An ultrawide tunable range single passband microwave photonic filter based on stimulated Brillouin scattering

A single passband microwave photonic filter with ultrawide tunable range based on stimulated Brillouin scattering is theoretically analyzed. Combining the gain and loss spectrums, tuning range with 44GHz is obtained without crosstalk by introducing two pumps. Adding more pumps, Tuning range multiplying with the multiplication factor equaling to the total quantity of pump can be achieved, which has potential application in microwave and millimeter wave wireless communication systems. ©2013 Optical Society of America OCIS codes: (070.0070) Fourier optics and signal processing; (290.5900) Scattering, stimulated Brillouin; (070.2615) Frequency filtering. References and links 1. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24, 201–229 (2006). 2. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE T Microw Theory 54(2), 832–846 (2006). 3. J. Yao, “Photonics for microwave signal filtering,” in IEEE Sarnoff Symposium, 2009. SARNOFF '09(2009), 1– 5. 4. V. R. Supradeepa, C. M. Long, R. Wu, F. Ferdous, E. Hamidi, D. E. Leaird, and A. M. Weiner, “Comb-based radiofrequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012). 5. R. Wu, C. M. Long, D. E. Leaird, and A. M. Weiner, “Directly generated Gaussian-shaped optical frequency comb for microwave photonic filtering and picosecond pulse generation,” IEEE Photon. Technol. Lett. 24(17), 1484–1486 (2012). 6. T. X. H. Huang, X. Yi, and R. A. Minasian, “A high-order FIR microwave photonic filter,” in International Topical Meeting on Microwave Photonics, 2009. MWP '09(2009), 1–4. 7. M. Song, C. M. Long, R. Wu, D. Seo, D. E. Leaird, and A. M. Weiner, “Reconfigurable and tunable flat-top microwave photonic filters utilizing optical frequency combs,” IEEE Photon. Technol. Lett. 23(21), 1618–1620 (2011). 8. Y. Dai and J. Yao, “Nonuniformly-spaced photonic microwave delayline filter,” Opt. Express 16(7), 4713–4718 (2008). 9. B. Vidal, J. L. Corral, and J. Martí, “All-optical WDM multi-tap microwave filter with flat bandpass,” Opt. Express 14(2), 581–586 (2006). 10. J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006). 11. X. Yi and R. A. Minasian, “Microwave photonic filter with single bandpass response,” Electron. Lett. 45(7), 362–363 (2009). 12. W. Zhang and R. A. Minasian, “Widely Tunable Single-Passband Microwave Photonic Filter Based on Stimulated Brillouin Scattering,” IEEE Photon. Technol. Lett. 23(23), 1775–1777 (2011). 13. W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phasemodulation to intensity-modulation conversion using a phase-shifted Fiber Bragg Grating,” IEEE T Microw Theory 60(5), 1287–1296 (2012). 14. M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Highly chirped single-bandpass microwave photonic filter with reconfiguration capabilities,” Opt. Express 19(5), 4566–4576 (2011). 15. T. X. H. Huang, X. Yi, and R. A. Minasian, “Single passband microwave photonic filter using continuous-time impulse response,” Opt. Express 19(7), 6231–6242 (2011). #181378 $15.00 USD Received 7 Dec 2012; revised 17 Jan 2013; accepted 17 Jan 2013; published 28 Jan 2013 (C) 2013 OSA 11 February 2013 / Vol. 21, No. 3 / OPTICS EXPRESS 2718 16. Y. M. Chang and J. H. Lee, “Tunable, single passband photonic microwave filter based on stimulated Brillouin scattering in nonlinear fiber,” in IEEE LEOS Annual Meeting Conference Proceedings, 2009. LEOS '09(2009), 654–655. 17. R. Pant, A. Byrnes, E. Li, D.-Y. Choi, C. G. Poulton, S. Fan, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and dynamically reconfigurable microwave photonic filter using stimulated Brillouin scattering,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides(Optical Society of America, 2012). 18. F. Zeng and J. Yao, “Investigation of phase-modulator-based all-optical bandpass microwave filter,” J. Lightwave Technol. 23, 1113– 1117(2005). 19. W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic Brillouin-based filter,” IEEE Photonics Journal 4(5), 1443–1455 (2012). 20. P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). 21. N. Guo, R. C. Qiu, S. S. Mo, and K. Takahashi, “60-GHz millimeter-wave radio: principle, technology, and new Results,” EURASIP J. Wirel. Commun. Netw. 2007, 1–48 (2007). 22. A. Loayssa, D. Benito, and M. José Garde, “Applications of optical carrier Brillouin processing to microwave photonics,” Opt. Fiber Technol. 8(1), 24–42 (2002).


Introduction
Microwave photonic filter (MPF) as a most powerful photonic signal process subsystem has been paid much attention to carrying equivalent function to those of an ordinary microwave filter within a radio frequency (RF) system or link.Compared with microwave filters implemented in the electrical domain, microwave photonic filters have many unique wonderful properties such as high frequency operation, large tunability and dynamic configurability, low and RF frequency independent loss, immunity to electromagnetic interference (EMI), and having potential application in radar, universal mobile telecommunications system, optically controlled phased array antennas, and radio-over-fiber systems [1][2][3][4].
Over the past decade a number of tap delay line based microwave photonics (MWP) filters have been proposed and experimentally demonstrated, such as high-order and high Q all-positive coefficients filter [5,6], and negative and complexity coefficients filters [7][8][9], aiming at realizing arbitrary bandpass filtering with flat top and sharp transition bands and achieving the tunability without the variation of the entire shape of the frequency response including the free spectral range (FSR) and the 3-dB bandwidth.
However, most microwave photonic filters employing optical delay line structures are limited by its intrinsic periodic spectral response.This is a significant drawback because it restricts the processing frequency to a fraction of FSR in order to avoid spectral overlapping.For wideband operation, it is important to realize microwave photonic filters which have a single passband without baseband response.Kinds of single passband filters have been reported [10][11][12][13][14][15][16][17].Among them, the technique based on stimulated Brillouin scattering (SBS) in optical fiber is an attractive approach for implementing high-resolution and large range tuning, and combining with phase modulation (PM) both modulator bias drift problem and baseband resonance can be eliminated.However, the basic tuning range of the present SBS based filters is limited within twice the range of brillouin frequency shift of fiber.
In this paper, we propose and analyze a single-bandpass MPF based on stimulated brillouin scattering together with phase modulation.By combining two adjacent pumps with accurate space, gain and loss of different pumps will overlap to be canceled with each other, and then tuning range multiplying can be obtained by numeric simulation.Theoretically, multiplication factor is equal to the pump quantity, and the continuous tuning range will reach the millimeter wave band when the factor is greater than three, which will lead to a potential application in microwave and millimeter wave wireless communication.

Operational principle
The conventional single passband MPF combining PM technique and SBS process has the configuration shown in Fig. 1.A continuous wave (CW) is sent to the phase modulator via polarization controller (PC).The polarization state of the light wave to the phase modulator is adjusted by the PC to minimize the polarization-dependent loss.The phase modulator is driven by a sinusoidal RF signal with a tunable angular frequency ω m generated by a vector network analyzer (VNA).After the interaction between modulated optical signal and counterpropagating pump wave, the output optical field via circulator is detected by photodetector and then translated to VNA to be analyzed Mathematically, for small signal modulation the normalized optical field E PM (t) at the output of the phase modulator can be expressed as [18]: Where J n (•) represents the nth-order Bessel function of the first kind with n = 0, 1 and m is the phase modulation index, and f c is the frequency of the laser and f m denotes the frequency of injected RF signal.Obviously, the two first-order sidebands are out of phase: denoted 0 and π in Fig. 2. If the phase-modulated signal is applied directly to the PD, no signal would be detected except dc since the beating between the optical carrier and the upper sideband will cancel completely the beating between the optical carrier and the lower sideband due to the fact that the two beat signals are out of phase with a balanced intensity.However, in Fig. 3(a), when introducing counterpropagating narrow linewidth pump wave launched from pump laser, the gain and loss spectrum separated by brillouin frequency shift ν B respectively to pump will be generated because of SBS process, which will lead to the broken of intensity balance between two sidebands, and then the corresponding RF signal can be detected by PD.
Since the gain and loss exists simultaneously, there will be two passband generated with the interval of 2ν B , so the SBS loss caused passband will restrict the channel bandwidth in practical application in order to avoid crosstalk.So the tunable range of conventional SBS based MPFs are confined within 2ν B .For the sake of broadening the available tuning range, a method based on loss compensation by another added pump is proposed shown in Fig. 1, where the single pump is replaced by two pumps boxed by red dotted line.When the frequency difference between the two pumps is accurately set as 2ν B , the gain of the second pump will compensate the loss caused by the first pump.Therefore the upper sideband after PM will not experience any gain or loss in the overlapping area, also the passband will not be shaped, which results in a broadened tuning range of 4ν B as shown in Fig. 3(b).According to this idea, more pumps can be used to increase the tuning range without limitation.
The SBS process occurs in the fiber between the upper sideband and the pump light wave causing the amplification in the gain spectrum region and the attenuation in the loss spectrum region which can be described as follows respectively [19]: Where g 0 and Γ B represent the line-center gain factor and Brillouin linewidth of the fiber, I p is the intensity of pump wave, and f is the frequency deviation from ν B .Following the SBS process, the optical field of the forward-propagating RF-modulated signal can be written as: Where L is the length of the fiber.Omitting the dc and the small second harmonic components, the optical power input into the PD is expressed approximately as: According to Eq. ( 2) and Eq. ( 3): ( ) The gain G﹑loss A and nonlinear phase shift φ g and φ α versus detuning from linewidth center are shown in Fig. 4.
Then the electronic field of the output RF signal at the PD can be given as: ℜ means the responsivity of PD to the input optical power.Then, the transfer function can be simplified as: In order to enlarge the tuning range, two adjacent pumps (f p1 and f p2 ) are employed with a permanent frequency space with 2ν B (namely f p2 -f p1 = 2ν B ). Then according to Eq. ( 4), after the SBS process, the optical power input into the PD can be rewritten as: From Eq. ( 6)~( 9) ( ) where k = 1、2.According to Eq. ( 11), the transfer function with two pumps can be expressed as: From Eq. ( 11) and Eq. ( 17), a general expression of transfer function with total N pumps can be derived to be:

Numeric simulation and discussion
In our numeric simulation, several parameters are assumed: -Gmax = -Amax = 5dB, Γ B = 30MHz, ν B = 11GHz [20].First, only one pump is considered, and the frequency space between carrier and pump is set to be 16GHz (f p -f c = 16GHz).After numeric simulation the frequency response is demonstrated in Fig. 5  Hence when three pumps are employed, the tunable range can reach 60GHz frequency band, which has potential application in 60GHz millimeter wave radio [21].Therefore by adding more pumps, the tuning range can be enlarged to 2ν B multiplying N, where N is equal to the total number of pump.The tunability is a critical property for MPFs.Two pumps are used to produce 4ν B of 44GHz tunable range, and then tuning the two pumps with the same pace, 44GHz continuous tunable range can be realized shown in Fig. 6.During this process, the space of the two pumps must be kept constant.The wavelength stability of laser is of vital importance for SBS related application [22].Although the high performance tunable laser has perfect wavelength stability of ± 1pm, the corresponding frequency fluctuation at 1550nm is about ± 125MHz.For the proposed cooperation of multi-pumps, the trouble caused by wavelength stability must be avoided.In Fig. 7, 1MHz detuning of the adjacent space error between two pumps will lead to a −30dB passband generation in the center of the SBS gain and loss spectrum overlapped region.The relationship between the frequency detuning and the undesired passband response is shown in Fig. 8, where the results have been normalized to the main lobe.Obviously, the tolerance is fairly small for laser, which is very difficult to be insured.Fortunately, potential solutions used to ensure the SBS stability can be realized by modulation or SBS based laser technologies.The modulation-technology-based schematic for our proposed MPF to eliminate the stability of SBS operation can be configured as Fig. 9, and the tunability can be realized by tuning f p .

Conclusion
A single passband tunable microwave photonic filter based on stimulated brillouin scattering is analyzed numerically.Employing two pumps, 44GHz tuning range is obtained free from crosstalk and the continuous tuning is achieved by changing the frequency space between pumps and carrier.The results also demonstrate that tuning range can be enlarged to 2ν B multiplying N which is the total quantity of pump.Overcoming the wavelength stability, the brillouin based filter has potential application in microwave and millimeter wave wireless communication.

Fig. 3 .
Fig. 3. (a) RF passband generation with the SBS process for a single pump (b) RF passband broadened generation with the SBS process for two pumps.

Fig. 4 .
Fig. 4. (a)SBS gain spectrum and (b) gain related nonlinear phase shift (c) SBS loss spectrum and (d) loss related nonlinear phase shift.
as the black curve.From the figure, two passband can be obtained, and the one at the lower frequency is excited by Brillouin gain centered at f 01 = 5GHz (f 01 equals f p -f c -ν B ) and the other one excited by Brillouin loss is centered at f 02 = 27GHz (f 02 equals f p -f c + ν B ). From the idea mentioned above, when another pump wave with frequency f p1 (f p1 = f p + 2ν B ) is added, the central frequency f 02 should move to 49GHz with passband space of 4ν B , which is confirmed by the purple cure shown in Fig.5.Compared with one pump, the tuning range has been doubled after adding another pump.Also in Fig.0.5 the blue curve shows the tripled tuning range with 6ν B with three pumps.

Fig. 5 .
Fig. 5. Comparison of frequency response in different number of pump.