010601-1 CHINESE OPTICS LETTERS / Vol. 9, No. 1 / January 10, 2011
Characteristics of light polarization in magneto-optic fiber
Bragg gratings with linear birefringence
Baojian Wu (
ÉÉÉ
êêê
)
∗
, Chongzhen Li (
ooo
ÂÂÂ
ýýý
), Kun Qiu (
¤¤¤
&&&
), and Liwei Cheng (
§§§
ááá
)
Key Lab of Broadband Optical Fiber Transmission and Communication Networks of the Ministry of Education,
University of Electronic Science and Technology of China, Chengdu 610054, China
∗
Corresponding author: bjwu@uestc.edu.cn
Received June 22, 2010; accepted August 11, 2010; posted online January 1, 2011
The coupling between guided optical waves in magneto-optic fiber Bragg gratings (MFBGs) with linear
birefringence is investigated using the eigen-mode and coupled-mode approaches. The relationship be-
tween the polarization-dependent loss (PDL) and the eigen states of polarization (SOPs) in the MFBGs
is discussed. Only the MFBGs with low linear birefringence are app lied to the peak PDL-based magnetic
field measurement, after which the linear dynamic range is determined using the relative magnitude of
linear and magnetically induced circular birefringence. In this letter, a theoretical model is presented to
explain the experimental results and help develop novel MFBG-based devices.
OCIS codes: 060.3735, 230.2240, 060.2300.
doi: 10.3788/COL201109.010601.
With the extensive applications of fiber Bra gg gratings
(FBGs) in optical communication systems
[1]
and opti-
cal sensors, co mposite or rare-earth-doped special FBGs
have also attracted attention for use in optical signal
processing
[2,3]
. Magneto-optic FBGs (MFBGs) comprise
a class of special FBGs asso ciated w ith the magneto-
optical (MO) effects, such as the Faraday effect. In prin-
ciple, the rare-earth-doped FBGs or writing FBGs on
strain-tuned yttrium-iron-garnet (YIG) fibers
[4]
should
be used for lar ge MO coefficients similar to those in
the mechanically microfabricated YIG planar gratings
[5]
.
The MFBGs are promising candidates for current or mag-
netic field sensor s and tunable dispersion compensation
modules
[6]
. Kersey et al. described a novel fiber probe for
monitoring alternating curre nt (AC) high magnetic fields
by detecting the shift in Bragg condition of FBGs due
to magnetically induced circular birefringence
[7]
. Arce-
Diego et al. compared the shift values for silica and
terbium-doped optical fibers
[8]
. The magnetic tunability
of the MFBGs is expected to have a unique advantage
over the often-used tuning schemes in compensating or
tracking speed due to the immediate magnetic field re-
sp onse of the MFBGs, which is free of any extra stretcher
(e.g., magnetostrictive rod).
In practice, the conventional FBGs used in optical com-
munications and fiber sensing may also be regarded as
MFBGs, to a cer tain extent, if the weak MO effects in
fibers are taken into account. However, a small linear
birefringence in standard fiber s can lead to the quench-
ing of the Faraday effect
[9]
. Thus, to utilize the intrin-
sic MO effects in the s ilica FBGs at the present time,
one has to recur to high-resolution detection technolo-
gies, such as unbalanced Mach-Zehnder interferometers
[9]
and polarization-dependent loss (PDL)
[10,11]
. However,
it should also be pointed out that the c oupling of guided
optical waves (GOWs) in the MFBGs tends to be more
complicated than the case in the magneto-optic fibers
because of the grating r e flec tion. To our knowledge,
thorough investigations have not yet been conducted on
the influence of linear birefringence on the propagation
characteristics of guided light in the MFBGs until now.
In this letter, we propose a theoretical model of MF-
BGs, which includes linear birefringence, MO effect (or
magnetically-induced c ircular birefringence), and grating
Bragg diffraction. In the MFBGs, the analytic expres-
sion of the eigen states of polarization (SOPs) can be
derived us ing the eigen-mode approach, in which the
above-mentio ned effects are introduced one by one as
perturbations into the MFBG systems. These effects,
as a whole, may also be taken into account through the
coupled-mode approach.
In linear birefringent MFBGs, the MO coupling of
two orthogonal linear polarization modes depends on the
phase mismatch resulting from linear birefringence just
as in MO film waveguides
[12]
. The Bragg grating struc-
ture is responsible for the coupling between the incident
and reflected light beams. In the following, the Fara-
day MO e ffect and refra ctive index modulation of FBGs
are added in succession into a linear birefringent fiber
system; a lightwave coupling problem in the linear bire -
fringent MFBGs is partitioned into two sub-problems of
x-invariant MO waveguides and MO waveguide gratings.
The first sub-problem is necessary for the perturbation
method to obtain the total optical field in the MFBGs
of interest. Provided that the GOWs are confined to
the fiber core for fundamental modes, the optical field
E(x, y, z, t) associated with the MO perturbation can be
restructured from the eigen modes by
E(x, y, z, t) =
1
2
F(y, z)
ˆyA
y
(x)e
j(ωt−β
y
x)
+ˆzA
z
(x)e
j(ωt−β
z
x)
+ c.c. , (1)
where the fast and slow axes of linearly birefringent fibers
are taken as the y a nd z axes, respectively; F(y, z) is
the normalized transversal distribution of the electric
field; A
y
(x) and A
z
(x) are the complex amplitudes; c.c.
designates the complex conjugate of the former terms;
β
y
= n
f
k
0
and β
z
= n
s
k
0
are the propagation constants
of the y- and z-polarized GOWs at the angular frequency
ω, respectively (where, n
s
and n
f
are the refractive in-
1671-7694/2011/010601(4)
c
2011 Chinese Optics Letters