CN113252087A - Annular loop single-mode optical fiber sensor based on Renner correction model and annular optical fiber loop design method thereof - Google Patents
Annular loop single-mode optical fiber sensor based on Renner correction model and annular optical fiber loop design method thereof Download PDFInfo
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Abstract
The invention discloses an annular loop single-mode optical fiber sensor based on a Renner correction model and an annular optical fiber loop design method thereof, and belongs to the technical field of optical fiber sensor design. The design method comprises the steps of firstly establishing a power loss model of an optical fiber ring of an undeformed annular loop, then establishing a deformation equation of the deformed annular loop, then establishing a correlation model of external displacement of the optical fiber of the annular loop and optical power attenuation on the basis of the deformation equation, and finally establishing a relative emission power loss model of the deformed loop and the undeformed loop of the optical fiber ring of the annular loop, and determining the relation between the appearance of the annular optical fiber loop and the loss power. The sensor designed by the design method simultaneously considers the conditions that the shape of the optical fiber ring is not changed, only the size is changed and the shape is changed, and the influence of optical fiber deflection, so that the sensor has wider application condition, avoids larger deviation between an actual measurement result and a theoretical prediction result, can be suitable for various application occasions, and can carry out measurement range and precision customization.
Description
Technical Field
The invention relates to an optical fiber sensor and a design method thereof, in particular to an annular loop single-mode optical fiber sensor based on a Renner correction model and an annular optical fiber loop design method thereof, and belongs to the technical field of optical fiber sensor design.
Background
An optical fiber is a flexible transparent fiber made of extruded glass or plastic, slightly thicker than human hair, usually consisting of a low refractive index transparent core, a transparent cladding material and a coating on the outermost layer. The optical fiber serves as an optical waveguide, and allows light to be totally reflected in the core. In optical fiber communications, Single Mode Fiber (SMF) is an optical fiber that directly transmits optical signals in transverse mode, operating at data rates of 100M/s or 1G/s, over transmission distances of at least 5 km. Typically, single mode optical fibers are used for long range signal transmission.
An optical fiber sensor is a sensor that converts the state of an object to be measured into a measurable optical signal. The working principle is that the light beam from the light source is transmitted to the modulator via the optical fiber, and the interaction between the light beam and the measured parameters in the modulator changes the optical properties of the light, such as light intensity, wavelength, frequency, phase, polarization state, etc. to form modulated light signal, which is then transmitted to the photoelectric device via the optical fiber and demodulated to obtain the measured parameters. In the whole process, the light beam is guided in through the optical fiber, passes through the modulator and then is emitted, wherein the optical fiber firstly plays the role of transmitting the light beam and secondly plays the role of an optical modulator. Therefore, the deformation of the optical fiber in the optical fiber sensor has a key influence on the intensity change of the optical signal.
In the prior art, during design of an annular single-mode fiber sensor, most of considerations are to change the use condition of laser signal intensity by only displacing an annular fiber in a radial direction (see the condition in fig. 2(b) of the specification), and no consideration is given to the use condition that the annular shape of the annular fiber is not changed and only the radius is changed (see the condition in fig. 2(a) of the specification) when the annular fiber is used, so that the laser signal intensity is changed. In addition, when the annular single-mode fiber sensor in the prior art is designed, the influence of deflection on an actual result is not considered, so that the deviation between theoretical prediction and an actual test result is large. In addition, the application range of the annular single-mode optical fiber sensor in the prior art is limited to be used in the mechanical performance test of the composite material, and the application scene is narrow.
Disclosure of Invention
In order to solve the technical problem, the invention provides an annular loop single-mode optical fiber sensor based on a Renner correction model and an annular optical fiber loop design method thereof.
The technical scheme of the invention is as follows:
the invention discloses a method for designing an annular optical fiber loop of an annular loop single-mode optical fiber sensor based on a Renner correction model, which mainly comprises the following steps:
s1, establishing a power loss model of the ring-shaped loop optical fiber ring which is not deformed, wherein the power loss model comprises the following steps:
wherein 1 ═ 2 pi (R + a), and α is a bending loss coefficient;
s2, establishing a deformation equation of the annular loop optical fiber ring deformation, including determining a deformation curvature rho under polar coordinates and determining a curvature radius R (theta) of the annular loop optical fiber through the deformation curvature rho,
the curvature ρ is:
θ∈[0，π/2]
where μ (θ) is the deflection equation and varies with θ; w is the displacement of the fiber optic ring under radial force; i is the moment of inertia of the cross section of the fiber; e is the effective Young's modulus of the fiber;
the radius of curvature R (θ) is:
wherein the content of the first and second substances,
ρ′＝dρ/dθ，ρ″＝dρ/dθ2；
s3, establishing a model of the correlation between the external displacement of the optical fiber ring of the annular loop and the optical power attenuation, as follows:
wherein α is a bending loss coefficient;
s4, establishing a relative emission power loss model of the deformed loop and the undeformed loop of the annular loop optical fiber loop, as follows:
the further technical scheme is as follows:
the bending loss coefficient α is determined by 2 α ═ Δ P/P derived from a loss equation, where P and Δ P are the power carried in the straight waveguide and the output power of the waveguide, respectively.
The further technical scheme is as follows:
the relationship between the bending loss coefficient alpha and the shape of the loop optical fiber is modeled as follows,
wherein R isclDenotes the radius of the cladding, RcTo achieve the critical radius for total internal reflection in the core.
The further technical scheme is as follows:
αmarcthe formula of the calculation model of (a) is as follows,
wherein r is the radius from the origin of the ring to the outer surface of the ring;
Reis an effective bending radius, and Re1.28(R + a), R being the actual bending radius, a being the radius of the core;
k is a free-space propagation constant,
K1(γ a) is a first order bessel function of the second type of modification;
β0the propagation constant of the leaky fundamental mode in the straight optical fiber is obtained by solving an eigenvalue equation of the guided fundamental mode;
The invention also discloses an annular loop single-mode optical fiber sensor based on the Renner correction model, and the optical fiber sensor is designed and molded based on the design method.
The further technical scheme is as follows:
the radius value of an optical fiber ring of an annular loop in the optical fiber sensor is 3-9 mm.
The further technical scheme is as follows:
the radius value of an optical fiber ring of an annular loop in the optical fiber sensor is 5-7 mm.
The further technical scheme is as follows:
the sensitivity of the optical fiber sensor is within the value range of the radius of the optical fiber ring of the annular loop, and is increased along with the reduction of the radius of the loop.
The further technical scheme is as follows:
the annular loop optical fiber ring of the optical fiber sensor can work in two different states, only the radius of the annular loop optical fiber ring changes and the shape of the annular loop does not change, or the acting force is applied to the annular loop optical fiber ring to enable the annular loop optical fiber ring to deform to generate a deformation displacement state.
The beneficial technical effects of the invention are as follows:
1. when the annular optical fiber loop of the optical fiber sensor is designed, two use conditions of the optical fiber sensor are considered, namely the condition that the radius of the annular loop optical fiber loop is changed and the shape of the annular loop is not changed, and the condition that acting force is applied to the annular loop optical fiber loop to deform the annular loop optical fiber loop to generate deformation displacement, so that the optical fiber sensor is more widely applicable;
2. when the annular optical fiber loop of the optical fiber sensor is designed, the influence of the deflection of an optical fiber material on an actual result is considered, and the condition that the actual measurement result has larger deviation with a theoretical prediction result is avoided;
3. the optical fiber sensor of the annular optical fiber loop designed by the invention can test the mechanical property of the material, can detect the pressure, the temperature, the vibration, the displacement, the hydrocarbon content and the like in real time, and can customize the measurement range and the precision according to different requirements.
Drawings
Fig. 1 is a schematic diagram of the bending loss of a single mode fiber leading to resonance phenomena caused by the coupling of light leaking back into the cladding and core, where the dashed arrows indicate radiation leaking from the fundamental mode.
FIG. 2 is a schematic diagram of a fiber loop sensor that can operate in two different ways: power attenuation caused by (a) radius changes and (b) displacement applied to the loop.
Fig. 3 is a comparison graph of theoretical models of Marcuse and Renner, showing power attenuation as the loop radius increases.
Fig. 4 is a schematic diagram of loop deformation due to applied force.
Fig. 5 is the theoretical model results for Marcuse and Renner showing the relative power decay as a function of the displacement calculated from the modified theoretical model. These theoretical models include the effect of flexibility in a 4, 5, 6, 7mm loop radius; the solid line represents the modified Marcuse model and the dashed line represents the modified Renner model; each set of solid and dashed lines from top right to bottom left represents the case of 7, 6, 5, 4mm loop radii in order.
FIG. 6 is a schematic structural diagram of an experimental apparatus according to an embodiment of the present invention; wherein (a) is a schematic diagram of a device suitable for keeping the annular loop circular and (b) is a schematic diagram of a device suitable for deforming the loop.
Fig. 7 is experimental data results obtained from two configurations of loop sensors, where fig. 7(a) is experimental measurements made using the device shown in fig. 6(a) (with the loop radius changed, but circular in shape), and fig. 7(b) is experimental measurements made using a 5mm radius loop deformed in accordance with the device shown in fig. 6 (b).
Fig. 8 is a graph comparing experimental measurements using the Marcuse theoretical model, the Renner theoretical model, the device of fig. 6(a) of the present application, and experimental measurements using prior art models.
Fig. 9 shows experimental measurements of the device of fig. 6(b) in dynamic and static measurement modes using the Marcuse modified theoretical model, the Renner modified theoretical model, and the sensor designed using the modified model of the present application, and comparing the theoretical results with the dynamic and static measurement results. Static measurements were made in 0.02mm displacement steps. The results show that at a given displacement of FOLS, the results for power decay at (a)5mm and (b)6mm radii.
Detailed Description
In order to make the technical means of the present invention clearer and to make the technical means of the present invention capable of being implemented according to the content of the specification, the following detailed description of the embodiments of the present invention is made with reference to the accompanying drawings and examples, which are provided for illustrating the present invention and are not intended to limit the scope of the present invention.
The present embodiment describes in detail the technical solution claimed in the present application, and uses a single mode fiber to explain in detail from the appearance design, theoretical calculation, and experimental results.
First, the appearance design
Mechanical bending of single mode fibers (fig. 1) results in laser light leaking out during propagation through the cladding and coating and results in a reduction in the transmitted power through the cladding and coating. Thus, forming a sharp bend or loop in the fiber can result in optical power loss in the core. In this case, the ratio of the light intensity (P) passing through the fiber loopR) From the output (P)out) Power and input (P)in) Calculating the ratio of the powers; similarly, the proportion (P ') of light intensity passing through the deformation loop'R) Calculated from the ratio of the output power to the input power of the deformation loop. Thus, the relative transmit power loss in a deformed loop compared to an undeformed loop is:
the transmitted intensity shows a tendency to decrease with respect to the ring radius. However, at a certain loop radius, a sharp increase in transmitted intensity is observed. These intermediate peaks occur because light leaking out of the core and reflecting off the core/cladding and coating/air interfaces couples with light in the core, creating whispering gallery modes. Two possible ways of varying the loop radius are shown in fig. 2, both of which can be used as a sensor concept design.
The following provides a theoretical model for estimating power loss due to macrobending of an optical fiber. However, models that assume infinite coating and cladding thickness are unpredictable in the presence of interference peaks and do not produce a linear relationship between loop radius and power loss. Thus, some modified methods may be used to predict the presence of the intermediate peak, including using ray optics theory, wave optics theory, and solving maxwell's equations in an equivalent cartesian coordinate system. However, previous models were limited to predicting the presence of intermediate peaks at certain loop radii in a circular loop and are not applicable to the physical concept of a deformed fiber loop. The focus of the work of this application is to develop a theoretical model for the working principle of this sensor based on the deformation of the soft material ring and will allow a more accurate prediction of the sensor performance.
Second, theoretical calculation
Marcuse (d. Marcuse) derives a power loss equation for a bent fiber assuming the fiber has an infinite cladding thickness by determining the field expansion coefficient in terms of the cylindrical wave. The field expansion is related to the guided mode field of the straight fiber to achieve an expansion coefficient, but the field of the curved waveguide, which is derived from the undistorted field of the straight fiber, is at a centrifugal orientation. Since the field varies in the direction perpendicular to the plane, by applying cylindrical polar coordinates, the solution of the external field of the curved dielectric waveguide is represented by superimposing the emerging cylindrical waves.
The hank equation H μ (2) (nkr) is used in an infinite cladding for waveguide external field solutions, where n is the refractive index of the cladding, k is the free space propagation constant, and r is the radius from the origin of the circular ring to the outer surface of the ring. The radiation loss caused by bending can be found by the loss equation 2 α ═ Δ P/P, where P and Δ P are the power carried in the straight waveguide and the output power of the waveguide, respectively. In the formula of curvature loss, the unit is dB/unit length and can be written as
αmarcAnd alpharenThe derivation of Marcuse and Renner (h.renner) is shown separately. ReDefined as the effective bend radius, which accounts for the dominant stress effect, V, kappa and gamma are
Where a is the radius of the core, k is the wavenumber associated with the free space wavelength λ, k is 2 π/λ; n isco、nclAnd nctRefractive indices of the core, cladding and coating, respectively; k1(γ a) is a first order bessel function of the second type of modification; beta is a0Is obtained by solving an eigenvalue equation of a radix modeThe propagation constant of the leaky fundamental mode of (a) in a straight optical fiber; r is the actual bend radius. With an elastic optical correction factor, for a silicon fibre of 1.28, a bending effect is obtained, i.e. an effective bending radius,
Re＝1.28(R+a)
there are several methods available to address the presence of interference peaks, and the method of Renner is used in this application. In the present work, the beamwidth of the transverse radiation field of the leaky modes in a bent fiber only increases as the square root of the distance from the core increases, so that it can be assumed that the cladding-coating interface is planar. The fundamental difference between the Marcuse model and the Renner model is that the Marcuse model assumes infinite cladding thickness around the core, while the Renner mode assumes finite fiber cladding. Assuming infinite cladding thickness eliminates the possibility of reflection from the cladding-coating interface back into the fiber core, and light leaking from the core is considered to be completely lost. In contrast, the Renner model assumes a finite cladding thickness, which allows back reflection from the cladding-coating interface toward the core. These back reflections in the actual fiber are measurable and can cause whispering gallery mode interference with the incident beam. The coated fiber has a bending loss coefficient of
RclDenotes the radius of the cladding, RcDefined as the critical radius to achieve total internal reflection in the core, i.e. to transmit the laser wave without loss. Once the shape of the loop is fixed, the bending loss factor is determined and the power loss can be calculated by simply multiplying the loop perimeter:
Figure 3 shows a comparison of two different radius circular ring models. It is clear that if the presence of the intermediate peak is neglected, the trend of the power loss can be approximated to a linear trend when the radius is between 4 and 7 mm. For example, data acquired at low frequencies or large steps may miss these peaks. At the same time, the use of a middle peak results in a very high sensitivity. This phenomenon allows the development of a dual range sensor.
One of the limitations of existing models is that they can only handle fiber loops in a circular configuration. The use of FOLS (fiber optical laser sensor) is based on the effect of deforming the loop, effectively changing the radius. Therefore, the deflection equation is applied to estimate the loss from a non-circular deformed ring (fig. 4). The problem sets the curvature as a function of the local angular coordinate θ rather than maintaining a constant value. The deformation equation for the annulus can be derived through material mechanics. Assuming symmetric deformation, only a quarter-ring is present, and the deformation of this ring in polar coordinates is estimated as:
θ∈[0，π/2]
μ (θ) is the deflection equation, will vary with θ; w is the displacement of the fiber optic ring under radial force; i is the moment of inertia of the cross section of the fiber; e is the effective young's modulus of the fiber.
The radius of curvature R (θ) may be calculated by the first and second derivatives of the curvature ρ.
ρ′＝dρ/dθ
ρ″＝dρ/dθ2
In order to establish a model related to the attenuation of the optical power to the external displacement, the above equations are combined to finally obtain:
the theoretical results of these two models are plotted in fig. 5, where the effect of flexibility is included in the prediction. Predictions are generated for various loop radii in the graph. The difference between the two models at the small displacement value, i.e. the improved Renner model, does not oscillate around the trend of the improved Marcuse mode, since each model is normalized to the power loss through the respective calculated undeformed loop.
Third, experimental results
The modified theoretical model was verified by experimental results using the experimental setup shown in fig. 6. The device includes a Corning SMF 28e fiber, a 1310nm single wavelength laser source (Thorlabs S1FC1310), a 90%/10% beam splitter (Fico P/N FC-210R1-8A), two photodetectors (Thorlabs DET410 and Newport 71617) connected to a data acquisition board (National Instruments NI USB-6221 DAQ). The apparatus also used a translation stage (Thorlabs MTS25/M), a CMOS camera (Nikon D7000) and a computer for instrument control, data recording and processing. FIG. 6 shows data acquisition in two device settings, where the loop of the first (a) remains circular, but can be changed in radius by pulling the fiber using a translation stage; wherein the loop of the second type (b) is mounted on the translation stage and is capable of deforming the anvil relative to the rigid. In both cases, a 10% signal is obtained using a beam splitter as a reference to normalize any fluctuations caused by the laser source or environmental conditions.
The experiment was carried out in two apparatuses as shown in fig. 6.
In the first case, fig. 6(a), the loop remains circular, but the radius of the loop changes. The loop is constructed by passing the optical fiber through a stainless steel tube fixed to a rigid support. The tube was cut to a length of 1.5mm to minimize the effect on the loop shape, with an inner diameter of 0.685mm selected to be slightly larger than twice the fiber diameter to avoid potential friction induced stresses while still holding the fiber in place. The translation stage is connected to the fiber to control the loop radius (fig. 6 a).
In the second case, the ring is mounted on a translation stage and deformed against a rigid anvil to deform the shape, as shown in fig. 6 (b). A digital camera is placed on top of the ring to capture images during ring deformation in order to measure the ring radius by image analysis.
Based on previous calculations, loops with radii less than 38.2mm produce a loss of strength. For loop radii close to this value, the losses are very small. However, consistent with the curve in fig. 3, the loss increases significantly in the range of 3-9mm with further reduction of the radius. Therefore, the test was performed within this radius value range. Fig. 7(a) shows experimental measurements performed using the configuration shown in fig. 6 (a). In this case, the loop remains circular, but the radius changes, and the intensity measurement is recorded. It can be seen that the loss increases with decreasing loop radius. The middle whispering gallery mode peaks are recorded at certain radius values, where the intensity shows a sharp peak. Fig. 7(b) shows experimental measurements made using the apparatus shown in fig. 6(b), in which an initial ring deformation of 5mm was recorded as the strength measurement. In this case, a similar behavior is also observed. The deformation of the loop results in a smaller effective radius and an increased power loss through the bend. In both cases, the experiment was repeated several times to ensure repeatability of the measurements, but for the sake of brevity, only two runs of data are shown in this particular example.
Experimental measurements corresponding to the device shown in fig. 6(a), in which a circular loop was tested, were compared to the Marcuse and Renner model in fig. 8. In this case, the loop remains circular at all times, but the radius is reduced. A close match between theoretical and experimental results was observed, especially at ring radii of 5 to 7 mm. The theoretical model can predict the position and intensity ratio of the intermediate peak well. However, since the transmission intensity is very low, the result deviates from the predicted result of a loop radius of 5mm or less, and therefore the intensity loss between the waveguide and the coupler is relatively high. Although best efforts have been made to minimize the loss of strength, it is unavoidable under the actual conditions expected for field work. It is also expected that at smaller loop radii, the effect of the electro-optic correction factor will become apparent.
In the next validation step, the model is modified to include the effect of flexibility, and the measurements on the sensor are taken in both dynamic and static measurement modes with the apparatus shown in fig. 6 (b). In the static mode, a displacement of 0.1mm is applied to the loop and a power measurement is obtained. In the dynamic mode, the displacement and power measurements are made continuously. All these results were obtained on 5 and 6mm rings, as shown in fig. 9(a) and (b). The results show that the sensitivity of this sensor increases with decreasing loop radius, as the peak becomes sharper. The modified Renner model enables the measurements of the sensors to be closely matched. These results indicate the possibility of using the improved Renner model to predict this sensor in an application.
The light sensor designed by the corrected model can detect pressure, temperature, vibration, displacement, hydrocarbon content and the like in real time according to use requirements, can customize range and precision according to different requirements, and is mainly applied to health monitoring of structures in civil engineering structures, aerospace structures, ships and energy sources.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, it should be noted that, for those skilled in the art, many modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (9)
1. A method for designing an annular optical fiber loop of an annular loop single-mode optical fiber sensor based on a Renner correction model is characterized by comprising the following steps:
s1, establishing a power loss model of the ring-shaped loop optical fiber ring which is not deformed, wherein the power loss model comprises the following steps:
wherein l is 2 pi (R + a), and α is a bending loss coefficient;
s2, establishing a deformation equation of the annular loop optical fiber ring deformation, including determining a deformation curvature rho under polar coordinates and determining a curvature radius R (theta) of the annular loop optical fiber through the deformation curvature rho,
the curvature ρ is:
where μ (θ) is the deflection equation and varies with θ; w is the displacement of the fiber optic ring under radial force; i is the moment of inertia of the cross section of the fiber; e is the effective Young's modulus of the fiber;
the radius of curvature R (θ) is:
wherein the content of the first and second substances,
ρ′＝dρ/dθ，ρ″＝dρ/dθ2；
s3, establishing a model of the correlation between the external displacement of the optical fiber ring of the annular loop and the optical power attenuation, as follows:
wherein α is a bending loss coefficient;
s4, establishing a relative emission power loss model of the deformed loop and the undeformed loop of the annular loop optical fiber loop, as follows:
2. the method of claim 1, wherein: the bending loss coefficient α is determined by 2 α ═ Δ P/P derived from a loss equation, where P and Δ P are the power carried in the straight waveguide and the output power of the waveguide, respectively.
3. The method of claim 2, wherein: the relationship between the bending loss coefficient alpha and the shape of the loop optical fiber is modeled as follows,
wherein R isclDenotes the radius of the cladding, RcTo achieve the critical radius for total internal reflection in the core.
4. The method of claim 3, wherein: alpha is alphamarcThe formula of the calculation model of (a) is as follows,
wherein r is the radius from the origin of the ring to the outer surface of the ring;
Reis an effective bending radius, and Re1.28(R + a), R being the actual bending radius, a being the radius of the core;
k is the free-space propagation constant and,
K1(γ a) is a first order bessel function of the second type of modification;
β0the propagation constant of the leaky fundamental mode in the straight optical fiber is obtained by solving an eigenvalue equation of the guided fundamental mode;
5. A ring-shaped loop single-mode optical fiber sensor based on a Renner correction model is characterized in that the sensor is designed and formed based on the design method of any one of claims 1 to 4.
6. The fiber optic sensor of claim 5, wherein: the radius value of an optical fiber ring of an annular loop in the optical fiber sensor is 3-9 mm.
7. The fiber optic sensor of claim 6, wherein: the radius value of an optical fiber ring of an annular loop in the optical fiber sensor is 5-7 mm.
8. The fiber optic sensor of claim 6, wherein: the sensitivity of the optical fiber sensor is within the value range of the radius of the optical fiber ring of the annular loop, and is increased along with the reduction of the radius of the loop.
9. The fiber optic sensor of claim 5, wherein: the annular loop optical fiber ring of the optical fiber sensor can work in two different states, only the radius of the annular loop optical fiber ring changes and the shape of the annular loop does not change, or the acting force is applied to the annular loop optical fiber ring to enable the annular loop optical fiber ring to deform to generate a deformation displacement state.
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