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

Yongchuan Xiao; Jing Guo; Kui Wu; Pengfei Qu; Huajuan Qi; Caixia Liu; Shengping Ruan; Weiyou Chen; Wei Dong

doi:10.1364/OE.21.002718

1. 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 [1–4].

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 [7–9], 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 [10–17]. 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.

2. 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

Fig. 1 Conventional configuration of the tunable single passband MPF. CW: Continuous Wave, PM: Phase Modulation, EDFA: Erbium-Doped Fiber Amplifier, PC: Polarization Controller, DSF: Dispersion-Shifted Fiber, VNA: Vector Network Analyzer, PD: Photodetector.

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Mathematically, for small signal modulation the normalized optical field E_PM(t) at the output of the phase modulator can be expressed as [18]:

\begin{array}{l} E (t) = J_{0} (m) \exp (j 2 π f_{c} t) \\ + J_{1} (m) \exp {j [2 π (f_{c} + f_{m}) t + \frac{π}{2}]} \\ - J_{1} (m) \exp {j [2 π (f_{c} - f_{m}) t - \frac{π}{2}]} \end{array}

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.

Fig. 2 Phase modulation spectrum.

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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.

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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]:

g (f) = \frac{g_{0} I_{p}}{2} \frac{{(Γ_{B} / 2)}^{2}}{f^{2} + {(Γ_{B} / 2)}^{2}} + j \frac{g_{0} I_{p}}{4} \frac{Γ_{B} f}{f^{2} + {(Γ_{B} / 2)}^{2}}

α (f) = - \frac{g_{0} I_{p}}{2} \frac{{(Γ_{B} / 2)}^{2}}{f^{2} + {(Γ_{B} / 2)}^{2}} - j \frac{g_{0} I_{p}}{4} \frac{Γ_{B} f}{f^{2} + {(Γ_{B} / 2)}^{2}}

Where g₀ 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:

E (t) = \exp (j 2 π f_{c} t) {\begin{cases} J_{0} (m) \\ + J_{1} (m) \exp [\begin{array}{l} {g [(f_{p} - ν_{B}) - (f_{c} + f_{m})] + α [(f_{p} + ν_{B}) - (f_{c} + f_{m})]} L \\ + j (2 π f_{m} t + \frac{π}{2}) \end{array}] \\ - J_{1} (m) \exp [j (- 2 π f_{m} t - \frac{π}{2})] \end{cases}}

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:

P \approx 2 J_{0} (m) J_{1} (m) {G (f_{m}) A (f_{m}) \cos [2 π f_{m} t + \frac{π}{2} + ϕ_{g} (f_{m}) + ϕ_{α} (f_{m})] - \cos (2 π f_{m} t + \frac{π}{2})}

According to Eq. (2) and Eq. (3):

\begin{array}{l} G (f_{m}) = \exp (Re [g (f_{p} - ν_{B} - (f_{c} + f_{m}))] L) \\ = \exp {\frac{g_{0} I_{p} L}{2} \frac{{(Γ_{B} / 2)}^{2}}{{[f_{p} - ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}}} \end{array}

\begin{array}{l} A (f_{m}) = \exp (Re [α (f_{p} + ν_{B} - (f_{c} + f_{m}))] L) \\ = \exp {- \frac{g_{0} I_{p} L}{2} \frac{{(Γ_{B} / 2)}^{2}}{{[f_{p} + ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}}} \end{array}

\begin{array}{l} ϕ_{g} (f_{m}) = Im [g (f_{p} - ν_{B} - (f_{c} + f_{m}))] L \\ = \frac{g_{0} I_{p} L}{4} \frac{Γ_{B} [f_{p} - ν_{B} - (f_{c} + f_{m})]}{{[f_{p} - ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}} \end{array}

\begin{array}{l} ϕ_{α} (f_{m}) = Im [α (f_{p} + ν_{B} - (f_{c} + f_{m}))] L \\ = - \frac{g_{0} I_{p} L}{4} \frac{Γ_{B} [f_{p} + ν_{B} - (f_{c} + f_{m})]}{{[f_{p} + ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}} \end{array}

The gain G﹑loss A and nonlinear phase shift ϕ_g and ϕ_α versus detuning from linewidth center are shown in 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.

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Then the electronic field of the output RF signal at the PD can be given as:

\begin{array}{l} E_{R F} (t) = ℜ < P > \\ \propto G (f_{m}) A (f_{m}) \cos [2 π f_{m} t + \frac{π}{2} + ϕ_{g} (f_{m}) + ϕ_{α} (f_{m})] - \cos (2 π f_{m} t + \frac{π}{2}) \end{array}

ℜ means the responsivity of PD to the input optical power. Then, the transfer function can be simplified as:

\begin{array}{l} {| H (f) |}^{2} = \frac{P_{R F}_{o u t}}{P_{R F}_{i n}} \\ \propto 1 + G (f_{m}) {}^{2}A (^{f_{m}) 2} - 2 G (f_{m}) A (f_{m}) \cos [ϕ_{g} (f_{m}) + ϕ_{α} (f_{m})] \end{array}

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:

P \approx 2 J_{0} (m) J_{1} (m) {\begin{cases} G_{1} (f_{m}) G_{2} (f_{m}) A_{1} (f_{m}) A_{2} (f_{m}) \cos [\begin{array}{l} 2 π f_{m} t + \frac{π}{2} + ϕ_{g 1} (f_{m}) \\ + ϕ_{α 1} (f_{m}) + ϕ_{g}_{2} (f_{m}) + ϕ_{α 2} (f_{m}) \end{array}] \\ - \cos (2 π f_{m} t + \frac{π}{2}) \end{cases}}

From Eq. (6)~(9)

\begin{array}{l} G_{k} (f_{m}) = \exp (Re {g (f_{p k} - ν_{B} - (f_{c} + f_{m}))} L) \\ = \exp {\frac{g_{0} I_{p k} L}{2} \frac{{(Γ_{B} / 2)}^{2}}{{[f_{p k} - ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}}} \end{array}

\begin{array}{l} A_{k} (f_{m}) = \exp (Re {α (f_{p k} + ν_{B} - (f_{c} + f_{m}))} L) \\ = \exp {- \frac{g_{0} I_{p k} L}{2} \frac{{(Γ_{B} / 2)}^{2}}{{[f_{p k} + ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}}} \end{array}

\begin{array}{l} ϕ_{g k} (f_{m}) = Im [g (f_{p k} - ν_{B} - (f_{c} + f_{m}))] L \\ = \frac{g_{0} I_{p k} L}{4} \frac{Γ_{B} [f_{p k} - ν_{B} - (f_{c} + f_{m})]}{{[f_{p k} - ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}} \end{array}

\begin{array}{l} ϕ_{α k} (f_{m}) = Im [α (f_{p k} + ν_{B} - (f_{c} + f_{m}))] L \\ = - \frac{g_{0} I_{p k} L}{4} \frac{Γ_{B} [f_{p k} + ν_{B} - (f_{c} + f_{m})]}{{[f_{p k} + ν_{B} - (f_{c} + f_{m})]}^{2} + {(Γ_{B} / 2)}^{2}} \end{array}

where k = 1、2.

According to Eq. (11), the transfer function with two pumps can be expressed as:

\begin{array}{l} {| H (f) |}^{2} = 1 + G_{1} (f_{m}) {}^{2}G_{2} (f_{m}) {}^{2}A_{1} (^{f_{m}) 2} A_{2} (^{f_{m}) 2} \\ - 2 G_{1} (f_{m}) G_{2} (f_{m}) A_{1} (f_{m}) A_{2} (f_{m}) \cos [\begin{array}{l} ϕ_{g 1} (f_{m}) + ϕ_{α 1} (f_{m}) \\ + ϕ_{g 2} (f_{m}) + ϕ_{α 2} (f_{m}) \end{array}] \end{array}

From Eq. (11) and Eq. (17), a general expression of transfer function with total N pumps can be derived to be:

\begin{array}{l} {| H (f) |}^{2} = 1 + \prod_{k = 1}^{N} G_{k} (f_{m}) {}^{2}A_{k} {(f_{m})}^{2} \\ - 2 [\prod_{k = 1}^{N} G_{k} (f_{m}) A_{k} (f_{m})] \cos {\sum_{k = 1}^{N} [ϕ_{g k} (f_{m}) + ϕ_{α k} (f_{m})]} \end{array}

3. Numeric simulation and discussion

In our numeric simulation, several parameters are assumed: ︱G︱_max = ︱A︱_max = 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 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 f₀₁ = 5GHz (f₀₁ equals f_p-f_c-ν_B) and the other one excited by Brillouin loss is centered at f₀₂ = 27GHz (f₀₂ 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 f₀₂ 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. 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.

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

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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.

Fig. 6 Filter continuous tuning within 44GHz range.

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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.

Fig. 7 Frequency response for two pumps with 1MHz offset.

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Fig. 8 Amplitude response for undesired passband at different frequency detuning.

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Fig. 9 Configuration of the proposed microwave photonic filter. LD: Laser Diode, CS-SSB: Carrier suppressed Single Sideband Modulation, CS-DSB: Carrier Suppressed Double Sideband Modulation.

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4. 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.

Acknowledgments

The authors are grateful to Science and Technology Development Plan of Jilin Province (Grant Nos.20110314, 20120324), the National Natural Science Foundation of China (Grant Nos.61077046, 61274068, 61275035) for the support in the work, and Chinese National Programs for High Technology Research and Development (Grant No.2013AA030902).

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

Abstract

1. Introduction

2. Operational principle

3. Numeric simulation and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (9)

Equations (18)

Optics Express