Supplementary data are available at Bioinformatics online.

A novel high-birefringence photonic crystal fiber (HB-PCF) with two zero-dispersion wavelengths (ZDWs) is designed, and an extraordinarily high modal birefringence of 1.56×10−2 is obtained at pump wavelength λp = 1850 nm. With the designed HB-PCF, the effect of the pump parameters on the modulation instability (MI) in the anomalous dispersion region close to the second ZDWs of the HB-PCF is comprehensively studied in this work. A broadband and tunable optical amplification is achieved by controlling the pump power and the pump wavelength based on the combined operation of Raman effect and cross phase modulation. By optimizing the pump parameters, the amplification bandwidth along the fiber slow axis reaches 152 nm for the pump power Pp = 280 W and the pump wavelength λp=1675 nm, while the gain bandwidth along the fiber fast axis is 165 nm for the pump power Pp = 600 W and the pump wavelength λp = 1818 nm.

We study the boundary value problem for a kind N-dimension nonlinear fractional differential system with the nonlinear terms involved in the fractional derivative explicitly. The fractional differential operator here is the standard Riemann-Liouville differentiation. By means of fixed point theorems, the existence and multiplicity results of positive solutions are received. Furthermore, two examples given here illustrate that the results are almost sharp.

Based on a designed high-birefringence photonic crystal fiber with two zero-dispersion wavelengths (ZDWs), the effect of fiber dispersion, pump power and pump wavelength on the modulation instability (MI) gain in the anomalous dispersion region is comprehensively analyzed in this paper. An asymmetric and broadband MI gain spectrum appears at the anti-Stokes band due to the different ZDWs along the fiber slow-and fast-axes. An optimal MI gain can be obtained when the pump wavelength (1675 nm) is slightly shorter than the second ZDW (1683 nm) and the pump power is 280 W. The optimal MI gain bandwidth finally reaches 152 nm and the gain profile is smoother.

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Based on a designed high-birefringence photonic crystal fiber (HB-PCF) with two zero-dispersion wavelengths (ZDWs), the effect of pump parameters and Raman scattering on the modulation instability (MI) gain is comprehensively analyzed in this paper. An interesting result is found, in that only when the pump wavelength lies within an approximately 10 nm range of the zero-dispersion points in the normal dispersion region of the HB-PCF does a broadband gain characteristic appear. The Raman effect results in a combination of the gain spectra from the Stokes and anti-Stokes band, which finally promotes the formation of broadband amplification. Moreover, there exist an optimal pump wavelength and a suitable pump power along the fast axis or the slow axis of the fiber. With these optimal pump parameters, the total MI gain bandwidth finally reaches 159 nm for the fiber fast axis and 162 nm for the fiber slow axis.