Theoretical and experimental analysis of staircase pulses in passive mode-locked fiber lasers

We report an experimental observation of staircase pulses generated from an Er:Yb co-doped fiber laser operating in the anomalous dispersion regime. The staircase pulses consist of two distinct square pulses associated with different wavelengths in a dual peak spectrum and they exhibit particular temporal characteristics. To establish a theory behind the experimental results, we simulate numerically the fiber oscillator by using a master equation and taking into consideration the gain inhomogeneities as well as other nonlinear variables.

Figure 1

Experimental setup of the nonlinear polarization evolution: isolator (PI-ISO), PC (polarization controller), and OC (output coupler).

Figure 2

Dominant operation of optical pulse distribution as a function of the pump power.

Figure 3

(a) Optical spectrum output and (b)square pulse temporal trace.

Figure 4

Radio-frequency spectrum output of the square pulse.

Figure 5

Staircase upward pulse: (a) optical spectrum and (b) temporal profile.

Figure 6

Staircase downward pulse: (a) optical spectrum and (b) temporal profile.

Figure 7

Spectral analysis of the pulse states.

Figure 8

(a) Temporal and (b) spectral distributions for a steady-state rectangular pulse with spectral doublet structure. $a=2.5$, $b=0.07$, $D_r=1.4$, $D_i=0.2$, $D_{i3}=0$, ${\sigma }_0=0.5$, $p=1$, $q=0.45$, $p_2=1$.

Figure 9

Transient process and the steady-state distributions (a) for the intensity $I\left(\tau \right)$ and (b) for the spectrum of a rectangular pulse in the case of $D_{i3}\ne 0$ ($D_{i3}=-1$ for $\zeta \le 1100$, $D_{i3}=1$ for $\zeta >1100$). Other parameters are the same as in Fig. 8.

Figure 10

(a) Temporal and (b) spectral distributions for a steady-state stepped pulse with spectral doublet structure in the case of a spectral inhomogeneity of an amplification. $a=0.5$, ${}_{i3}=-1$, $D_0=4$, $h_1=h_2=0.8$, $b_1=b_2=0.0005$. Other parameters are the same as in Fig. 8.

Figure 11

(a) Temporal and (b) spectral distributions for a steady-state stepped pulse with a spectral doublet structure in the case of a spectral inhomogeneity of an amplification. $D_{i3}=1$, other parameters are the same as in Fig. 10.