ptimization of reversible LPFG for sensing application
unita P. Ugale, Vivekanand Mishra ∗
lectronics Engineering Department, S. V. National Institute of Technology, Ichchhanath, Surat, Gujarat, India
r t i c l e i n f o
rticle history:eceived 29 January 2013ccepted 3 June 2013
a b s t r a c t
We report here for the first time to our knowledge the characterization of mechanically induced longperiod fiber gratings in novel MSM fiber structure. Reversible grating of same period and length was
eywords:PFGeversible gratings
induced in single mode fiber, multimode fiber and novel multimode-singlemode-multimode (MSM) fiberstructure. The spectral response of reversible LPFG in SMF is verified experimentally as well as fromsimulation results and then compared with the experimental spectral response of reversible LPFG inmultimode fiber and MSM fiber structure. Reversible LPFG in novel MSM fiber structure is the mostoptimized and suitable grating for sensing application. For this grating we have obtained single resonantwavelength over a wide wavelength range and maximum transmission loss peak of around 20 dB.
SM fiber structure
. Introduction
Long period fiber grating (LPFG) is the special case of FBG. Itas first suggested by Vengsarkar and coworkers in 1996 [1]. LPFG
an be formed by introducing periodic longitudinal perturbationsf refractive index along the core of a single mode fiber. It canouple light between fundamental core mode and co-propagatingladding modes at specific resonance wavelength. The period of aypical LPFG ranges from 100 �m to 1000 �m. The cladding modesf LPFG are absorbed by the polymer coating of the fiber, hence theransmission spectrum consists of number of rejection bands at theesonance wavelengths. In contrast to the Bragg grating, LPFG doesot produce reflected light and can serve as spectrally selectivebsorber. Therefore it is also called as transmission grating.
LPFGs formed by mechanically-induced technique have gener-ted great interest due to its versatility in the process of fabrication.n these gratings the fiber is subject to periodical stress, whichesults in alternated regions under compression and stretching thatodulate the refractive index via the photo elastic effect. These
ratings need neither a special fiber nor an expensive writing deviceor fabrication. These gratings also offer advantages of being sim-le, inexpensive, erasable, and reconfigurable and also give flexibleontrol of transmission spectrum.
. LPFG mathematical model
If a periodical pressure is applied on the waveguide, a longeriod grating is formed owing to the photo elastic effect and the
microbending effect. In this section, the theoretical framework todescribe the long period fiber gratings (LPFG) is discussed. Theenergy of the core mode LP01 is coupled into that of the claddingmodes LP1m if the phase matching condition as follows is satisfied[1].
2�ncoeff
�−
2�ncleff
�= 2�
�(1)
where neffco is the effective index of the core mode, neff
cl is theeffective index of cladding mode.
For a given periodicity � one can induce mode-couplingbetween the fundamental mode and several different claddingmodes, a property that manifests itself as a set of spiky losses atdifferent wavelengths in the transmission spectrum. In design ofoptical filters concatenation of gratings are required and the rela-tively close spaced resonance peaks of cladding modes can causeserious difficulties to generate a desired spectrum.
The coupled mode equations describe their complex amplitude,Aco(z) and Acl(z) [2].
dAco(z)dz
= iKco−coAco(z) + is
2Kco−clAcl(z)e−i2ız
dAcl(z)dz
= iKcl−coAco(z)ei2ız + is
2Kcl−clAcl(z)
(2)
where Aco and Acl are the slowly varying amplitudes of the coreand cladding modes, Kco-co, Kcl-cl and Kco-cl = K*
cl-co are the couplingcoefficients, s is the grating modulation depth and
Fig. 1. Plot of effective index of the fundamental core mode as a function of wave-length. For calculation of effective indices of the circularly symmetric, forwardpropagating cladding modes, consider a multimode step index structure ignoring
12 S.P. Ugale, V. Mishra /
ı = �(
ncoeff
− ncleff
/� − 1/�)
is the detuning from the resonant
avelength. The coupling is determined by the transverse fields ofhe resonant modes Ei and the average index of the grating �ni
ij = ωε0n
4
∫n(r)Ei(r)E∗
j (r)dr (3)
According to coupled mode theory, grating transmission is aunction of coupling coefficient Kij.
Assuming the detuning from resonant wavelength is balancedy the dc coupling, simplified expression for grating transmission
s given by
(Z) = cos2(KZ) (4)
Cross coupling coefficient K depends on the grating index profilend field profiles of the resonant modes.
The analysis given by Erdogan [3] is followed for the calculationf core and effective cladding refractive index.
Consider a step index fiber with three layers: central core withefractive index n1, cladding with refractive index n2 and the exter-al medium with refractive index n3 is considered. The core radius
s a and the cladding is assumed to extend to infinity.Variation of effective index neff
co of fundamental LP01 guidedode as a function of wavelength is calculated by using the follow-
ng equations:The normalized frequency of the fiber is given by V.
= 2�a
�
√n2
1 − n22 (5)
Normalized index difference
= n1 − n2
n1(6)
The approximate value of index as a function of wavelength isiven by Sellmeier equation:
2(�) = 1 +M∑
i=1
Ai�2
�2 − �2i
(7)
The commonly used wave-guide parameters u and w are givens follows:
=√
k21 − ˇ2
01 (8)
=√
ˇ201 − k2
2 (9)
here
1 = 2�n1
�, k2 = 2�n2
�, ˇ01 = 2�neff
co
�(10)
The characteristic equation for a LP0m guided propagation in aeakly guiding fiber (n1≈n2) is
1u
J1(ua)J0(ua)
= 1w
k1(wa)k0(wa)
(11)
Where m is radial order of mode. Jp, kp are Bessel and modifiedessel functions of order p. The characteristic equation was solvedumerically to obtain the curve in Fig. 1.
the presence of core. The eigen value equation for the LP0m cladding mode can thenbe approximated by that of a uniform dielectric cylinder surrounded by an infinitemedium.
(J′1(u(m)
clb)
u(m)cl
J1(u(m)cl
b)+ K ′
1(w(m)cl
b)
w(m)cl
K1(w(m)cl
b)
)
×(
K21
J′1(u(m)cl
b)
u(m)cl
J1(u(m)cl
b)+ K2
2
K ′1(w(m)
clb)
w(m)cl
K1(w(m)cl
b)
)
=(
ˇ(m)cl
b
)2
⎛⎜⎜⎝ 1[(
u(m)cl
)2+(
w(m)cl
)2]⎞⎟⎟⎠
2
(12)
u(m)cl
and w(m)cl
are the wave-guide parameters for cladding
u(m)cl
=√
k22 −(
ˇ(m))2
(13)
w(m)cl
=√(
ˇ(m))2 − k2
3 (14)
ˇ(m) = 2�n(m)cl
�and (15)
ncl(m)eff
=√
n22 −(
�
2�
)2( jm
b
)2
(16)
where jm are the roots of the Bessel function of order zero(J0(jm) = 0). Effective index difference between the fundamentalcore mode and cladding modes as a function of wavelength is cal-culated and plotted in Fig. 2. The phase match curves betweenthe fundamental core mode and the cladding modes with differ-ent diffraction orders for a step index single-mode fiber are shownin Figs. 3 and 4.
3. Experiment and result analysis
Reversible grating is induced in a single mode fiber, from Corn-ing (SMF28) with a period of 600 �m. The grating is characterizedby passing a light from broadband source SLED, having center wave-length of 1530 nm, and the bandwidth of 69 nm, and the response
is observed on optical spectrum analyzer, which is shown in Fig. 5.The resulting resonant wavelengths are compared with the the-oretical results from phase matching curve shown in Fig. 3. andsummarized in Table 1.
Essentially, fiber gratings are fibers with modulated refractiveindex of the core and are mostly fabricated in single mode fibers.However, recently, it has been reported that fiber gratings formedin multimode fibers also are useful in many applications [4,5].
Multimode fibers (MMFs) offer more flexibility in grating designand performance characteristics compared to single-mode fiber,multimode fibers have a merit of easy coupling with inexpensivelight sources and other optical components due to their large core,so gratings in multimode are preferred to yield lower cost sys-tems. Therefore, optical fiber gratings in multimode fibers have alsoreceived attention in recent years.
In single mode fibers there exists only one core mode (LP01) andmany cladding modes (LP1m), the core–cladding coupling occurs atcertain specific wavelengths. However, in the case of a multimodefiber with a large number of core modes and cladding modes, thecore–cladding power coupling occurs at all wavelengths and thewavelength dependence is not resolved [6,7].
Reversible grating is induced in Multimode fiber (62.5/125 �m),from Corning with a period of 600 �m and then it is characterized,the spectral response is observed on optical spectrum analyzer,which is shown in Fig. 6.
As compared to reversible LPFG in single mode fiber, thesegratings have more number of transmission dips in the spectralresponse; the corresponding resonant wavelengths are summa-rized in Table 2.
Single mode gratings gave better response (resonant loss peaksof up to ∼7 dB) as compared to multimode gratings (resonant losspeaks of up to ∼5 dB). But multimode fiber has its own advantagesbecause of large core diameter, such as easy coupling with inex-pensive light sources and other optical components. Therefore thesystem cost reduces. Thus to combine the advantages of both sin-gle mode fiber and multimode fiber, a novel MSM fiber structure isprepared to induce the reversible LPFG.
A schematic diagram of the MSM fiber structure used in experi-
ment is shown in Fig. 7. The sample is prepared by splicing a 15 cmlong section of SMF (SMF-28TM) using a Sumitomo Type39 fusionsplicer in between two MMFs (62.5/125). The loss at both spliceswas 0.02 dB.
Fig. 6. Complete transmission spectrum of reversible LPFG in multi mode fiber.
Table 2Resonance wavelengths for reversible LPFG in multimode fiber.
Grating period Resonance wavelengths for different modes (nm)
Fig. 8. Spectral response of MLPFG in MSM fiber structure.
The reversible LPFG with period of 600 �m and length = 70 mms induced in single mode fiber in MSM structure. Light is launchedrom a broadband source to the lead-in MMF, through the devicereversible LPFG) to the lead-out MMF and spectrally resolved usingn optical spectrum analyzer (OSA) (Prolite60).
The transmission spectrum of reversible LPFG in MSM fiber
tructure is plotted in Fig. 8, the input power spectrum is also shownor comparison purpose. The peak loss of around 20 dB is obtained,hich is much greater than maximum loss of 8 dB in single modeLPFG and 5 dB in multimode fiber.
[
[
125 (2014) 111– 114
4. Conclusion
The theoretical framework to describe the long period fiber grat-ing (LPFG) is discussed and then the comparison of theoretical andpractical resonance wavelengths for reversible LPFG in single modefiber is done. It is found that the practical results are in close agree-ment with theoretical values.
As compared to LPFG in single mode fiber (SMF28), LPFG in mul-timode fiber have more number of transmission dips in the spectralresponse.
Reversible LPFG in MSM fiber structure gives single transmissiondip. Resonant loss peak strength is around 20 dB, which is muchgreater than maximum loss of 8 dB in single mode reversible LPFGand 5 dB in multimode fiber.
Thus the response of grating is very impressive. There is a sin-gle resonant wavelength over a wide wavelength range (only onecladding mode satisfying Bragg condition). This offers extremelywide tunable range without worrying about overlap among differ-ent bands in sensing application.
Acknowledgment
This work is partially supported by the Department of Scienceand Technology of India.
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