Observations of existence and instability dynamics of near-zero-dispersion temporal Kerr cavity solitons

Dissipative Kerr cavity solitons (CSs) are persisting pulses of light that manifest themselves in driven optical resonators and that have attracted significant attention over the last decade. Whilst the vast majority of studies have revolved around conditions where the resonator exhibits strong anomalous dispersion, recent studies have shown that solitons with unique characteristics and dynamics can arise under conditions of near-zero-dispersion driving. Here, we report on experimental studies of the existence and stability dynamics of Kerr CSs under such conditions. In particular, we experimentally probe the solitons' range of existence and examine how their breathing instabilities are modified when group-velocity dispersion is close to zero, such that higher-order dispersion terms play a significant role. On the one hand, our experiments directly confirm earlier theoretical works that predict (i) breathing near-zero-dispersion solitons to emit polychromatic dispersive radiation, and (ii) that higher-order dispersion can extend the range over which the solitons are stable. On the other hand, our experiments also reveal a novel cross-over scenario, whereby the influence of higher-order dispersion changes from stabilising to destabilising. Our comprehensive experiments sample soliton dynamics both in the normal and anomalous dispersion regimes, and our results are in good agreement with numerical simulations and theoretical predictions.

Figure 1

Simplified depiction of the experimental setup. The inset depicts the second-order group-velocity dispersion coefficient of the cavity as a function of wavelength, the dashed orange lines indicate the position of the zero-dispersion-wavelength. AM, amplitude modulator; DSF, dispersion-shifted fibre; ECDL, external-cavity diode laser; EDFA, erbium-doped fibre amplifier; OSA, optical spectrum analyzer; OSC, oscilloscope.

Figure 2

(a) Red curve shows CS bifurcation curve for X = 150 and $d_3=1.12$; green curve shows corresponding results in the absence of higher-order dispersion $[{\beta }_3={\beta }_4=0]$ and stimulated Raman scattering $[f_{\mathrm{R}}=0]$. Vertical dashed-dotted lines labeled as ${\mathrm{\Delta }}_{\mathrm{H}2}$ and ${\mathrm{\Delta }}_{\mathrm{H}3}$ indicate the detunings at which breathing solitons emerge in the absence and presence of higher-order terms, respectively. Blue curves show CW solutions for X = 150. Solid (dashed) curves correspond to stable (unstable) solutions. (b), (c) Blue (orange) curves show experimentally measured (numerically simulated) CS energy per round-trip and time-averaged spectrum at $\mathrm{\Delta }=44.5$, respectively. (d) and (e) are as in (b) and (c), respectively, but with $\mathrm{\Delta }=18$. The positions of both measurements along the CS bifurcation curves are indicated in (a) by green circles. Insets in (c) and (e) show the dispersive wave spectral components in more detail.

Figure 3

The right panel shows a pseudocolor plot of experimentally measured spectra at various detuning values, obtained through vertically concatenating 72 individual spectral measurements with parameters as in Fig. 2. The left panel shows a corresponding plot of high resolution spectral measurements around the dispersive wave spectral profile; note that the latter measurements are centered at the wavelength of the strongest dispersive radiation peak and encompass a spectral window of 20 nm. In both panels, the predicted positions of the CS Hopf bifurcation points in the presence and absence of higher-order terms, ${\mathrm{\Delta }}_{\mathrm{H}3}$ and ${\mathrm{\Delta }}_{\mathrm{H}2}$ [same values shown in Fig. 2], are indicated by the yellow arrows, respectively.

Figure 4

Bifurcation characteristics of CSs with parameters as in Fig. 2 over a range of normalized detunings and driving powers; solutions within the green, orange, and purple patches are stable, oscillatory, and spatio-temporally chaotic, respectively. Black solid lines delineate the existence boundaries of CSs in the absence of higher-order terms (pure LLE model) whilst the black dashed line shows the corresponding Hopf bifurcation point ${\mathrm{\Delta }}_{\mathrm{H}2}$. Blue and red dots correspond to experimental measurements of stable and unstable CSs, respectively.

Figure 5

Bifurcation characteristic of single-peak CSs with normal-dispersion driving and $d_3=1.07$ over a range of normalized detunings and driving powers. The green patch indicates the parameter range within which normal-dispersion CS exist and are predicted to be stable; note that there are no instabilities for the considered parameters. For comparison, the solid-grey curves delineate the existence boundaries of anomalous-dispersion CSs with $d_3=1.12$, whilst dashed- and dotted-grey curves indicate the corresponding instability boundaries (data extracted from Fig. 4). Blue dots correspond to experimental measurements of stable CSs (no unstable CSs were observed for the considered parameters). The insert shows a pseudocolor plot of spectral measurements at $X=120$ and for various detunings (corresponding to data points enclosed by the dashed-orange rectangle). Note that, due to experimental error, a data point near $X=150$ and $\mathrm{\Delta }=20$ is missing. However, by observing the stability state of its neighbours, it is reasonable to assume the CS at this position will be stable.

Figure 6

(a) Upper-detuning-limit of soliton range of existence as a function of deviation from the ZDW, ${\lambda }_{\mathrm{p}}-{\lambda }_{\mathrm{zdw}}$, where ${\lambda }_{\mathrm{p}}$ and ${\lambda }_{\mathrm{zdw}}$ are the driving wavelength and ZDW, respectively. The dashed-red line indicates the detuning-limit of the zero-dispersion soliton that exists when ${\beta }_2=0$ (or equivalently $d_3=\infty$). (b) Temporal profiles of simulated CSs at $\mathrm{\Delta }=20$ for normal-dispersion driving (orange-solid curve), anomalous-dispersion driving (blue-dashed curve), and driving exactly at the ZDW (grey circles).