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摘要：采用数值计算的方法研究了了纤芯折射率对光纤Bragg光栅群时延的影响。结果表明：随着纤芯折射率的增大光纤Bragg光栅的群时延量不断减小，时延峰值产生红移，且移动的幅度较大；同时一定带宽的谐振峰两边的旁瓣加强，整体呈现递减趋势。这些规律为设计新型的光器件提供理论参考。
关键词：光纤Bragg光栅；群时延；光器件
中图分类号：TN012文献标识码：A
Influence of core index on group delay of fiber Bragg gratings
Yunbo Shang
(Gansu Construction Vocational Technical College, Lanzhou, 730050, China)
Abstract: The influence of core index on group delay of fiber Bragg gratings were investigated by numerical simulation method. The results indicate that the group delay decreases with core index increasing. The group delay curves are red-shifted and the degrees of the increasing. A certain bandwidth of resonance peaks on both sides of the side lobe. Present the downward trend. This provides theoretical basis for designing the Optical device based on fiber Bragg gratings.
Key words: fiber Bragg gratings; group delay; the Optical device
光纖Bragg光栅（FBG）作为一种新型的无源光子器件[1]，它具有损耗低、体积小、成本低、对偏振不敏感、连接简单等优点[2-3]，且通过滤波效应可实现慢光延迟器等[4] 被广泛的应用于光纤通信与传感领域中[5]，成为近十年来光学领域研究的热点之一。
1理论分析
设纤芯半径为，相对折射率差为的光纤Bragg光栅的沿z轴向的分布为 [6]
（1）
式中为纤芯折射率，为直流有效折射率的变化，为调制深度，为光栅周期。
根据耦合模理论，利用“同步近似”，在波导边界条件下，可得到基于振幅系数[7-9]的光纤Bragg光栅的群时延为[10]
（2）
2计算结果及分析
设=5，=1.06cm，N=20000，n0=1.46，=0.002，=0.0001及=1可得FBG的时延谱。保持其它参数不变，分别取纤芯折射率为1.3，1.4和1.5，通过计算可得FBG时延谱，如图1所示。可以看出，随着的增大FBG的群时延量不断减小；时延峰值波长向长波长方向移动，即产生红移，且移动的幅度较大；同时一定带宽的谐振峰两边的旁瓣加强。
图1 对FBG群时延的影响图2 时延量的最大值随的变化规律
图2更加直观的说明了随着的增大，FBG的时延量呈现出递减的趋势，且减小的幅度较大。为制作基于光纤Bragg光栅的传感器提供了理论依据。
在实际允许的参数范围限制内，当继续增大参数，将会产生更低的群时延峰。
3结论
通过以上的理论分析和数值计算讨论了纤芯半径对光纤Bragg光栅群时延的影响。结果表明：随着纤芯折射率的增大光纤Bragg光栅的群时延量不断减小；时延峰值产生红移，且移动的幅度较大；同时一定带宽的谐振峰两边的旁瓣加强，整体呈现递减趋势。
参考文献:
[1] Hill K O, Fujii Y, Johnson D C, et al. Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication [J]. Appl Phys Lett, 1978, 32(10): 647-649.
[2] Shang-Lin Hou, Yun-bo Shang, Yan-Jun Liu, Jing-li Lei, and Yongzhao Xu. Influence of Grating Period of Uniform Fiber Bragg Grating on Slow Light Delay. In: PIERS. SuZhou, 2011.
[3] Liu Chao, Pei Li, Li Zhuo-Xuan, et al. Characteristics of the fiber Bragg grating based all-fiber acousto-optic modulator[J]. Acta Physica Sinica, 2013, 62(3): 0342081-0342087.
[4] Song Minqing, Hou Shanglin, Zhang Baoxia et al. Invesrigation on slow light of photonic crystal fiber Bragg gratings[J]. Infrared and Laser Engineering, 2013, 42(6):1547-1552.
[5] Zhang Sen, Wang Zhen, Liu Menghua et al. Development and application of optical fiber sensing technology[J]. Optical Fiber ＆Electric Cable, 2007, 3(3):1-8.
[6] Erdogan T. Fiber grating spectra [J]. Lightwave Technol, 1997, 15(8): 1277-1282.
[7] Kogelnik H, Shank C V. Coupled-wave theory of distributed feedback lasers [J]. Appl Phys
Lett, 1972, 43(5): 2327-2335.
[8] Kogelnik H. Theory of optical waveguides in Guided-Wave Optoelectronics [M]. T. Tamir, Ed. New York: Springer-Verlag, 1990.
[9] Ball G A, Glenn W H, Morey W W. Programmable fiber optical delay line [J]. IEEE Photon. Technol Lett, 1994, 6(6): 741-743.
[10] Shang-Lin Hou, Yun-bo Shang, Yan-Jun Liu, Jing-li Lei, and Yongzhao Xu. Influence of Grating Period of Uniform Fiber Bragg Grating on Slow Light Delay. In: PIERS. SuZhou, 2011.
关键词：光纤Bragg光栅；群时延；光器件
中图分类号：TN012文献标识码：A
Influence of core index on group delay of fiber Bragg gratings
Yunbo Shang
(Gansu Construction Vocational Technical College, Lanzhou, 730050, China)
Abstract: The influence of core index on group delay of fiber Bragg gratings were investigated by numerical simulation method. The results indicate that the group delay decreases with core index increasing. The group delay curves are red-shifted and the degrees of the increasing. A certain bandwidth of resonance peaks on both sides of the side lobe. Present the downward trend. This provides theoretical basis for designing the Optical device based on fiber Bragg gratings.
Key words: fiber Bragg gratings; group delay; the Optical device
光纖Bragg光栅（FBG）作为一种新型的无源光子器件[1]，它具有损耗低、体积小、成本低、对偏振不敏感、连接简单等优点[2-3]，且通过滤波效应可实现慢光延迟器等[4] 被广泛的应用于光纤通信与传感领域中[5]，成为近十年来光学领域研究的热点之一。
1理论分析
设纤芯半径为，相对折射率差为的光纤Bragg光栅的沿z轴向的分布为 [6]
（1）
式中为纤芯折射率，为直流有效折射率的变化，为调制深度，为光栅周期。
根据耦合模理论，利用“同步近似”，在波导边界条件下，可得到基于振幅系数[7-9]的光纤Bragg光栅的群时延为[10]
（2）
2计算结果及分析
设=5，=1.06cm，N=20000，n0=1.46，=0.002，=0.0001及=1可得FBG的时延谱。保持其它参数不变，分别取纤芯折射率为1.3，1.4和1.5，通过计算可得FBG时延谱，如图1所示。可以看出，随着的增大FBG的群时延量不断减小；时延峰值波长向长波长方向移动，即产生红移，且移动的幅度较大；同时一定带宽的谐振峰两边的旁瓣加强。
图1 对FBG群时延的影响图2 时延量的最大值随的变化规律
图2更加直观的说明了随着的增大，FBG的时延量呈现出递减的趋势，且减小的幅度较大。为制作基于光纤Bragg光栅的传感器提供了理论依据。
在实际允许的参数范围限制内，当继续增大参数，将会产生更低的群时延峰。
3结论
通过以上的理论分析和数值计算讨论了纤芯半径对光纤Bragg光栅群时延的影响。结果表明：随着纤芯折射率的增大光纤Bragg光栅的群时延量不断减小；时延峰值产生红移，且移动的幅度较大；同时一定带宽的谐振峰两边的旁瓣加强，整体呈现递减趋势。
参考文献:
[1] Hill K O, Fujii Y, Johnson D C, et al. Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication [J]. Appl Phys Lett, 1978, 32(10): 647-649.
[2] Shang-Lin Hou, Yun-bo Shang, Yan-Jun Liu, Jing-li Lei, and Yongzhao Xu. Influence of Grating Period of Uniform Fiber Bragg Grating on Slow Light Delay. In: PIERS. SuZhou, 2011.
[3] Liu Chao, Pei Li, Li Zhuo-Xuan, et al. Characteristics of the fiber Bragg grating based all-fiber acousto-optic modulator[J]. Acta Physica Sinica, 2013, 62(3): 0342081-0342087.
[4] Song Minqing, Hou Shanglin, Zhang Baoxia et al. Invesrigation on slow light of photonic crystal fiber Bragg gratings[J]. Infrared and Laser Engineering, 2013, 42(6):1547-1552.
[5] Zhang Sen, Wang Zhen, Liu Menghua et al. Development and application of optical fiber sensing technology[J]. Optical Fiber ＆Electric Cable, 2007, 3(3):1-8.
[6] Erdogan T. Fiber grating spectra [J]. Lightwave Technol, 1997, 15(8): 1277-1282.
[7] Kogelnik H, Shank C V. Coupled-wave theory of distributed feedback lasers [J]. Appl Phys
Lett, 1972, 43(5): 2327-2335.
[8] Kogelnik H. Theory of optical waveguides in Guided-Wave Optoelectronics [M]. T. Tamir, Ed. New York: Springer-Verlag, 1990.
[9] Ball G A, Glenn W H, Morey W W. Programmable fiber optical delay line [J]. IEEE Photon. Technol Lett, 1994, 6(6): 741-743.
[10] Shang-Lin Hou, Yun-bo Shang, Yan-Jun Liu, Jing-li Lei, and Yongzhao Xu. Influence of Grating Period of Uniform Fiber Bragg Grating on Slow Light Delay. In: PIERS. SuZhou, 2011.