12 CHINESE OPTICS LETTERS / Vol. 6, No. 1 / January 10, 2008
A new demodulation technique for optical fiber
interferometric sensors with [3 × 3] directional couplers
Tingting Liu (
444
ËËËËËË
), Jie Cui (
www
###
), Desheng Chen (
),
Ling Xiao (
(((
), and Dexing Sun (
,,,
)
Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080
Received March 15, 2007
Optical fiber interferometric sensors based on [3 × 3] couplers have been used in many fields. A new
technique is proposed to demodulate output signals of this kind of sensors. The technique recovers the
signal of interest by fitting coefficients of elliptic (Lissajous) curves between each fiber pair. Different from
other approaches, this technique eliminates the dependence on the idealization of [3 × 3] coupler, provides
enhanced tolerance to the variance of photoelectric converters, and is anti-polarization in a certain extent.
The main algorithm has been successfully demonstrated both by numerical simulation and experimental
result.
OCIS codes: 060.2370, 070.6020, 060.1810, 120.3180.
Single-mode fiber interferometric sensors have drawn
a great deal of attention due to their high accuracy,
high sensitivity, and immunity of electromagnetic dis-
turbance. Optical fiber interferometric sensors base d
on [3 × 3] couplers have been used to detect acoustic,
magnetic, temperature perturbations and delamination
in comp osites
[1,2]
. Use of [3 × 3] directional couplers in
interferometer has been proposed early in 1980
[3]
, and
it was repo rted that it could solve the signal fading
problem
[3−5]
. Sheem et al. analyzed the waveguide the-
ory of [3 × 3] couplers, and gave the output expressions
in which the coefficients of three channels are equal
[4]
.
Furthermore, scattering matrix theory was also used to
describe the property of [3×3] couplers
[6,7]
. This theory is
simple and straightforward compare d with the waveguide
theory, but the latter is clearer and exacter in physical
conception.
The key of interferometic fiber-optic sensors is demod-
ulation technique. In 1982, Koo et al. proposed a sim-
ple demodulator
[8]
according to the output expressions
of [3 × 3] coupler given by Sheem. References [9 − 11]
described a conventional demodulation technique which
involved differentiation, cross-multiplication, summing
and integration etc. and required different gains for
three outputs, when the output phase differ e nce s were
120
◦
. Although the demodulation methods described
above se em straightforward, there are many difficulties
in implementation. For example, imperfection during the
fabrication of [3 × 3] couplers will lead the splitting ratio
to deviate from 1:1:1 and the output differences to de-
viate fro m ±120
◦
. The asymmetry of couplers and the
variance of photoelectric converter s will both cause am-
plitude fluctuations at the outputs. These factors will de-
grade the demodulation per formance and measurement
precision.
In this paper, a new demodula tion technique is pre-
sented. We establish the output mathematical model of
[3×3] fiber coupler which is a little different from Sheem’s
result using waveguide theory, and further obtain general
expressions synthesizing the practical condition of cou-
pler. The demodulation algorithm is described, which
utilizes the elliptic curve between any two of the three
outputs.
Figure 1 is an o ptica l fiber hydrophone using Mach-
Zehnder interferometer (MZI) with C
1
a [2 × 2] coupler
and C
2
a [3 × 3] directional coupler. Let z = 0 denote
the input port of [3 × 3 ] coupler and z = L denote its
output port. Let a
i
(z) (i = 1, 2, 3) be the complex ampli-
tudes of thr e e waves in the [3×3] coupler at the reference
point z. a
i
(z) are governed by a set of linear differential
equations
[3,4]
da
i
dz
+ jK
i,i+1
a
i+1
+ jK
i,i+2
a
i+2
= 0,
i = 1, 2, 3, i + 3 := i, (1)
where K
i,k
(= K
k,i
) is the coupling coefficient betwee n
the ith and the kth waveguides, and := means equiva-
lence. Ass uming that K
12
= K
23
= K
31
= K for math-
ematical simplicity, then the s olutions for a
i
in this case
are
[3]
a
i
(z) = c
i
e
jKz
+ be
−2jKz
,
3
X
i=1
c
i
= 0, (2)
where c
i
and b are constants.
According to the principle of MZI, we assume that the
inputs of [3 × 3] directiona l coupler are a
1
(0) = r
1
e
jφ
1
,
a
2
(0) = r
2
e
j(φ
1
+φ)
, a
3
(0) = 0. The first leg a
1
(0) cor-
responds to the reference arm with the initial phase
φ
1
and amplitude r
1
; the second leg a
2
(0) corresponds
to the signal arm where φ denotes the phase shift relative
Fig. 1. Schematic diagram of optical fiber hydrophone with
MZI. PD: photoelectric detector.
1671-7694/2008/010012-04
c
2008 Chinese Optics Letters