Study on a four-channel frequency division multiplexing multi-longitudinal mode
fiber-ring laser sensor array by beat frequency modulation technology
Jintaozhang1, 2*, YunlongZhang2, KunLi2, XuefengChen2, XiujuanYu2, YoulongYu1,
ShengchunLiu2*
1.
School of Instrument Science and Optic-Electronics Engineering, Hefei
University of Technology, Hefei, 230009, China
2.
Institute of Fiber Optics, Heilongjiang University, 150080, Harbin, China
*Corresponding author: [email protected], [email protected]
Abstract: Base on beat frequency modulation technology, a four-channel frequency
division multiplexing multi-longitudinal mode fiber-ring laser sensor array is
proposed and experimentally demonstrated by measuring the strains applied to one
laser sensors. The fiber-ring laser sensor as a sensing element is formed by a fiber
Bragg grating, a 3dB coupler and a section of Er3+ fiber. By analyzing the photonic
generation of beat signals and the theory of strain measurement, a relationship
describing the strain applied to the fiber-ring cavity and the beat frequency shift has
been obtained. Combining the frequency division multiplexing technology with the
beat frequency modulation, the system has the capability of multiplexing and
addressing more sensors. The responses of different beat frequency shift to the strain
are
−0.584kHz/με@782.698MHz
and
−0.891kHz/με@1185.911MHz
,
respectively which are in good agreement with the theoretical expectations. The
proposed system offers a cost-effective, high accuracy and high stability for
multi-parameter measurement.
Keywords: frequency division multiplexing, multi-longitudinal mode, fiber-ring laser
sensor, beat frequency shift
0. Introduction
In recent years, owing to the distinguished advantages such as high sensitivity,
electro-magnetic immunity, low cost and compactness, the conventional fiber Bragg
grating (FBG) sensors belonging to passive fiber sensors have been extensively
studied and applied in measurement of many physical parameters, such as strain,
temperature, pressure, vibration and acceleration, etc.1-5 Thus it can be thought that
the FBG sensor systems are successful enough in fiber sensors. However, for the
distributed sensing system, the decrease of light source power for individual sensing
unit with the increase of the multiplexing numbers of the sensors will cause the
degradation of sensing performance inevitably6-8. Fortunately, the rapid development
of fiber laser technology provides good candidates to solve this issue9-12. The
multi-longitudinal mode fiber-ring laser (MMFRL) sensor based on beat frequency
demodulation technology is one of the preferred methods13-14.
In
this
paper,
a
four-channel
frequency-division-multiplexing
(FDM)
multi-longitudinal mode fiber-ring laser sensor array by beat frequency modulation
technology is formed. Four similar sensing units are connected by 1*4 coupler, and
each unit contains one FBG and one fiber ring which is formed by a section of fiber,
one 3-dB fiber coupler. When the pump power is greater than the threshold of any of
the four laser sensors, multiple modes laser will be oscillated simultaneously in this
fiber-ring cavity and many beat frequency signals are generated by any two laser
modes, which is used as a sensing signal in the experiment. The beat frequency signal
containing the strain applied to the fiber-ring cavity is detected by a photo detector
(PD). And then the strain applied to the fiber-ring cavity can be monitored by
measuring the beat frequency shift of the any two mode lasers and the sensing unit
also can be addressed by beat frequency signal.
1. Principle and experiments
1480nm
Laser
FBG1
Stationary Translation
stage
Stage
Er3+
3dB
1
1*4
Coupler
Ch1
Ch2
Ch3
Ch4
FBG2
FBG3
Er3+
Er3+
3dB
3dB
PD
FBG4
RFSA
Er3+
3dB
2
3
Fig.1 Schematic configuration of the four-channel FDM-MMFRL array system
The schematic configuration of the proposed four-channel FDM-MMFRL array by
beat frequency modulation technology is shown in Fig.1. Each of the fiber-ring
resonator cavities of the MMFRL used as sensing unit is formed by an active fiber
ring, a section of Er3+ fiber and a FBG reflector. The fiber ring contains a 3dB fiber
coupler and a section of fiber.
The output port 2 and port 3 of the 3dB coupler are
spliced as a fiber ring, and a section of Er3+ fiber is spliced before port 1 of the 3dB
coupler and the FBG to offer enough gain. And the output port of the MMFRL is
spliced to the output port of the 1*4 coupler successively. The 1480 nm pump laser
(Pf=350mw) is launched into the MMFRLs through an isolator (ISO, Operating
wavelength
is
1480nm,
Isolates
degree ≥ 42dB ),
a
1480/1550nm
wavelength-division-multiplexer (WDM) and a 1*4 coupler. When the quartered
pump power is higher than the threshold power, many laser modes can stably
established in each MMFRL within the reflected band of the FBG. The light contains
sensing information from the fiber-ring resonator cavity of each MMFRL output
through the 1*4 coupler and the WDM to the PD (Newport Model 1544, 3dB
bandwidth is 12GHz) to get the electrical beat signal, and the frequency of which can
be measured by the frequency spectrum analyzer (FSA, R&S FSP30, Frequency range
is 9KHz-30GHz).
When the1480nm pump laser is enough robust, there are many longitudinal modes
with the same frequency spacing 𝑣𝑖 established in the fiber-ring laser cavity. It can
be expressed as:
𝑣𝑖 =
𝑖𝑐
2𝑛𝐿
= 𝑖𝑣
(1)
Where L is the effective cavity length, n is the effective refractive index, c is the
light velocity in vacuum and i is used to denote multiples of the beat frequency.
All the modes produced in the same fiber-ring resonant cavity are coherent,
therefore, the beat frequency between any two different longitudinal modes can be
expressed as:
𝑓𝑁 = 𝑣𝑚 − 𝑣𝑘 =
(𝑚−𝑘)𝑐
2𝑛𝐿
=
𝑁𝑐
2𝑛𝐿
= 𝑁𝑣
(2)
Where 𝑣𝑚 , 𝑣𝑘 are two different longitudinal modes in the fiber-ring resonator
cavity, N=m-k is used to denote the beat frequency.
When micro-strain applied on the fiber-ring cavity, the effective length of the
MMFRL cavity is changed, the beat frequency shift d𝑓𝑁 given by14:
d𝑓𝑁 = −𝑁
𝑐
2𝑛𝐿
(
𝛿𝑛
𝑛
+
𝛿𝐿
𝐿
𝛿𝑛
) = −𝑓𝑁 (
𝑛
+
𝛿𝐿
𝐿
) = −𝑓𝑁 (1 − 𝑃𝑒 )𝜀
(3)
Where 𝑃𝑒 is the photo-elastic constant whose value is about 0.22, 𝜀 is the
micro-strain applied to the laser cavity. Equation (3) indicates that the applied strain
determined by the beat frequency ship and the higher frequency has the higher
sensing sensitivity of the sensor.
The maximum number of multiplexing sensors in this proposed system K is related
to the sensor measurement range 𝜀, the predetermined non-overlapping maximum
observation frequency of the beat frequency signal f, the effective cavity length L, and
the mechanical tensile region length of the laser cavity l.
Provided the maximum laser cavity length is 𝐿𝑚𝑎𝑥 , according to Eq. (2), the
minimum beat frequency of laser sensor and the maximum beat frequency series can
be written respectively as:
𝑣𝑚𝑖𝑛 =
N=[
𝑐
(4)
2𝑛𝐿𝑚𝑎𝑥
𝑓
𝑣𝑚𝑖𝑛
]
(5)
In order to avoid the overlap between two beat frequency signals in adjacent series
and ensure the function of addressing sensors, the maximum beat frequency series N
should satisfy the following equation:
(𝑁 − 1)𝑣𝑚𝑎𝑥 = 𝑓
(6)
Provided the sensor with the same measurement range, that the maximum number
of multiplexing sensors of this sensing array:
k=[
𝑓
𝑣𝑚𝑖𝑛
]×
𝑣𝑚𝑖𝑛 2
𝑓−𝑣𝑚𝑖𝑛
×
𝐿
𝑙𝑓𝑁 (1−𝑝𝑐 )𝜀
2. Experiment and results
+1
(7)
Fig.2 the optical spectrum of the MMFRL array
The fiber Bragg gratings shown in Fig.1 have the same 3dB bandwidth and
reflectivity which are about 0.29nm and 90% respectively, and the center wavelengths
are about 1536nm, 1540nm, 1544nm and 1548nm respectively. The optical spectrum
of the MMFRL array is shown in Fig.2. The MMFRL cavity with the lengths of
4.2880m, 4.2641m, 4.2538m and 4.2486m, corresponds to the resonant frequencies of
23.72MHz, 23.83MHz, 23.92MHz and 24.03MHz. The EDF lengths with absorption
coefficient 10dB/m @ 1530 nm used in the four MMFRL sensors are 0.8340m,
0.8915m, 0.8775m and 0.7910m respectively. When the pump is 250mW, the
four-channel MMFRL sensor array remains a stable laser output. The maximum of the
threshold power for single sensor is about 4.7mW. Consequently a large number of
non-overlapping beat signals can be observed from 23.72MHz to 1.8GHz, and the
output beat signals of the sensor array system around 800MHz and 1.2GHz are shown
in Fig.3 (a) and (b). According to the Eq. (7), when the maximal strain of the MMFRL
sensor reaches 5000με, 𝑣𝑚𝑖𝑛 is 23.72MHz and the observation frequency 𝑓𝑁 is
about 1.2 GHz, then the corresponding maximum multiplexing sensor number of this
sensing array system is 20.
(a) 800MHz
(b) 1.2GHz
Fig.3 Beat frequency spectrums of this system around different frequency
As shown in Fig.1, the ring laser cavity of Ch1 is attached to the micro-displacement
platform to induce the micro-strain to the ring laser cavity. The mechanical tensile
region length of the laser cavity is 1.200m and the cavity length of the laser is
4.2880m. The beat frequency spectrums of sensor array system around 1.2GHz on
different strains are shown in Fig.4. When the applied strain is zero, the output beat
frequencies of sensor array are 1185.91MHz, 1191.73MHz, 1196.15MHz and
1201.27MHz successively. And the output frequencies of the Ch1 are 1185.82MHz,
1185.73MHz, 1186.64MHz and 1185.55MHz when the strains are 100με, 200με,
300με and 400με, respectively. From Fig.4, there have some small polarization noise.
It mainly from two aspects: One, practical fibers are not perfectly circularly
symmetric. As a result, the two orthogonal polarization modes of the laser cavity can
be laser simultaneously. Two, the refractive index change of FBG is different at every
direction, so the cavity of laser have fast and slow axis. As FBG laser, when the laser
cavity is very short, the effect of the low and fast axis of FBG is obvious. It needs to
be well controlled to generate single-polarization laser15. But, in MMFRL sensor, the
cavity length of the MMFRL is relativity long, the fiber birefringence and the
refractive index change of FBG can be mixed into polarization effect and the
polarization noise of each direction can be mean. The beat signal amplitude of two
polarizations is smaller than the beat signal of two longitudinal. So we can distinguish
two different signals.
Fig.4 Beat frequency spectrums of this system around 1200 MHz on different
strains. PN: polarization noise；BF：beat frequency signal
As shown in Fig.5, The experimental responses of beat frequency to the applied
strains
around
different
frequency
are
−0.584kHz/με@782.698MHz
and −0.891kHz/με@1185.911MHz, respectively. They are in good agreement with
the theoretical values, which are −0.610kHz/με@782.698MHz and −0.926khz/
με@1185.911MHz, respectively.
It is worth to mention that the stability of the beat frequency signals depends on the
temperature and the pump power. But, in this paper the temperature change of the
environment can be neglected and the fluctuation of the pump power used in the
system is less than 50μw, so the effect can also be ignored.
Fig.5 Responses of the different frequency to the strains
3. Discussion and conclusion
In this paper, a four-channel frequency division multiplexing multi-longitudinal
mode fiber-ring laser sensor array by beat frequency modulation technology has been
proposed. The fiber-ring laser array has ultrahigh stability and low threshold. When a
strain is applied to any one sensor of this fiber laser array, the value of the strain can
be achieved and the sensor can be addressed simultaneously by directly measuring the
beat frequency. The experimental results are in good agreement with the theoretical
values. The number of multiplexed sensors in this proposed system is more than 20,
and, it means that the system has the ability to address and measure more than twenty
sensors at the same time. Therefore, the proposed MMFRL sensing system can
provide a structure simple, ultrahigh stability, high sensitivity, all electrical and
low-cost multiplexing and demodulation method for strain, temperature, stress and
displacement etc. measuring simultaneously.
Acknowledgments
This work was supported in part by the National Nature Science Foundation of
China under Grant (60877043); by the Provincial Nature Science Foundation of
Heilongjiang Province under Grant (F201435) and by the High Level Innovation
Teams of Heilongjiang University under Grant (HD-028).
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