Multiple microwave frequencies measurement based on stimulated Brillouin scattering with improved measurement range Yongchuan Xiao,1 Jing Guo,1 Kui Wu,1 Wei Dong,1,* Pengfei Qu,2 Xindong Zhang,1 Shengping Ruan,1 and Weiyou Chen1,* 1
State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China 2 Chongqing Optoelectronics Research Institute, Chongqing 400060, China *[email protected]
Abstract: We numerically investigate the operational principle and performance of stimulated Brillouin scattering based multiple microwave frequency signals measurement. The unknown signals are processed specially to generate a gain region which is measured by phase modulation to amplitude modulation converting. By sweeping the vector network analyzer, both single and multiple frequencies measurement can be achieved. The loss spectrum generated by one of the pumps is fully compensated by the gain spectrum of the other pump, which increases the measurement range from 2νB to 4νB. ©2013 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (290.5900) Scattering, stimulated Brillouin; (350.4010) Microwaves.
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#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31740
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1. Introduction Frequency measurement ranging from subgigahertz to millimeter (mm)-wave frequency is of great importance for the application in modern radar system and electronic warfare, which has been widely investigated in electric domain [1]. Over the past few decades, photonic assisted microwave measurement techniques have been developed due to its inherent advantages compared with electronic techniques, such as large bandwidth, light weight, small size, low loss, and immunity to electromagnetic interference [2]. Recently, a number of photonic approaches have been demonstrated to implement microwave frequency measurement. Instantaneous frequency measurement (IFM) based on microwave power or optical power comparison of two channels is realized by constructing amplitude comparison function (ACF). Several methods have been proposed to construct ACF using, such as, dispersion induced microwave or optical power penalties [3–8], polarization domain interferometer [9], and optical filter or filter subsystem [10–12]. Also an on-chip photonic IFM system has been demonstrated which is a promising solution to resist environmental disturbance [13].To avoid frequency ambiguities, a monotone interval is chosen to get a unique mapping between power ratio value and microwave frequency. A steep ACF over the entire range of measurement is required since flat ACF will increase the measurement error. Although IFM with large measurement range and high resolution can be realized, only single frequency signal measurement is accurate. Multiple frequency signals measurement which is highly desired in realistic spectrally-cluttered environment has also been demonstrated. An electrically tuned fiber Bragg grating is used to realize frequency scanning measurement ranging from 2 to 9 GHz in [14]. In [15], a photonic based channelized receiver is presented using phase-shifted chirped fiber Bragg grating and photodetector array. A system based on frequency-time mapping for two 20 GHz spaced RF signals measurement utilizing a dispersive medium is reported in [16]. A two-tone RF signals measurement is presented in [17] by processing interferogram which is measured by sweeping tunable laser, and 15MHz resolution is experimentally demonstrated. Another similar version which can realize real-time measurement with limited resolution is proposed in [18]. A method using a spectrally sliced incoherent source is proposed in [19], in which two etalons with different free space range are employed and 5 GHz channel spacing and ± 2.5 GHz accuracy are achieved. In [20], a seven bands simultaneous and parallel instantaneous frequency measurements with ± 500 MHz error over the entire 1–40 GHz band is demonstrated.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31741
In [21], a technique combining stimulated Brillouin scattering (SBS) and phase modulation to amplitude modulation (PM to AM) conversion is proposed, and less than 30MHz measurement error has been demonstrated. But the vector network analyzer (VNA) in [21] is only used to provide probe signals; additional synchronization digital oscilloscope is needed to complete the measurement. In this paper, a novel configuration is proposed, where the VNA not only provides probe signals but also performs frequency measurement so that the oscilloscope is removed. We have theoretically analyzed the operational principle and measurement performance. By extending the scheme from one pump to two pumps, the measurement range is broadened from 2νB to 4νB for multiple frequencies measurement. 2. Operational principle The schematics of the proposed microwave frequency measurement are shown in Fig. 1. The phase modulator is driven by a sinusoidal microwave signal with scanning frequency fm generated by a VNA. If the phase-modulated signal is applied directly to photodetector (PD), no signal would be detected, except a 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 beat signals are out of phase with a balanced intensity. In the proposed scheme, the unknown signal is up-converted by dual parallel MachZehnder modulator (DPMZM) to generate the SBS pump and the VNA launched sweeping frequencies act as probe signals. When sidebands generated by phase modulation locate in the pump induced gain region, amplification caused by SBS process will be achieved to break the balance of sideband intensity. Hence the PM to AM conversion will be realized which will be displayed in VNA after detecting, and then the unknown frequency will be obtained since the pump is specially processed so that the frequency interval between gain region and carrier is equal to unknown frequency. The SBS process is usually described as nonlinear interaction between two counter-propagating waves via an acoustic wave. If a particular phase matching condition is satisfied (namely fprobe = fpump-νB), fraction of pump wave is scattered off into the probe wave, so that the global effect of the SBS process demonstrates a generation of narrowband gain resonance around the frequency of fpump-νB, resulting in an exponential growth for the probe wave. On the contrary, the energy transfer can be regarded as the generation of a loss resonance around the frequency of fpump + νB as far as the pump wave is concerned. Thus, the SBS interaction leads to a downshifted gain region where a counter-propagating signal is amplified and an upshifted loss region where the counter-propagating signal is attenuated. First, only one pump is employed as is shown in Fig. 1(a). The light source provided by laser diode (LD) with the frequency fc is divided into two paths. The upper path is phasemodulated by VNA launched microwave signals. The lower path is modulated by DPMZM1 and DPMZM2 which are driven by Brillouin frequency shift νB and unknown signal fx respectively, to generate carrier-suppressed upper sideband [22]. Therefore the final output performs as pump wave with the frequency separated by fx + νB away from carrier. The phasemodulated signals whose states of polarization are aligned by polarization controller (PC) are sent into a dispersion shift fiber (DSF) to interact with the counter-propagating pump wave. Thus the PM to AM conversion at fx will be realized which will be observed by VNA after PD detecting. The spectrum processing of one-pump based frequency measurement is shown in Fig. 2(a). Both biases of DPMZM1 and DPMZM2 are controlled to obtain only the first-order upper sidebands. So the gain region is centered at fx to realize PM to AM conversion. Noting that another frequency centered at fx + 2νB also will cause PM to AM conversion because of SBS caused attenuation. When multiple frequency signals are measured simultaneously, especially when existing two frequencies separated by 2νB, the high frequency signal cannot be measured correctly because the gain region corresponding to high frequency signal pump will be superimposed by low frequency signal pump induced loss region. So the measurement range is limited within 2νB for simultaneous measurement of multiple frequency signals if only one pump is applied.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31742
Second, an extended scheme based on two pumps shown in Fig. 1(b) is designed to reach wider range. When the two pumps are spectrally separated by 2νB with the same power, the loss spectrum of pump 1 can be fully compensated by the gain spectrum of pump 2 [23]. The global effect of gain-loss compensation manifests that the spectral space between gain and loss region is broadened from 2νB to 4νB, which will lead to a doubled measurement range for multiple frequency signals. The spectral process is shown in Fig. 2(b). Firstly, DPMZM1 is specially driven by 2νB to generate SSB-SC modulation. And secondly, the unknown signal fx is injected according to DPMZM2 with the same modulation pattern. At last, the amplitude modulator is biased at the minimum transmission point to generate a double-sideband suppressed carrier (DSB-SC) modulation. For the amplitude modulator, the driven frequency is specially set to be νB to generated two sidebands separated by 2νB where the lower sideband is used to perform frequency measurement and the higher sideband is used to implement gain and loss compensation. Since the space between gain and loss can be expanded to 3νB and 4νB by introducing pump 3 and pump 4 in a similar way, it is easily inferred that there is no theoretical limitation on the range of the SBS based frequency measurement.
Fig. 1. Schematics of photonic assisted single and multiple microwave frequencies measurement. (a) One pump is applied; (b) Gain and loss compensation based two pumps are applied. LD: Laser Diode, DSF: Dispersion-Shifted Fiber, OI: Optical Isolator, PC: Polarization Controller, OC: Optical Circulator.
Fig. 2. The spectrum processing of frequency measurement: (a) for one pump and (b) for two pumps.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31743
3. Numeric simulation and discussion Under small signal modulation, only the optical carrier and the two first-order sidebands are considered, and the output optical field after the PM is given by
π π E (t ) = J 0 (m) exp ( j 2π f c t ) + J1 (m) exp j 2π ( f c + f m )t + − J1 (m) exp j 2π ( f c − f m )t − 2 2 (1) where fc is optical carrier frequency and fm is microwave modulation frequency, Jn (•) represents the nth-order Bessel function of the first kind with n = 0, ± 1, and m is the phase modulation index. In this paper, the first-order upper sideband is selected to be processed by SBS. The Brillouin gain and loss can be expressed as [24]: g( f ) =
g 0 ( Δν B / 2 ) g Δν B f +j 0 2 2 2 2 f + ( Δν B / 2 ) 4 f + ( Δν B / 2 )2
(2)
g 0 ( Δν B / 2 ) g Δν B f −j 0 2 2 f 2 + ( Δν B / 2 )2 4 f + ( Δν B / 2 )2
(3)
a( f ) = −
2
2
where g0 = gBIpLeff⁄Aeff, νB denotes Brillouin frequency shift and ΔνB is the Brillouin linewidth, f is the frequency offset to the center of Brillouin linewidth of gain (for g(f)) or loss (for a(f)), gB is line center gain, IP is power of pump wave, Leff and Aeff are effective fiber length and effective mode area of DSF respectively. When considering SBS process, the optical field before PD can be given by: J m 0( ) g ( f − ν ) − ( f + f ) + a ( f + ν ) − ( f + f ) B c m B c m p p E ( t ) = exp ( j 2π f c t ) + J1 ( m ) exp π + j 2π f m t + 2 − J ( m ) exp − j 2π f t + π m 1 2 (4)
{
}
where fp is equal to fc + νB + fx according to Fig. 2, and fx is the unknown frequency. So Eq. (4) can be rewritten as: J 0 ( m ) + J1 ( m ) exp g ( f x − f m ) + a ( f x + 2ν B − f m ) + E ( t ) = exp ( j 2π f c t ) − J m exp − j 2π f t + π m 1( ) 2
π j 2π f m t + 2 (5) Omitting the dc and the small second harmonic components, the optical power input into the PD is expressed approximately as:
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31744
π π P ≈ 2 J 0 (m) J1 (m) G ( f m ) A( f m ) cos 2π f m t + + φg ( f m ) + φa ( f m ) − cos(2π f m t + ) 2 2 (6)
According to Eq. (2) and Eq. (3): 2 g ( Δν B / 2 ) G ( f m ) = exp Re g ( f x − f m ) = exp 0 2 2 2 ( f x − f m ) + ( Δν B / 2 )
{
}
(7)
2 g ( Δν B / 2 ) A ( f m ) = exp Re a ( f x + 2ν B − f m ) = exp − 0 2 2 2 ( f x + 2ν B − f m ) + ( Δν B / 2 ) (8)
{
}
ν B ( f x − fm ) g φg ( f m ) = Im g ( f x − f m ) = 0 4 ( f x − f m )2 + ( Δν B / 2 )2 φa ( f m ) = Im a ( f x + 2ν B − f m ) = −
(9)
Δν B ( f x + 2ν B − f m ) g0 4 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2
(10)
Therefore, the output electric field after detecting can be given as: Eout (t ) = ℜ < P >
π π (11) ∝ G ( f m ) A( f m ) cos 2π f m t + + φg ( f m ) + φa ( f m ) − cos(2π f m t + ) 2 2 ℜ means the responsivity of PD to the input optical power. In the numerical simulation, several parameters are assumed: g0 = 5, νB = 10GHz, ΔνB = 40MHz.The calculation results are shown in Fig. 3. Figure 3(a) demonstrates that only one single frequency signal is input to be measured at a time, and fx equals 1GHz﹑5GHz﹑10GHz﹑15GHz﹑25GHz﹑35GHz and 48GHz respectively. It can be seen that PM to AM conversion has occurred in both gain and loss region with permanent interval of 2νB. When multiple unknown frequencies are input simultaneously, fp is replaced by fpk, and fpk = fc + νB + fxk (where k = 1, 2, 3…N, and N is total number of unknown frequencies), the optical field is given by π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 E ( t ) = exp ( j 2π f c t ) N + J1 ( m ) exp g ( f xk − f m ) + a ( f xk + 2ν B − f m ) + k =1
π j 2π f m t + 2 (12)
Thus, from Eq. (11) the output electric field for multiple frequencies simultaneous measurement can be given as: Eout (t ) = ℜ < P > π N φgk ( f m ) π N ∝ ∏ Gk ( f m ) Ak ( f m ) cos 2π f m t + + − cos(2π f m t + ) 2 2 k =1 k =1 +φak ( f m )
(13)
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31745
The numerical result of multiple frequencies measurement for single pump at frequencies of fx1 = 1GHz, fx2 = 5GHz, fx3 = 10GHz and fx4 = 15GHz is shown in Fig. 3(b).
Fig. 3. Only one pump is adopted: (a) single frequency is input at a time; (b) multiple frequencies are input simultaneously
Noting that when multiple signals are input simultaneously, especially when existing two frequencies fx1 and fx2, where fx2 = fx1 + 2νB, fx2 cannot be observed because of overlapping of gain and loss region as is shown in Fig. 4(a), but it can be detected if only fx2 is measured shown in Fig. 4(b) as a comparison. Thus the measurement range of multiple frequencies is limited within 2νB.
Fig. 4. (a) fx1 = 5GHz and fx2 = 25GHz are measured simultaneously; (b) fx = 25GHz is measured only
Then two pumps with spectral space of 2νB are designed to broaden the available measurement range. The optical field before PD is written as: π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 E ( t ) = exp ( j 2π f c t ) + J m exp g ( f x − f m ) + a ( f x + 2ν B − f m ) + 1( ) + g ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m )
π j 2π f m t + 2
(14) so the output electronic field can be given as:
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31746
π π Eout (t )∝ GG ( f m ) AA( f m ) cos 2π f m t + + φgg ( f m ) + φaa ( f m ) − cos(2π f m t + ) 2 2 (15) where
{
}
GG ( f m ) = exp Re g ( f x − f m ) + g ( f x + 2ν B − f m )
2 g g0 ( Δν B / 2 ) ( Δν B / 2 ) 0 = exp + 2 2 2 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2 2 ( f x − f m ) + ( Δν B / 2 ) (16) 2
{
}
AA ( f m ) = exp Re a ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m )
2 g g0 ( Δν B / 2 ) ( Δν B / 2 ) = exp − 0 − 2 2 2 2 2 ( f x + 4ν B − f m ) + ( Δν B / 2 ) 2 ( f x + 2ν B − f m ) + ( Δν B / 2 ) (17) 2
φgg ( f m ) = Im g ( f x − f m ) + g ( f x + 2ν B − f m ) =
ν B ( f x − fm ) ν B ( f x + 2ν B − f m ) g0 g + 0 2 2 4 ( f x − f m ) + ( Δν B / 2 ) 4 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2
φaa ( f m ) = Im a ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m ) Δν B ( f x + 2ν B − f m ) g0 g0 =−
4
( f x + 2ν B − f m )
2
+ ( Δν B / 2 )
2
−
4
(18)
Δν B ( f x + 4ν B − f m )
( f x + 4ν B − f m )
2
+ ( Δν B / 2 )
(19) 2
When performing multi-frequency measurement, the optical field is: π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 N g ( f xk − f m ) + a ( f xk + 2ν B − f m ) E (t ) = exp ( j 2π f c t ) (20) + J m exp k =1 + g ( f xk + 2ν B − f m ) + a ( f xk + 4ν B − f m ) 1( ) π + j 2π f m t + 2
Hence the output electronic field of multiple frequencies measurement for two pumps can be expressed as: π N φggk ( f m ) π N Eout (t )∝ ∏ GGk ( f m ) AAk ( f m ) cos 2π f m t + + − cos(2π f m t + ) 2 k =1 +φaak ( f m ) 2 k =1 (21) The numeric results of single frequency measurement based on two pumps are shown in Fig. 5(a), where the interval between gain and loss has been doubled. The multi-frequency measurement at frequencies of fx1 = 5GHz, fx2 = 15GHz, fx3 = 25GHz and fx4 = 35GHz is shown in Fig. 5(b), and the available measurement range increases to 4νB.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31747
Fig. 5. Two pumps are adopted: (a) Single frequency is input at a time; (b) Multiple frequencies are input simultaneously
The accuracy for our proposed scheme depends on both the step of frequency-scanning of VNA and the principle used to realize frequency measurement. In principle, the frequency information of the microwave signal depends on the Brillouin frequency shift νB, which is related to pump wavelength, surrounding temperature and the applied strain on the fiber, and it can be given as:
νB =
2nVa
(22)
λp
where n is the refractive index, Va is the speed of acoustic wave and λp is the wavelength of pump light. So, 2nVa Δν B = Δ λ p
2Δ ( nVa ) 2nVa − 2 Δλ p = λp λp
(23)
The first term on the right-hand side of the equation is caused by changes in temperature ΔT and strain Δε, which can be written as [25] Δν B1 =
2Δ ( nVa )
λp
= CT ΔT + Cε Δε
(24)
here, CT is the temperature coefficient and Cε is the strain coefficient for the fiber, and CT is near 1MHz/°C and Cε is near 0.05MHz/με. In practical frequency measurement, the strain is constant but the surrounding temperature will fluctuate leading to the deviation of νB, so the temperature control is required. The last term on the right-hand side of Eq. (2) is rewritten as: Δν B 2 =
2nVa
λ p2
Δλ p
(25)
It is caused by wavelengths variation of pumps which is inevitable for our proposed frequency measurement system because the pumps are generated by injecting the unknown frequencies with SSB-SC, which means that the pump wavelengths will change with different incoming unknown frequencies; hence the measurement error is introduced. In our proposed scheme, λp is the carrier at 1.55μm and the corresponding νB is 10GHz, and the relationship between ΔνB2 and Δλp is shown in Fig. 6. For our proposed one pump and two pumps scheme, the measurement range is from 0 to 20GHz and 40GHz, so the corresponding Δλp varies from 80pm to 240pm and 400pm, which means the maximum error is 1.54MHz and 2.58MHz. Therefore, if the temperature fluctuation is controlled within 0.05°C and the strain is kept to be a constant, the surrounding fluctuation caused error can be neglected [26]. If the scanning
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31748
step of VNA is less than the maximum error caused by the variation of νB, the measurement accuracy for the proposed system is less than ± 3MHz, or the accuracy is determined by the scanning step of VNA.
Fig. 6. ΔνB2 versus Δλp
For simultaneous measurement of multiple frequency signals the distinguishable frequency interval is crucial. When two frequencies of 10 GHz and 10.036GHz are input at different moment, they can be identified easily as is shown in Fig. 7(a). But if they are input simultaneously, the result indicates that the frequency peak has deviated. The reason is that the space between the two measured frequencies is too close which leads to the overlap of these adjacent gain regions. Moreover, identification for those frequencies will be a difficulty when they get close too much. In order to distinguish the adjacent unknown frequencies, here it is assumed that the valley amplitude shown in Fig. 7(b) must be 3dB lower than both of the two peaks. By calculating, the valley amplitude reduces with the increase of frequency space because of the diminishment of overlapping as is shown in Fig. 8(a). The minimum frequency space of 35.8MHz corresponding to 3dB valley is achieved. Meanwhile, the relationship between frequency offset and the frequency space is given in Fig. 8(b), and the maximum offset is 2.3MHz at the space of 35.8MHz. However, when the two unknown frequencies are separated by more than 120MHz, the frequency offset can be neglected. So when multiple simultaneous signals are measured, additional measurement error caused by overlapping the adjacent frequencies must be considered if they get too close. The measurable frequency number is determined by the ratio of the maximum measurement range to the minimum distinguishable frequency interval. Although large measurement range and high accuracy for multiple frequency signals measurement can be implemented, high resolution frequency sweeping over the whole measurement range will be time-consumption. The tradeoff between measurement range and accuracy must be made to get the frequency measurement close to real time.
Fig. 7. (a) fx1 = 10GHz and fx2 = 10.036GHz are measured individually; (b) fx1 = 10GHz and fx2 = 10.036GHz are measured simultaneously
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31749
Fig. 8. (a) Normalized amplitude of valley versus frequency space; (b) Frequency offset versus frequency space
4. Conclusion
Single and multiple frequency signals measurement based on SBS in combination with PM to AM conversion has been proposed and analyzed. Compared with one pump scheme, measurement range for MFSM has been broadened from 2νB to 4νB when two pumps are applied. The measurement error less than 10 MHz has been obtained. The minimum frequency space of 35.8MHz with 2.3MHz frequency offset has been get for simultaneous signals measurement. Although frequency sweeping is adopted, it is still a promising solution for frequency measurement with large range, high accuracy and high real-time. 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).
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31750
State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China 2 Chongqing Optoelectronics Research Institute, Chongqing 400060, China *[email protected]
Abstract: We numerically investigate the operational principle and performance of stimulated Brillouin scattering based multiple microwave frequency signals measurement. The unknown signals are processed specially to generate a gain region which is measured by phase modulation to amplitude modulation converting. By sweeping the vector network analyzer, both single and multiple frequencies measurement can be achieved. The loss spectrum generated by one of the pumps is fully compensated by the gain spectrum of the other pump, which increases the measurement range from 2νB to 4νB. ©2013 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (290.5900) Scattering, stimulated Brillouin; (350.4010) Microwaves.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31740
16. L. V. T. Nguyen, “Microwave photonic technique for frequency measurement of simultaneous signals,” IEEE Photon. Technol. Lett. 21(10), 642–644 (2009). 17. B. Vidal, T. Mengual, and J. Marti, “Photonic technique for the measurement of frequency and power of multiple microwave signals,” IEEE Trans. Microw. Theory Tech. 58(11), 3103–3108 (2010). 18. B. Vidal, “Photonic approach for instantaneous frequency and power measurement of simultaneous microwave signals,” in Proceedings of International Topical Meeting on Microwave Photonics, (IEEE, 2011), 192–194. 19. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic approach for multiple-frequency-component measurement using spectrally sliced incoherent source,” Opt. Lett. 35(3), 438–440 (2010). 20. L. A. Bui and A. Mitchell, “Parallel all-optical instantaneous frequency measurement system using channel labeling,” IEEE Photon. Technol. Lett. 24(13), 1118–1120 (2012). 21. S. Zheng, S. Ge, X. Zhang, H. Chi, and X. Jin, “High-resolution multiple microwave frequency measurement based on stimulated Brillouin scattering,” IEEE Photon. Technol. Lett. 24(13), 1115–1117 (2012). 22. B. Vidal, T. Mengual, and J. Marti, “Photonic microwave filter with single bandpass response based on Brillouin processing and SSB-SC,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2009), 1–4. 23. K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32(3), 217–219 (2007). 24. W. Zhang and R. A. Minasian, “Switchable and tunable microwave photonic Brillouin-based filter,” IEEE Photon. J. 4(5), 1443–1455 (2012). 25. X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12), 4152– 4187 (2011). 26. W. Li, N. H. Zhu, and L. X. Wang, “Brillouin-assisted microwave frequency measurement with adjustable measurement range and resolution,” Opt. Lett. 37(2), 166–168 (2012).
1. Introduction Frequency measurement ranging from subgigahertz to millimeter (mm)-wave frequency is of great importance for the application in modern radar system and electronic warfare, which has been widely investigated in electric domain [1]. Over the past few decades, photonic assisted microwave measurement techniques have been developed due to its inherent advantages compared with electronic techniques, such as large bandwidth, light weight, small size, low loss, and immunity to electromagnetic interference [2]. Recently, a number of photonic approaches have been demonstrated to implement microwave frequency measurement. Instantaneous frequency measurement (IFM) based on microwave power or optical power comparison of two channels is realized by constructing amplitude comparison function (ACF). Several methods have been proposed to construct ACF using, such as, dispersion induced microwave or optical power penalties [3–8], polarization domain interferometer [9], and optical filter or filter subsystem [10–12]. Also an on-chip photonic IFM system has been demonstrated which is a promising solution to resist environmental disturbance [13].To avoid frequency ambiguities, a monotone interval is chosen to get a unique mapping between power ratio value and microwave frequency. A steep ACF over the entire range of measurement is required since flat ACF will increase the measurement error. Although IFM with large measurement range and high resolution can be realized, only single frequency signal measurement is accurate. Multiple frequency signals measurement which is highly desired in realistic spectrally-cluttered environment has also been demonstrated. An electrically tuned fiber Bragg grating is used to realize frequency scanning measurement ranging from 2 to 9 GHz in [14]. In [15], a photonic based channelized receiver is presented using phase-shifted chirped fiber Bragg grating and photodetector array. A system based on frequency-time mapping for two 20 GHz spaced RF signals measurement utilizing a dispersive medium is reported in [16]. A two-tone RF signals measurement is presented in [17] by processing interferogram which is measured by sweeping tunable laser, and 15MHz resolution is experimentally demonstrated. Another similar version which can realize real-time measurement with limited resolution is proposed in [18]. A method using a spectrally sliced incoherent source is proposed in [19], in which two etalons with different free space range are employed and 5 GHz channel spacing and ± 2.5 GHz accuracy are achieved. In [20], a seven bands simultaneous and parallel instantaneous frequency measurements with ± 500 MHz error over the entire 1–40 GHz band is demonstrated.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31741
In [21], a technique combining stimulated Brillouin scattering (SBS) and phase modulation to amplitude modulation (PM to AM) conversion is proposed, and less than 30MHz measurement error has been demonstrated. But the vector network analyzer (VNA) in [21] is only used to provide probe signals; additional synchronization digital oscilloscope is needed to complete the measurement. In this paper, a novel configuration is proposed, where the VNA not only provides probe signals but also performs frequency measurement so that the oscilloscope is removed. We have theoretically analyzed the operational principle and measurement performance. By extending the scheme from one pump to two pumps, the measurement range is broadened from 2νB to 4νB for multiple frequencies measurement. 2. Operational principle The schematics of the proposed microwave frequency measurement are shown in Fig. 1. The phase modulator is driven by a sinusoidal microwave signal with scanning frequency fm generated by a VNA. If the phase-modulated signal is applied directly to photodetector (PD), no signal would be detected, except a 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 beat signals are out of phase with a balanced intensity. In the proposed scheme, the unknown signal is up-converted by dual parallel MachZehnder modulator (DPMZM) to generate the SBS pump and the VNA launched sweeping frequencies act as probe signals. When sidebands generated by phase modulation locate in the pump induced gain region, amplification caused by SBS process will be achieved to break the balance of sideband intensity. Hence the PM to AM conversion will be realized which will be displayed in VNA after detecting, and then the unknown frequency will be obtained since the pump is specially processed so that the frequency interval between gain region and carrier is equal to unknown frequency. The SBS process is usually described as nonlinear interaction between two counter-propagating waves via an acoustic wave. If a particular phase matching condition is satisfied (namely fprobe = fpump-νB), fraction of pump wave is scattered off into the probe wave, so that the global effect of the SBS process demonstrates a generation of narrowband gain resonance around the frequency of fpump-νB, resulting in an exponential growth for the probe wave. On the contrary, the energy transfer can be regarded as the generation of a loss resonance around the frequency of fpump + νB as far as the pump wave is concerned. Thus, the SBS interaction leads to a downshifted gain region where a counter-propagating signal is amplified and an upshifted loss region where the counter-propagating signal is attenuated. First, only one pump is employed as is shown in Fig. 1(a). The light source provided by laser diode (LD) with the frequency fc is divided into two paths. The upper path is phasemodulated by VNA launched microwave signals. The lower path is modulated by DPMZM1 and DPMZM2 which are driven by Brillouin frequency shift νB and unknown signal fx respectively, to generate carrier-suppressed upper sideband [22]. Therefore the final output performs as pump wave with the frequency separated by fx + νB away from carrier. The phasemodulated signals whose states of polarization are aligned by polarization controller (PC) are sent into a dispersion shift fiber (DSF) to interact with the counter-propagating pump wave. Thus the PM to AM conversion at fx will be realized which will be observed by VNA after PD detecting. The spectrum processing of one-pump based frequency measurement is shown in Fig. 2(a). Both biases of DPMZM1 and DPMZM2 are controlled to obtain only the first-order upper sidebands. So the gain region is centered at fx to realize PM to AM conversion. Noting that another frequency centered at fx + 2νB also will cause PM to AM conversion because of SBS caused attenuation. When multiple frequency signals are measured simultaneously, especially when existing two frequencies separated by 2νB, the high frequency signal cannot be measured correctly because the gain region corresponding to high frequency signal pump will be superimposed by low frequency signal pump induced loss region. So the measurement range is limited within 2νB for simultaneous measurement of multiple frequency signals if only one pump is applied.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31742
Second, an extended scheme based on two pumps shown in Fig. 1(b) is designed to reach wider range. When the two pumps are spectrally separated by 2νB with the same power, the loss spectrum of pump 1 can be fully compensated by the gain spectrum of pump 2 [23]. The global effect of gain-loss compensation manifests that the spectral space between gain and loss region is broadened from 2νB to 4νB, which will lead to a doubled measurement range for multiple frequency signals. The spectral process is shown in Fig. 2(b). Firstly, DPMZM1 is specially driven by 2νB to generate SSB-SC modulation. And secondly, the unknown signal fx is injected according to DPMZM2 with the same modulation pattern. At last, the amplitude modulator is biased at the minimum transmission point to generate a double-sideband suppressed carrier (DSB-SC) modulation. For the amplitude modulator, the driven frequency is specially set to be νB to generated two sidebands separated by 2νB where the lower sideband is used to perform frequency measurement and the higher sideband is used to implement gain and loss compensation. Since the space between gain and loss can be expanded to 3νB and 4νB by introducing pump 3 and pump 4 in a similar way, it is easily inferred that there is no theoretical limitation on the range of the SBS based frequency measurement.
Fig. 1. Schematics of photonic assisted single and multiple microwave frequencies measurement. (a) One pump is applied; (b) Gain and loss compensation based two pumps are applied. LD: Laser Diode, DSF: Dispersion-Shifted Fiber, OI: Optical Isolator, PC: Polarization Controller, OC: Optical Circulator.
Fig. 2. The spectrum processing of frequency measurement: (a) for one pump and (b) for two pumps.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31743
3. Numeric simulation and discussion Under small signal modulation, only the optical carrier and the two first-order sidebands are considered, and the output optical field after the PM is given by
π π E (t ) = J 0 (m) exp ( j 2π f c t ) + J1 (m) exp j 2π ( f c + f m )t + − J1 (m) exp j 2π ( f c − f m )t − 2 2 (1) where fc is optical carrier frequency and fm is microwave modulation frequency, Jn (•) represents the nth-order Bessel function of the first kind with n = 0, ± 1, and m is the phase modulation index. In this paper, the first-order upper sideband is selected to be processed by SBS. The Brillouin gain and loss can be expressed as [24]: g( f ) =
g 0 ( Δν B / 2 ) g Δν B f +j 0 2 2 2 2 f + ( Δν B / 2 ) 4 f + ( Δν B / 2 )2
(2)
g 0 ( Δν B / 2 ) g Δν B f −j 0 2 2 f 2 + ( Δν B / 2 )2 4 f + ( Δν B / 2 )2
(3)
a( f ) = −
2
2
where g0 = gBIpLeff⁄Aeff, νB denotes Brillouin frequency shift and ΔνB is the Brillouin linewidth, f is the frequency offset to the center of Brillouin linewidth of gain (for g(f)) or loss (for a(f)), gB is line center gain, IP is power of pump wave, Leff and Aeff are effective fiber length and effective mode area of DSF respectively. When considering SBS process, the optical field before PD can be given by: J m 0( ) g ( f − ν ) − ( f + f ) + a ( f + ν ) − ( f + f ) B c m B c m p p E ( t ) = exp ( j 2π f c t ) + J1 ( m ) exp π + j 2π f m t + 2 − J ( m ) exp − j 2π f t + π m 1 2 (4)
{
}
where fp is equal to fc + νB + fx according to Fig. 2, and fx is the unknown frequency. So Eq. (4) can be rewritten as: J 0 ( m ) + J1 ( m ) exp g ( f x − f m ) + a ( f x + 2ν B − f m ) + E ( t ) = exp ( j 2π f c t ) − J m exp − j 2π f t + π m 1( ) 2
π j 2π f m t + 2 (5) Omitting the dc and the small second harmonic components, the optical power input into the PD is expressed approximately as:
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31744
π π P ≈ 2 J 0 (m) J1 (m) G ( f m ) A( f m ) cos 2π f m t + + φg ( f m ) + φa ( f m ) − cos(2π f m t + ) 2 2 (6)
According to Eq. (2) and Eq. (3): 2 g ( Δν B / 2 ) G ( f m ) = exp Re g ( f x − f m ) = exp 0 2 2 2 ( f x − f m ) + ( Δν B / 2 )
{
}
(7)
2 g ( Δν B / 2 ) A ( f m ) = exp Re a ( f x + 2ν B − f m ) = exp − 0 2 2 2 ( f x + 2ν B − f m ) + ( Δν B / 2 ) (8)
{
}
ν B ( f x − fm ) g φg ( f m ) = Im g ( f x − f m ) = 0 4 ( f x − f m )2 + ( Δν B / 2 )2 φa ( f m ) = Im a ( f x + 2ν B − f m ) = −
(9)
Δν B ( f x + 2ν B − f m ) g0 4 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2
(10)
Therefore, the output electric field after detecting can be given as: Eout (t ) = ℜ < P >
π π (11) ∝ G ( f m ) A( f m ) cos 2π f m t + + φg ( f m ) + φa ( f m ) − cos(2π f m t + ) 2 2 ℜ means the responsivity of PD to the input optical power. In the numerical simulation, several parameters are assumed: g0 = 5, νB = 10GHz, ΔνB = 40MHz.The calculation results are shown in Fig. 3. Figure 3(a) demonstrates that only one single frequency signal is input to be measured at a time, and fx equals 1GHz﹑5GHz﹑10GHz﹑15GHz﹑25GHz﹑35GHz and 48GHz respectively. It can be seen that PM to AM conversion has occurred in both gain and loss region with permanent interval of 2νB. When multiple unknown frequencies are input simultaneously, fp is replaced by fpk, and fpk = fc + νB + fxk (where k = 1, 2, 3…N, and N is total number of unknown frequencies), the optical field is given by π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 E ( t ) = exp ( j 2π f c t ) N + J1 ( m ) exp g ( f xk − f m ) + a ( f xk + 2ν B − f m ) + k =1
π j 2π f m t + 2 (12)
Thus, from Eq. (11) the output electric field for multiple frequencies simultaneous measurement can be given as: Eout (t ) = ℜ < P > π N φgk ( f m ) π N ∝ ∏ Gk ( f m ) Ak ( f m ) cos 2π f m t + + − cos(2π f m t + ) 2 2 k =1 k =1 +φak ( f m )
(13)
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31745
The numerical result of multiple frequencies measurement for single pump at frequencies of fx1 = 1GHz, fx2 = 5GHz, fx3 = 10GHz and fx4 = 15GHz is shown in Fig. 3(b).
Fig. 3. Only one pump is adopted: (a) single frequency is input at a time; (b) multiple frequencies are input simultaneously
Noting that when multiple signals are input simultaneously, especially when existing two frequencies fx1 and fx2, where fx2 = fx1 + 2νB, fx2 cannot be observed because of overlapping of gain and loss region as is shown in Fig. 4(a), but it can be detected if only fx2 is measured shown in Fig. 4(b) as a comparison. Thus the measurement range of multiple frequencies is limited within 2νB.
Fig. 4. (a) fx1 = 5GHz and fx2 = 25GHz are measured simultaneously; (b) fx = 25GHz is measured only
Then two pumps with spectral space of 2νB are designed to broaden the available measurement range. The optical field before PD is written as: π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 E ( t ) = exp ( j 2π f c t ) + J m exp g ( f x − f m ) + a ( f x + 2ν B − f m ) + 1( ) + g ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m )
π j 2π f m t + 2
(14) so the output electronic field can be given as:
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31746
π π Eout (t )∝ GG ( f m ) AA( f m ) cos 2π f m t + + φgg ( f m ) + φaa ( f m ) − cos(2π f m t + ) 2 2 (15) where
{
}
GG ( f m ) = exp Re g ( f x − f m ) + g ( f x + 2ν B − f m )
2 g g0 ( Δν B / 2 ) ( Δν B / 2 ) 0 = exp + 2 2 2 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2 2 ( f x − f m ) + ( Δν B / 2 ) (16) 2
{
}
AA ( f m ) = exp Re a ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m )
2 g g0 ( Δν B / 2 ) ( Δν B / 2 ) = exp − 0 − 2 2 2 2 2 ( f x + 4ν B − f m ) + ( Δν B / 2 ) 2 ( f x + 2ν B − f m ) + ( Δν B / 2 ) (17) 2
φgg ( f m ) = Im g ( f x − f m ) + g ( f x + 2ν B − f m ) =
ν B ( f x − fm ) ν B ( f x + 2ν B − f m ) g0 g + 0 2 2 4 ( f x − f m ) + ( Δν B / 2 ) 4 ( f x + 2ν B − f m )2 + ( Δν B / 2 )2
φaa ( f m ) = Im a ( f x + 2ν B − f m ) + a ( f x + 4ν B − f m ) Δν B ( f x + 2ν B − f m ) g0 g0 =−
4
( f x + 2ν B − f m )
2
+ ( Δν B / 2 )
2
−
4
(18)
Δν B ( f x + 4ν B − f m )
( f x + 4ν B − f m )
2
+ ( Δν B / 2 )
(19) 2
When performing multi-frequency measurement, the optical field is: π J 0 ( m ) − J1 ( m ) exp − j 2π f m t + 2 N g ( f xk − f m ) + a ( f xk + 2ν B − f m ) E (t ) = exp ( j 2π f c t ) (20) + J m exp k =1 + g ( f xk + 2ν B − f m ) + a ( f xk + 4ν B − f m ) 1( ) π + j 2π f m t + 2
Hence the output electronic field of multiple frequencies measurement for two pumps can be expressed as: π N φggk ( f m ) π N Eout (t )∝ ∏ GGk ( f m ) AAk ( f m ) cos 2π f m t + + − cos(2π f m t + ) 2 k =1 +φaak ( f m ) 2 k =1 (21) The numeric results of single frequency measurement based on two pumps are shown in Fig. 5(a), where the interval between gain and loss has been doubled. The multi-frequency measurement at frequencies of fx1 = 5GHz, fx2 = 15GHz, fx3 = 25GHz and fx4 = 35GHz is shown in Fig. 5(b), and the available measurement range increases to 4νB.
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31747
Fig. 5. Two pumps are adopted: (a) Single frequency is input at a time; (b) Multiple frequencies are input simultaneously
The accuracy for our proposed scheme depends on both the step of frequency-scanning of VNA and the principle used to realize frequency measurement. In principle, the frequency information of the microwave signal depends on the Brillouin frequency shift νB, which is related to pump wavelength, surrounding temperature and the applied strain on the fiber, and it can be given as:
νB =
2nVa
(22)
λp
where n is the refractive index, Va is the speed of acoustic wave and λp is the wavelength of pump light. So, 2nVa Δν B = Δ λ p
2Δ ( nVa ) 2nVa − 2 Δλ p = λp λp
(23)
The first term on the right-hand side of the equation is caused by changes in temperature ΔT and strain Δε, which can be written as [25] Δν B1 =
2Δ ( nVa )
λp
= CT ΔT + Cε Δε
(24)
here, CT is the temperature coefficient and Cε is the strain coefficient for the fiber, and CT is near 1MHz/°C and Cε is near 0.05MHz/με. In practical frequency measurement, the strain is constant but the surrounding temperature will fluctuate leading to the deviation of νB, so the temperature control is required. The last term on the right-hand side of Eq. (2) is rewritten as: Δν B 2 =
2nVa
λ p2
Δλ p
(25)
It is caused by wavelengths variation of pumps which is inevitable for our proposed frequency measurement system because the pumps are generated by injecting the unknown frequencies with SSB-SC, which means that the pump wavelengths will change with different incoming unknown frequencies; hence the measurement error is introduced. In our proposed scheme, λp is the carrier at 1.55μm and the corresponding νB is 10GHz, and the relationship between ΔνB2 and Δλp is shown in Fig. 6. For our proposed one pump and two pumps scheme, the measurement range is from 0 to 20GHz and 40GHz, so the corresponding Δλp varies from 80pm to 240pm and 400pm, which means the maximum error is 1.54MHz and 2.58MHz. Therefore, if the temperature fluctuation is controlled within 0.05°C and the strain is kept to be a constant, the surrounding fluctuation caused error can be neglected [26]. If the scanning
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31748
step of VNA is less than the maximum error caused by the variation of νB, the measurement accuracy for the proposed system is less than ± 3MHz, or the accuracy is determined by the scanning step of VNA.
Fig. 6. ΔνB2 versus Δλp
For simultaneous measurement of multiple frequency signals the distinguishable frequency interval is crucial. When two frequencies of 10 GHz and 10.036GHz are input at different moment, they can be identified easily as is shown in Fig. 7(a). But if they are input simultaneously, the result indicates that the frequency peak has deviated. The reason is that the space between the two measured frequencies is too close which leads to the overlap of these adjacent gain regions. Moreover, identification for those frequencies will be a difficulty when they get close too much. In order to distinguish the adjacent unknown frequencies, here it is assumed that the valley amplitude shown in Fig. 7(b) must be 3dB lower than both of the two peaks. By calculating, the valley amplitude reduces with the increase of frequency space because of the diminishment of overlapping as is shown in Fig. 8(a). The minimum frequency space of 35.8MHz corresponding to 3dB valley is achieved. Meanwhile, the relationship between frequency offset and the frequency space is given in Fig. 8(b), and the maximum offset is 2.3MHz at the space of 35.8MHz. However, when the two unknown frequencies are separated by more than 120MHz, the frequency offset can be neglected. So when multiple simultaneous signals are measured, additional measurement error caused by overlapping the adjacent frequencies must be considered if they get too close. The measurable frequency number is determined by the ratio of the maximum measurement range to the minimum distinguishable frequency interval. Although large measurement range and high accuracy for multiple frequency signals measurement can be implemented, high resolution frequency sweeping over the whole measurement range will be time-consumption. The tradeoff between measurement range and accuracy must be made to get the frequency measurement close to real time.
Fig. 7. (a) fx1 = 10GHz and fx2 = 10.036GHz are measured individually; (b) fx1 = 10GHz and fx2 = 10.036GHz are measured simultaneously
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31749
Fig. 8. (a) Normalized amplitude of valley versus frequency space; (b) Frequency offset versus frequency space
4. Conclusion
Single and multiple frequency signals measurement based on SBS in combination with PM to AM conversion has been proposed and analyzed. Compared with one pump scheme, measurement range for MFSM has been broadened from 2νB to 4νB when two pumps are applied. The measurement error less than 10 MHz has been obtained. The minimum frequency space of 35.8MHz with 2.3MHz frequency offset has been get for simultaneous signals measurement. Although frequency sweeping is adopted, it is still a promising solution for frequency measurement with large range, high accuracy and high real-time. 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).
#193017 - $15.00 USD Received 27 Jun 2013; revised 26 Nov 2013; accepted 30 Nov 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031740 | OPTICS EXPRESS 31750
