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The theoretical derivation of optical time-domain fractional Fourier transformation is achieved and implemented. Based on the understanding of fractional Fourier transformation, we propose a new method for analyzing the influence of combined effects of dispersion and self-phase modulation on the propagation of optical pulses. And the simulation results show that when the dispersion is dominant in the transmission, a fractional Fourier transformation with a negative order number will help reduce the broadening of optical pulses induced by the dispersion. On the other hand, when the self-phase modulation is dominant, a positive order fractional Fourier transmission can help eliminate the pulse splitting effect.
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Keywords:
- optical propagation /
- fractional fourier transformation /
- dispersion /
- self-phase modulation
[1] Agrawal G P 2001 Nonlinear Fiber Optics 3rd edition
[2] Sano A, Miyamoto Y, Kuwahara S, Toba H 2000 J. Lightwave Technol. 18 1519
[3] Green A G, Mitra P P, Wegener L G L 2003 Opt. Lett. 28 2455
[4] Hayase S, Kikuchi N, Sekine K, Sasaki S 2004 OSA/OFC ThM3
[5] Shen S, Chang C C, Sardesai H P, Binjrajka V, Weiner A M 1999 J. Lightwave Technol. 17 452
[6] Schimpf D N, Seise E, Limpert J, Tünnermann A 2009 Opt. Express 17 4997
[7] Nakazawa M, Hirooka T 2005 J. Opt. Soc. Am. B 22 1842
[8] Ng T T, Parmigiani F, Ibsen M, Zhang Z W, Petropoulos P, Richardson D J 2008 IEEE Photon. Technol. Lett. 20 1097
[9] Teng S Y, Cheng C F, Liu M, Liu L R, Xu Z Z 2003 Acta Phys. Sin. 52 316 (in Chinese) [藤树云、程传福、刘 曼、刘 立人、徐至展 2003 52 316] 〖10] Pei L, Ning T G, Li T J, Dong X W, Jian S S 2005 Acta Phys. Sin. 54 1630 (in Chinese) [裴 丽、宁提纲、李唐军、董小伟、简水生 2005 54 1630]
[10] Li Q L, Li Q S, Lin L B 2006 Chin. Phys. 15 2306
[11] Zhang J Z, Wang Y C, Wang A B 2008 Chin. Phys. B 17 3264
[12] Essiambre R J, Agrawal G P 1995 J. Opt. Soc. Am. B 12 2420
[13] Hanna M, Porte H, Goedgebuer J P, Rhodes W T 1999 Opt. Lett. 24 732
[14] Liu J S 2004 Acta Phys. Sin. 53 3014 (in Chinese) [刘劲松 2004 53 3014]
[15] Almeida L B 1994 IEEE Trans on Signal Processing 42 3084
[16] Li W, Qiao Y J, Han Q S, Zhang H 2009 Chin. Opt. Lett. 7 679
[17] Sinkin O V, Holzlhner R, Zweck J, Menyuk C R 2003 J. Lightwave. Technol. 21 61
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[1] Agrawal G P 2001 Nonlinear Fiber Optics 3rd edition
[2] Sano A, Miyamoto Y, Kuwahara S, Toba H 2000 J. Lightwave Technol. 18 1519
[3] Green A G, Mitra P P, Wegener L G L 2003 Opt. Lett. 28 2455
[4] Hayase S, Kikuchi N, Sekine K, Sasaki S 2004 OSA/OFC ThM3
[5] Shen S, Chang C C, Sardesai H P, Binjrajka V, Weiner A M 1999 J. Lightwave Technol. 17 452
[6] Schimpf D N, Seise E, Limpert J, Tünnermann A 2009 Opt. Express 17 4997
[7] Nakazawa M, Hirooka T 2005 J. Opt. Soc. Am. B 22 1842
[8] Ng T T, Parmigiani F, Ibsen M, Zhang Z W, Petropoulos P, Richardson D J 2008 IEEE Photon. Technol. Lett. 20 1097
[9] Teng S Y, Cheng C F, Liu M, Liu L R, Xu Z Z 2003 Acta Phys. Sin. 52 316 (in Chinese) [藤树云、程传福、刘 曼、刘 立人、徐至展 2003 52 316] 〖10] Pei L, Ning T G, Li T J, Dong X W, Jian S S 2005 Acta Phys. Sin. 54 1630 (in Chinese) [裴 丽、宁提纲、李唐军、董小伟、简水生 2005 54 1630]
[10] Li Q L, Li Q S, Lin L B 2006 Chin. Phys. 15 2306
[11] Zhang J Z, Wang Y C, Wang A B 2008 Chin. Phys. B 17 3264
[12] Essiambre R J, Agrawal G P 1995 J. Opt. Soc. Am. B 12 2420
[13] Hanna M, Porte H, Goedgebuer J P, Rhodes W T 1999 Opt. Lett. 24 732
[14] Liu J S 2004 Acta Phys. Sin. 53 3014 (in Chinese) [刘劲松 2004 53 3014]
[15] Almeida L B 1994 IEEE Trans on Signal Processing 42 3084
[16] Li W, Qiao Y J, Han Q S, Zhang H 2009 Chin. Opt. Lett. 7 679
[17] Sinkin O V, Holzlhner R, Zweck J, Menyuk C R 2003 J. Lightwave. Technol. 21 61
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