Temporal Cavity Soliton in a Coherently Driven Active Fiber Resonator

Temporal cavity solitons (CSs) in passive optical resonators have attracted significant attention over the last decade [1], [2]. However, real life applications are still lagging behind, mostly because very little power can be injected in, or extracted from, a high finesse resonator. Even if solitons in mode-locked lasers (MLLs) can circumvent this problem, the noise coming from the gain medium causes timing jitter that hinder their use for some applications. [3]. Here, we show that incorporating an optical amplifier in a passive cavity but keeping the system below the lasing threshold allows to excite a new kind of temporal soliton, named active cavity soliton (ACS), that combines the advantages of MLL and passive cavity solitons. When the gain dynamics is much slower than the roundtrip time t
R
, such driven resonator is described by the following generalized Lugiato-Lefever equation [4]\begin{equation*}{t_R}\frac{{\partial u(T,\tau )}}{{\partial T}} = \left({ - \frac{\Lambda }{2} + \frac{{{g_0}{L_e}/2}}{{1 + {{\left({{P_{sat}}{t_R}}\right)}^{ - 1}}\int_0^{{t_R}} {|u(T,\tau ){|^2}} {\text{d}}\tau }} - i{\delta _0} - i\frac{{{\beta _2}L}}{2}\frac{{{\partial ^2}}}{{\partial {\tau ^2}}} + i\gamma L|u(T,\tau ){|^2}}\right)u(T,\tau ) + \sqrt {{\theta _{{\text{in}}}}{P_s}} ,\tag{1}\end{equation*}where u is the intracavity electric field envelope, Λ is the intrinsic intracavity loss, L is the length of the resonator, γ its nonlinear parameter and β
2
the average group velocity dispersion. T=nt
R
, where n is an integer, is a slow time. τ is a time reference traveling at the group velocity, P
s
is the driving power and δ
0
the phase detuning from the closest cavity resonance. g
0
is the unsaturated gain, L
e
is the amplifier length and P
sat
is the gain saturation power. The experimental set-up, depicted in Fig. 1a, is a fiber resonator (L=50 m) incorporating a short erbium doped fiber (L
e
=34 cm) pumped at 1480 nm (P
p
=1 W) and two couplers (99/1 and 90/10), driven by a highly coherent continuous wave laser. At low driving powers, the finesse is 248, which corresponds to 2.5% effective loss. At higher driving powers, the gain saturates when on resonance. It prevents the spontaneous formation of solitons but not their existence. Figure 1b shows the cavity resonance and the ACS peak power existence branch, obtained by bifurcation analysis of Eq. (1) when θ
in
P
s
=11 mW. The homogeneous solution shows no bistability nor modulation instability. Unlike passive resonators, the soliton branch is disconnected from the homogeneous state and forms an isola [5]. This disconnection makes external excitation of ACSs necessary. To show it, we first stabilize the intracavity power at 60 mW (6.5% of effective loss, see black dot in Fig. 1b). We then excite solitons with a single optical pulse [6] and record the output on a 10 GHz oscilloscope. A short pulse leaving the cavity at each roundtrip time following the addressing pulse is shown in Fig. 1c.