Topological Anderson Random Laser

Abstract

Topological lasers and random lasers embody two contrasting strategies for disorder management in photonics: the former suppresses disorder via protected edge transport, while the latter exploits multiple scattering for feedback. Here, we theoretically demonstrate that these seemingly incompatible paradigms can be unified through a topological Anderson random laser (TARL), where disorder itself induces a topological phase that enables robust lasing. Starting from a trivial photonic lattice, we show that engineered disorder drives the system into a topological Anderson insulator regime, generating emergent chiral edge states that serve as boundary-selective lasing channels. Remarkably, the TARL exhibits rapid mode selection toward a single edge state, producing an ultranarrow emission spectrum and enhanced slope efficiency optimized near disorder strength with maximal topological mobility gap. Furthermore, they exhibit single-mode-like coherence properties, deviating from Kardar-Parisi-Zhang behavior in conventional chiral topological lasers, while remaining significantly more robust against local perturbations than conventional random lasers. Our findings establish a disorder-enabled flexible route to topologically protected single-mode lasing and introduce a fundamentally new design principle for robust, high-coherence photonic light sources.

Figures (10)

• Figure 1: Band structure and topological phase characteristics.(a) Band structure of a cylindrical QWZ lattice with width $N_{y}=20$ and parameter $u=-1$. (b) Phase diagram in the $w$-$u$ plane determined by the Bott index $C_B$ with $E_{f}=0$, the TAI phase appears in the purple area. (c) Eigenvalue distribution of a finite TAI system with $N_{x}=20, N_{y}=20, u=-2.1$, and disorder strength $W=3.5$. The horizontal axis shows the eigenvalue $\omega$, and the vertical axis indicates the edge population $I_E$. The color map represents the IPR, characterizing the localization of each eigenstate. (d) Bott index $C_B$ evaluated over different disorder strength $W$ and Fermi energy $E_{f}$, showing the closure of the trivial band gap (orange) followed by the emergence of a disorder-induced topological mobility gap (purple).
• Figure 2: Single-mode lasing behavior in TARLs. (a) Schematic demonstration of how the TARL supports a single edge mode that dominates the lasing dynamics. (b) Time-resolved power spectral density (PSD) for the TARL (left panel) and a conventional QWZ-based TL (right panel), highlighting the rapid single-mode selection in the TARL case. (c) The normalized PSD (blue bars) averaged over initial fluctuations and the density of states (red line) of the TARL system. The gray shaded region marks the pumping frequency window. The parameters for the TARL (conventional TL) are: $u=-2.1$ and $W=3.5$ ($u=-1$ and $W=0$). Other parameters are $P=0.5$, $\gamma=0.1$.
• Figure 3: Eigenfrequencies and normalized GMO factors $\eta_j$ of all modes for (a) the TARL with $u=-2.1$, $W=3.5$ and (b) the conventional TL with $u=-1$, $W=0$. Black (red) circles denote bulk (edge) modes.
• Figure 4: Slope efficiency of the TARL. (a) Laser output intensity $I$ as a function of pump strength $P/\gamma$ for different disorder strengths $W$. (b) Slope efficiency $S$ as a function of disorder strength $W$. The results are averaged over 100 realizations of disorder reconfiguration, with the shaded region indicating the 95% confidence interval. The efficiency is maximized near the disorder value $W\simeq 4$ that corresponds to the largest topological mobility gap [see Fig. \ref{['fig:1']}(c)]. Other parameters are the same as that in Fig. \ref{['fig:2']}.
• Figure 5: Robustness of the TARL against local perturbations. (a) and (b) the real-space patterns of the steady laser with defects (white squares) introduced in the bulk and boundary, respectively. (c) The normalized PSDs (blue bars and yellow bars) corresponding to the defects in (a) and (b), respectively. (d) The normalized PSD disorder reconfigurations of $3$ sites (blue bars) and $20$ sites (yellow bars) compared with the disorder configuration in Fig. \ref{['fig:2']}. The gray dashed line marks the position of the PSD peak in Fig. \ref{['fig:2']}(c). Other parameters are the same as in Fig. \ref{['fig:2']}.