Wideband true-time-delay beam former that
employs a tunable chirped fiber grating prism
Yunqi Liu,Jianping Yao,and Jianliang Yang
Afiber grating prism that consists of four tunable chirped-grating delay lines for wideband true-time-
delay beam forming is propod and demonstrated.The chirped gratings are produced by u of the
grating bending technique in which a uniform grating is surface mounted on a simply supported beam.
We obtained chirped gratings with different chirp rates by bending the uniform gratings with different
bone
beam deflections.Four linear chirpedfiber gratings with identical spectral width but linearly incread
grating length are fabricated.The spectra and time-delay respons of the tunable chirped gratings are
measured.A chirped-grating prism for wideband true-time-delay beam forming by u of four chirped少儿英语歌曲大全
gratings is constructed and tested experimentally.We obtained different time delays by tuning the
wavelength of the optical carrier.The propod true-time-delay beam former with a four-element
phad-array steerer is suitable for continuous beam forming at microwave frequencies up to20GHz.
©2003Optical Society of America
OCIS codes:060.0060,060.2330,060.2340,060.2430,230.1480.
1.Introduction
Photonic true-time-delay͑TTD͒beam forming has been considered a good alternative for wideband phad-array antenna͑PAA͒systems thanks to its many advantages,such as immunity to electromag-netic interference,low loss,small size,lightweight, and the possibility of controlling veral arrays by u of wavelength division multiplexing.1–9A prom-ising way to achieve TTD beam forming is to u a fiber grating prism͑FGP͒,which can be built by u of arrays of discretefiber Bragg gratings͑FBGs͒or chirped gratings.For discrete FBG-bad FGPs,1–4 the prism is constructed by u of a number of dis-crete FBGs with different center wavelengths written at different physical locations of thefiber delay lines. The spacing between any adjacent gratings deter-mines the time delay,which in turn det
ermines the beam-pointing direction of the array antenna.The discrete FGB-bad approach assures broadband TTD operation but allows only discrete beam-pointing angles.It can produce a minimum time delay of approximately10ps and is suitable for beam forming at microwave frequencies of less than3 GHz.4For a chirped-grating-bad FGP that us linear chirpedfiber gratings,3–8the TTD unit allows continuous beam steering and produces smaller time delays.In most approaches in which a single chirped grating is ud,6,7multiple tunable lar sources are required.Different time delays are pro-duced by tuning the wavelength spacing of optical carriers that are reflected at different locations of the chirped grating.The u of just onefiber-chirped grating for the whole TTD system avoids the time-delay inaccuracies induced by the position mis-matches of many gratings.For an N-channel TTD unit,N tunable lar sources͑TLSs͒with equally incread or decread wavelength spacing controlled by a programmable multiwavelength controller should be incorporated into the system,which caus the whole system to be bulky and expensive.In the discrete FGP,to increa the operating frequency, one can replace thefirst delay line by a chirped-grating delay line,9leading to a discrete-chirped FGP. We recently reported that the discretely chirped FGP allows for discrete beam forming at higher microwave frequencies whereas the complex TTD system re-mains the same.9
To increa the operating frequency,we propo and demonstrate a four-channel chirped-grating-
银河护卫队 彩蛋
When this rearch was performed,Y.Liu and J.Yang were with
the Photonics Rearch Group,School of Electrical and Electronic
Engineering,Nanyang Technological University,Singapore
639798.Y.Liu͑yqliu@ee.cityu.edu.hk͒is now with the Depart-
ment of Electronic Engineering,City University of Hong Kong,Tat
Chee Avenue,Kowloon,Hong Kong.J.Yao is with the School of
Information Technology and Engineering,University of Ottawa,
Ottawa K1N6N5,Canada.
Received9August2002;revid manuscript received10Janu-
ary2003.
0003-6935͞03͞132273-05$15.00͞0
关于国庆节的英语手抄报
©2003Optical Society of America
1May2003͞Vol.42,No.13͞APPLIED OPTICS2273
bad FGP.The propod FGP,which consists of
怎么样英语four linear chirped-grating-bad delay lines,can
function at higher microwave frequencies with con-
tinuous beam steering.The chirped gratings ud
in the system were produced by u of the grating
bending technique.The chirp rate of each chirped
grating was tuned by bending a uniformed FBG sur-
face mounted on a simply supported beam.Four
chirped gratings with identical spectral width and
linearly incread grating length were produced and
were ud to construct the chirped-grating prism.
We show that the propod TTD unit with a four-
element phad-array steerer is suitable for beam
forming at frequencies up to20GHz.
2.Principles and Theoretical Analysis
Figure1shows the experimental tup of the tunable
chirped FGP beam former for a four-element wide-
band PAA system.The tunable lar source was
externally modulated with an electro-optic modulator ͑EOM͒.A polarization controller was incorporated between the tunable lar source and the EOM to
olorcontrol the polarization state.The modulated light
feeds a group of N single-modefibers through an
equal-path1:N power divider͑Nϭ4͒.Eachfiber
delay line includes a linear chirpedfiber grating.
The different peak-reflection wavelengths of the
chirped gratings were controlled to within the tun-
able range of the tunable lar source.Four optical
circulators were ud to direct the modulated light to
the FGP.The reflected light was time delayed in
accordance with the particular grating address.
Each wavelength was associated with a different
round-trip time delay.For the propod system,the
time delays associated with wavelengthC are iden-
tical in all four delay lines of the prism,whereC is
the reflection wavelength that corresponds to the
midpoints of the chirped gratings.The N photode-
tectors recover the individually time-delayed micro-
wave signals that feed the N antenna–radiator
elements.The time delay of the microwave signal
depends on the locations from which the light is re-flected at the gratings,and we can control it by tuning the wavelength of the optical carrier.So we can control the scanning angle of the radiation pattern by tuning the wavelength of the TLS.To ensure an acceptable signal-to-noi ratio at the output of the photodetectors,an erbium-dopedfiber amplifier was incorporated into the system in front of the1ϫ4 coupler to compensate for inrtion loss.
The steering angle resolution of the TTD unit can be expresd as2
minϭarcsin͑4nf m d min͞c͒,(1) where nϭ1.5is the effective refractive index of the fiber core,d min is the minimum grating spacing,f m is the maximum microwave frequency,and c is the free-space speed of light.The beam-pointing angle of the system that corresponds to the mainlobe of array antenna0can be expresd as
sin0ϭ
c⌬t d
d PAA
,(2)
where d PAA is the element spacing of the antenna array,and⌬t d is the time-delay difference between adjacent channels.For the propod system,the ra-diation angle of the PAA can be expresd as
sin0ϭ
c⌬
d PAA
k1ϭ
2n⌬d
d PAA
,(3)
where k1is the chirp rate of thefirst chirpedfiber grating,⌬is the wavelength tuning step of the tun-able lar source,and⌬d is the grating location dif-ference between adjacent delay lines with respect to the wavelengths fromC toCϩ⌬.Figure2shows the configuration of the relative grating location dif-ference that determines the radiation angle of the PAA system.The midpoints of the four chirped gratings have the same wavelengthC and the iden-tical time delay.Then the grating location differ-ence at this point is equal to0,which corresponds to 0°radiation angle.We determined the
beam-Fig.1.Experimental tup of the tunable chirpedfiber grating prism beam former for a four-element wideband PAA system. 2274APPLIED OPTICS͞Vol.42,No.13͞1May2003
pointing direction by the grating location difference that can be controlled by changing the wavelength tuning step and that is independent of the microwave frequency.Therefore,the FGP is a TTD beam former and is suitable for wideband applications.From Eq.͑3͒,the radiation angle can be expresd as
sin 0ϭk ⌬ϭk ͑L ϪC ͒,
(4)
where L is the output wavelength of the TLS,k ϭck 1͞d PAA is a constant determined by the chirp rate of the first chirped grating and the PAA element spac-ing.
The far-field pattern of the N -element pha array with element spacing of d PAA is given by 9
AF ͑͒ϭ͉f ͉͑͒ϭ
ͯ
sin ͑N ͞2͒
N sin ͑͞2͒
ͯ
,
(5)͑͒ϭϪd PAA sin ϩ␣,
(6)
receivewhere ␣ϭn 2⌬d ,ϭ2͞m ,m is the wavelength of the microwave signal,and is the radiation angle.
3.Experimental Results and Discussions
Figure 3shows the experimental tup for the time-delay measurements.The light of the TLS is nt to the EOM through the polarization controller.A 10-GHz microwave signal from the signal generator is applied to the modulator.The modulated light is re flected by the chirped fiber grating at the different locations of the delay line.The index-matching gel is ud to reduce the Fresnel re flection at the fiber end.The re flected light is split into two beams.
One is nt to the optical spectrum analyzer ͑OSA ͒.The other is ampli fied by the erbium-doped fiber am-pli fier and then converted to an electrical signal by a high-speed photodetector.The detected signal is nt to the oscilloscope ͑Agilent DCA 86100A ͒.The microwave signal generated by the signal generator is also nt to the oscilloscope to compare the time delay with the detected time-delayed signal.The tunable lar source lects a desired time delay by lection of the corresponding re flection point at the chirped fiber grating by tuning its output wave-length.
One can tune the chirp rates of the four fiber grat-ings by bending the uniform FBGs surface mounted on one side of a simply supported beam.10The sim-ply supported beam has a length of 100mm and a thickness of 4.5mm,who midpoint is de flected by u of a high-precision micrometer.With this tech-nique,four chirped fiber gratings with identical spec-tral widths but linearly incread grating length are produced and tested.The grating lengths are 1.5,3,4.5,and 6mm.The spectral width of the tunable chirped gratings is approximately 11nm.The cen-ter wavelength of the chirped gratings is approxi-mately C ϭ1553.0nm.We ud the OSA with a high-resolution tunable lar source to measure the spectrum of the fiber gratings.The output power of the TLS was kept constant at the wavelength range from 1520to 1620nm.The ripples of the broadband light source were then excluded from the measure-ments of the grating spectrum.The spectrum of the fiber grating can be measured more accurately than the method by simple u of an OSA with a broad-band source becau of the high wavelength resolu-tion of the TLS.The time-delay respons of the four chirped fiber gratings were measured experi-mentally at 10GHz.The time delay associated with wavelength C was lected as the reference for time-delay measurements.
Figure 4shows the re flection spectra and time-delay respons of the four chirped fiber gratings.Note that the time-delay respon is not linear around the longest and shortest wavelengths.
So we ud only the central ctions of the gratings that correspond to a range of 1548.5–1557.5nm of their spectra for the experiment.The bending of the grat-ings leads to grating ripples in the re flection spectra,which induces the signal fluctuation at the antenna array.The largest ripples ari at the two sides of the re flection spectra that correspond to the shortest and longest wavelengths.The large ripples do not affect the signal amplitude of the TTD unit becau only the central ctions of the gratings are ud for the experiments.For the TTD unit,the small-signal fluctuations found at the central grating ctions can be compensated in the electronic domain.2Becau the beam-pointing angle is determined only by the time delays of the N -channel time-delayed signals,the ripples of the grating re flection do not affect the antenna beam-pointing angle.The only effect of the grating re flection fluctuation that is due to bending on the TTD unit is its effect on the channel coef fi
-Fig.2.Con figuration of the relative grating location difference that determines the radiation angle of t
he PAA
system.
Fig.3.Experimental tup for the time-delay measurements:TLS,tunable lar source;Osci,oscilloscope;SG,signal generator;OSA,optical spectrum analyzer;PD,photodetector;IMG,index-matching gel.
1May 2003͞Vol.42,No.13͞APPLIED OPTICS
2275
cients of the four-channel beam-forming system,which further affects the mainlobe width and the mainlobe-to-sidelobe ratio.By using the electronic equalization technique,2,8we compensated for the re-flection fluctuation that is due to grating bending in the experiments.The measured time delays of the four tunable chirped-grating delay lines at 10-GHz microwave frequency are plotted as a function of the optical wavelength in Fig.5.The measured disper-sion rates of the four delay lines are 13.7,18.8,24.1,and 29.4ps ͞nm.The R -squared values of the data fitting are higher than 0.99,which means good lin-earity of the time-delay characteristics.The small deviation of the time-delay measurements away from linearity could be attributed to the position uncer-tainties of the gratings and the time-delay measure-
ment errors.For the tunable chirped gratings,the two gratings with a shorter grating length have a better linear time-delay respon than the other two with a longer grating length.The strain induced by beam tuning in the fiber has poor linearity for the longer gratings,which leads to a poorer linearity of the time-delay respon.In practical systems,a longer supported beam can be adopted to eliminate or to reduce the nonlinearity of the time-delay respon.Bad on the four linear chirped fiber gratings,we constructed a four-element TTD unit.For the TTD unit shown in Fig.1,the available maximum micro-wave frequency was determined by the minimum dis-tance allowed in the grating be
tween adjacent wavelengths.9As described in Ref.11,the rf power degradation limits the available maximum micro-wave frequency for the conventional intensity modulation –direct detection scheme.The maxi-mum microwave frequency that corresponds to the first Ϫ3-dB signal bandwidth of the rf power degra-dation can be expresd as 11
f de
g ϭ͑c ͞4C 2␦͒1͞2,
(7)
where ␦is the chirp rate of the chirped fiber grating.For our system,C ϭ1553.0nm,␦ϭ29.4ps ͞nm,and the maximum microwave frequency is calculated to be approximately 32.5GHz.When the microwave frequency is clo to this frequency,the dominant rf power degradation aris becau of the chromatic dispersion of the chirped grating.Then the single-sideband modulation technique should be adopted in place of the current modulation scheme.7For
TTD
学习化妆技巧
Fig.4.Re flection spectra and time-delay respons of the four chirped fiber
gratings.
Fig.5.Experimental time-delay measurements of tunable fiber grating delay lines at the microwave frequency of 10GHz:E ,grating 1;ᮀ,grating 2;‚,grating 3;ϫ,grating 4.2276
APPLIED OPTICS ͞Vol.42,No.13͞1May 2003
applications,Ϫ3-dB power degradation could be too large.To maintain a good signal level,we consider the first Ϫ1-dB signal bandwidth of the rf power deg-radation to be acceptable,which corresponds to 20GHz for the propod system.11So the TTD unit with the tunable chirped-grating prism can be ud for wideband PAA beam forming at microwave fre-quencies up to 20GHz without any dominant rf power degradation.It can also be deduced from Eq.͑3͒that the steering angle resolution of the TTD unit can be incread if we decrea the wavelength tun-ing step of the TLS.When continuous wavelength tuning is provided,continuous PAA beam steering is thus realized.
To avoid the existence of more than one mainlobe in the radiation patterns,the array element spacing of the PAA system is t to be half of the wavelength of the microwave frequency.12For a 10-GHz micro-wave signal,the element spacing should be d PAA ϭ15mm.Equation ͑4͒can be expresd as
sin 0ϭ0.212ϫ͑L Ϫ1553.0͒.
(8)
We can control the radiation angle by changing the output wavelength of the TLS.Figure 6shows the relationship between the tunable wavelength of the optical source and the PAA radiation angle.It can be en that radiation angle scanning has a higher wavelength nsitivity at the broadside radi-ation ͑0°angle ͒than that near the end-fire array ͑Ϫ90°or 90°angle ͒.The radiation pattern scans at angles from Ϫ72.5°to 72.5°when the wavelength of the tunable lar is tuned from 1548.5to 1557.5nm.We note that the beam-pointing accuracy is deter-mined by the time delays of the time-delayed signals,which is determined by the time-delay linearity of the chirped gratings.Figure 5shows that the time-delay characteristics of the four chirped gratings has high linearity.In the propod TTD system,the high-precision TLS is ud so that highly accurate PAA beam pointing can be obtained.The radiation patterns can be calculated by u of Eqs.͑5͒and ͑6͒for the four-element PAA system.Note that the mainlobe of the radiation pattern is quite broad since only four array elements are ud in the system shown in Fig.1.9,12The propod four-channel TTD
beam-forming unit can be extended to many channels by u of different feed geometry 12to genera
te a pencil-shaped beam.As the element number in-creas,a much-narrower mainlobe would be ob-tained and the mainlobe-to-sidelobe ratio would be signi ficantly incread.
4.Conclusion
A FGP that consists of four tunable chirped-grating delay lines has been propod and demonstrated.To the best of our knowledge,this is the first exper-imental demonstration of an optical TTD beam-forming network by u of tunable chirped gratings that can function at microwave frequencies up to 20GHz.It should be noted that the chirp tuning tup and the TTD unit were built on a highly stable optical table.For a practical system,proper packaging of the chirped gratings and other optical components were employed to ensure a high degree of system stability.
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Fig.6.Relationship between the tunable wavelength of the opti-cal source and the PAA radiation angle.
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