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A novel theory, namely, Fourier mode coupling (FMC) theory for fiber Bragg gratings (FBGs) is proposed in this paper. During analyzing coupled modes of FBGs, the Fourier transform relations among the amplitude coefficients of coupled modes are found for the first time. The general expressions of reflective and transmissive spectra of FBGs are deduced from the combination of Fourier transform with the well-known coupled-mode theory. In the proposed FMC theory, the spectral characteristics of the FBG are achieved by the calculation of coupled modes in the spatial domain spectrum, which is the Fourier transform result of refractive index perturbation in the FBG. The FBG spectrum based on the FMC theory is simulated here, and compared with those obtained from the coupled mode theory and pure Fourier transform. The comparison shows that the FMC theory for and the derived spactra of FBGs are in accordance with the coupled mode theory and the practical spectra of the FBG respectively. The FMC theory has many features, these being simple, clear, direct, accurate and fast, which could be used as a universal tool for fast spectrum analysis of any FBG with an arbitrary distribution of refractive index perturbation along the fiber axis.
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Keywords:
- fiber-optic component /
- fiber Bragg grating /
- Fourier mode coupling /
- spectral characteristics
[1] Lam D K W, Garside B K 1981 Appl. Opt. 20 440
[2] Yamada M, Sakuda K 1987 Appl. Opt. 26 3474
[3] Poladian L 1993 Phys. Rev. E 48 4758
[4] Bouzid A, Abushagur M A G 1997 Appl. Opt. 36 558
[5] Peral E, Capmany J 1997 J. Lightwave Technol. 15 1295
[6] Kogelnik H 1976 Bell Sys. Tech. J. 55 109
[7] Kogelnik H 1990 Theory of Optical Waveguides in Guided-wave Optoelectronics (Berlin: Springer-Verlag)
[8] Erdogan T, Sipe J E 1996 J. Opt. Soc. Am. A 13 296
[9] Erdogan T 1997 J. Opt. Soc. Am. A 14 1760
[10] Erdogan T 1997 J. Lightwave Technol. 15 1277
[11] Lee K S, Erdogan T 2001 Electron. Lett. 37 156
[12] Wang Y H, Ren W H, Liu Y, Tan Z W, Jian S S 2008 Acta Phys. Sin. 57 363 (in Chinese) [王燕花、任文华、刘 艳、谭中伟、简水生 2008 57 363]
[13] Qiu K, Wu B J, Wen F 2009 Acta Phys. Sin. 58 1726 (in Chinese) [邱 昆、武保剑、文 峰 2009 58 1726]
[14] Wang M G, Wei H, Jian S S 2003 Acta Phys. Sin. 52 609 (in Chinese) [王目光、魏 淮、简水生 2003 52 609]
[15] Shu X W, Huang D X, Deng G H, Shi W, Jiang S 2000 Acta Phys. Sin. 49 1731 (in Chinese) [舒学文、黄德修、邓桂华、施 伟、江 山 2000 49 1731]
[16] Ouellette F, Cliche J F, Gagnon S 1994 J. Lightwave Technol. 12 1728
[17] Weller-Brophy L A, Hall D G 1985 J. Opt. Soc. Am. A 2 864
[18] Weller-Brophy L A, Hall D G 1988 Appl. Opt. 27 963
[19] Kashyap R 1999 Fiber Bragg Gratings (San Diego: Academic Press)
[20] Zheng J L, Wang R, Fang T, Lu L, Pu T, Chen X F 2009 Acta Phys. Sin. 58 7017 (in Chinese) [郑吉林、王 荣、方 涛、卢 麟、蒲 涛、陈向飞 2009 58 7017]
[21] Mazzetto E, Someda C G, Acebron J A, Spigler R 2005 Opt. Quantum Electron. 37 755
[22] Marcuse D 1974 Theory of Dielectric Optical Waveguide (New York: Academic Press)
[23] Fang J X, Cao Z Q, Yang F Z 1987 Physical Foundation of Optical Waveguide Technology (Shanghai: Shanghai Jiaotong University Press)(in Chinese)[方俊鑫、曹庄琪、杨傅子 1987光波导技术物理基础 (上海:上海交通大学出版社)]
[24] Shu X W 2000 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [舒学文 2000 博士学位论文 (武汉:华中理工大学)]
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[1] Lam D K W, Garside B K 1981 Appl. Opt. 20 440
[2] Yamada M, Sakuda K 1987 Appl. Opt. 26 3474
[3] Poladian L 1993 Phys. Rev. E 48 4758
[4] Bouzid A, Abushagur M A G 1997 Appl. Opt. 36 558
[5] Peral E, Capmany J 1997 J. Lightwave Technol. 15 1295
[6] Kogelnik H 1976 Bell Sys. Tech. J. 55 109
[7] Kogelnik H 1990 Theory of Optical Waveguides in Guided-wave Optoelectronics (Berlin: Springer-Verlag)
[8] Erdogan T, Sipe J E 1996 J. Opt. Soc. Am. A 13 296
[9] Erdogan T 1997 J. Opt. Soc. Am. A 14 1760
[10] Erdogan T 1997 J. Lightwave Technol. 15 1277
[11] Lee K S, Erdogan T 2001 Electron. Lett. 37 156
[12] Wang Y H, Ren W H, Liu Y, Tan Z W, Jian S S 2008 Acta Phys. Sin. 57 363 (in Chinese) [王燕花、任文华、刘 艳、谭中伟、简水生 2008 57 363]
[13] Qiu K, Wu B J, Wen F 2009 Acta Phys. Sin. 58 1726 (in Chinese) [邱 昆、武保剑、文 峰 2009 58 1726]
[14] Wang M G, Wei H, Jian S S 2003 Acta Phys. Sin. 52 609 (in Chinese) [王目光、魏 淮、简水生 2003 52 609]
[15] Shu X W, Huang D X, Deng G H, Shi W, Jiang S 2000 Acta Phys. Sin. 49 1731 (in Chinese) [舒学文、黄德修、邓桂华、施 伟、江 山 2000 49 1731]
[16] Ouellette F, Cliche J F, Gagnon S 1994 J. Lightwave Technol. 12 1728
[17] Weller-Brophy L A, Hall D G 1985 J. Opt. Soc. Am. A 2 864
[18] Weller-Brophy L A, Hall D G 1988 Appl. Opt. 27 963
[19] Kashyap R 1999 Fiber Bragg Gratings (San Diego: Academic Press)
[20] Zheng J L, Wang R, Fang T, Lu L, Pu T, Chen X F 2009 Acta Phys. Sin. 58 7017 (in Chinese) [郑吉林、王 荣、方 涛、卢 麟、蒲 涛、陈向飞 2009 58 7017]
[21] Mazzetto E, Someda C G, Acebron J A, Spigler R 2005 Opt. Quantum Electron. 37 755
[22] Marcuse D 1974 Theory of Dielectric Optical Waveguide (New York: Academic Press)
[23] Fang J X, Cao Z Q, Yang F Z 1987 Physical Foundation of Optical Waveguide Technology (Shanghai: Shanghai Jiaotong University Press)(in Chinese)[方俊鑫、曹庄琪、杨傅子 1987光波导技术物理基础 (上海:上海交通大学出版社)]
[24] Shu X W 2000 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [舒学文 2000 博士学位论文 (武汉:华中理工大学)]
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