Stability analysis and quantum-limited noise properties of the Soliton-similariton fiber laser

Abstract

Soliton-similariton fiber lasers have demonstrated exceptional operational stability, maintaining continuous mode-locking for weeks despite large intracavity spectral and temporal breathing. We present the first stability study of this laser, rigorously establishing that the anomalous dispersion segment that supports the soliton is the cause of this robustness. Specifically, we perform linear stability analysis of the laser employing a Jacobian-based eigenvalue decomposition and show that the eigenvalues lie within the unit circle, leading to a positive stability margin, which is indicative of the robustness of the laser against small perturbations. Furthermore, the stability margin is observed to increase with the length of the anomalous fiber segment, clearly establishing its role in pulse stabilization. Critically, integrated pulse timing jitter and relative intensity noise as obtained from quantum noise-limited laser simulations are shown to be anti-correlated to the stability margin, further validating the results of the Jacobian analysis and establishing an unequivocal link between the reported noise performance of the soliton-similariton laser to the underlying pulse stabilization mechanism mediated by the anomalous segment. The direct link of the linear stability analysis to the underlying nonlinear physics of the laser, together with its significantly lower computational overhead, establishes it as a highly effective predictive framework for assessing laser noise performance, enabling novel approaches for designing quantum noise-limited ultrafast sources.

Figures (9)

• Figure 1: Schematic of the soliton-similariton fiber laser cavity. Pulse propagates clockwise through erbium-doped fiber amplifier (EDFA, red fiber, $+\beta_2$), Coupler 1, OFS-980 fiber (green, $+\beta_2$), bandpass filter and saturable absorber (BPF/S.A., green/blue box), SMF-28 fiber (orange, $-\beta_2$), and Coupler 2. Output couplers (orange) extract light from the cavity: Coupler 1 with 5% coupling ratio provides the main output, while Coupler 2 with 1% coupling ratio serves as a monitoring tap. The pump laser is coupled via wavelength-division multiplexer (WDM). The schematic of the all-normal-dispersion fiber laser is obtained by replacing the SMF-28 passive fiber (orange line) with a positive-dispersion fiber (green dashed line).
• Figure 2: Pulse formation dynamics and steady-state output at the two output ports of the soliton-similariton fiber laser.Left ($\mathrm{OC}_1$): Similariton output after the normal-dispersion segment. Right ($\mathrm{OC}_2$): Soliton output after the anomalous segment. Panels (a,e): steady-state temporal intensity (black) with parabolic/solitonic fits (green dashed) and their respective chirp (red, right axis). Panels (b,f): temporal evolution over 300 round trips showing convergence from noise. Panels (c,g): steady-state spectra centered at $1550\,\mathrm{nm}$. Panels (d,h): spectral evolution over round trips. All intensities are normalized. $\mathrm{R.T}$ represents round trips
• Figure 3: Steady-state output of the all-normal dispersion fiber laser. The anomalous segment in Fig. \ref{['fig:laser_schematic']} is replaced by a normal-dispersion fiber. The normalized temporal intensity and spectral power are shown after 300 round trips.
• Figure 4: Convergence dynamics and intracavity evolution for soliton-similariton and all-normal fiber lasers.(a,c) Phase-space trajectories in the Poincaré plane $(T_{\mathrm{RMS}}, \omega_{\mathrm{RMS}})$ for five independent quantum-noise initial conditions (marked ×) converging to fixed points (filled dots) for (a) soliton-similariton and (c) all-normal configurations. Both cavities exhibit wide basins of attraction, but the convergence character differs. The soliton-similariton laser shows oscillatory relaxation due to competing soliton and similariton dynamics, while the all-normal variant converges smoothly via purely dissipative pulse shaping. The number of round-trips taken to reach steady state for each noise is slightly different; however, the plot shown is for a fixed round-trip of 250. (b,d) Intracavity Poincaré maps reveal pulse evolution through successive cavity elements once the steady state has been reached. Closed trajectories confirm fixed-point operation in both systems, with arrows indicating propagation direction.
• Figure 5: Linear stability comparison. Top row: soliton-similariton laser. Bottom row: All-normal fiber laser. (a,c) Eigenvalues $\mu$ of the round-trip linearization in the complex plane; the unit circle marks the stability boundary $|\mu|=1$. The colorbar encodes the absolute value of eigenvalues $|\mu_i|$. (b,d) Sorted magnitudes $|\mu|$ with the red dashed line at $|\mu|=1$. All eigenvalues of the soliton-similariton laser cavity lie inside the unit circle and exhibit a larger spectral gap($1-\rho_{\mathbf{J}}$), indicating greater robustness of the fixed point. In contrast, the all-normal variant design has several eigenvalues ($|\mu|>1$) outside the unit circle, indicating that the fixed point associated with it is susceptible to perturbation.