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Optics Communications 266 (2006) 532–535

Generation of millimeter-wave in optical pulse carrier by usingan apodized Moire fiber grating

Qing Ye *, Feng Liu, Ronghui Qu, Zujie Fang

Lab of Information Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, PR China

Received 25 February 2006; received in revised form 19 May 2006; accepted 22 May 2006

Abstract

A novel scheme is proposed to transform a Gaussian pulse to a millimeter-wave frequency modulation pulse by using an apodizedMoire fiber Bragg grating in radio-over-fiber system. The relation between the input and output pulses is analyzed theoretically by Fou-rier transformation method and the requirements for the proposed fiber grating are presented. An apodized Moire fiber Bragg grating isdesigned and its characteristics are studied. It is shown that the proposed device is feasible, and the new scheme is believed to be an effec-tive solution for the generation of millimeter-wave sub-carrier in future radio-over-fiber systems.� 2006 Elsevier B.V. All rights reserved.

PACS: 42.81.�i; 84.40.�x; 42.81.Qb

Keywords: Millimeter-wave pulses; Apodized Moire fiber grating; Radio-over-fiber systems

1. Introduction

As personal communication developing, demand on itscapacity has increased rapidly. Frequency of the wirelesscarrier will increase to millimeter-wave (MMW) range[1,2]. To extend the MMW propagation distance, opticalcarrier via fiber links between base station (BS) and centraloffice (CO) is supposed to be one of the most promisingtechnologies, which is referred to radio-over-fiber (ROF).One of the key issues in ROF is the generation of MMWsub-carrier modulated optical signals. The basic idea is touse the two-wave mixing to generate difference frequencyin the tens GHz range. Several papers have been publishedon this topic [3–7]. For example, Braun et al. [6] proposed ascheme to generate low-phase-noise MMW using opticalsideband injection locking. Bordonalli et al. [7] improvedthe above scheme and reported a MMW signal generationby combining optical sideband injection locking with opti-cal phase-lock loop techniques for two fiber-coupled DFB

0030-4018/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2006.05.041

* Corresponding author.E-mail address: yeqing_siom@126.com (Q. Ye).

lasers. Apart from the above continuous-wave microwaveand MMW signal generation devices, Levinson et al. [8]put forward a method of synthesizing complex frequencymodulation form microwave and MMW pulses by usingdispersion and Kerr effect in optical fiber systems, anddemonstrated the generation of electrical pulses modulatedat a controllable microwave frequency using a Mach–Zehnder interferometer and a chirped fiber grating. Veryrecently, they also demonstrated [9] a broad MMWmodulated pulses generation with a linear frequencychirp by using two fiber Bragg gratings and a mode-lockedfiber laser. However, the above schemes need the stablecontrol of the length of optical paths in the interferometerand the fiber birefringence, which is not easy in practicalapplications. Therefore, making use of some specialstructure passive devices to realize several to tens GHzmodulated light-wave will be an attractive idea.

In this paper, we propose a novel scheme to transforman optical pulse to a MMW modulated pulse by using aapodized Moire fiber Bragg grating. The grating has a typ-ical reflection spectrum of two peaks that will correspond-ingly change the spectrum of the incident optical pulse.

Fig. 1. A conceptual scheme of the proposed ROF system.

Fig. 2. The response function of fiber grating for the generation of MMWmodulated pulse.

Q. Ye et al. / Optics Communications 266 (2006) 532–535 533

Thus, the reflected spectrum becomes a combination of twodifferent wavelengths in frequency domain, and then intime domain a pulse modulated at difference frequency willbe generated by two-wave mixing. Moreover, due to Moirefiber Bragg grating [10–13] is fabricated usually by reading-in two different period fiber Bragg gratings in the sameposition of fiber to form optical Moire stripe refractiveindex distribution, the different wavelength will be reflectedin the same position. So it may also overcome the effect offiber grating’s time delay on MMW modulated pulse andavoids mixing two waves with different time delays of thegratings. By using the proposed apodized Moire fiberBragg grating filter, a novel ROF system can be designedas shown conceptually in Fig. 1. Optical signal pulses canbe transmitted via a conventional fiber link from a CO toa BS. At the BS, the pulse will be reflected by the proposedfiber grating to form a MMW modulation pulse. Theformed MMW modulation pulse will be transformed intoa MMW by a high-speed detector, and finally transmittedinto the free space by the antennas in the BS. In this paper,theoretical analysis on relations among the original pulsewidth, generated pulse width, MMW frequency, andparameters of the fiber grating will be derived, require-ments of related components will be discussed, and simula-tions will be given for some typical cases.

2. Theoretical analysis

In the proposed ROF scheme, a key component is thefiber Bragg grating as a filter to change the spectrum ofthe input optical pulse. The effect of a FBG on input pulsescan be described by its spectral response function HFBG(x).A Gaussian optical pulse input is considered in the analy-sis, whose spectrum can be expressed as:

eE inðxÞ ¼1

2E0s0 exp

�ðx� x0Þ2s20

8

" #; ð1Þ

where x0 is the pulse central angle frequency, s0 is the full-width at 1/e maximum and E0 is the pulse amplitude. Therequested output pulse is also a Gaussian pulse, but mod-ulated by a given MMW frequency of f, expressed as:

Eout ¼ E1 exp �2t2=s21

� �expðix0tÞ cosðpftÞ; ð2Þ

where s1 and E1 are the full-width at 1/e maximum and theamplitude of the output pulse. The corresponding spectrumis

eEoutðxÞ ¼1

2E1s1 exp

�p2f 2s21

8

� �exp

�ðx� x0Þ2s21

8

" #

� coshpf ðx� x0Þs2

1

4

� �: ð3Þ

Then the required spectral response function of FBG canbe obtained to be

HFBGðxÞ ¼ eEoutðxÞ=eE inðxÞ

¼ E1s1

E0s0

exp�p2f 2s2

1

8

� �exp

�ðx� x0Þ2ðs21 � s2

0Þ8

" #

� coshpf ðx� x0Þs2

1

4

� �: ð4Þ

The above expression is a Gauss line-type which is mod-ified by a hyperbolic secant function, and it depicts that therequired response function of FBG possesses double-wave-length characteristic as shown in Fig. 2. Apparently, it is easyto understand from the expression that the width of the out-put pulse s1 should be larger than that of the input pulse s0 inorder to keep the response function of FBG converging. Theresponse function (4) has two peaks, approximately at

x� � x0 � �pf 1� exp�p2f 2s2

1

2

� �þ s2

0

s21

� �� �pf : ð5Þ

To get a dispersion component with the response functionof Eq. (4), a Moire fiber Bragg grating may be one of theoptimal candidates, which can realize a two-peak reflectionspectrum by forming Moire fringes refractive index distri-bution along the length of the fiber grating. Generally,the reflection spectrum of a conventional Moire FBG isnot exactly coincident with the requested spectral responseof Eq. (4) and some side-modes are existent. However, aproper apodization technology of the index distributioncan hopefully help to make it as close to the requestedone as possible; and the apodization technologies in FBGfabrication are now mature enough to meet the designrequirements [14,15]. Since the maximum of FBG responsefunction HFBG, termed as m, must be less than 1 as a pas-

0.0

0.2

0.4

0.6

0.8

1.0

1554.4 1554.8 1555.2 1555.6 1556.0

0.0

0.2

0.4

0.6

0.8

1.0

(b)

Ref

lect

ivity

(a)

534 Q. Ye et al. / Optics Communications 266 (2006) 532–535

sive dispersion component, the reflected optical field will bereduced. From Eq. (4), the ratios of the field amplitudesand the pulse energies can be deduced as

E1=E0 ¼2ms0

s1

exp�p2f 2s2

0

8

� �; ð6Þ

I1=I0 ¼2m2s0

s1

exp�p2f 2s2

0

4

� �; ð7Þ

where I0 and I1 are the energies of the input pulse and out-put pulse. It is shown that there exists an optimal value ofthe input pulse width s0,

ffiffiffi2p

=pf , for the maximum outputpulse energy. Additionally, it also means that the MMW-modulated optical pulse should be amplified before trans-ferring to wireless MMW. Fortunately, fiber amplifiersand UTC-PD MMW detectors [16,17] have developed withgood performance and low price.

The required response function of Eq. (4) has anotherparameter, the full width at 1/e maximum intensity, dx,which can be deduced to be

dx ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip2f 2s4

0 þ 4 s21 � s2

0ð Þp

s21 � s2

0

: ð8Þ

Each peak-width of the spectrum will decide the output pulsewidth and affect the detection precision of the high-speedPD, which can be met by precise design of the Moire FBG.

1554.4 1554.8 1555.2 1555.6 1556.0

0.0

0.2

0.4

0.6

0.8

1.0

1554.4 1554.8 1555.2 1555.6 1556.0

(c)

Wavelength (nm)

Fig. 3. The response spectra of the FBG: (a) the required; (b) withoutapodized Moire fiber grating; (c) with apodized Moire fiber grating.

3. Design of fiber grating and numerical simulation

Eqs. (4)–(8) have given the requirements for a FBG thatcan transform a Gaussian pulse to a MMW modulatedpulse for a given frequency. Based on the above theoreticalanalysis, an apodized Moire FBG is designed to satisfy therequirements of the dispersion component for waveformtransform. For a Moire fiber grating, its peak–peak spaceof the reflection spectrum may be adjusted by controllingthe number of p phase shift points, and the spectrumwidths may be adjusted by controlling the grating lengthand the related refractive index modulation amplitude.Furthermore, a proper apodized function added to Moirefringe of the fiber grating can match the reflection spectrumshape with the required response function basically.Fig. 3(a) shows the required fiber gating response spectrumfor forming 60 GHz MMW modulation pulse obtainedfrom Eq. (4). Figs. 3(b) and (c) display the reflection spec-tra of the designed Moire fiber grating with parameters ofs0 = 7.5 ps, s1 = 100 ps, m = 1. In the Moire FBG numer-ical simulation, two refractive index modulation periodsK1 and K2, which is chosen to form Moire fringe refractiveindex distribution, are 536.93 nm and 537.10 nm, respec-tively. Their corresponding reflection spectrum frequencyspace is 60 GHz (0.48 nm) approximately. A rise-cosinefunction, j(z) = (b + cos[2(z � L/2)/L])/(b + 1) with thefiber grating length L and the adjusting parameter b, isadded to the Moire FBG refractive index modulation pro-file to control the side-modes of the reflection spectrum(Fig. 3(c)). A comparison of Fig. 3(a)–(c) shows that an

apodized Moire fiber grating can basically realize the spec-trum shape matching with that of the required responsefunction. Additionally, from Eq. (8), the angle frequencywidth dx of each spectrum can be obtained to be40.17 GHz (0.0512 nm). Then the length L and the relativerefractive index modulation amplitude Dnmax of the Moirefiber grating are requested to be 33.1 mm and 3 · 10�4 torealize both the maximum peak-reflectivity and the reflec-tion spectrum widths matching. Fig. 4 shows the corre-sponding refractive index modulation profile of theapodized Moire FBG for b = �0.5 and 20 p phase shiftpoints are formed along the length of the grating.

0 5 10 15 20 25 30 35-3

-2

-1

0

1

2

3

FBG Length (mm)

X 10-4

Ref

ract

ive

inde

x m

odua

ltion

Fig. 4. The relative refractive index modulation profile along the apodizedMoire FBG.

-200 -100 0 100 200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Nor

mal

ized

inte

nsity

(a.

u.)

Time (ps)

the output pulse from apodized Moire FBG

the required pulse

Fig. 5. The comparison of the output pulse from apodized Moire FBGand the required pulse.

Q. Ye et al. / Optics Communications 266 (2006) 532–535 535

Fig. 5 shows a simulated waveform of a MMW modu-lated optical pulse by using the above designed Moire fibergrating. The solid and dashed curves represent therequested pulse and the generated pulse. It is seen thatthe output pulse reflected from the designed fiber gratingis coincident with the requested pulse basically, includingits shape and modulation frequency. The narrow inputGaussian pulse is now broadened by the reflection of thefiber grating and a required MMW modulation frequencyis modulated to the output optical pulse. But the pulseenergy is lost because the FBG is a passive component.By using Eq. (7) it is easy to obtain the energy ratio ofthe output to the input pulse by integration of the inputand output pulse waveform. When the peak reflectivity ofFBG is taken to be 1, the energy ratio is calculated to be0.091. So it is required to implement an amplification ofabout 10.4 dB to resume the initial input energy.

Although the above analysis is given for Gaussian pulse,it is easy to obtain similar theories for other kinds of wave-forms, such as chirped Gaussian pulses, hyperbolic secantpulses. They have similarly qualitative relations, but differa little quantitatively. Especially it should be noticed tohyperbolic secant soliton pulse, it may keep steady pulseshape for a long fiber-link and solve the dispersion effecton the supershort pulse transmission.

4. Conclusion

In conclusion, a novel scheme has been proposed totransform a Gaussian pulse to a MMW modulation pulseby designing a twin-peak fiber grating filter. Making useof the Fourier transformation method, the response func-tion of the requested fiber grating is obtained, and an apod-ized Moire FBG is designed to realize their transmissionspectra matching. The simulation result shows that the out-put pulse from the designed fiber grating is coincident withthe required pulse. The proposed scheme may have advan-tages, such as less dispersion influence in fiber propagation,low cost, easy to implement, etc. It is shown that the pro-posed device is feasible, and will be an effective solutionfor future ROF communication network MMW sub-car-rier generation.

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