Intracavity dynamics in high-power mode-locked fiber lasers

A theoretical model is developed which characterizes the intracavity pulse evolutions in high-power fiber lasers. It is shown that experimentally observed dynamics of the key pulse parameters can be described by a reduced model of ordinary differential equations. Critical in driving the intracavity dynamics is the amplitude and phase modulations generated by the discrete elements in the laser. The theory gives a simple geometrical description of the intracavity dynamics and possible operation modes of the laser cavity. Furthermore, it provides a simple and efficient method for optimizing the performance of complex multiparametric laser systems.

Figure 1

Peak-power (a) and pulse duration (b) modulations from the discrete action of the saturable absorber (3) on a Gaussian pulse for the parameter values $l_0=0.3$ (solid), 0.5 (dashed black), and 0.7 (dashed gray).

Figure 2

Temporal (a) and spectral (b) solutions from numerical simulation of (1) with gain (2) in the net-anomalous dispersion regime. Dispersion map parameters are $d_1=1$, $L_1=1$, and $d_2=-0.9$, $L_2=1$. Dissipative parameters are $g_0=2$, $e_0=1$, $\nu =0.05$, $\alpha =0.1$, $l_0=0.5$, $p_{\mathrm{s}}=3$, and $\rho =0.5$. Note that the saturable absorber (SA) and output coupler (OC) are applied at the end of the map resulting in last two pulses. Gray shade corresponds to the gain segment.

Figure 3

Evolution of pulse parameters over two map periods from full simulations (solid) and the reduced system (dashed) for the laser setup in Fig. 2. The results from application of the saturable absorber (SA) and output coupler (OC) are shown for both the full (circle) and reduced (gray diamonds) models. Shaded regions correspond to the gain segment.

Figure 4

Poincaré map of stable mode-locking operation of Fig. 2. The jump condition associated with the saturable absorber results in the flow moving to the black diamond, while that associated with the output coupler moves the phase point to the gray circle. The solid lines correspond to the full model (1–4), and the dashed lines correspond to the reduced model (10, 11, 12, 13) illustrating good agreement. Gray segments correspond to the gain fiber segment.

Figure 5

Temporal (a) and spectral (b) solutions from numerical simulation of (1) with gain (2) in the net-normal dispersion regime. The laser setup is the same as in Fig. 2 but with $d_2=-1.2$. Gray shade corresponds to the gain segment.

Figure 6

Evolution of pulse parameters over two map periods from full simulations (solid) and the reduced system (dashed) for the laser setup in Fig. 5. The results from application of the saturable absorber (SA) and output coupler (OC) are shown for both the full (circle) and the reduced (gray diamonds) models. Shaded regions correspond to the gain segment.

Figure 7

Temporal (a) and spectral (b) solutions from numerical simulation of (1) with gain (2) for an all-normal dispersion laser. Dispersion map parameters are $d_1=-1$, $L_1=3$, $d_2=-1$, $L_2=0.6$, and $d_3=-1$, $L_3=1$, and $\gamma =2$. Dissipative parameters are $g_0=30$, $e_0=1$, $\nu =0$, $\alpha =0$, $l_0=0.5$, $p_{\mathrm{s}}=3$, $\rho =0.7$, and ${\Omega }_f=0.8$. Note that the saturable absorber (SA), output coupler (OC), and spectral filter (SF) are applied in series resulting in the last three pulses in the map. Gray shade corresponds to the gain segment.

Figure 8

Evolution of pulse parameters over two map periods from full simulations (solid) and the reduced system (dashed) for the laser setup in Fig. 7. The results from application of the saturable absorber (SA), output coupler (OC), and spectral filter (SF) are shown for both the full (circle) and reduced (gray diamonds) models. Shaded regions correspond to the gain segment.

Figure 9

Temporal profiles of the pulse solution from the full governing Eqs. (1, 2) (solid) as well as the ansatz (22) with parameter values given by the solutions to the reduced Eq. (23) (dashed) at four distinct locations in the cavity. (a) At the beginning of the gain segment; (b) at the end of the gain segment; (c) after the output coupler; and (d) after spectral filtering.

Figure 10

Spectral profiles of the pulse solution from the full governing Eqs. (1, 2) (solid) as well as the ansatz (22) with parameter values given by the solutions to the reduced Eq. (23) (dashed) at the same four distinct locations in the cavity as in Fig. 9.

Figure 11

Output pulse energies as a function of spectral filter bandwidth values ${\Omega }_f$ for two laser configurations from both the full governing Eqs. (1, 2) (diamonds) and the reduced model (23). All parameters are the same as in Fig. 7, but the order of the saturable absorber and the output coupler are switched. All output energies are normalized by the output pulse energy of the laser system considered in Fig. 7. The output pulse energies are significantly increased in the configuration where the output coupler precedes the saturable absorber.