Performance analysis on an instantaneous microwave frequencymeasurement with tunable range and resolution based on a singlelaser source

Jing Li a,b, TiGang Ning a,b, Li Pei a,b,n, Wei Jian a,b, Jingjing Zheng a,b, Haidong You a,b,c,Hongyao Chen a,b, Chan Zhang a,b

a Key Laboratory of All Optical Network & Advanced Telecommunication Network of EMC, Beijing Jiaotong University, Beijing 100044, Chinab Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, Chinac Science and Information College, Qingdao Agricultural University, Qingdao 266109, Shandong, China

a r t i c l e i n f o

Article history:Received 4 February 2014Received in revised form19 March 2014Accepted 1 April 2014

Keywords:Instantaneous microwave measurementMeasurement rangeResolution

a b s t r a c t

A prototype of instantaneous microwave frequency measurement with tunable range and resolutionbased on a single laser source is proposed and analyzed. In the proposal, one polarization modulator(PolM) followed by a section of dispersion compensating fiber (DCF), a polarization beam splitter (PBS)and two photodiodes (PDs) are used as the key component. To obtain an amplitude comparison function(ACF), the lightwave from a laser source should be first oriented at an angle of α (αa01 or 901) relativeto one principal axis of PolM. After transmission of DCF, the PBS is connected with principal axis 7451 tothat of PolM. Then, by monitoring and processing the microwave power of two optical paths via two PDs,frequency of microwave signal can be easily estimated. It is found that the measurement range can bestretched by simply adjusting α. Its performance is first analyzed by theory and then verified bysimulations. Since the proposal is characteristic with its tunable measurement range and resolution, afrequency measurement range as large as 13.2 GHz with a measurement resolution of 70.15 GHz isobtained.

& 2014 Published by Elsevier Ltd.

1. Introduction

Photonic instantaneous microwave frequency measurement(IFM) has been a topic of interest over the past few years. Onetypical photonic IFM owns many advantages, such as high band-width, low loss, and immunity to electro-magnetic interference(EMI) [1,2], over a conventional electronic system. Due to itsinherent advantages, IFM can find many applications, one of whichis in the field of electronic warfare (EW). Normally, the unknownmicrowave signal is required to be frequency identified before sentto the second level receiver for further processing. Thus it is of greatimportance to identify the frequency of a specially interceptedmicrowave signal from radar or communication. Recently, varioustechniques have been proposed to implement photonic IFM. Forexample, the IFM can be realized by using a coherent optical RFchannelizer [3,4], complementary optical filter [5–7], and disper-sion-induced power-fading functions [8–17]. For all photonic IFM,the following two characteristics should be met: 1) a wide

measurement range to satisfy application with frequency fromfew hundreds of megaHertz to hundreds of giga-Hertz; 2) a highmeasurement resolution in order to avoid error frequency identi-fication. It is found that the approaches in [8–17, which is based onthe monitoring of the microwave power of an optical microwavesignal that experiences different power penalties, is a promisingsolution for IFM with a large frequency measurement range and arelatively high resolution. However, for most cases [8–12], themeasurement range and resolution are fixed for a given system,which is not desirable for EW applications requiring a specificmeasurement range and a high resolution. Typically, the measure-ment range and resolution are two complementary features whichcannot be satisfied simultaneously, which means that a highermeasurement resolution results in a smaller measurement range. Tosolve this problem, the major task is to stretch the measurementrange without degrading the resolution. Therefore, many researchesfocus on an IFM system with tunable measurement range andresolution [13–17]. For example, it can be realized by applyingadjustable dispersion via tuning two optical wavelength with alarge wavelength spacing [13]. But the tuning range is limited tofew giga-Hertz due to the relatively small dispersion changesresulting from the wavelength tuning. Then in [14], one single lasersource incorporating a dual-output Mach–Zehnder modulator is

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Optics & Laser Technology

http://dx.doi.org/10.1016/j.optlastec.2014.04.0030030-3992/& 2014 Published by Elsevier Ltd.

n Corresponding author at: Key Laboratory of All Optical Network & AdvancedTelecommunication Network of EMC, Beijing Jiaotong University, Beijing 100044,China.

E-mail address: lipei@bjtu.edu.cn (L. Pei).

Optics & Laser Technology 63 (2014) 54–61

employed. By tuning the laser's wavelength, the measurementrange can be extended. But the scheme still requires a hugewavelength tuning so as to reach a relatively higher dispersionchanges. In [15], a reconfigurable IFM system based on a dual-parallel Mach Zehnder modulator and a Mach–Zehnder modulatoris proposed. According to the research, the measurement range canbe tuned by adjusting laser wavelength or bias voltage. But theapproach will suffer from the bias drift problem. In [16], the samegroup proposed an IFM system based on stimulated Brillouinscattering. By varying the reference driving frequency, the measure-ment range as well as the resolution can be tuned. But the schemestill suffers from bias drift problem and a relatively complexarchitecture. In [17], an IFM system based on a polarizationmodulator is proposed. By simply adjusting the polarization angle,the measurement range as well as the resolution can be tuned. Butthe scheme requires two laser sources with equal power and a largewavelength spacing so as to provide enough dispersion and anoptical filter to separate lightwaves, which might be costful andcomplex in architecture.

In this work, we report a simplified IFM system with tunablemeasurement range and resolution. The key component is apolarization modulator (PolM) followed by 2 km dispersion com-pensating fiber (DCF), a polarization beam splitter (PBS) and twophotodiodes (PDs). By monitoring the microwave power, a mono-tonically decreasing amplitude comparison function (ACF) can beobtained. Since the ACF is dependent on the polarization angle ofincident light α, the measurement range of the proposed IFMsystem can be stretched by simply adjusting α. It is found that biasdrift (within �20�20%) has little impact on the range andresolution. The key significances associated with our proposalare the single-wavelength operation and filter-less architecture,which will simplify the IFM system a lot when compared withprevious reported approaches [13–17].

2. Model and theory

Fig. 1 shows the schematic setup of the proposed IFM withtunable range. The lightwave from the continuous-wave (CW)laser is first coupled to the polarization modulator (PolM). The keycomponent, PolM, can be considered as a special phase modulatorthat supports transverse electric (TE) and transverse magnetic(TM) modes with complementary phase modulation indices. Thepolarization controller (PC1) is used to align the incident light tomake sure that its polarization direction is 451 relative to oneprincipal axis of the PolM (y). Supposing that the unknownmicrowave signal is VRF(t)¼VRFsinΩt, where VRF and Ω¼2πƒRFdenote the magnitude and angular frequency, respectively. Then

the output optical field after PolM can be expressed as follows:

ExEy

" #pE0ejω0t

sin αexpðjmU sin Ωtþ jφÞcos αexpð� jmU sin ΩtÞ

" #ð1Þ

where E0 is magnitude of optical carrier,ω0 is angular frequency ofoptical carrier, φ¼πVbias/Vπ is the bias-induced phase shift, andm¼ πVRF=

ffiffiffi2

pVπ is modulation index, where Vπ denotes half-wave

voltage of the PolM. Under small signal modulation, Eq. (1) can besimply concluded as

ExEy

" #¼ E0ejω0t

∑1

n ¼ �1sin αJnðmÞexpðjnΩtþ jφÞ

∑1

n ¼ �1cos αJnð�mÞexpðjnΩtÞ

266664

377775 ð2Þ

where Jn is the Bessel function of the first kind of order n. Thesignal in Eq. (2) is then launched into a spool of 2 km DCF(D¼�160 ps/km nm). Since the DCF we use is only 2 km in length,the walk off effect between two orthogonal polarized light paths isnegligible. The transmission function of the DCF is similar to thatof the single mode fiber [18,19]. It can be expressed as (neglectingthe constant phase and higher order terms)

HðωÞ ¼ exp � jλ20DL4πc

ðω�ω0Þ2" #

ð3Þ

where λ0 is the optical wavelength, c is the speed of light invacuum, L is fiber length and D is chromatic dispersion parameter.The optical field after the DCF becomes

ExEy

" #¼ E0ejω0t

∑1

n ¼ �1sin αJnðmÞexpðjnΩtþ jφnþ jφÞ

∑1

n ¼ �1cos αð�1ÞnJnðmÞexpðjnΩtþ jφnÞ

266664

377775 ð4Þ

where φn ¼ �n2λ20DLΩ2=4πc is dispersion-induced phase shift.

A polarization beam splitter (PBS) is then connected with theDCF via PC2 with principal axis 7451 to that of the PolM, asshown in Fig. 1. The two ports (Port 1 and Port 2) correspond totwo complementary output transfer functions [20]. Tuning thebias voltage of the PolM to let φ¼901, Eqs. (5) and (6) show thedetail expression of optical signals at Port 1 and Port 2:

EPort1ðtÞ ¼ffiffiffi2

p

2E0ejω0t ∑

1

n ¼ �1j sin αh

þð�1Þn cos α�JnðmÞexpðjnΩtþ jφnÞ ð5Þ

Fig. 1. Schematic setup of the proposed IFM with tunable range (CW—continuous wave; PC—polarization controller; RF—radio frequency; PolM—polarization modulator;fiber; PBS—polarization beam splitter; DCF—dispersion compensating fiber; PD—photodiode).

J. Li et al. / Optics & Laser Technology 63 (2014) 54–61 55

EPort2ðtÞ ¼ffiffiffi2

p

2E0ejω0t ∑

1

n ¼ �1

j sin α�ð�1Þn cos α

" #JnðmÞexpðjnΩtþ jφnÞ

ð6ÞIf the optical signals in Eqs. (5) and (6) are sent to two PDs (PD1

and PD2 as shown in Fig. 1) for square-law detection, the ac termsof the photocurrents are

iPD1ðtÞp R1 E0j j2J1ðmÞJ0ðmÞ sin �λ20DLΩ2

4πc�2α

!" #sin Ωt ð7Þ

iPD2ðtÞp R2 E0j j2J1ðmÞJ0ðmÞ sin �λ20DLΩ2

4πcþ2α

!" #sin Ωt ð8Þ

Assuming these two PDs in use are with the same sensitivityR1¼R2. Comparing the microwave power from two PDs at thepost-processing stage (as shown in Fig. 1), we can obtain theamplitude comparison function (ACF) as

ACF¼ PPD1

PPD2¼

sin 2 �λ20DLΩ2

4πc �2α� �

sin 2 �λ20DLΩ2

4πc þ2α� � ð9Þ

As expressed in the equation, the ACF is independent of the laserpower and modulation index (small signal modulation index). Onlytwo variables, say dispersion DL and polarization angle α, areincluded in Eq. (9). To evaluate the spectrum property of the ACF,parameters are set as shown in Table 1.

Fig. 2(a) plots the power fading of PPD1 and PPD2 in Case A. In thefigure, the notch point of PPD1 is around 6.6 GHz. After the ACFconverting, the measurement range can be considered as the bandfrom DC to 6.6 GHz, which is 0–6.6 GHz. Then by adjusting α viathe PC1 placed between the CW and PolM, the notch point will beshifted; thus the measurement range is stretched as well. Fig. 2(b) investigates the ACF under four different Cases (A–D inTable 1). For example, when α is adjusted from 101 to 201, 301,and 401, the measurement range can be stretched to around 0–9.3 GHz, 0–11.4 GHz and 0–13.2 GHz, respectively. The bandwidthhas been extended from around 6.6 GHz to as large as 13.2 GHz.

Also note that the measurement range can be further extendedby decreasing the dispersion DL in Eq. (9). In our case, we just needto vary the length of DCF. To prove that theory, Fig. 3 plots the ACFat Case D (α¼401) and different dispersions DL: (a) �320 ps/nm;(b) �240 ps/nm; and (c) �160 ps/nm.

Note that the notch point of an ACF curve shifts to a highfrequency band. From Eq. (9), the maximum frequency ƒMAX of IFMcan be calculated as

f MAX ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4α=ð�2πλ20DL=cÞ

q; 0 3 oαo45 3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2π�4αð Þ=ð�2πλ20DL=cÞq

; 45 3 oαo90 3

8><>: ð10Þ

It has to be mentioned that when α is adjusted from 0–451 to45–901, the ACF curve will be reversed. In that case, ƒMAX willcorrespond to the peak point. In our work, α can be controlled byPC1 within the range of 0–451. Thus by solving Eq. (10), a specialmeasurement range can be set with the optimum values of DL andα. To simplify the discussion, we will focus on the feature of

Table 1Parameter setting.

Symbol Case A Case B Case C Case D

DL (ps/nm) �320 �320 �320 �320α (deg) 10 20 30 40

Cases A–D represent the parameter setting corresponding to Fig. 2; DL is thedispersion parameter at 1550 nm.

Fig. 2. Calculated results of (a) power fading functions and ACF at Case A and(b) ACF for Cases A–D corresponding to Table 1.

Fig. 3. Calculated ACF at Case D (α¼401) and different dispersions DL¼�320,�240, and �160 ps/nm.

J. Li et al. / Optics & Laser Technology 63 (2014) 54–6156

tunable range and resolution by adjusting α. The dispersion DL isset as a constant value.

3. Simulation and discussion

To investigate its mechanism, simulations are preformed via anOptiSystem 10.0. The setup can be found in Fig. 1. The CW laser works

at a carrier wavelength of 1550 nm, linewidth of 0.8 MHz and powerof �10 dBm. Then PC1 is employed to align the inject polarizationdirection at the PolM, which is designed via a Matlab program and aprogrammable module based on its characteristic. The injectedpolarization angle is adjusted to α relative to one principal axis ofthe PolM. The PolM is biased at quadrature point (φ¼901). Then 2 kmDCF is used as the dispersive element (D¼�160 ps/km nm). Afterthat, the PC2 followed by a PBS is connected. As stated in Section II, the

Fig. 4. Setup to find the optimum polarization alignment of PC2.

Fig. 5. Simulated optical power versus α (0–901) at different β¼151, 301, 451, 601,and 751.

Fig. 6. Calculated (line) and simulated (mark) power fading and ACF at α¼401.

Fig. 7. (a) Estimated frequency at α¼101 when input frequency tuned from 6.7 to18.7 GHz. (c) Estimation errors.

J. Li et al. / Optics & Laser Technology 63 (2014) 54–61 57

principal axis of the PBS should be aligned 7451 to that of the PolM.In the simulation, that angle can be set easily. But in practice, we needto find the optimum polarization alignment of the PC2 at first. Thetesting setup is shown in Fig. 4.

The PolM is terminated first, which means no driven signal isapplied. The detail procedure lies as follow: first, we set PC2 to arandom angle (βa01 or 901) and fix it. Then, we rotate PC1 to tuneα from 01 to 901. Next, by monitoring the optical power via anoptical power meter (OPM), we can draw an optical power curveas shown in Fig. 5. Five different β are considered: (a) β¼151; (b)β¼301; (c) β¼451; (d) β¼601; (e) β¼751. Note that the opticalpower remains constant only if β¼451 is satisfied. In other cases

(βa451), the optical power varies with respect to the selection ofα. Based on the relationship in Fig. 5, we can set the PC2 easily.

Then we apply RF signals to PolM to verify the mechanism inFig. 1. By adjusting the polarization angle α to 101 via PC1(corresponding to Case A), Fig. 6 shows the calculated (line) andsimulated (marks) power fading of PPD1 and PPD2 and the ACF. Asshown in the figure, the calculated and simulated results matchwell. The measurement range can be found as 0–6.6 GHz.

Based on such a relationship in Fig. 6, we can easily estimate theunknown frequency. Fig. 7(a) shows the calculated (line) andsimulated (marks) estimated frequencies against the input fre-quency. Then in Fig. 7(b), the estimated error is obtained as around

Fig. 8. Estimation frequency at different α (a) 201, (c) 301, and (e) 401. Estimated errors at different α (b) 201, (d) 301, and (f) 401.

J. Li et al. / Optics & Laser Technology 63 (2014) 54–6158

70.1 GHz when measurement range is from 0 to 6.6 GHz. It has tobe mentioned that the primary distortion in simulation comes fromthe terminal noise of two PD (100e�24W/Hz). Because of that, thecurve (calculation) and marks (simulation) in Fig. 7 are not perfectlymatched. Also note that the estimation errors near the notch point(6.6 GHz) are relatively high. It is mainly induced by the finiteresponse of ACF at notch point.

Then we stretch the measurement range by adjusting α to 201,301 and 401. The estimation frequency and estimation errors areillustrated in Fig. 8(a)–(f). There is a trade-off between the measure-ment range and the measurement errors. As shown in the figures, alarger measurement range will result in a lower measurementresolution. Table 2 shows the measurement ranges, bandwidthand errors at different α. For example, with α adjusted to 201, 301,and 401, the measurement range has been successfully extended to0–9.3 GHz, 0–11.4 GHz and 0–13.2 GHz, respectively. However, dueto the impact of terminal noise of two PDs, the resolution decreasesto around 70.12 GHz, 70.18 GHz and 70.53 GHz.

In order to improve the IFM system's resolution, we separatethe whole 13.2 GHz band to four different sections. In each section,different measurement ranges with a similar resolution areapplied. The parameter setting list can be found in Table 3. Fig. 9(a) and (b) plots the estimated frequency and errors. In the entiremeasurement range from 0 to 13.2 GHz, the measurement error(or resolution) can be controlled within 70.15 GHz, which is animprovement than in Fig. 8(e) and (f).

In the above verification, bias state of PolM is maintained atquadrature point (Vbias¼Vπ/2). In practice, Vbias may drift due tothe environment perturbation and the limited device's accuracy. Itwill affect the feature of the proposed IFM system. Therefore, it isnecessary to discuss the impact of bias drift. To evaluate it, werewrite the bias voltage as Vbias¼(1þΔV/Vπ)Vπ/2, where ΔV/Vπdenotes the bias drift. To quantify the impact of ΔV/Vπ, Fig. 10(a)–(d) illustrates the estimation errors at bias drift (a) 710%, (b)720%, (c) 730%, and (d) 740%. Apparently, when ΔV/Vπ is small(�20�20%), the estimation errors can still maintained at accep-table range (70.3 GHz), as shown in Fig. 9(a) and (b). But whenΔV/Vπ increases to 730% or 740%, the estimation errors becomemuch higher, around 70.5 GHz and 70.8 GHz, as shown in Fig. 10(c)–(d). Also note that around four boundary frequencies (6.6 GHz,9.3 GHz, 11.4 GHz and 13,2 GHz), the errors change dramatically. Itis because the ACF curves are slightly shifted to a lower frequencywhen the bias state drifts from the quadrature point. However, theimpact will not be serious if the bias is carefully controlled.

Normally, by using bias voltage control circuit, the bias drift ofPolM can be controlled within a range of �20�20%.

4. Conclusion

We have proposed and analyzed a novel approach for IFM basedon a single laser source and filter-less architecture. The keycomponent is a PolM followed by a section of DCF and a PBS. Withcarefully adjustment of the polarization angles, two outputs of PBScorrespond to two complementary output transfer functions of thePolM. By monitoring the microwave power via two PDs, a mono-tonically decreasing ACF can be obtained. Since the ACF is depen-dent on the polarization angle of incident light α, the measurementrange of the proposed IFM system can be stretched by simplyadjusting α. In order to verify the mechanism, simulations arecarried out. In the simulation, the measurement range can bestretched from 0–6.6 GHz to 0–9.3 GHz, 0–11.4 GHz and 0–13.2GHz by tuning α from 101 to 201, 301 and 401, respectively. Besides,the trade-off issue between measurement range and resolution canbe alleviated by separating the entire band into four different ones(0–6.6 GHz, 6.6–9.3 GHz, 9.3–11.4 GHz and 11.4–13.2 GHz). In that

Fig. 9. (a) Estimated frequency using parameter setting in Table 3 when inputfrequency tuned from 0 to 13.2 GHz. (c) Estimation errors.

Table 3Parameter setting list.

Measurement ranges (GHz) α (deg) Bandwidth (GHz) Resolution (GHz)

0–6.6 10 6.6 70.156.6–9.3 20 2.7 70.159.3–11.4 30 2.1 70.1511.4–13.2 40 1.8 70.15

Table 2Measurement ranges, bandwidth and resolution.

α (deg) Measurement ranges (GHz) Bandwidth (GHz) Resolution (GHz)

10 0–6.6 6.6 70.1020 0–9.3 9.3 70.1230 0–11.4 11.4 70.1840 0–13.2 13.2 70.53

J. Li et al. / Optics & Laser Technology 63 (2014) 54–61 59

way, a relative high resolution (70.15 GHz) can be obtained for awide measurement range (0–13.2 GHz). It is also found that the biasdrift (within �20�20%) has little impact on the resolution, which isa desirable feature for defense applications. During our analysis, theimpact of fiber nonlinearities is not included since the desired ACF(as expressed in Eq. (9)) is independent of laser power. Thus we canemploy relatively small laser power to minimize the impact of fibernonlinearities in practice.

The major advantage of our proposal is that only one CW laseris used as the source and no optical filter is required, which willresult in a simple and cost-effective architecture. However, thedisadvantage of the proposal is that in order to tune the measure-ment range and resolution, the polarization angle of incidentlightwave needs careful adjustment and maintenance; otherwise,the results (i.e. estimation errors) will change. However, since thatimpact has already proved to be small in [17], it will not be aconcern in practice.

Acknowledgments

This work is supported by the Fundamental Research Funds forthe Central Universities (No. 2014JBM013)

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