Study On The Spectral Characteristics And Sensing Properties Of Cascaded LPFG

As a transmission type optical fiber passive device,the resonant wavelength and loss peak amplitude of Long-period fiber grating(LPFG)are very sensitive to the changes of the environment.In the field of optical fiber sensing,compared with fiber Bragg grating(FBG),there is a higher sensitivity to the change of strain,temperature and environmental refractive index,and has the advantages of strong resistance to electromagnetic interference,small size,light quality,high temperature resistance,corrosion resistance,high sensitivity,high resolution and high stability.It has made a good development and application in the field of optical fiber sensing and communication,such as marine ships,large structures,aeronautics and astronautics,nuclear industry and petrochemical,electric power and so on.In this paper,the spectral characteristics of single LPFG and cascaded LPFGs were analyzed based on coupled mode theory and transfer matrix method,and simulation was carried out at the same time.Finally,the axial strain sensing characteristics of single and cascaded LPFGs were experimentally studied.The experimental results show that the loss peak amplitude of the transmission spectrum varied linearly with the change of the axial strain,and the sensitivity of the axial strain was higher.The cascaded LPFGs were embedded in the Sagnac loop higher than the directly cascaded LPFGs sensitivity.Both of them had a sensitivity of 7～8 times of a single LPFG.The main contents of this paper are as follows:1.The coupled mode equation of LPFG was derived by using the coupled mode theory.The coupling rate(t=、t×),the coupling depth(|κ|L),the effective refractive index(neff),the propagation constant(β),the resonant wavelength(λres)and the bandwidth(△λ)of the LPFG were simulated and analyzed by the Matlab model equation.The simulation results show that in the range of 0<|κ|L≤π,with the increased of the average effective refractive index modulation(δneff),the self coupling rate t= gradually decreased until δneff= 3.875×10-5,and the minimum value was zero,then gradually increased until δneff = 7.75×10-5,and the maximum value was 1,and the change of the cross coupling rate was just opposite to the change.Under the condition of under coupling,△λ of transmission spectrum was narrowed and the transmission became smaller with the increased of the grating length.Under the condition of full coupling,△λ of transmission spectrum was narrowed and the transmission became smaller with the increased of the grating length.Under the over coupling condition,△λ of transmission spectrum was narrowed and the transmittance became smaller with the increase of the grating length;△λ of transmission spectrum became narrower and the transmission became larger with the increased of the length of the grating.With the increased of the number of cladding modes,the effective refractive index neffcl of the first order of v cladding modes decreased gradually,and the effective refractive index neffco of the core model decreased linearly with the increased of the wavelength.β of core modes and the cladding modes had a good linear relationship with the wavelength.With the increased of δneff,the grating’s λres was linear red shift approximately,△λ was narrowed gradually,and the larger of δneff,the narrower the trend was.In addition,the transfer matrix method was used to simulate the influence of the parameters such as the length of the grating(L),the period(A),δneff,the DC self coupling coefficient(σ)and the AC cross coupling coefficient(κ)on the transmission spectrum in the LPFG transmission spectrum.The simulation results show that with the increased of L,△λ of transmission spectrum of grating decreased and the loss peak deepened.With the increase ofΛ of grating,the resonant peak was red shifted and △λ broadened.With the increased ofδneff,λres was red shifted,△λ of LPFG gradually decreased,the loss peak deepened,and the side bands became more obvious.With the increased of wavelength,there was almost without change of σ(as a constant).With the increase of σ,the transmission of the corresponding wavelength increased.With the increased of κ,△λ of transmission spectrum widened gradually.2.Based on the coupled mode theory and the M-Z interferometer principle,the coupling and interference mechanism of cascaded LPFGs were analyzed,and the influence of D and △neff to S was analyzed.Finally,the transmission matrix method was used to simulate the transmission spectrum.The simulation results show that the distance between the adjacent two interference peaks of the cascaded LPFGs transmission spectrum was inversely proportional to the effective refractive index difference of the grating and the center distance of D.The optimum cascade structure required the transmission of the two gratings to be 3dB and the coupling depth be|κ|L=π/4.3.The axial strain sensing characteristics of single LPFG,cascaded two LPFGs and cascade LPFGs embedded in Sagnac ring were experimentally studied.The experimental results show that with the increased of axial strain,the amplitude of the loss peak of a single LPFG became larger and the sensitivity was-1.284×10-2 dB·με-1.The amplitude of the loss peak of the transmission spectrum became larger and the sensitivity reached up to-9.174×10-2dB·με-1,when two LPFGs were cascaded,and the amplitude of the loss peak of the cascaded LPFGs embedded in the Sagnac loop was gradually increasing and the sensitivity attained-10.118×10-2 dB·με-1.The above of them had good repeatability of direction,and the sensitivity of cascaded LPFGs was 7～8 times of a single LPFG.