance notch of the ring resonator, an amplitude variation is also observed in the measured amplitude response of the phase shifter.
Fig. 4 Measured responses of the MPPS (a) continuous RF phase tuning (b) superimposed RF power variations at various RF phase shifts. Inset: Optical response of the phase shifter.
As the MPPS is implemented based on a single microring configuration, the RF power variation due to the high extinction ratio of the microring filter can be minimized by reducing the loss of the microring and optimizing the coupling coefficient between the straight waveguide and racetrack waveguide [16]. Moreover, the use of cascaded dual microring resonators to implement phase shifting can also be adopted to present a more controllable RF power variation [30].
3.3 Microwave Photonics Subsystem
Combining the two operations into one MWP subsystem as depicted in Fig. 2, we now demonstrate that the two functions can be cascaded and controlled separately. Figure 5(a) shows the RF frequency response of the MWP filter with a passband centered at 20.828 GHz. The phase of the generated RF passband was then varied by altering the carrier wavelengths to achieve a MPPS operation that covers a continuous phase tuning range of about 200° within the filter passband, as shown in Fig. 5(b). The resulting variations in the RF power responses of approximately ± 3dB as the carrier was tuned to realize different RF phase shifts are shown in Fig. 5(a). This variation in power is a result of the subsequent carrier attenuation due to the notch response of the phase shifter. Nevertheless, the shape factor of the bandpass filter remains essentially the same, with just 2 MHz difference at −20dB bandwidth as the phase was tuned continuously.
Fig. 5 Measured RF responses (a) Superimposed RF spectra at various RF phase shifts of the bandpass filter response at 20.828 GHz (b) Continuous RF phase tuning at passband
To further demonstrate the validity of our scheme, we tested the operation of the cascaded signal processors at a different pump frequency which produced a shift in the centre frequency of the RF bandpass filter, showing a new passband at around 30.828 GHz in Fig. 6(a). Figure 6(b) shows the accompanying RF phase shifts for the new bandpass filter as the carrier wavelength is tuned. As before, the tuning of the carrier wavelength to achieve different RF phase shifts between 0 and 215° contributed to around ± 3dB in power variations. We can see that despite the change in the pump frequency of the first photonic RF signal processor, the performance of the second photonic RF signal processor remains relatively unaffected as it is still able to provide continuous RF phase shifts around the passband of the newly shifted bandpass filter. This is due to the wideband operation of the RF phase shifter as illustrated in Fig. 4(a) where the phase change is almost independent of the RF frequencies starting from 20 GHz onwards across the full tuning range of the phase shifter. The same phase shifts can thus be maintained as the RF filter is tuned within the operation bandwidth of the phase shifter.
Fig. 6 Measured RF responses (a) Superimposed RF spectra at various RF phase shifts of the bandpass filter response at 30.828 GHz (b) Continuous RF phase tuning at passband
Regarding the noise figure of the system, as with conventional microwave photonic links, the noise figure is high because the normal electrical-to-optical and optical-to-electrical conversion processes introduce considerable losses. Also there is noise generated by spontaneous emission noise of the Brillouin process which arises from scattering from thermally generated acoustic waves, and there are coupling losses to the silicon photonics chip. The losses in the system can be compensated by using optical amplification. Moreover, the noise figure can be reduced by using a low-noise RF amplifier before the optical modulator.
However, it is worth mentioning that just for the purpose of concept demonstration, the phase shifter operation was facilitated by varying the wavelength of the laser source. This is due to the absence of active tuning elements on the phase shifting component. As such, the center frequency of the optical bandpass filter used to select the pump signal for the SBS process in the first photonics RF processor needed to be tuned continuously as the laser wavelength was varied to achieve different phase shifts. Nevertheless, if the phase control is accomplished instead by using a microheater to individually tune the ring resonator [31], the dependence between the two photonics RF processors components can be completely eliminated thus potentially enabling isolated phase tuning without affecting the tunability of the MPBF. Photonic integration of the current SBS-based setup to develop a more compact and lightweight MBPF system is also possible in the near future with recent developments in on-chip SBS demonstrating SBS enhancement in nanoscale devices that is able to achieve sufficient gain within a very short length [32]. Meanwhile, the effective SBS gain in highly nonlinear waveguides can be increased by the presence of a photonic bandgap structure, thus providing potential solutions to achieve power-efficient on-chip integrated SBS [33].
4. Conclusion
We have presented a novel and practical system that is capable of executing multiple cascaded signal processing functions comprising a MWP bandpass filter and a phase shifter, while providing a separate control for each function. This is realized by cascading two signals processors where the first is a stimulated Brillouin scattering (SBS) based MWP bandpass filter, followed by an on-chip phase shifter based on a single all-pass microring resonator. Experimental results have demonstrated a single bandpass MWP filter with a 3-dB bandwidth of around 15MHz and out-of-band ratio of more than 40dB. At the same time, the system is also able to perform independent, continuous, filter shape-invariant, phase control with a tuning range of approximately 0-215°, strongly indicating that the system is able to carry out individually controlled signal processing for each of the photonic RF processor without interfering with the functionality of the other signal processor.
Acknowledgments
This work was supported by the Australian Department of Defence.
References and links
1. R. A. Minasian, E. H. W. Chan, and X. Yi, “Microwave photonic signal processing,” Opt. Express 21(19), 22918–22936 (2013). [CrossRef] [PubMed]
2. A. J. Seeds, “Microwave photonics,” IEEE Trans. Microw. Theory Tech. 50(3), 877–887 (2002). [CrossRef]
3. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013). [CrossRef]
4. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
5. J. Wang, F. Zeng, and J. P. Yao, “All-optical microwave bandpass filters implemented in a radio-over-fiber link,” IEEE Photonics Technol. Lett. 17(8), 1737–1739 (2005). [CrossRef]
6. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]
7. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Wideband 360° microwave photonic phase shifter based on slow light in semiconductor optical amplifiers,” Opt. Express 18(6), 6156–6163 (2010). [CrossRef] [PubMed]
8. A. Loayssa and F. J. Lahoz, “Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006). [CrossRef]
9. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010). [CrossRef]
10. J. F. Diehl, J. M. Singley, C. E. Sunderman, and V. J. Urick, “Microwave photonic delay line signal processing,” Appl. Opt. 54(31), F35–F41 (2015). [CrossRef] [PubMed]
11. D. Zhu, S. Pan, S. Cai, and D. Ben, “High-performance photonic microwave downconverter based on a frequency-doubling optoelectronic oscillator,” J. Lightwave Technol. 30(18), 3036–3042 (2012). [CrossRef]
12. J. P. Yao, G. Maury, Y. L. Guennec, and B. Cabon, “All-optical subcarrier frequency conversion using an electrooptic phase modulator,” IEEE Photonics Technol. Lett. 17(11), 2427–2429 (2005). [CrossRef]
13. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]
14. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “All-optical microwave bandpass filter and phase shifter using a broadband optical source and an optical phase modulator,” Opt. Lett. 37(10), 1661–1663 (2012). [CrossRef] [PubMed]
15. Y. Zhang, F. Zhang, and S. Pan, “A microwave photonic system with switchable functions based on cascaded polarization modulators,” in 2014 13th International Conference on Optical Communications and Networks (ICOCN, 2014), pp. 1–3.
16. Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photonics Technol. Lett. 21(1), 60–62 (2009). [CrossRef]
17. D. B. Adams and C. K. Madsen, “A novel broadband photonic RF phase shifter,” J. Lightwave Technol. 26(15), 2712–2717 (2008). [CrossRef]
18. B. Vidal, T. Menguak, and J. Marti, “Photonic microwave filter with single bandpass response based on Brillouin processing and SSB-SC,” in Proc. IEEE. Int. Meeting on Microwave Photonics (MWP, 2009), pp. 1–4.
19. W. Zhang and R. A. Minasian, “Widely tunable single-passband microwave photonic filter based on stimulated Brillouin scattering,” IEEE Photonics Technol. Lett. 23(23), 1775–1777 (2011). [CrossRef]
20. J. W. Goodman, Statistical Optics (John Wiley and Sons, 2000).
21. T. Chen, X. Yi, L. Li, and R. Minasian, “Single passband microwave photonic filter with wideband tunability and adjustable bandwidth,” Opt. Lett. 37(22), 4699–4701 (2012). [CrossRef] [PubMed]
22. S. Hu, L. Li, X. Yi, and C. Yu, “Ultraflat widely tuned single bandpass filter based on stimulated Brillouin Scattering,” IEEE Photonics Technol. Lett. 26(14), 1466–1469 (2014). [CrossRef]
23. W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic Brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012). [CrossRef]
24. M. Nikles, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997). [CrossRef]
25. A. Zadok, A. Eyal, and M. Tur, “Gigahertz-wide optically reconfigurable filters using stimulated Brillouin scattering,” J. Lightwave Technol. 25(8), 2168–2174 (2007). [CrossRef]
26. W. Wei, L. Yi, Y. Jaouën, and W. Hu, “Bandwidth-tunable narrowband rectangular optical filter based on stimulated Brillouin scattering in optical fiber,” Opt. Express 22(19), 23249–23260 (2014). [CrossRef] [PubMed]
27. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]
28. G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III-V/silicon photonics for on-chip and intra-chip optical interconnects,” Laser Photonics Rev. 4(6), 751–779 (2010). [CrossRef]
29. J. K. Doylend and A. P. Knights, “The evolution of silicon photonics as an enabling technology for optical interconnection,” Laser Photonics Rev. 6(4), 504–525 (2012). [CrossRef]
30. M. Pu, L. Liu, W. Xue, Y. Ding, H. Ou, K. Yvind, and J. M. Hvam, “Widely tunable microwave phase shifter based on silicon-on-insulator dual-microring resonator,” Opt. Express 18(6), 6172–6182 (2010). [CrossRef] [PubMed]
31. M. Pu, L. Liu, W. Xue, Y. Ding, H. Ou, K. Yvind, J. M. Hvam, and J. M. Hvam, “Widely tunable microwave phase shifter based on silicon-on-insulator dual-microring resonator,” Opt. Express 18(6), 6172–6182 (2010). [CrossRef] [PubMed]
32. B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013). [CrossRef]
33. M. Merklein, I. V. Kabakova, T. F. Büttner, D. Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Enhancing and inhibiting stimulated Brillouin scattering in photonic integrated circuits,” Nat. Commun. 6, 6396 (2015). [CrossRef] [PubMed]
