Theoretical and experimental investigation of the intensity response
of DFB-FL to external acoustic excitation
P.P. Wang
a
, J. Chang
a,
n
, C.G. Zhu
a
, Y.J. Zhao
a,b
, Z.H. Sun
b
, X.L. Zhang
b
, G.D. Peng
a,b,c
a
School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan 250100, PR China
b
Laser Institute of Shandong Academy of Science, Jinan 250014, PR China
c
Photonics & Optical Communications Group, School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney 2052, Australia
article info
Article history:
Received 10 November 2012
Received in revised form
8 January 2013
Accepted 14 January 2013
Available online 11 February 2013
Keywords:
Intensity response
Distributed-Feedback fiber laser
Intensity-type acoustic sensor
abstract
The inten sity response of Distributed-Feedback fiber laser (DFB-FL) to external acoustic excitation has
been investigated theoretically and experimentally. The transfer function for external acoustic
excitation modulation has been obtained, and the intensity response characteristics of DFB-FL to
external acoustic excitation are described by simulation. Through experiments we observe a signal of
16.5 kHz with 25 dB in the DFB-FL RIN spectrum as the external acoustic pressure is 10.25 Pa. The
signal power obtained in time domain is 0.033
m
W and acoustic pressure sensitivity which is calculated
as –169.8 dB re
m
W/
m
Pa at 16.5 kHz, which confirms that DFB-FL has the potential to be used as an
intensity-type acoustic sensor.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Distributed-Feedback fiber laser (DFB-FL) acoustic sensors have
attracted much attention for more than 10 years and have found a
number of potentially useful applications for its high-performance
and miniaturization [1–3]. The DFB-FL relative intensity noise (RIN)
plays an important role in determining the minimum detectable
signal and has been investigated by many researchers [4–6]. Granch
et al. have modeled the RIN of Er
3þ
doped DFB-FL according to the
rate equations; the transfer functions for pump perturbation and loss
modulation have been derived. Lina Ma et al. have modeled the RIN
characteristics of DFB-FL with external laser injection, and the RIN
enhancement for each sensing unit in the array could be evaluated
exactly. Furthermore, the influence of external environment on DFB-
FL characteristics calls for attention, which needs to be eliminated
because the extra intensity introduced during exciting procedure can
reduce accuracy and sensitivity of the sensors. When there is external
acoustic excitation applied on the phase-shift grating, the fiber is
physically lengthened or shortened due to the elasticity of the fiber,
and the refractive index of the fiber is modified because of the photo-
elasticity [7]. These two physical effects give rise to changes in both
the Bragg reflection wavelength
l
B
¼2n
eff
L
and the DFB-FL output
power fluctuation. As a result, the effect of external acoustic excita-
tion modulation which may contribute significantly to the DFB-FL
intensity should be analyzed and discussed. On the other hand, we
could obtain the fixed external acoustic excitation signal intensity
through the filtering system. It means that the DFB-FL has the
potential to be used as an intensity-type acoustic sensor [8–9]. In
theformerworkofourlaboratory,wehavedonealotofbasic
experimental research and parts of the experimental results have
been publishe d [10,12]. In this paper, we present the theoretical
model of the intensity response of DFB-FL to external acoustic
excitation firstly, and an experimental configuration is designed to
demonstrate the intensity response. The acoustic pressure sensitivity
at 16.5 kHz and the frequency response at frequencies ranging from
5 kHz to 16.5 kHz are obt ained by experiments.
2. Theoretical model
The rate equations of an Er
3 þ
doped DFB-FL can be given by
Eq. (1) in terms of excited ion density n
2
and cavity photon
density q [5] :
dn
2
dt
¼ W
P
þW
a
ðÞ
1n
2
ðÞ
n
2
W
e
þ
1
t
2
dq
dt
¼ W
e
n
2
N
0
W
a
1n
2
ðÞN
0
q
t
c
ð1Þ
where the pu mp absorption W
p
,signalabsorptionW
a
and signal
emission W
e
are denoted as
W
P
¼
G
p
s
P
P=A
c
h
n
P
, W
a
¼
s
a
cq=n ¼ qr
qa
, W
e
¼
s
e
cq=n ¼ qr
qe
ð2Þ
Here r
qa
¼
s
a
c/n, r
qe
¼
s
e
c/n,andwedefine
D
r
q
¼r
qa
þr
qe
.
t
c
is the
lifetime of laser photons within the cavity which can be expressed as
t
c
¼nl
e
/c
g
,
g
¼ln(14exp(
k
l)) is the cavity loss, and the other
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Optics & Laser Technology
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.optlastec.2013.01.014
n
Corresponding author. Tel.: þ86 136 05310806.
E-mail address: changjun@sdu.edu.cn (J. Chang).
Optics & Laser Technology 49 (2013) 227–230