Nonlinear combining and compression in multicore fibers

We demonstrate numerically light-pulse combining and pulse compression using wave-collapse (self-focusing) energy-localization dynamics in a continuous-discrete nonlinear system, as implemented in a multicore fiber (MCF) using one-dimensional (1D) and 2D core distribution designs. Large-scale numerical simulations were performed to determine the conditions of the most efficient coherent combining and compression of pulses injected into the considered MCFs. We demonstrate the possibility of combining in a single core 90% of the total energy of pulses initially injected into all cores of a 7-core MCF with a hexagonal lattice. A pulse compression factor of about 720 can be obtained with a 19-core ring MCF.

Figure 1

Schematic depiction of the considered MCF waveguide with 7 (left) and 19 (right) cores arranged in a circle.

Figure 2

Schematic depiction of the considered multicore fiber with hexagonal and square geometry and 2D numbering of cores.

Figure 3

Dependence of the percentage of total energy $E$ combined in the core with pulse compression (a) and the pulse-width compression factor in the logarithmic scale (b) on the initial pulses [Eq. (15)]; parameters $P$ and $\tau$ for the 7-core MCF with ring core configuration and modulation coefficient $M=0.3$. The isoline $E=E_{\mathrm{cr}}=4\pi$ is indicated by the yellow dots; the level $H=0$ is depicted by white dashes.

Figure 4

Evolution of the input Gaussian pulses [Eq. (15)] with the parameters $P=0.5,\tau =2.0$, and $M=0.3$ injected in all cores of the 7-core ring MCF (best combining) (a). Corresponding input intensity distribution in core 7 (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 83.5% of total input energy $E$ is combined in core 7. The pulse width (FWHM) is reduced by $5.74\mathrm{x}$. The peak power increases in $19.5\mathrm{x}$.

Figure 5

Evolution of the input Gaussian pulses [Eq. (15)] with the parameters $P=0.436,\tau =42.5$, and $M=0.3$ injected in all cores of the 7-core ring MCF (best compression) (a). Corresponding input intensity distribution in core 7 (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 35.8% of total input energy $E$ is combined in the 7th core. The pulse width (FWHM) is reduced by $307.6\mathrm{x}$. The peak power increases in $123.7\mathrm{x}$.

Figure 6

Dependence of the percentage of total energy $E$ combined in the core with pulse compression (a) and the pulse-width compression factor in the logarithmic scale (b) on the initial pulses [Eq. (15)]; parameters $P$ and $\tau$ for the 19-core MCF with ring core configuration and modulation coefficient $M=0.3$. The isoline $E=E_{\mathrm{cr}}=4\pi$ is indicated by the yellow dots; the level $H=0$ is depicted by white dashes.

Figure 7

Evolution of the input Gaussian pulses [Eq. (15)] with the parameters $P=0.09,\tau =4.33$, and $M=0.3$ injected in all cores of the 19-core ring MCF (best combining) (a). The input intensity distribution in core 19 (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 80.0% of total input energy $E$ is combined in the 19th core. The pulse width (FWHM) is reduced by $12.7\mathrm{x}$. The peak power increases in $111.0\mathrm{x}$.

Figure 8

Evolution of the input Gaussian pulses [Eq. (15)] with the parameters $P=0.0545,\tau =184.0$, and $M=0.3$ injected in all cores of the 19-core ring MCF (best compression) (a). The input intensity distribution in core 19 (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 10.9% of total input energy $E$ is combined in the 19th core. The pulse width (FWHM) is reduced by $720.4\mathrm{x}$. The peak power increases in $314.8\mathrm{x}$.

Figure 9

Dependence of the percentage of total energy $E$ combined in the core with pulse compression (a) and the pulse-width compression factor in the logarithmic scale (b) on the initial pulses [Eq. (15)]; parameters $P$ and $\tau$ for the 7-core hexagonal MCF without modulation. The level $H=H_c$ is depicted by white dashes.

Figure 10

Evolution of the input Gaussian pulses [Eq. (16)] with the parameters $P=0.687$ and $\tau =1.775$ injected in all cores of the hexagonal 7-core MCF (best combining) (a). The input intensity distribution in the central core (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 91.6% of total input energy $E$ is combined in the core (0,0). The pulse width (FWHM) is reduced by $6.37\mathrm{x}$. The peak power increases in $37.7\mathrm{x}$.

Figure 11

Evolution of the input Gaussian pulses [Eq. (16)] with the parameters $P=536$ and $\tau =3.2$ injected in all cores of the hexagonal 7-core MCF (best compression) in the logarithmic scale (a). The input intensity distribution in the central core (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scales. 16.6% of total input energy $E$ is combined in the core (0,0). The pulse width (FWHM) is reduced by $256.3\mathrm{x}$. The peak power increases in $21.85\mathrm{x}$.

Figure 12

Dependence of the percentage of total energy $E$ combined in the core with pulse compression (a) and the pulse-width compression factor (b) on the initial pulses [Eq. (15)]; parameters $P$ and $\tau$ for the 19-core hexagonal MCF without modulation. The level $H=H_c$ is depicted by white dashes.

Figure 13

Evolution of the input Gaussian pulses [Eq. (16)] with the parameters $P=0.36$ and $\tau =1.69$ injected in all cores of a hexagonal 19-core MCF (best combining) (a). The input intensity distribution in the central core (dashed red line) and the distribution at compression point (solid blue line) are shown in logarithmic (b) and normal (c) scale. 80.9% of total input energy $E$ is combined in the core (0,0). The pulse width (FWHM) is reduced by $7.3\mathrm{x}$. The peak power increases in $103.4\mathrm{x}$.

Figure 14

Dependence of the percentage of total energy $E$ combined in the core with pulse compression (a) and the pulse-width compression factor in the logarithmic scale (b) on the initial pulses [Eq. (17)] parameters $P$ and $\tau$ for hexagonal 19-core MCF with modulation coefficient $M=0.3$. The level $H=H_c$ is depicted by white dashes.