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Effect of frequency chirping on supercontinuum generation in dispersion flatted and dispersion decreasing fiber
Physics Letters A 333 (2004) 415–419 www.elsevier.com/locate/pla
Effect of frequency chirping on supercontinuum generation in dispersion flatted and dispersion decreasing fiber ✩ Jin Wei ∗ , Xu Wencheng, Chen Zhaoxi, Xu Yongzhao, Yu Bingtao, Cui Hu, Liu Songhao Institute of Quantum Electronics, South China Normal University, Guangzhou 510631, China Received 26 April 2004; received in revised form 29 October 2004; accepted 1 November 2004 Available online 11 November 2004 Communicated by A.P. Fordy
Abstract The effect of frequency chirping on supercontinuum (SC) generation in dispersion flatted and dispersion decreasing fiber has been studied by numerical simulation based on the total field nonlinear Schrödinger equation. Our results show that a positive initial frequency chirp can significantly broaden the supercontinuum spectrum by up to approximate 80 nm, and the SC intensity increase about 5 dB. A range of optimal positive frequency chirps is identified to obtain the maximized supercontinuum bandwidth. The mechanism of this enhancement is also discussed detailedly through the evolutions of temporal and spectral width related to different pre-chirped pulses. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Tg; 42.65.Re Keywords: Supercontinuum; Frequency chirp; Dispersion flatted and dispersion decreasing fiber
Generation of supercontinuum (SC) in optical fibers is a promising method to obtain ultrashort pulses over a wide spectral range, which has great potential for many applications such as optical metrology, spectroscopy, biomedical optics, and optical communications, especially in the OTDM and DWDM systems [1]. Recently, generation of supercontinuum in special designed fibers such as dispersion shifted fiber (DSF) [2], dispersion decreasing fiber (DDF) [3], dispersion flatted fiber (DFF) [4], photonic crystal fibers [5,6] and tapped fibers [7], becomes attractive methods. It is shown that dispersion flatted and dispersion decreasing fiber (DFDF) is quite appropriate ✩ Supported by the Excellent Teacher Foundation of Guangdong Province (Q02084) and Natural Science Foundation of Guangdong Province (No. 980030). * Corresponding author. E-mail address: [email protected] (W. Jin).
0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.11.003
416
W. Jin et al. / Physics Letters A 333 (2004) 415–419
for generating SC pulses with a flatly broadened spectrum, which is therefore regarded as the most utilizable SC source for optical communication system [8–10]. Several schemes focused on the SC generation in DFDF provide detailed discussion about the effects of input pulse parameter and fiber characteristics on the SC bandwidth and flatness. It is clearly seen that the initial chirp of the input pulse has a significant effect on pulse evolution in fibers. Z. Zhu et al. have discussed the effect of frequency chirping on SC generation in photonic crystal fibers and found that the initial linear chirp increases the SC bandwidth and improves the coherence [6]. Wu Yue et al. found that the SC bandwidth reduces by both the positive and negative frequency chirps in DDF [3]. However, to our best knowledge, no detailed report has been found that discusses the influence of initial frequency chirp on the generation of supercontinuum in DFDF. In this Letter, we analyzed the effects of frequency chirp on SC generation in DFDF. The results show that a positive frequency chirp can significantly broaden the supercontinuum spectrum. Considering the wideband spectrum of supercontinuum pulses, we use the total field Schrödinger equation instead of temporal Schrödinger equation to model the pulse propagation inside the DFDF fibers [8,9,11–13]. ∂Atotal(z, Ω) = −i∆(Ω)Atotal(z, Ω) ∂z − Γ (Ω)Atotal(z, Ω) 2 Ω −i 1+ Qker r FT Ω Atotal(z, τ )Atotal(z, τ ) ω0 2 Ω SRaman FT Ω Atotal(z, τ ) . −i 1+ QRaman FT Ω Atotal(z, τ ) × FT −1 τ ω0
(1)
Where Atotal(z, τ ) is the electric field amplitude, z is the longitudinal along the fiber, τ = t − z/Vg , Vg represent the group velocity of the wave with a frequency of ω0 in the fiber. Atotal(z, Ω) is the Fourier transform of Atotal(z, τ ). FT Ω stands for direct Fourier transform and FT −1 τ for the inverse Fourier transform. On the right-hand side of Eq. (1), the first line second line represents the linear part of the system, including dispersion and fiber loss. ∆(Ω) is the fiber dispersion which can be described as: ∆(Ω) =
∞
(k) Ω
β0
k
k!
k=2
,
(k)
β0 =
dkβ (ω0 ). dωk
The second and third lines are responsible for nonlinear effects: the former originates from Kerr-effect and the latter from stimulated Raman scattering (SRS). Where (3)
Qker r =
ω0 3χ1111 cµ0 Pscale , c n0 4n0 Aeff
QRaman =
Pscale ω0 GRaman . c Aeff
(3) And χ1111 is the (1, 1, 1, 1) components of the Kerr susceptibility sensor, GRaman is the Raman gain coefficient factor. Aeff = πω2 , where ω is the spot size of the best Gaussian approximation for the field ψ(r). The profile and distribution of chromatic dispersion in an optical fiber and the intensity and duration of the optical pump pulse are very important to the SC generation. Here we introduce an idealized dispersion characteristic in a DFDF, chromatic dispersion D(λ, z) expressed as: z 2 , D(λ, z) = −k(λ − λ0 ) + Dmax 1 − (2) z0
where k has a negative value in the case of a convex dispersion profile and Dmax is the peak value at the input. Length z0 is defined as the propagation distance after which the chromatic dispersion becomes negative (normal dispersion) at all wavelengths. In this Letter, we assume k = 0.0001 ps/(nm3 /km), Dmax = 6 ps/nm/km, z0 = dkβ 2πc 600 m and fiber length z = 720 m. According to βk = dω k |ω=ωc , ω = λ , λ = λ0 = 1550 nm, the GVD coefficients
W. Jin et al. / Physics Letters A 333 (2004) 415–419
417
derivatives as follows:
λ20 z Dmax 1 − , 2πc z0 λ30 z β3 (λ0 , z) = 2D 1 − , max (2πc)2 z0 λ40 z 2 6Dmax 1 − − 2kλ0 , β4 (λ0 , z) = − (2πc)3 z0 λ50 z 2 β5 (λ0 , z) = 24D 1 − − 24kλ max 0 . (2πc)4 z0
β2 (λ0 , z) = −
The input pulses are assumed to have the form
Cτ 2 τ A(0, τ ) = P0 sech exp −i 2 , T0 2T0
(3) (4) (5) (6)
(7)
where P0 is the peak power, T0 is related to the full wave half maximum (FWHM) of the input pulse by TFWHM ≈ 1.763T0, and C is the parameter representing the initial linear frequency chirp. The specific values of other parameters used in simulation are given as follows: Aeff = 50 µm2 , n2 = 3.2 × 10−20 m2 /W, P0 = 2.23 W, TFWHM = 4 ps. Fig. 1 shows the SC spectrum curves when the chirp coefficient C takes the values of −1.0, 0 and 1.5 with the corresponding SC spectral widths of 8, 221 and 303 nm. We notice that the intensity of SC spectrum in the case of C = 1.5 is higher than that without initial chirp though the flatness is diminished slightly. The spectrum related to negative chirp is neither broad nor flatness. The SC bandwidth broadens from 221 nm (C = 0) to 303 nm (C = 1.5) by imposing an initial frequency chirp on the input pulses. Fig. 2 plots the 27-dB SC bandwidth as a function of chirp parameter C. We notice that there is a wide range of optimal positive chirp that maximizes the SC bandwidth, in this case it is approximately from 1 to 2. And the pulse could not evolve into SC spectrum in the case of negative chirp or larger positive chirp. It is interesting that this dependence of SC bandwidth on C is quite different from that in dispersion decreasing fibers, where the SC bandwidth reduces by the frequency chirp (both positive and negative). To better understand how initial chirp influence the pulse compression and accordingly why there is a wide range of optimal positive chirp that maximizes the SC bandwidth, we plot temporal and spectral width of the pulse on a function of propagating distance with initial chirp as −1.0, 0, 1.5, 2.5, as displayed in Fig. 3.
Fig. 1. SC spectrum curves with different frequency chirp C.
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W. Jin et al. / Physics Letters A 333 (2004) 415–419
Fig. 2. 27-dB SC bandwidth as a function of the chirp coefficient.
(a)
(b)
Fig. 3. (a) Temporal width on a function of propagating distance with different chirp. (b) Spectral width on a function of propagating distance with different chirp.
Consider the solid curves that represent the pulse without initial chirp. We can see that the pulse width reduces monotonously with the propagating distance before the point of 600 m and becomes wide after that point due to optical wave breaking, while spectrum broadens drastically near the point of 600 m. This can be understood as fallows. SC generation in fused-silica optical fiber is regarded as the result of two constituent processes: pulse compression and spectral shaping. Pulse compression creates the high peak powers necessary to achieve significant nonlinear action in fibers. Spectral shaping results from the combined effects of pulse shape evolution with propagation and the generation of new spectral components by high-intensity portions of the pulse through nonlinearities. In the case of negative chirp as showed in Fig. 3 in dot curves, the pulse width increases slightly at a distance of about 100 m and then decreases to approximate 1.5 ps at the distance of 600 m, while the spectrum width almost remains as narrow as input. The reason is that at the initial stage of propagation, the interplay of initial chirp and dispersion dominates the pulse due to the relatively high dispersion and low nonlinearity. When an optical pulse is negatively chirped, the frequency at its leading edge is higher than that at its trailing edge. In the condition of β2 < 0, the initial chirp adds to the dispersion-induced chirp. As a result, the net chirp is enhanced leading to pulse broadening. With a further increase in propagation distance, the |β2 | decreases and the nonlinear compression becomes the crucial effect on the pulse. And therefore the pulse width decreases. But both the compression and the SC generation are not satisfied due to the initial broadening of the pulse width.
W. Jin et al. / Physics Letters A 333 (2004) 415–419
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In contrast, as for the dash curves which corresponding to the pulse with an initial positive chirp of 1.5, we notice that the pulse width is always narrower and the spectrum width is always broader than that without chirping along the whole propagating distance. When an optical pulse is positively chirped, the frequency at its leading edge is lower than that at its trailing edge. In the condition of β2 < 0, the initial chirp compensates the dispersion-induced chirp and enhances the chirp created by SPM. As a result the initial pulse compression is enhanced and higher peak power is obtained, and thus a broader and stronger SC spectrum is generated. The dot-dash curves correspond to a positive chirp of 2.5. In this case, the large positive chirp over compensates the dispersion-induced chirp at the initial stage of propagation where the dispersion is relatively high and thus the chirp created by SPM is small correspondingly. And therefore the pulse width decreases rapidly at a distance before 250 m, and increases slightly during the distance of 250 to 450 m. After that, the domination of dispersioninduced chirp gives way to the chirp created by SPM, and the pulse width decrease correspondingly. But the final compression and broadening of spectrum is not satisfied due to the undulation in the compressing process. According to the descriptions above, we can see the different chirped pulses have different SC spectral and temporal width evolutions in the DFDF. When the pump pulse has a negative or too large positive chirp, the pulse will not be compressed properly, and therefore cannot evolve into SC pulse, while a slight positive chirp can enhance the compression and force the pulse to generate a broader spectrum. In other words, there must be an optimal chirp that can best help to compress the pulse and generate the widest spectrum. In inclusion, we have studied the effects of initial linear chirp on the SC generation in DFDF. The results show that a proper positive chirp can significantly enhance the SC generation. We have also analyzed the relationship between the SC bandwidth and the chirp coefficient and found that there is a wide range of optimal positive chirps which can maximize the SC bandwidth. The evolution of pulse width and spectrum width is shown and the mechanism is discussed that the initial chirp broadens the SC spectrum.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
H. Sotobayashi, W. Chujo, A. Konishi, T. Ozeki, J. Opt. Soc. Am. B 19 (11) (2002) 2803. A. Mussot, T. Sylvestre, L. Provino, H. Maillotte, Opt. Lett. 28 (19) (2003) 1820. Y. Wu, C.-Y. Lou, M. Han, T. Wang, Y.-Z. Gao, Chin. Phys. 11 (2002) 578. F. Futami, et al., IEICE Trans. Electron. E82-C (1999) 1531. N.I. Nikolov, T. Srensen, O. Bang, A. Bjarklev, J. Opt. Soc. Am. B 20 (11) (2003) 2329. Z. Zhu, T.G. Brown, Opt. Exp. 12 (4) (2004) 689. W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, P.St.J. Russell, J. Opt. Soc. Am. B 19 (9) (2002) 2148. K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, T. Morioka, Electron. Lett. 33 (1997) 1806. K. Mori, H. Takara, S. Kawanishi, J. Opt. Soc. Am. B 18 (12) (2001) 1780. T. Okuno, M. Onishi, M. Nishimura, IEEE Photon. Technol. Lett. 10 (1) (1998) 72. B. Gross, J.T. Manassah, J. Opt. Soc. Am. B 9 (1992) 1813. G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, New York, 1995. P.L. Francois, J. Opt. Soc. Am. B 8 (2) (1991) 276.
Effect of frequency chirping on supercontinuum generation in dispersion flatted and dispersion decreasing fiber ✩ Jin Wei ∗ , Xu Wencheng, Chen Zhaoxi, Xu Yongzhao, Yu Bingtao, Cui Hu, Liu Songhao Institute of Quantum Electronics, South China Normal University, Guangzhou 510631, China Received 26 April 2004; received in revised form 29 October 2004; accepted 1 November 2004 Available online 11 November 2004 Communicated by A.P. Fordy
Abstract The effect of frequency chirping on supercontinuum (SC) generation in dispersion flatted and dispersion decreasing fiber has been studied by numerical simulation based on the total field nonlinear Schrödinger equation. Our results show that a positive initial frequency chirp can significantly broaden the supercontinuum spectrum by up to approximate 80 nm, and the SC intensity increase about 5 dB. A range of optimal positive frequency chirps is identified to obtain the maximized supercontinuum bandwidth. The mechanism of this enhancement is also discussed detailedly through the evolutions of temporal and spectral width related to different pre-chirped pulses. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Tg; 42.65.Re Keywords: Supercontinuum; Frequency chirp; Dispersion flatted and dispersion decreasing fiber
Generation of supercontinuum (SC) in optical fibers is a promising method to obtain ultrashort pulses over a wide spectral range, which has great potential for many applications such as optical metrology, spectroscopy, biomedical optics, and optical communications, especially in the OTDM and DWDM systems [1]. Recently, generation of supercontinuum in special designed fibers such as dispersion shifted fiber (DSF) [2], dispersion decreasing fiber (DDF) [3], dispersion flatted fiber (DFF) [4], photonic crystal fibers [5,6] and tapped fibers [7], becomes attractive methods. It is shown that dispersion flatted and dispersion decreasing fiber (DFDF) is quite appropriate ✩ Supported by the Excellent Teacher Foundation of Guangdong Province (Q02084) and Natural Science Foundation of Guangdong Province (No. 980030). * Corresponding author. E-mail address: [email protected] (W. Jin).
0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.11.003
416
W. Jin et al. / Physics Letters A 333 (2004) 415–419
for generating SC pulses with a flatly broadened spectrum, which is therefore regarded as the most utilizable SC source for optical communication system [8–10]. Several schemes focused on the SC generation in DFDF provide detailed discussion about the effects of input pulse parameter and fiber characteristics on the SC bandwidth and flatness. It is clearly seen that the initial chirp of the input pulse has a significant effect on pulse evolution in fibers. Z. Zhu et al. have discussed the effect of frequency chirping on SC generation in photonic crystal fibers and found that the initial linear chirp increases the SC bandwidth and improves the coherence [6]. Wu Yue et al. found that the SC bandwidth reduces by both the positive and negative frequency chirps in DDF [3]. However, to our best knowledge, no detailed report has been found that discusses the influence of initial frequency chirp on the generation of supercontinuum in DFDF. In this Letter, we analyzed the effects of frequency chirp on SC generation in DFDF. The results show that a positive frequency chirp can significantly broaden the supercontinuum spectrum. Considering the wideband spectrum of supercontinuum pulses, we use the total field Schrödinger equation instead of temporal Schrödinger equation to model the pulse propagation inside the DFDF fibers [8,9,11–13]. ∂Atotal(z, Ω) = −i∆(Ω)Atotal(z, Ω) ∂z − Γ (Ω)Atotal(z, Ω) 2 Ω −i 1+ Qker r FT Ω Atotal(z, τ )Atotal(z, τ ) ω0 2 Ω SRaman FT Ω Atotal(z, τ ) . −i 1+ QRaman FT Ω Atotal(z, τ ) × FT −1 τ ω0
(1)
Where Atotal(z, τ ) is the electric field amplitude, z is the longitudinal along the fiber, τ = t − z/Vg , Vg represent the group velocity of the wave with a frequency of ω0 in the fiber. Atotal(z, Ω) is the Fourier transform of Atotal(z, τ ). FT Ω stands for direct Fourier transform and FT −1 τ for the inverse Fourier transform. On the right-hand side of Eq. (1), the first line second line represents the linear part of the system, including dispersion and fiber loss. ∆(Ω) is the fiber dispersion which can be described as: ∆(Ω) =
∞
(k) Ω
β0
k
k!
k=2
,
(k)
β0 =
dkβ (ω0 ). dωk
The second and third lines are responsible for nonlinear effects: the former originates from Kerr-effect and the latter from stimulated Raman scattering (SRS). Where (3)
Qker r =
ω0 3χ1111 cµ0 Pscale , c n0 4n0 Aeff
QRaman =
Pscale ω0 GRaman . c Aeff
(3) And χ1111 is the (1, 1, 1, 1) components of the Kerr susceptibility sensor, GRaman is the Raman gain coefficient factor. Aeff = πω2 , where ω is the spot size of the best Gaussian approximation for the field ψ(r). The profile and distribution of chromatic dispersion in an optical fiber and the intensity and duration of the optical pump pulse are very important to the SC generation. Here we introduce an idealized dispersion characteristic in a DFDF, chromatic dispersion D(λ, z) expressed as: z 2 , D(λ, z) = −k(λ − λ0 ) + Dmax 1 − (2) z0
where k has a negative value in the case of a convex dispersion profile and Dmax is the peak value at the input. Length z0 is defined as the propagation distance after which the chromatic dispersion becomes negative (normal dispersion) at all wavelengths. In this Letter, we assume k = 0.0001 ps/(nm3 /km), Dmax = 6 ps/nm/km, z0 = dkβ 2πc 600 m and fiber length z = 720 m. According to βk = dω k |ω=ωc , ω = λ , λ = λ0 = 1550 nm, the GVD coefficients
W. Jin et al. / Physics Letters A 333 (2004) 415–419
417
derivatives as follows:
λ20 z Dmax 1 − , 2πc z0 λ30 z β3 (λ0 , z) = 2D 1 − , max (2πc)2 z0 λ40 z 2 6Dmax 1 − − 2kλ0 , β4 (λ0 , z) = − (2πc)3 z0 λ50 z 2 β5 (λ0 , z) = 24D 1 − − 24kλ max 0 . (2πc)4 z0
β2 (λ0 , z) = −
The input pulses are assumed to have the form
Cτ 2 τ A(0, τ ) = P0 sech exp −i 2 , T0 2T0
(3) (4) (5) (6)
(7)
where P0 is the peak power, T0 is related to the full wave half maximum (FWHM) of the input pulse by TFWHM ≈ 1.763T0, and C is the parameter representing the initial linear frequency chirp. The specific values of other parameters used in simulation are given as follows: Aeff = 50 µm2 , n2 = 3.2 × 10−20 m2 /W, P0 = 2.23 W, TFWHM = 4 ps. Fig. 1 shows the SC spectrum curves when the chirp coefficient C takes the values of −1.0, 0 and 1.5 with the corresponding SC spectral widths of 8, 221 and 303 nm. We notice that the intensity of SC spectrum in the case of C = 1.5 is higher than that without initial chirp though the flatness is diminished slightly. The spectrum related to negative chirp is neither broad nor flatness. The SC bandwidth broadens from 221 nm (C = 0) to 303 nm (C = 1.5) by imposing an initial frequency chirp on the input pulses. Fig. 2 plots the 27-dB SC bandwidth as a function of chirp parameter C. We notice that there is a wide range of optimal positive chirp that maximizes the SC bandwidth, in this case it is approximately from 1 to 2. And the pulse could not evolve into SC spectrum in the case of negative chirp or larger positive chirp. It is interesting that this dependence of SC bandwidth on C is quite different from that in dispersion decreasing fibers, where the SC bandwidth reduces by the frequency chirp (both positive and negative). To better understand how initial chirp influence the pulse compression and accordingly why there is a wide range of optimal positive chirp that maximizes the SC bandwidth, we plot temporal and spectral width of the pulse on a function of propagating distance with initial chirp as −1.0, 0, 1.5, 2.5, as displayed in Fig. 3.
Fig. 1. SC spectrum curves with different frequency chirp C.
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W. Jin et al. / Physics Letters A 333 (2004) 415–419
Fig. 2. 27-dB SC bandwidth as a function of the chirp coefficient.
(a)
(b)
Fig. 3. (a) Temporal width on a function of propagating distance with different chirp. (b) Spectral width on a function of propagating distance with different chirp.
Consider the solid curves that represent the pulse without initial chirp. We can see that the pulse width reduces monotonously with the propagating distance before the point of 600 m and becomes wide after that point due to optical wave breaking, while spectrum broadens drastically near the point of 600 m. This can be understood as fallows. SC generation in fused-silica optical fiber is regarded as the result of two constituent processes: pulse compression and spectral shaping. Pulse compression creates the high peak powers necessary to achieve significant nonlinear action in fibers. Spectral shaping results from the combined effects of pulse shape evolution with propagation and the generation of new spectral components by high-intensity portions of the pulse through nonlinearities. In the case of negative chirp as showed in Fig. 3 in dot curves, the pulse width increases slightly at a distance of about 100 m and then decreases to approximate 1.5 ps at the distance of 600 m, while the spectrum width almost remains as narrow as input. The reason is that at the initial stage of propagation, the interplay of initial chirp and dispersion dominates the pulse due to the relatively high dispersion and low nonlinearity. When an optical pulse is negatively chirped, the frequency at its leading edge is higher than that at its trailing edge. In the condition of β2 < 0, the initial chirp adds to the dispersion-induced chirp. As a result, the net chirp is enhanced leading to pulse broadening. With a further increase in propagation distance, the |β2 | decreases and the nonlinear compression becomes the crucial effect on the pulse. And therefore the pulse width decreases. But both the compression and the SC generation are not satisfied due to the initial broadening of the pulse width.
W. Jin et al. / Physics Letters A 333 (2004) 415–419
419
In contrast, as for the dash curves which corresponding to the pulse with an initial positive chirp of 1.5, we notice that the pulse width is always narrower and the spectrum width is always broader than that without chirping along the whole propagating distance. When an optical pulse is positively chirped, the frequency at its leading edge is lower than that at its trailing edge. In the condition of β2 < 0, the initial chirp compensates the dispersion-induced chirp and enhances the chirp created by SPM. As a result the initial pulse compression is enhanced and higher peak power is obtained, and thus a broader and stronger SC spectrum is generated. The dot-dash curves correspond to a positive chirp of 2.5. In this case, the large positive chirp over compensates the dispersion-induced chirp at the initial stage of propagation where the dispersion is relatively high and thus the chirp created by SPM is small correspondingly. And therefore the pulse width decreases rapidly at a distance before 250 m, and increases slightly during the distance of 250 to 450 m. After that, the domination of dispersioninduced chirp gives way to the chirp created by SPM, and the pulse width decrease correspondingly. But the final compression and broadening of spectrum is not satisfied due to the undulation in the compressing process. According to the descriptions above, we can see the different chirped pulses have different SC spectral and temporal width evolutions in the DFDF. When the pump pulse has a negative or too large positive chirp, the pulse will not be compressed properly, and therefore cannot evolve into SC pulse, while a slight positive chirp can enhance the compression and force the pulse to generate a broader spectrum. In other words, there must be an optimal chirp that can best help to compress the pulse and generate the widest spectrum. In inclusion, we have studied the effects of initial linear chirp on the SC generation in DFDF. The results show that a proper positive chirp can significantly enhance the SC generation. We have also analyzed the relationship between the SC bandwidth and the chirp coefficient and found that there is a wide range of optimal positive chirps which can maximize the SC bandwidth. The evolution of pulse width and spectrum width is shown and the mechanism is discussed that the initial chirp broadens the SC spectrum.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
H. Sotobayashi, W. Chujo, A. Konishi, T. Ozeki, J. Opt. Soc. Am. B 19 (11) (2002) 2803. A. Mussot, T. Sylvestre, L. Provino, H. Maillotte, Opt. Lett. 28 (19) (2003) 1820. Y. Wu, C.-Y. Lou, M. Han, T. Wang, Y.-Z. Gao, Chin. Phys. 11 (2002) 578. F. Futami, et al., IEICE Trans. Electron. E82-C (1999) 1531. N.I. Nikolov, T. Srensen, O. Bang, A. Bjarklev, J. Opt. Soc. Am. B 20 (11) (2003) 2329. Z. Zhu, T.G. Brown, Opt. Exp. 12 (4) (2004) 689. W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, P.St.J. Russell, J. Opt. Soc. Am. B 19 (9) (2002) 2148. K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, T. Morioka, Electron. Lett. 33 (1997) 1806. K. Mori, H. Takara, S. Kawanishi, J. Opt. Soc. Am. B 18 (12) (2001) 1780. T. Okuno, M. Onishi, M. Nishimura, IEEE Photon. Technol. Lett. 10 (1) (1998) 72. B. Gross, J.T. Manassah, J. Opt. Soc. Am. B 9 (1992) 1813. G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, New York, 1995. P.L. Francois, J. Opt. Soc. Am. B 8 (2) (1991) 276.