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LCFBG是光栅周期Λ(z)沿光栅轴向呈线性变化的啁啾光纤布拉格光栅。由于不同栅区位置处的光栅周期对应不同的布拉格反射波长,根据布拉格反射波长公式:
$$ {\lambda _D}{\text{(}}z{\text{) = }}2{n_{eff}}{{\varLambda}} (z) $$ (1) 可知,LCFBG可具有很宽的反射带宽。公式(1)中,neff为LCFBG纤芯的有效折射率,光栅周期Λ(z)
可表示为: $$ {{\varLambda}} (z){\text{ = }}{{{\varLambda}} _0} + \frac{C}{{2{n_{eff}}}}z $$ (2) 式中:Λ0为LCFBG栅区中心位置对应的初始光栅周期,啁啾系数
$C{\text{ = }}\dfrac{{{\rm{d}}{\lambda _D}}}{{{\rm{d}}z}}$ [12]。由光栅周期啁啾化引入的相移量为:$$ \frac{1}{2}\frac{{{\rm{d}}\phi }}{{{\rm{d}}z}} = - \frac{{4\pi {n_{eff}}z}}{{\lambda _D^2(z)}}\frac{{{\rm{d}}{\lambda _D}}}{{{\rm{d}}z}} = - C\frac{{4\pi {n_{eff}}z}}{{\lambda _D^2(z)}} $$ (3) 从上式可以看出,LCFBG的相移变化与有效折射率、光栅周期等参数密切相关。而这些参数对诸如温度、应力等外界条件的变化较为敏感。当温度发生变化时,光栅周期和有效折射率都将发生如下变化[13]:
$$ n_{eff}{'}{\text{ = }}{n_{eff}}{\text{ + }}\Delta {n_{eff}}{\text{ = }}{n_{eff}}(1 + \xi \Delta { T}) $$ (4) $$ {\varLambda {'}}(z) = \varLambda (z) + \Delta \varLambda {\text{ = }}\varLambda (z)(1 + \alpha \Delta { T}) $$ (5) 式中:ξ为热光系数;α为热膨胀系数;ΔT为温度变化量。同时,布拉格波长也将发生漂移:
$$ \lambda _D{'}(z) = {\lambda _D}(z) + (\alpha + \xi ){\lambda _D}(z)\Delta T $$ (6) 根据公式(3)可知,如果对LCFBG栅区某一局部位置进行加热(如图1所示),其栅区的线性啁啾特性将会被破坏,在该位置处的相移量将会发生突变。这将和啁啾相移光纤光栅一样,在其透射禁带中会产生一窄带透射峰。通过改变LCFBG局部加热点的位置z、温度
ΔT、宽度ΔL和数量等参数,其透射禁带中透射峰的透射率、中心波长、带宽以及透射峰个数亦将随之发生变化。 -
根据上述理论分析,采用光纤光栅传输矩阵法,对局部点加热的LCFBG输出光谱特性进行了理论模拟。设定宽带高反LCFBG栅区中心位置对应的布拉格波长λ0=1550 nm,栅区长度L=15 mm,有效折射率neff=1.453,啁啾系数C=2 nm/cm,此时透射禁带宽度约为2.45 nm(不是透射谱带宽)。需要说明的是,在数值模拟过程中,没有考虑在LCFBG栅区局部加热位置两侧存在的热传导现象。
当对LCFBG栅区中心位置处进行局部点加热,且加热宽度ΔL=0.25 mm时,在温度变化
ΔT分别为110 ℃、135 ℃和150 ℃的情况下,其透射光谱图如图2(a)所示。从图中可以看出,当ΔT在135 ℃附近时,温度变化引起的相移突变量Δφ接近π,窄带透射峰的透射率接近100%,且其中心波长位于LCFBG透射禁带的中心位置附近。随着温度变化量 ΔT增大,该窄带透射峰的中心波长将向长波长方向移动,且由于相移突变量Δφ具有周期性,透射峰中心波长将在小于透射禁带宽度的一定范围(Δλ=0.34 nm)内,随ΔT以周期约为225 ℃的规律变化。同时,窄带透射峰的透射率以相同的温度变化周期发生规律性变化,如图2(b)所示。该周期的大小主要受加热宽度ΔL的影响,如图2(c)所示。随着加热宽度的增加,该周期值逐渐减小,且减小趋势逐渐平缓,而窄带透射峰在透射禁带范围内的扫描范围 Δλ基本上不随加热宽度的增加而发生变化。 图 2 (a)
ΔL=0.25 mm,不同ΔT时的LCFBG透射谱;(b) ΔL=0.25 mm时,窄带透射峰中心波长和透射率与ΔT之间的变化关系;(c)窄带透射峰中心波长(或透射率)的变化周期及其中心波长扫描范围与ΔL之间的关系 Figure 2. (a) Transmission spectrum of LCFBG under the different temperature changes ΔT and ΔL=0.25 mm; (b) Central wavelength and transmittance of narrow-band transmission peaks versus ΔT under ΔL=0.25 mm; (c) Period and scanning range of the central wavelength (or transmittance) of narrow-band transmission peaks versus ΔL
图3(a)为加热位置仍在LCFBG栅区中心位置处,温度变化ΔT=135 ℃时,不同加热宽度ΔL对应的透射谱。透射峰的中心波长随着加热宽度的增加而在LCFBG透射禁带中较小范围内发生红移。当加热宽度ΔL=0.25 mm时,透射峰的透射率接近100%,且其对应的中心波长处于透射禁带的中心位置附近。在此条件下,加热宽度每改变大约0.45 mm,透射峰中心波长和透射率均完成一次周期性变化,如图3(b)所示。该周期的大小随着加热温度变化量
ΔT的增加而逐渐减小,如图3(c)所示。 图 3 (a) ΔT=135 ℃,ΔL为不同值时LCFBG的透射谱;(b) ΔT=135 ℃时,窄带透射峰中心波长和透射率与加热宽度之间的变化关系;(c) 窄带透射峰中心波长(或透射率)的变化周期与ΔT之间的关系
Figure 3. (a) Transmission spectrum of LCFBG under the different heating width ΔL and ΔT=135 ℃; (b) Central wavelength and transmittance of narrow-band transmission peaks versus ΔL; (c) Period of the central wavelength (or transmittance) of narrow-band transmission peaks versus
ΔT 由上述数值模拟结果可知,无论是改变温度变化量ΔT,还是改变加热宽度ΔL,主要都是影响LCFBG栅区被加热部分的相移突变量Δφ。而由Δφ的变化引起的透射峰波长的漂移,其变化范围明显小于透射禁带的宽度。
当加热宽度
ΔL=0.25 mm,温度变化ΔT=135 ℃时,对距LCFBG栅区一端z=6.5 mm、7.5 mm和8.5 mm处分别进行加热,其透射光谱如图4(a)所示。当加热位置位于LCFBG栅区中心时,其窄带透射峰中心波长亦位于透射禁带的中间位置,而当局部加热点分别位于栅区中心两侧对称位置时,其产生的透射峰亦相对于透射禁带中心呈对称分布。若在LCFBG整个栅区范围改变加热位置,则可在整个透射禁带范围内实现窄带透射峰,其中心波长与加热位置呈现线性变化规律,如图4(b)所示。除在LCFBG栅区边缘位置外,加热位置的变化对窄带透射峰的透射率影响较小。LCFBG啁啾系数C的大小决定了透射峰波长随加热位置的变化速率。从图4(b)可知,对啁啾系数较大的LCFBG栅区进行局部点加热,可实现窄带透射峰波长的快速调谐。而若想实现窄带透射峰波长的精细调谐,则LCFBG的啁啾系数要较小。 图 4 (a)局部加热点的中心位置距LCFBG栅区一端6.5 mm、7.5 mm和8.5 mm时的LCFBG透射谱;(b)窄带透射峰中心波长和透射率与加热位置的关系
Figure 4. (a) Transmission spectrum of LCFBG under the local heating points located at 6.5 mm,7.5 mm and 8.5 mm from one end of the LCFBG, respectively; (b) Central wavelength and transmittance of transmission peaks versus heating position
Investigation of the spectral characteristics of a linearly chirped fiber Bragg grating with local point heating
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摘要: 对线性啁啾光纤光栅(LCFBG)进行局部点加热时,在不同加热温度、加热宽度和加热位置情况下的输出光谱特性进行了研究。通过数值模拟发现,改变栅区局部加热点的温度和宽度,对透射禁带中窄带透射峰的透射率有较为明显的影响,其透射峰的中心波长也将会发生一定的漂移;透射峰的中心波长与栅区局部加热点的位置存在线性对应关系,且透射峰波长变化范围可覆盖整个透射禁带;LCFBG啁啾系数的大小,决定了改变加热位置导致的透射峰波长的调谐速率。基于理论研究结果,以热敏打印头的加热阵列为加热源,对LCFBG栅区进行局部点加热时的输出光谱特性进行了实验研究,得到了重复性和稳定性都较好、可多波长调谐的窄带透射峰。在实验误差范围内,实验结果与数值模拟得到的结论较为一致。Abstract: The output spectrum characteristics of a linearly chirped fiber Bragg grating (LCFBG) under localized point heating with different heating temperatures, widths and positions were investigated. The numerical simulation shows that the heating temperature and heating width applied onto the LCFBG have an obvious influence on the transmissivity and central wavelength of narrow-band transmission peaks in the transmission bandgap. The central wavelengths of the transmission peaks have a good linear relationship with the local heating positions of the LCFBG and can shift in the whole transmission bandgap region. The chirp coefficient of the LCFBG determines the wavelength tuning velocity of the transmission peaks induced by the change in the heating position. Based on the theoretical results, the spectral characteristics of the LCFBG are investigated experimentally using a commercial thermal printhead as a local heating source. The narrow-band transmission peaks are realized with high performance in terms of reproducibility, stability and potential multiwavelength tunability. The experimental results are in good agreement with those of the numerical simulation within the experimental error.
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图 2 (a)
ΔL=0.25 mm,不同ΔT时的LCFBG透射谱;(b) ΔL=0.25 mm时,窄带透射峰中心波长和透射率与ΔT之间的变化关系;(c)窄带透射峰中心波长(或透射率)的变化周期及其中心波长扫描范围与ΔL之间的关系 Figure 2. (a) Transmission spectrum of LCFBG under the different temperature changes ΔT and ΔL=0.25 mm; (b) Central wavelength and transmittance of narrow-band transmission peaks versus ΔT under ΔL=0.25 mm; (c) Period and scanning range of the central wavelength (or transmittance) of narrow-band transmission peaks versus ΔL
图 3 (a) ΔT=135 ℃,ΔL为不同值时LCFBG的透射谱;(b) ΔT=135 ℃时,窄带透射峰中心波长和透射率与加热宽度之间的变化关系;(c) 窄带透射峰中心波长(或透射率)的变化周期与ΔT之间的关系
Figure 3. (a) Transmission spectrum of LCFBG under the different heating width ΔL and ΔT=135 ℃; (b) Central wavelength and transmittance of narrow-band transmission peaks versus ΔL; (c) Period of the central wavelength (or transmittance) of narrow-band transmission peaks versus
ΔT 图 4 (a)局部加热点的中心位置距LCFBG栅区一端6.5 mm、7.5 mm和8.5 mm时的LCFBG透射谱;(b)窄带透射峰中心波长和透射率与加热位置的关系
Figure 4. (a) Transmission spectrum of LCFBG under the local heating points located at 6.5 mm,7.5 mm and 8.5 mm from one end of the LCFBG, respectively; (b) Central wavelength and transmittance of transmission peaks versus heating position
图 6 (a)热敏打印头4个区域同时工作时的红外热成像图;(b)加热阵列上某一工作区域在不同加热宽度和不同加热占空比情况下的温度变化曲线
Figure 6. (a) Infrared thermal imaging of four heating regions on the thermal printhead with a duty ratio of 90%; (b) Temperature curves of one heating region with different consecutive heating elements on the heating array versus heating duty ratio
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