Two-color flat-top solitons in microresonator-based optical parametric oscillators

We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator-based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we found the effect of the transformation of the flat-top platicon profile at half-frequency into the bell-shaped bright soliton profile upon frequency scan. For platicon excitation one needs simultaneous accurate matching of the microresonator free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were found for the different generation methods, and properties of the generated platicons were studied for various combinations of the medium parameters.

Figure 1

FW (left panels) and SH (right panels) field distribution (upper line) and spectrum (bottom line, logarithmic scale) evolution upon forward pump frequency scan ${\alpha }_2=-11.0+0.002\tau$ at $b_{21}=0.05, b_{22}=-0.05, f=15, \varepsilon =0.4$. ${\mu }_{1,2}$ are mode numbers, ${\mu }_2=0$ corresponds to the pumped mode, ${\mu }_1=0$ corresponds to the mode nearest to the half pump frequency. All quantities are plotted in dimensionless units.

Figure 2

Profiles of the FW and SH components of the generated patterns for ${\alpha }_2=\pm 8.0$ and ${\alpha }_2=\pm 3.0$ at $f=15, \varepsilon =0.4$ for $b_{21}=0.05, b_{22}=-0.05$. All quantities are plotted in dimensionless units.

Figure 3

FW and SH intracavity powers $U_1$ and $U_2$ vs pump frequency detuning ${\alpha }_2$ upon forward pump frequency scan ${\alpha }_2=-11.0+0.002\tau$ at $b_{21}=0.05, b_{22}=-0.05, f=15, \varepsilon =0.4$. All quantities are plotted in dimensionless units.

Figure 4

Platicon generation domains for different values of the modulation depth and fixed pump amplitude (left panel) and for different pump amplitudes and fixed modulation depth (right panel) at $b_{21}=0.05, b_{22}=-0.05$ and $b_{21}=-0.05, b_{22}=0.05$. All quantities are plotted in dimensionless units.

Figure 5

FW field distribution evolution upon forward pump frequency scan ${\alpha }_2=-11.0+0.002\tau$ at $b_{21}=0.05, f=15, \varepsilon =0.4$ for $b_{22}=-0.02$ (left panel) and $b_{22}=-0.01$ (right panel). All quantities are plotted in dimensionless units.

Figure 6

$U_1\left({\alpha }_2\right)$ (left) and FW spectrum (right) for different values of $b_{22}$ at $b_{21}=0.05, f=15, \varepsilon =0.4$. ${\mu }_1=0$ corresponds to the mode nearest to the half pump frequency. All quantities are plotted in dimensionless units.

Figure 7

Profiles of the platicon components for different FSRs mismatch values at $f=15, \varepsilon =0.4, b_{21}=0.05, b_{22}=-0.05$. All quantities are plotted in dimensionless units.

Figure 8

FW (left panels) and SH (right panels) field distribution (upper line) and spectrum (bottom line, logarithmic scale) evolution upon forward pump frequency scan ${\alpha }_{20}=-15.0+0.002\tau$ at $b_{21}=0.05, b_{22}=-0.05, f=15, \mathrm{\Delta }=2{\kappa }_2$. ${\mu }_{1,2}$ are mode numbers, ${\mu }_2=0$ corresponds to the pumped mode, ${\mu }_1=0$ corresponds to the mode nearest to the half pump frequency. All quantities are plotted in dimensionless units.

Figure 9

Profiles of the FW and SH components of the generated patterns for different detuning values at $f=15, \mathrm{\Delta }=2{\kappa }_2, b_{21}=0.05, b_{22}=-0.05$. All quantities are plotted in dimensionless units.

Figure 10

FW and SH intracavity powers $U_1$ and $U_2$ vs pump frequency detuning ${\alpha }_{20}$ upon forward frequency scan ${\alpha }_{20}=-15.0+0.002\tau$ at $b_{21}=0.05, b_{22}=-0.05, f=15, \mathrm{\Delta }=2{\kappa }_2$. All quantities are plotted in dimensionless units.

Figure 11

Platicon generation domains for different values of the pumped mode shift and fixed pump amplitude (left panel) and different pump amplitudes and fixed pumped mode shifts (right panel) at $b_{21}=0.05, b_{22}=-0.05$ and $b_{21}=-0.05, b_{22}=0.05$. All quantities are plotted in dimensionless units.

Figure 12

Profiles of the platicon components for different FSRs mismatch values at $f=15, \mathrm{\Delta }=2{\kappa }_2, b_{21}=0.05, b_{22}=-0.05$. All quantities are plotted in dimensionless units.