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The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength

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Abstract

Supercontinuum generation with femtosecond pulses in photonic crystal fibers with two zero-dispersion wavelengths (ZDWs) is investigated numerically. The role of the higher ZDW is examined for 5 fiber designs with a nearly constant lower ZDW. It is found that the resulting spectrum is mainly determined by self-phase modulation in the first few mm of fiber, followed by soliton self-frequency shift and amplification of dispersive waves. It is demonstrated how femtosecond soliton pulses can be generated with any desired center wavelength in the 1020–1200 nm range by adjusting the fiber length. Further, the generation of a bright-bright soliton-pair from an initial single red-shifted soliton is found. The soliton-pair has one color in the anomalous dispersion region and the other color in the normal dispersion region, which has not previously been described for bright-bright soliton-pairs.

©2005 Optical Society of America

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Corrections

Michael H. Frosz, Peter Falk, and Ole Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength: erratum," Opt. Express 15, 5262-5263 (2007)
https://opg.optica.org/oe/abstract.cfm?uri=oe-15-8-5262

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Supplementary Material (4)

Media 1: AVI (247 KB)     
Media 2: AVI (298 KB)     
Media 3: AVI (944 KB)     
Media 4: AVI (865 KB)     

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Figures (7)

Fig. 1.
Fig. 1. Left: Calculated dispersion profiles for 5 triangular PCFs with pitch ʌ and relative air-hole size d/ʌ given in the inset. Right: Wavelength λ DW of dispersive waves vs. the soliton center wavelength λ S. The color labelling is the same in both figures.
Fig. 2.
Fig. 2. Calculated spectrograms up to z = 6 mm in the ʌ = 1.0 μm (left) and the ʌ = 1.1 μm fiber (right). The white horizontal lines indicate the ZDWs. pitch1p0_6mm_dB.avi (0.2 MB), pitch1p1_6mm_dB.avi (0.3 MB). 210 computation points were used.
Fig. 3.
Fig. 3. Left: power spectra after 6 mm of propagation in the ʌ = 1.0 μm fiber. Blue, solid: full simulation; green, dotted: no delayed Raman response; red, dashed: only dispersion terms are β¯2 and β¯3. Right: phase mismatch κ for degenerate FWM at a peak power P 0 = 15 kW and λ 0 = 804 nm, when β¯2 ,β¯4,…, β¯4 are included (blue, solid) and when only β¯2 is included (red, dashed) in Eq. (9).
Fig. 4.
Fig. 4. Power spectra after 6 mm (left) and 6 cm (right) of propagation. The input spectrum is indicated as a thin black line.
Fig. 5.
Fig. 5. Left: spectrogram for the 1.2 μm PCF up to z = 60 cm (pitch1p2_60cm_dB.avi, 0.9 MB). Right: spectrogram for the 1.3 μm PCF up to z = 52 cm (pitch1p3_52cm.avi, 0.9 MB). The white horizontal lines indicate the ZDWs.
Fig. 6.
Fig. 6. A close-up of the spectrogram for the 1.2 μm PCF at z = 60 cm. It is seen that the pulse generated in the normal dispersion region has not changed its width significantly over several centimeters. The white horizontal lines indicate the ZDWs.
Fig. 7.
Fig. 7. (a) The red-infrared part of the pulse spectrum output from the ʌ = 1.3 μm PCF at various fiber lengths.

Equations (11)

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A z = i m 2 i m β ¯ m m ! m A t m + [ 1 + i ω 0 t ] [ A ( z , t ) t R ( t′ ) A ( z , t t′ ) 2 d t′ ] ,
β 2 ( ω ) = β ¯ 2 + β ¯ 3 [ ω ω 0 ] + 1 2 β ¯ 4 [ ω ω 0 ] 2 + 1 6 β ¯ 5 [ ω ω 0 ] 3 +
β ¯ m = β m ( ω 0 ) = ( d m β d ω m ) ω = ω 0 ,
S ( z , t , ω ) = e iωt′ e [ t′ t ] 2 α 2 A ( z , t′ ) d t′ 2 ,
A z = i β 2 ( ω sol ) 2 2 A t 2 + iγA A 2 ,
A z = i m 2 i m β m ( ω sol ) m ! m A t m .
β 2 ( ω sol ) 2 T sol 2 = m 2 β m ( ω sol ) m ! [ ω DW ω sol ] m ,
T sol = T 0 2 N 1 = T 0 2 ( γ P 0 T 0 2 β 2 ( ω sol ) | ) 1 ,
κ = 2 γ P 0 + Ω 2 β ¯ 2 + 2 4 ! Ω 4 β ¯ 4 + 2 6 ! Ω 6 β ¯ 6 +
β 1 ( ω ) = β 1 ( ω A ) + β 2 ( ω A ) [ ω ω A ] + β 3 ( ω A ) 2 [ ω ω A ] 2 ,
Δ ω = 2 β 2 ( ω A ) β 3 ( ω A ) ,
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