Abstract

In this paper, we present a novel configuration for an all-fiber tunable infinite impulse response optical filter using stimulated Brillouin scattering. By applying the Brillouin acoustic waves within the coupling area of an optical coupler, we can control its transmissivity and so to affect the spectral response of the IIR optical filter. In this paper, we explain the principle of operation of the proposed device and experimentally demonstrate the ability to control the spectral response of an optical filter based on fiber ring resonator configuration.

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

1. Introduction

Microwave photonic filters realized for signal processing have been of great interest due to their advantages over electronic counterparts: flexible tunability, immunity to electromagnetic interference, low losses, reconfigurability, etc. [14]. Many applications of microwave photonic filters can be found in wireless networks, radar systems, satellite communications, warfare systems, and similar [4].

Fiber optic technology is one of the most used realizations of microwave photonic filters. There are many techniques reported for fiber optic filter realization: using delay lines [58], mode-locked laser [9], incoherent light sources [10], or stimulated Brillouin scattering effect [1114].

In this work, we focus on infinite impulse response (IIR) filters, which in comparison to finite impulse response filters (FIR) require fewer stages, can be made more compact, and have sharper response [6,15]. The IIR filter used in this work is based on previous work from Ref. [6] where the filter is constructed in a fiber optic ring structure with two fiber optic couplers (see Fig. 1).

 figure: Fig. 1.

Fig. 1. Schematic diagram of an optical ring resonator.

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In this paper we propose a new technique for the realization of an all-fiber tunable IIR optical filter using the Brillouin effect. Among the mentioned fiber optic techniques, stimulated Brillouin scattering (SBS) is a favorable nonlinear effect for achieving a tunable optical filter, due to its several advantages: high gain/loss, wide frequency tunability, and narrow bandwidth of 10-30 MHz [16,17]. The SBS has been used in many ways to achieve tunability, which include: SBS induced sideband amplification [12], polarization control [11], SBS induced frequency change of electro-optic modulator [18], manipulation of directly modulated laser pump [19], etc.

Here we take advantage of the SBS effect in a quite different way. In SBS, the interference pattern created by two counter-propagating optical waves (usually called pump and Stokes) generates density variations in the fiber, i.e. acoustic wave through a process called electro-striction. Those density variations modify the dielectric constant of the fiber and create an effective periodic grating in it, which scatters the pump wave, while the backscattered light is downshifted in its frequency, resulting in optical power transfer from the pump wave to the Stokes wave [20,21].

In this work, we exploit this phenomenon by introducing the SBS effect and generation of acoustic waves inside the coupling area of the coupler that is used in our IIR filter. The presence of such periodic grating within the coupler may affect the coupling of the relevant coupled wavelength and thus preventing the complete signal transmission. This process will affect the notch depth of the filter spectral response and make it lower. In that way, by controlling the presence and the intensity of a pump wave in the system, tunability of the notch depth of the IIR filter may be achieved. To our knowledge, this is the first time that the SBS is used to tune the filter response in an optical filter in such configuration.

2. Theoretical background

2.1 IIR optical filter

An optical IIR filter that is constructed in a fiber optic ring structure with a fiber optic coupler (which is in fact an optical fiber Fabry-Perot interferometer) can be seen in Fig. 1.

The amplitude spectral response of the filter is given by [6]:

$$|{H(\nu )} |= \frac{{{t_1}{t_2}}}{{\sqrt {1 + r_1^2r_2^2 - 2{r_1}{r_2} \cdot \cos (2\pi \nu \Delta t)} }}$$
where r1, t1, r2, and t2 are splitting ratios of the coupler, Δt is the round-trip time of the ring, and ν the frequency. Note that R + T=1 for $r_\textrm{i}^2 = \textrm{R}$ and $t_\textrm{i}^2 = \textrm{T}$. The response of the ideal filter with different coupling ratios, and for Δt = 5 ns is given in Fig. 2.

 figure: Fig. 2.

Fig. 2. IIR filter response versus fiber optic coupler ratios.

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It can be seen that the depth of the notches and the sharpness of the passband depend on the coupling ratios. This is the ideal case, where the losses in the fiber loop, connectors/splices, and inequality of the couplers are neglected. Thus, controlling the coupling ratio of couplers can be used for controlling the depth of filter transmission.

2.2 Optical couplers

Several different techniques can be used to make a fiber coupler. One common technique is the fused fiber coupler in which the cores of two single-mode fibers are brought close together in a central region such that the spacing between the cores is comparable to their diameters [22]. In this case, a transfer of optical power from one core to another may occur under suitable conditions [22].

If we consider a directional coupler made up of two fibers with identical propagation constants, it can be shown that the coupling coefficient between those two fibers depends on some different parameters such as refractive index, the distance between fibers, fiber core radius, etc [22]. Thus, the coupling ratio may be controlled by controlling one of those parameters. The common method for getting such variable-ratio couplers is to adjust the relative lateral positions of the mated fibers of the coupler with a mechanical micrometer. In general, the tunable filters need to have fast tunability. However, the rates of changes in the coupling ratio that may be achieved by this method are very slow relative to the required tunability rates and thus a faster mechanism is required for this purpose.

2.3 Brillouin effect

In our proposed system we suggest modifying the fiber refractive index to control the coupling ratio of the filter, and so to control the filter transmission. Such modification of the refractive index may be done using the Brillouin effect. The Brillouin effect is a non-linear effect that is caused by an interaction between two counter-propagating optical waves (called pump and Stokes) with two different frequencies within an optical fiber. The interference pattern created by those two waves generates density variations in the fiber, i.e., an acoustic wave that has a frequency equal to the difference between the frequencies of the two optical waves. Those density variations modify the dielectric constant of the fiber through a process called electro-striction. The dielectric constant changes from its original value $\varepsilon$ to the value$\varepsilon + \Delta \varepsilon$[20]:

$$\Delta \varepsilon = \rho _0^{ - 1}{\gamma _e}\tilde{\rho }(z,t)$$
Where ${\rho _0}$ is the mean density of the medium, ${\gamma _e}$is the electro-strictive constant and $\tilde{\rho }(z,t)$ is the change in the material density distribution, given by [20]:
$$\tilde{\rho }(z,t) = {\varepsilon _0}{\gamma _e}{q^2}\frac{{{A_P}A_S^\ast }}{{\Omega _B^2 - {\Omega ^2} - i\Omega {\Gamma _B}}}{e^{i(\Omega t - qz)}} + c.c$$
Where ${\varepsilon _0}$ is the dielectric constant of the vacuum, q is the acoustic wave-number, ${\Omega _B}$ is the Brillouin frequency shift, $\Omega $ is the frequency differences between the pump and the Stokes, ${A_P}$ and ${A_S}$ are the amplitudes of the pump and Stokes waves respectively, and ${\Gamma _B}$ is the Brillouin linewidth, which is inversely proportional to the phonon lifetime.

Another configuration where this effect can be obtained is called SBS generator, which means that only the pump wave is applied externally, and both the Stokes and acoustic fields grow from noise within the interaction region. For that configuration, the back-reflected Stokes signal is downshifted in frequency. For an incident pump wave of sufficient intensity, the spontaneously scattered light can become quite intense, so the incident and scattered light fields can then beat together, giving rise to density and pressure variations through electrostriction [20].

In this work, we will use the configuration of SBS generator. The interaction between two optical waves, i.e. the inserted pump wave and the back-reflected Stokes wave, will generate density variations that will modify the dielectric constant of the fiber as we explained above. We built our system such that these periodic changes in the refractive index are generated within the coupling area of an optical coupler that is used for building the IIR filter. This periodic grating leads to changes in the refractive index within the coupler [23], and so the coupling coefficient and the splitting ratio of the coupler are also changed. As can be seen in Fig. 2, changing the splitting ratio of the coupler leads to a change in the notch depth of the filter transmission. In that way, by controlling the presence of a pump wave in the system, an optical IIR filter with a tunable notch depth based on a ring resonator configuration may be realized. A flow diagram that explains the influence of the Brillouin effect on the transmission spectrum of IIR filter can be seen in Fig. 3.

 figure: Fig. 3.

Fig. 3. A flow diagram: The influence of the SBS process on the filter's depth step-by-step.

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Controlling the depth of the filter by using the pump allows us to control the transmission on the filtered frequencies. Without a pump wave, those frequencies will be blocked by the filter and when we turn on the pump those frequencies will pass through the system, while the transmission depends on the pump intensity. Thus, such a device could be used for the realization of many all-fiber optical components such as switches and modulators [24].

3. Experimental results

A schematic diagram of the experimental setup can be seen at Fig. 4.

 figure: Fig. 4.

Fig. 4. Schematic diagram of the experimental setup.

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A polarized laser source with a wavelength of 1550 nm, linewidth of 1 MHz and power of 12 dBm was used as an input signal. The input signal was modulated in amplitude with a sine form with different frequencies between 1 MHz to 1.1 MHz with steps of 250 Hz by an electro-optic modulator (EOM). The RF carrier was produced by a network analyzer (NWA). The polarization controller (PC) was used to match the laser polarization to the EOM. The signal was then amplified by an erbium-doped fiber amplifier (EDFA) for increasing its intensity and was inserted into the IIR filter. The IIR filter was built with two polarization-maintaining couplers with energy splitting factors of 90/10 and 99/1 (i.e. R1 = 0.9 and R2 = 0.99). A long single-mode silica fiber (core diameter 8 μm, cladding diameter 125 μm, SILITEC fibers), not polarization-maintaining with a length of 12.6 km was used to create the Brillouin effect. Since SBS is a non-linear effect, the optical power of the pump wave must exceed a certain threshold value to become significant. This threshold value is inversely proportional to the fiber length, so a relatively long fiber is required to get the Brillouin effect. This fiber was spliced to the 90% branch of the first coupler so the Brillouin acoustic wave that is generated in the long fiber could travel from the long fiber to the coupling area of the coupler. Note that the intensity of the acoustic wave is proportional to the multiplication of the pump and Stokes intensities [20]. That means that the acoustic wave is stronger where those intensities are stronger. Since the pump intensity decreases along the fiber, while the back-reflected Stokes is amplified, the maximum value of the acoustic wave is expected to be very close to the input of the pump, i.e., in the coupling area of the fiber (see Fig. 4). The other connections in this system were performed by optical connectors. Thus, the loop length in our filter was 12.6 km, so the free spectral range (FSR) of the filter was:

$$FSR = \frac{c}{{n \cdot L}} \approx 16kHz$$
Note that the linewidth of the laser source (1 MHz) is greater than the FSR of the filter. Thus, the light inside the loop will not undergo constructive interference, and the RF filtering will happen at the receiver's end (i.e. the optical detector), where multiple replicas of the laser light are detected at the same time. For that reason, a polarization controller inside the loop to optimize the contrast of the filter response is not required. A polarized laser source with a wavelength of 1546 nm and power of 4 dBm was used as a pump wave to generate the Brillouin acoustic wave. The pump wave was amplified to 26 dBm by EDFA and was inserted into the loop by using an optical circulator. At the filter output, an array waveguide grating (AWG) was used to separate the filtered signal and the back-reflected Stokes signal from the Brillouin effect. The filtered signal was detected by an IR detector that was connected to the NWA.

By using the NWA the above-mentioned modulation frequencies were used to calculate the transfer function of the filter. The transfer function was measured with and without the pump. For each case, an average of five measurements was taken. The results can be seen in Fig. 5.

 figure: Fig. 5.

Fig. 5. Experimental results: The transfer function of the IIR filter: without the Brillouin effect (blue line) and with the Brillouin effect.

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4. Discussion

The results are shown in Fig. 5. One can see that the FSR of the filter is about 16 kHz, with a good agreement with the theoretical value. It can also be seen that the depth of the spectral response changes with the pump signal, from -2.3 dB with the pump off to -1.6 dB with the pump on, i.e., a difference of 0.7 dB. Those results show the influence of the acoustic Brillouin wave on the filter's transmission. However, in previous works better results with a tunability of about 3 dB in the notch depth were achieved [24]. Also, the spectral response of the experimental filter that was measured by the NWA is not as sharp as the response of the theoretical filter, although we used high coupling ratios for the couplers. Numerical simulation of the above-illustrated setup shows that for the coupling ratios that we used in our experiment; the filter response should be as illustrated in Fig. 6.

 figure: Fig. 6.

Fig. 6. Simulation results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 and length of 12.6 km (amplitude in logarithmic scale).

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The simulation results show that the depth of the spectral response should be about -40 dB, compared to the -2.3 dB we got in our experiment. This difference between the theory and the experimental may be explained by the loss of the long fiber we used to generate the Brillouin effect. In our experiment, we used 12.6 km fiber which means that we have losses of about 2.52 dB (for typical attenuation value of 0.2 dB to km). Additional optical losses in the experimental system are the connector losses (about 0.2 dB) and the circulator insertion loss (0.75 dB). If we insert those losses into our simulation, the accepted simulated filter transmission becomes more similar to the experimental results, as can be seen in Fig. 7.

 figure: Fig. 7.

Fig. 7. Simulation results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 and fiber loss of 12.6 km fiber (amplitude in logarithmic scale).

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One can see that similar to the experimental results, the depth of the simulated filter transmission is about -2.3 dB which means that our results have good agreement with the theory. In the experiment, when we turned the pump on, we got a depth of only -1.6 dB. The numerical simulation shows that such a change in the transmission depth corresponds to a change of the coupling ratio from 90% to 65%, as can be seen in Fig. 8.

 figure: Fig. 8.

Fig. 8. Simulation Results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 (blue line) compared to the case of 35/65 and 1/99 (red line): (a) Ideal filter transmission; (b) Filter with the long fiber loss.

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Figure 8(a) shows the transmission of the filter for the case, in which we simulated short fiber of only 1 m and without circulator losses. In that case, a significant change in the filter depth of more than 10 dB results from the change in the coupling ratio. Figure 8(b) shows the calculation of the transmission of the same filter by using the long fiber. In this case, the simulation results are very similar to the experimental results presented in Fig. 5, in which the change in the transmission depth was minor. It means that by using shorter fiber length, a more significant change in the transmission depth may be achieved. However, the long fiber is required to achieve the Brillouin effect. This problem may be solved by designing a different configuration for the filter, in which the long fiber that is used to generate the Brillouin effect will be out of the loop. This may be applied by splicing the long fiber to a different port of the coupler, which is not connected to the loop of the filter as can be seen in Fig. 9.

 figure: Fig. 9.

Fig. 9. Schematic diagram of the proposed tunable filter with shorter loop length.

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This configuration allows us to apply the same concept of controlling the filter's transmission depth by the Brillouin effect since it enables us to modify the dielectric constant of the coupler so that the long fiber is placed out of the filter's loop. In this scheme, the acoustic vibrations that will be generated in the long fiber due to the Brillouin effect will change the refractive index of the coupler that is connected to this long fiber (the right coupler in Fig. 9). Then according to Eq. (1) we will get a change in the filer's transmission. In that way, we can get the same effect using short fiber for the loop, and so to reduce the optical loss and to achieve higher FSR to the filter, and more effective depth tunability. It is important to note that the influence of the Brillouin effect on the filter's transmission is due to the change in the refractive index caused by the Brillouin effect, and is not related to the interaction between the two optical waves (i.e., the pump and the Stokes). Thus, the desired effect can occur also in the scheme of Fig. 9.

As we mentioned above, such a device can be used for the realization all-fiber optical components such as switches and modulators. To clarify this point, we will give an example that is based on the experimental results presented in Fig. 5. According to those results, the frequency of about 1 MHz has transmission of -2.3 dB where the pump is off. While we are turning the pump on, its transmission will change to -1.6 dB. So, controlling the transmission of such signal is possible by controlling the presence of the pump in the system. Moreover, according to Eq. (3) in our manuscript, we can see that the Brillouin effect depends on the intensity of the pump wave, so different intensities of pump wave are expected to give us different values for the signal transmission. Thus, modulating the pump will allow us to modulate the input signal. The speed of modulation will be depending on the possible modulation rate of the pump wave, and will be limited by the Brillouin phonon lifetime, which is about 10 ns [21,22].

5. Conclusions

In this paper we proposed a new technique for controlling an all-fiber IIR optical filter using SBS. We presented preliminary experimental results which demonstrate the potential of the proposed method for the realization of a tunable optical filter, by achieving a change of about 0.7 dB in the depth of the spectral response of the filter. Such a device could be used for the realization of many all-fiber optical components such as modulators and switches. In future work, an improvement of the filter may be realized, by using the short loop configuration, and a narrower laser source for the input signal.

Funding

Hrvatska Zaklada za Znanost (2016-06-1307).

Disclosures

The authors declare no conflict of interest.

References

1. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]  

2. J. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” J. Lightwave Technol. 31(4), 571–586 (2013). [CrossRef]  

3. R. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Tech. 54(2), 832–846 (2006). [CrossRef]  

4. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]  

5. Z. Zalevsky, A. Shemer, V. Eckhouse, D. Mendlovic, and S. Zach, “Radio frequency photonic filter for highly resolved and ultrafast information extraction,” J. Opt. Soc. Am. A 22(8), 1668 (2005). [CrossRef]  

6. Z. Zalevsky, A. Shemer, D. Mendlovic, and S. Zach, “Passive and periodically ultra fast RF-photonic spectral scanner,” Opt. Express 14(18), 8367 (2006). [CrossRef]  

7. L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010). [CrossRef]  

8. Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019). [CrossRef]  

9. E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

10. W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019). [CrossRef]  

11. W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013). [CrossRef]  

12. J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016). [CrossRef]  

13. D. Marpaung, B. Morrison, M. Pagani, R. Pant, D. Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Low-power, chip-based stimulated brillouin scattering microwave photonic filter with ultrahigh selectivity,” Optica 2(2), 76 (2015). [CrossRef]  

14. W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012). [CrossRef]  

15. C. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18(6), 860–868 (2000). [CrossRef]  

16. S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015). [CrossRef]  

17. C. Feng, S. Preussler, and T. Schneider, “The influence of dispersion on stimulated-brillouin- scattering-based microwave photonic notch filters,” J. Lightwave Technol. 36(22), 5145–5151 (2018). [CrossRef]  

18. W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012). [CrossRef]  

19. W. Wei, L. Yi, Y. Jaouën, and W. Hu, “Arbitrary-shaped Brillouin microwave photonic filter by manipulating a directly modulated pump,” Opt. Lett. 42(20), 4083 (2017). [CrossRef]  

20. R.W. Boyd, Nonlinear Optics, 3rd ed., pp. 429–471, Academic press, Burlington, Massachusetts (2008). [CrossRef]  

21. G. P. Agrawal, “Stimulated Brillouin scattering,” Chapter 9 in Nonlinear Fiber Optics, 4th ed., pp. 329–333, Academic Press, Burlington, Massachusetts (2008).

22. G. P. Agrawal, “Fibers couplers,”, chapter 2 in Applications of non-linear fiber optics, pp. 62–111, Academic press, Burlington, Massachusetts (2001). [CrossRef]  

23. G. Shabtay and Z. Zalevsky, “Fiber Bragg gratings as interleavers,” J. Opt. Netw. 2(2), 19–37 (2003).

24. R. K. Varshney, B. Nagaraju, A. Singh, B. P. Pal, and A. K. Kar, “Design and realization of an all-fiber broadband tunable gain equalization filter for DWDM signals,” Opt. Express 15(21), 13519–13530 (2007). [CrossRef]  

References

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  1. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
    [Crossref]
  2. J. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” J. Lightwave Technol. 31(4), 571–586 (2013).
    [Crossref]
  3. R. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Tech. 54(2), 832–846 (2006).
    [Crossref]
  4. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  5. Z. Zalevsky, A. Shemer, V. Eckhouse, D. Mendlovic, and S. Zach, “Radio frequency photonic filter for highly resolved and ultrafast information extraction,” J. Opt. Soc. Am. A 22(8), 1668 (2005).
    [Crossref]
  6. Z. Zalevsky, A. Shemer, D. Mendlovic, and S. Zach, “Passive and periodically ultra fast RF-photonic spectral scanner,” Opt. Express 14(18), 8367 (2006).
    [Crossref]
  7. L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
    [Crossref]
  8. Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
    [Crossref]
  9. E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).
  10. W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
    [Crossref]
  11. W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
    [Crossref]
  12. J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
    [Crossref]
  13. D. Marpaung, B. Morrison, M. Pagani, R. Pant, D. Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Low-power, chip-based stimulated brillouin scattering microwave photonic filter with ultrahigh selectivity,” Optica 2(2), 76 (2015).
    [Crossref]
  14. W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012).
    [Crossref]
  15. C. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18(6), 860–868 (2000).
    [Crossref]
  16. S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015).
    [Crossref]
  17. C. Feng, S. Preussler, and T. Schneider, “The influence of dispersion on stimulated-brillouin- scattering-based microwave photonic notch filters,” J. Lightwave Technol. 36(22), 5145–5151 (2018).
    [Crossref]
  18. W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012).
    [Crossref]
  19. W. Wei, L. Yi, Y. Jaouën, and W. Hu, “Arbitrary-shaped Brillouin microwave photonic filter by manipulating a directly modulated pump,” Opt. Lett. 42(20), 4083 (2017).
    [Crossref]
  20. R.W. Boyd, Nonlinear Optics, 3rd ed., pp. 429–471, Academic press, Burlington, Massachusetts (2008).
    [Crossref]
  21. G. P. Agrawal, “Stimulated Brillouin scattering,” Chapter 9 in Nonlinear Fiber Optics, 4th ed., pp. 329–333, Academic Press, Burlington, Massachusetts (2008).
  22. G. P. Agrawal, “Fibers couplers,”, chapter 2 in Applications of non-linear fiber optics, pp. 62–111, Academic press, Burlington, Massachusetts (2001).
    [Crossref]
  23. G. Shabtay and Z. Zalevsky, “Fiber Bragg gratings as interleavers,” J. Opt. Netw. 2(2), 19–37 (2003).
  24. R. K. Varshney, B. Nagaraju, A. Singh, B. P. Pal, and A. K. Kar, “Design and realization of an all-fiber broadband tunable gain equalization filter for DWDM signals,” Opt. Express 15(21), 13519–13530 (2007).
    [Crossref]

2019 (2)

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

2018 (1)

2017 (1)

2016 (1)

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

2015 (2)

D. Marpaung, B. Morrison, M. Pagani, R. Pant, D. Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Low-power, chip-based stimulated brillouin scattering microwave photonic filter with ultrahigh selectivity,” Optica 2(2), 76 (2015).
[Crossref]

S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015).
[Crossref]

2013 (2)

W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
[Crossref]

J. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” J. Lightwave Technol. 31(4), 571–586 (2013).
[Crossref]

2012 (2)

W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012).
[Crossref]

W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012).
[Crossref]

2010 (1)

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

2009 (1)

2007 (1)

2006 (3)

2005 (1)

2003 (1)

2000 (1)

Agrawal, G. P.

G. P. Agrawal, “Stimulated Brillouin scattering,” Chapter 9 in Nonlinear Fiber Optics, 4th ed., pp. 329–333, Academic Press, Burlington, Massachusetts (2008).

G. P. Agrawal, “Fibers couplers,”, chapter 2 in Applications of non-linear fiber optics, pp. 62–111, Academic press, Burlington, Massachusetts (2001).
[Crossref]

Boyd, R.W.

R.W. Boyd, Nonlinear Optics, 3rd ed., pp. 429–471, Academic press, Burlington, Massachusetts (2008).
[Crossref]

Capmany, J.

Capmany, J. J.

Choi, D. Y.

chuan Xiao, Y.

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

Ding, W.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Dong, W.

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

Eckhouse, V.

Eggleton, B. J.

Feng, C.

Feng, X.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Gasulla, I.

Gu, J.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Hu, Q.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Hu, W.

Huang, D.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Jaouën, Y.

Jia, Z.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Kar, A. K.

Li, M.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Li, P.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Li, W.

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
[Crossref]

Li, X.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Liu, J. G.

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

Lloret, J.

Luther-Davies, B.

Madden, S. J.

Madsen, C.

Marpaung, D.

Mendlovic, D.

Minasian, R.

R. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Tech. 54(2), 832–846 (2006).
[Crossref]

Minasian, R. A.

W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012).
[Crossref]

W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012).
[Crossref]

Mora, J.

Morrison, B.

Nagaraju, B.

Ortega, B.

Pagani, M.

Pal, B. P.

Pant, R.

Pastor, D.

Preussler, S.

C. Feng, S. Preussler, and T. Schneider, “The influence of dispersion on stimulated-brillouin- scattering-based microwave photonic notch filters,” J. Lightwave Technol. 36(22), 5145–5151 (2018).
[Crossref]

S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015).
[Crossref]

qi Li, J.

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

Sales, S.

Sancho, J.

Schneider, T.

C. Feng, S. Preussler, and T. Schneider, “The influence of dispersion on stimulated-brillouin- scattering-based microwave photonic notch filters,” J. Lightwave Technol. 36(22), 5145–5151 (2018).
[Crossref]

S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015).
[Crossref]

Shabtay, G.

Shemer, A.

Shi, D.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Shi, Z.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Singh, A.

Varshney, R. K.

Wang, L.

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

Wang, L. X.

W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
[Crossref]

Wei, W.

Wen, J.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Xu, E.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Yang, C. W.

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

Yao, J.

Yi, L.

Yu, Y.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Zach, S.

Zalevsky, Z.

Zhang, W.

W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012).
[Crossref]

W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012).
[Crossref]

Zhang, X.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Zhang, X. D.

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

Zhang, Z.

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

Zhou, L.

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Zhu, N.

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Zhu, N. H.

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
[Crossref]

IEEE Photonics J. (2)

W. Li, L. X. Wang, and N. H. Zhu, “All-optical microwave photonic single-passband filter based on polarization control through stimulated brillouin scattering,” IEEE Photonics J. 5(4), 5501411 (2013).
[Crossref]

W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic brillouin-based filter,” IEEE Photonics J. 4(5), 1443–1455 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (2)

W. Li, C. W. Yang, L. Wang, J. G. Liu, and N. H. Zhu, “Tunable single-notch microwave photonic filter based on non- sliced ASE source,” IEEE Photonics Technol. Lett. 31(10), 731–734 (2019).
[Crossref]

W. Zhang and R. A. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated brillouin scattering,” IEEE Photonics Technol. Lett. 24(14), 1182–1184 (2012).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

R. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Tech. 54(2), 832–846 (2006).
[Crossref]

J. Lightwave Technol. (5)

J. Opt. Netw. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

L. Zhou, X. Zhang, E. Xu, Y. Yu, X. Li, and D. Huang, “A novel tunable cascaded IIR microwave photonic filter,” Opt. Commun. 283(14), 2794–2797 (2010).
[Crossref]

Z. Shi, J. Wen, Z. Jia, D. Shi, M. Li, N. Zhu, and W. Li, “Tunable single notch microwave photonic filter based on delay lines,” Opt. Commun. 448, 15–18 (2019).
[Crossref]

Opt. Eng. (1)

S. Preussler and T. Schneider, “Stimulated brillouin scattering gain bandwidth reduction and applications in microwave photonics and optical signal processing,” Opt. Eng. 55(3), 031110 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optica (1)

Optoelectron. Lett. (1)

J. qi Li, Y. chuan Xiao, W. Dong, and X. D. Zhang, “Dual-band bandpass tunable microwave photonic filter based on stimulated brillouin scattering,” Optoelectron. Lett. 12(4), 276–279 (2016).
[Crossref]

Other (4)

R.W. Boyd, Nonlinear Optics, 3rd ed., pp. 429–471, Academic press, Burlington, Massachusetts (2008).
[Crossref]

G. P. Agrawal, “Stimulated Brillouin scattering,” Chapter 9 in Nonlinear Fiber Optics, 4th ed., pp. 329–333, Academic Press, Burlington, Massachusetts (2008).

G. P. Agrawal, “Fibers couplers,”, chapter 2 in Applications of non-linear fiber optics, pp. 62–111, Academic press, Burlington, Massachusetts (2001).
[Crossref]

E. Xu, Q. Hu, W. Ding, J. Gu, X. Feng, Z. Zhang, and P. Li, “Tunable microwave photonic filter based on mode-locked fiber laser,” in 2017 International Topical Meeting on Microwave Photonics (MWP), IEEE (2017).

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Figures (9)

Fig. 1.
Fig. 1. Schematic diagram of an optical ring resonator.
Fig. 2.
Fig. 2. IIR filter response versus fiber optic coupler ratios.
Fig. 3.
Fig. 3. A flow diagram: The influence of the SBS process on the filter's depth step-by-step.
Fig. 4.
Fig. 4. Schematic diagram of the experimental setup.
Fig. 5.
Fig. 5. Experimental results: The transfer function of the IIR filter: without the Brillouin effect (blue line) and with the Brillouin effect.
Fig. 6.
Fig. 6. Simulation results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 and length of 12.6 km (amplitude in logarithmic scale).
Fig. 7.
Fig. 7. Simulation results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 and fiber loss of 12.6 km fiber (amplitude in logarithmic scale).
Fig. 8.
Fig. 8. Simulation Results: The transfer function of the IIR filter with couplers of 10/90 and 1/99 (blue line) compared to the case of 35/65 and 1/99 (red line): (a) Ideal filter transmission; (b) Filter with the long fiber loss.
Fig. 9.
Fig. 9. Schematic diagram of the proposed tunable filter with shorter loop length.

Equations (4)

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| H ( ν ) | = t 1 t 2 1 + r 1 2 r 2 2 2 r 1 r 2 cos ( 2 π ν Δ t )
Δ ε = ρ 0 1 γ e ρ ~ ( z , t )
ρ ~ ( z , t ) = ε 0 γ e q 2 A P A S Ω B 2 Ω 2 i Ω Γ B e i ( Ω t q z ) + c . c
F S R = c n L 16 k H z