Implications of a zero-nonlinearity wavelength in photonic crystal fibers doped with silver nanoparticles

Photonic crystal fibers doped with silver nanoparticles exhibit a Kerr nonlinearity that can be positive or negative depending on the input wavelength and which vanishes at a specific wavelength. The existence of negative nonlinearity allows soliton formation even in the normal-dispersion region of the fiber, and the zero-nonlinearity wavelength (ZNW) acts as a barrier for the Raman-induced redshift of solitons. We adopted the variational principle to understand the role of the zero-nonlinearity point on Raman redshift and verified its prediction numerically for fundamental and higher-order solitons. We show how the simultaneous presence of a ZNW and a zero-dispersion wavelength affects soliton evolution inside such fibers and find a number of unique features such as the position and the spectral bandwidth of the dispersive wave that change with the location of the ZNW.

Figure 1

(a) Schematic cross section of the proposed fiber. (b) Fundamental mode field distribution calculated at the operating wavelength of 880 nm.

Figure 2

(a) Raman-induced spectral shift at $\xi =20$ of a second-order soliton $(N=2)$ in the absence (red pulse) (dark gray pulse) and presence (pink pulse) (light gray pulse) of a ZNW. (b) Spectral evolution inside the PCF in the two cases. The arrow marks the absence of a ZNW. (c) Frequency shifts with distance as predicted by the variational technique for $N=1$; blue squares represent numerical data that agree with the dashed blue line. The dashed blue line (upper) represents the negative higher-order nonlinear coefficient and the dotted red line represents the positive higher-order nonlinear coefficient. The black solid line (middle) indicates the absence of higher-order nonlinear coefficient. (d) Variational prediction comparing soliton spectrum at a distance of $\xi =8$ with the input spectrum (dotted curve). Red dot at the peak shows the extent of RIFS.

Figure 3

Spectral (a) and temporal (b) evolution of the pulse over 3 m. Black and pink vertical lines in (a) mark the ZDW (1023 nm) and the ZNW (1374 nm), respectively. (c) GVD and nonlinear profiles of the PCF as a function of wavelength. (d) Spectrogram at 1.2 m where DW initiates. (e) Phase-matched curve; a red circle indicates the location of DW. (f) Spectrogram at 2 m.

Figure 4

Spectral (a) and temporal (b) evolution of the pulse over 3 m. Black and pink vertical lines in (a) mark the ZDW (1023 nm) and the ZNW (1205 nm), respectively. (c) GVD and nonlinear profiles of the PCF as a function of wavelength. (d) Spectrogram at 1.5 m. (e) Phase-matching curve; a red circle indicates the wavelength of the DW. (f) Spectrogram at 2 m.

Figure 5

Spectral (a) and temporal (b) evolution over 3 m. Black and pink vertical lines in (a) mark the ZDW (1023 nm) and the ZNW (1135 nm), respectively. (c) GVD and nonlinear profiles of the PCF. (d) Spectrogram at 1.3 m. (e) Phase-matching curve; a red circle indicates the location of DW. (f) Spectrogram at 2 m.

Figure 6

Spectral (a) and temporal (b) evolution over 3 m. Black and pink vertical lines in (a) mark the ZDW (1023 nm) and the ZNW (1073 nm), respectively. (c) GVD and nonlinear profiles of the PCF. (d–f) are the spectrograms corresponding to 1.7, 2, and 3 m. Notice that the DW blueshifts along the length of the fiber.

Figure 7

Spectral (a) and temporal (b) evolution when the ZDW and ZNW coincide at 1023 nm. (c,d) are the spectrograms at 2 and 4 m, respectively. Fiber dispersion is modified in (e,f) such that the ZDW is absent but ZNW coincides at 1023 nm [pink vertical line in (e)].

Figure 8

(a) Variation of DW wavelength with the ZNW both numerically (dot-dashed line) and analytically from phase-matched Eq. (15) (circle). (b) Same variation over a wider range of ZNW. The horizontal line shows the wavelength of DW when ZNW does not exist. (c) Variation of ZNW with the filling factor f. (d) Variation of spectral bandwidth width of DW with the ZNW. Bandwidth is defined as the difference between the two points that are 10 dB below the peak intensity of the DW. The horizontal line shows the width of DW when ZNW does not exist.