“…The curvature C (defined as the inverse of bending radius R) is calculated by C = 2h/[h 2 + (L/2) 2 ], where L and h are the distance of the fixed points and the central vertical displacement of the grating, respectively. As it is known that bending of a fiber induces a refractive index perturbation that depends linearly on the distance from fiber axis, with a value of zero at the center and increasing/decreasing on the inside/outside of the bend, the coupling coefficients to cladding modes change accordingly [37]. Here, for the still symmetric TMFBG1, bending is expected to shift the centers of the mode patterns in the direction of the bend and to cause a decrease of the coupling to modes of the M = 1 family (as well as to some very weak coupling to modes of the M = 0 family since the bend-induced refractive index is asymmetric).…”
The lower order cladding mode resonances of a fiber Bragg grating (FBG) are sensitive to fiber bending but their spectral density makes their response to bending very complex. In this work we present a simple method to reduce and control the number of low order cladding mode resonances via FBGs written in a two-mode fiber (TMF) with an ultrafast laser. Owing to the larger core size of the TMF, a slight break of the cylindrical asymmetry of the grating patterns can be induced when using femtosecond side-irradiation with a small change in the writing condition. This allows us to control the mode families coupled by the grating, and in particular to those modes that have positive or negative bending responses along certain bend directions. Experimental results demonstrate that several lower-order neighboring-cladding mode pairs coupled by the asymmetric TMFBG have antagonistic loss responses (by several dB) for different bending directions, thus allowing full 2D bending measurements with many applications in shape sensing. Finally, this device has similar advantages as tilted FBGs, i.e. temperature de-correlation and the possibility of increasing the signal to noise ratio by averaging simultaneous measurements on several pairs of resonances.
“…The curvature C (defined as the inverse of bending radius R) is calculated by C = 2h/[h 2 + (L/2) 2 ], where L and h are the distance of the fixed points and the central vertical displacement of the grating, respectively. As it is known that bending of a fiber induces a refractive index perturbation that depends linearly on the distance from fiber axis, with a value of zero at the center and increasing/decreasing on the inside/outside of the bend, the coupling coefficients to cladding modes change accordingly [37]. Here, for the still symmetric TMFBG1, bending is expected to shift the centers of the mode patterns in the direction of the bend and to cause a decrease of the coupling to modes of the M = 1 family (as well as to some very weak coupling to modes of the M = 0 family since the bend-induced refractive index is asymmetric).…”
The lower order cladding mode resonances of a fiber Bragg grating (FBG) are sensitive to fiber bending but their spectral density makes their response to bending very complex. In this work we present a simple method to reduce and control the number of low order cladding mode resonances via FBGs written in a two-mode fiber (TMF) with an ultrafast laser. Owing to the larger core size of the TMF, a slight break of the cylindrical asymmetry of the grating patterns can be induced when using femtosecond side-irradiation with a small change in the writing condition. This allows us to control the mode families coupled by the grating, and in particular to those modes that have positive or negative bending responses along certain bend directions. Experimental results demonstrate that several lower-order neighboring-cladding mode pairs coupled by the asymmetric TMFBG have antagonistic loss responses (by several dB) for different bending directions, thus allowing full 2D bending measurements with many applications in shape sensing. Finally, this device has similar advantages as tilted FBGs, i.e. temperature de-correlation and the possibility of increasing the signal to noise ratio by averaging simultaneous measurements on several pairs of resonances.
“…All of these results can be understood from the basic coupling mechanism in FBGs, and TFBGs in particular. Using coupled-mode theory under weak coupling approximation, the coupling coefficient between the core mode and a cladding mode can be expressed as follows 21 :…”
Section: Resultsmentioning
confidence: 99%
“…2). As mentioned in 21 for standard FBGs, when the fiber is bent with a curvature C in direction δ, the refractive index perturbation can be written as , where k is equal to , with n the refractive i n dex, v the Poisson ratio, and P 11 and P 12 are the photoelastic constants of silica glass.…”
In this work, a compact fiber-optic 3D shape sensor consisting of two serially connected 2° tilted fiber Bragg gratings (TFBGs) is proposed, where the orientations of the grating planes of the two TFBGs are orthogonal. The measurement of the reflective transmission spectrum from the pair of TFBGs was implemented by Fresnel reflection of the cleaved fiber end. The two groups of cladding mode resonances in the reflection spectrum respond differentially to bending, which allows for the unique determination of the magnitude and orientation of the bend plane (i.e. with a ± 180 degree uncertainty). Bending responses ranging from −0.33 to + 0.21 dB/m−1 (depending on orientation) are experimentally demonstrated with bending from 0 to 3.03 m−1. In the third (axial) direction, the strain is obtained directly by the shift of the TFBG Bragg wavelengths with a sensitivity of 1.06 pm/με.
“…As shown in Fig. 7(a) , if the cross-section of the fiber is set to x-y plane, coordinate transformation allows the bent fiber to be expressed, with modified refractive index distribution 23 Figure 7 ( a ) Schematic of a circularly bent fiber, ( b ) Refractive index distribution of an unstressed (up), bent fiber (down), ( c ) E-field distribution of straight fiber, ( d ) E-field distribution of bent fiber in a certain degree, and ( e ) and ( f ) magnified schematic evolution of the fundamental mode with fiber bend (the average power of the E-field is forced to move out the fiber dip and eventually loss out fiber). …”
A highly sensitive fiber-optic accelerometer based on detecting the power output of resonances from the core dip is demonstrated. The sensing probe comprises a compact structure, hereby a short section of specific core (with a significant core dip) fiber stub containing a straight fiber Bragg grating is spliced to another single-mode fiber via a core self-alignment process. The femtosecond laser side-illumination technique was utilized to ensure that the grating inscription region is precisely positioned and compact in size. Two well-defined core resonances were achieved in reflection: one originates from the core dip and the other originates from fiber core. The key point is that only one of these two reflective resonances exhibits a high sensitivity to fiber bend (and vibration), whereas the other is immune to it. For low frequency (<10 Hz) and weak vibration excitation (<0.3 m/s2) measurement, the proposed sensor shows a much higher resolution (1.7 × 10−3 m/s2) by simply monitoring the total power output of the high-order core mode reflection. Moreover, the sensor simultaneously provides an inherent power reference to eliminate unwanted power fluctuations from the light source and transmission lines, thus providing a means of evaluating weak seismic wave at low frequency.
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