Introduction

Over the past decade, topological photonics has revolutionized photonic science by enabling robust unidirectional light propagation that is inherently immune to backscattering and structural imperfections1,2,3,4,5,6,7. Among various platforms, glass-based waveguide arrays have driven major advances in both linear and nonlinear topological photonics and relevant quantum simulators8,9,10,11,12,13,14,15,16,17,18,19. However, the inherently high pump thresholds and intrinsically low gain of glass platforms fundamentally exclude their viability for supporting actively reconfigurable topological devices. To circumvent this limitation, the non-Hermitian topological experiments in glass have adopted a “low-loss-for-gain” strategy, where engineered waveguide losses (e.g., through controlled bending or absorption modulation) artificially mimic gain effects14,20,21. These workarounds incur substantial propagation losses, severely limiting their utility for truly active topological photonics and quantum information processing.

Recent progress in topological photonics has extended beyond passive architectures, giving rise to topological lasers that harness the interplay between non-Hermitian dynamics, nonlinear interactions, and topological band structures14,22,23,24,25,26,27,28. These systems have garnered considerable interest owing to their unique physical phenomena and potential for applications in electro-optics and integrated photonics. Unlike traditional lasers, topological laser emission occurs in a topologically protected state, offering robustness against structural defect and disorder, inherent from underlying topological properties of the photonic system24,29,30,31,32,33,34,35,36,37.

While topologically protected lasing has been demonstrated in microcavities and microring resonators based on semiconductor materials, these platforms still face notable limitations38,39,40,41. Notably, they exhibit comparatively lower pump efficiency and output power than conventional lasers. Moreover, their laser modes are fixed in spatial position, lacking reconfigurability. The static nature of these lasing modes poses a major obstacle for practical applications, because the topological lasing is restricted to specific regions, such as interfaces between topologically distinct regions, leaving much of the footprint of the device unused. Furthermore, as the pump power increases, nonlinear saturation effects in semiconductor materials destroy edge localization and induce bulk modes, preventing topological lasing at arbitrary sites30. As a result, the concept of topological lasing in non-Hermitian optical systems remains largely confined to fundamental research.

Femtosecond laser direct writing has become an established technique for waveguide fabrication in optical materials. However, in crystalline systems, this method predominantly produces Type-II modifications that that are typically with poor mode coupling control in waveguide arrays42. In contrast, we demonstrate that the Nd:BaLaGa3O7 crystal43 overcomes this limitation, enabling stable, low-loss Type-I waveguides (<0.6 dB/cm) with exceptional transverse coupling feature in photonic lattices, while simultaneously preserving high optical gain inside the waveguide cores. This unique dual capability is critical for achieving path-selective, high-performance topological waveguide laser generation and output.

In this work, we theoretically and experimentally demonstrate the active topological lasing at arbitrary site of Su–Schrieffer–Heeger (SSH) waveguide arrays fabricated on a self-grown disordered laser crystal (Nd:BaLaGa3O7). Using this all-solid-state laser platform (Fig. 1a, b), we achieve the single-mode, continuous-wave (CW) lasing at wavelength of 1060 nm under 808 nm light pump, delivering an output power exceeding 100 mW (corresponding to power density above 2.5 MW/cm2), far exceeding values reported in other topological laser systems. For instance, our platform delivers an output power more than two orders of magnitude greater than reported semiconductor topological lasers—surpassing typical values of ~6 μW44, 2 mW (peak power)34 or 4 kW/cm2 (10 W over a 500 × 500 μm2 area)35. Crucially, the fabricated waveguide exhibits exceptional long-term stability, as evidenced by the maintained waveguiding transmission and lasing output with no obvious degradation after three years at room temperature. This robustness directly validates the practical potential of our approach and paves the way for developing viable topological laser devices.

Fig. 1: Topological lasing in the presence of material gain.
Fig. 1: Topological lasing in the presence of material gain.
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a Diagram of gain-induced topologically protected laser in the active waveguide laser system. Mirror 1 and 2 (M1 and M2) form a parallel resonant cavity. b Energy level diagram of the active medium Nd3+.The pump energy excites electrons to the 4F3/2 energy level, leading to spontaneous emission of multiple photons that manifests as broadband random noise. Photons with wavelength of 1060 nm oscillate inside the resonator, generating stimulated emission that drives stable gain, while other photons that do not contribute to the oscillations dissipate through competitive suppression mechanisms. c, d Simulated propagation field as a function of the evolutionary distance along the waveguide array. Field evolution when excited at either an edge trivial site (c) or an arbitrary interface site (d), in the passive (i) and active (ii) environments, respectively.

Results and Discussion

In contrast to the previously mentioned semiconductor-based topological laser platforms, our system employs an all-solid-state waveguide laser architecture that offers superior performance, including a higher stimulated emission cross-section, lower intrinsic loss, as well as excellent thermal conductivity and beam quality. These advantages enable even conventional sites lasers to maintain high-quality output modes and narrow linewidths. Leveraging these benefits, we have not only achieved robust topological lasing at topological edge states, but also observed topological edge lasing at trivial lattice terminals (Fig. 1c)— a phenomenon that has not been reported before. Remarkably, leveraging the high-gain properties of solid-state waveguide lasers, we demonstrate the topological lasing at arbitrarily positioned topological interface sites within the lattice (Fig. 1d), effectively unlocking lasing beyond fixed geometric boundaries. We notice that an earlier work reported the emergence of interface modes at the centre of a zigzag chain of polariton micropillars via local non-Hermitian pumping in an SSH chain45. This theoretical prediction provides a related conceptual framework, and our work demonstrates reconfigurable lasing at site-selective modes that is experimentally realized in an all–solid-state laser platform. Furthermore, we reveal that the parity-time (PT) symmetry phase transition of such interface modes occur at higher gain threshold that is locally introduced at a single site, distinct from conventional PT phase transitions triggered by large-scale gain/loss distributions on the lattice14,27,46,47,48,49. Our findings crucial advance the understanding of the interaction between lasers and topological structures, and open avenues for fully utilizing device footprints and realizing on-demand, reconfigurable laser output at selectable site.

We numerically discover that topological edge modes and interface modes at arbitrary position can emerge from trivial sites when gain is introduced at single boundary/intermediate site in the SSH model, as detailed in Supplementary Note 1. To gain deeper insight into this interplay between non-Hermitian effect and topological phase transition, we analytically investigate two representative cases based on SSH model with intracell coupling v and intercell coupling w. In the first example, we consider a non-Hermitian semi-infinite SSH chain with gain iΓ applied to the leftmost site (highlighted in red in Fig. 2a). To analytically capture the non-Hermitian behaviour, we model the interaction between the second leftmost boundary site and the remainder of the system as a self-energy term Σ(E) (see the derivation in Supplementary information and also in ref. 50), leading to an effective edge Hamiltonian, which reads:

$${H}_{eff}(E)=\left(\begin{array}{cc}i\Gamma & v\\ v & 0\end{array}\right)+\varSigma (E),$$
(1)

where E is the energy of the edge modes. Solving the eigenvalue of Eq. (1) yields the analytic expression for the eigenenergy,

$$E=\frac{i{\Gamma }^{2}-i{w}^{2}\pm \sqrt{-{\Gamma }^{4}+4{\Gamma }^{2}{v}^{2}-2{\Gamma }^{2}{w}^{2}-{w}^{4}}}{2\Gamma }$$
(2)

The complex energy curves produced from Eq. (2) show exactly agreement with numerical results, as illustrated in Fig. 2c. At low gain (Γ>w), two edge modes (red curves), verified by the spatial distribution of wave function in Fig. 2e, emerge distinctly from the bulk continuum (blue-shaded region), remaining degenerate in imaginary part of their energy. As the gain increases beyond a critical threshold \(\Gamma=v+\sqrt{{v}^{2}-{w}^{2}}\), these two edge modes coalesce at an exceptional point (EP) and undergoes a PT phase transition. Notably, since Γ is real-valued, this PT phase transition occurs only when the bulk lattice on the right is in a trivial phase (v > w), consistent with our numerical findings. In the PT-broken regime, the two edge modes exhibit zero real energy and differ in imaginary energy component. Topological lasing is expected to occur on edge mode with the larger imaginary part, corresponding to the higher gain. These edge modes retain the topological properties inherited from the bulk. Consequently, lasing in such modes is topologically protected and robust against structural disorder, as confirmed in our subsequent experiments.

Fig. 2: Schematic diagrams of SSH model and corresponding band structures and wavefunction distributions.
Fig. 2: Schematic diagrams of SSH model and corresponding band structures and wavefunction distributions.
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a, b Schematic of gain-induced semi-infinite SSH model (a), and infinite SSH model (b) supporting topological edge modes. In (a), the boundary is designated as the gain at leftmost lattice site together with its coupled neighbour site, while the bulk region on the right contributes with self-energy to the boundary. In (b), the interface region is designated as an arbitrary intermediate site together with its coupled neighbour site, and it accounts for self-energy from both left and right semi-infinite segments of the bulk. Red-coloured site represents the gain site. c, d The complex spectra and parity-time (PT) phase transition of topological edge modes (c) and topological interface modes (d). Red-coloured curves represent bands of edge (interface) modes, blue-dotted curves and purple-dotted curves are projection of edge (interface) modes on real-energy plane and imaginary-energy plane, respectively, and blue-shaded regions are bulk bands. e, f Wavefunction profile variations over the lattice as a function of the gain parameter Γ, for the schematic shown in (a) and (b), respectively. The purple and blue arrows indicate the location of edge states emergence and PT phase transition. Coupling parameters v = 0.95 and w = 0.208 are used consistently throughout the manuscript unless otherwise specified.

Intriguingly, the mechanism of inducing the topological modes can be generalized to arbitrary sites within the lattice, as demonstrated in our second example. We consider an infinitely SSH model with gain (or loss) introduced at an arbitrary intermediate site, denoted by the red dot in Fig. 2b. To define an interface, the gain site can always be grouped with its neighbouring site, where the interaction between them is v. The corresponding effective interface Hamiltonian for such group region becomes (details in Supplementary note 4)

$${H}_{eff}(E)=\left(\begin{array}{cc}i\Gamma+\varSigma {(E)}_{2,2} & v\\ v & \varSigma {(E)}_{2,2}\end{array}\right)$$
(3)

The eigenvalue of the effective Hamiltonian is solved accordingly:

$$E=\pm \frac{\sqrt{2{v}^{2}+2{w}^{2}-{\Gamma }^{2}\pm \sqrt{({\Gamma }^{2}-4{v}^{2})({\Gamma }^{2}-4{w}^{2})}}}{\sqrt{2}}$$
(4)

The analytic complex eigenenergies of the effective Hamiltonian are plotted (red curves) in Fig. 2d, displaying behaviours analogous to the first example. As the gain increases, the curve exhibits two EPs indicating two PT-phase transitions. However, only the transition occurring in the complex domain (Im(E) ≠ 0) is relevant for our case, as interface modes appear only after the eigenvalue branches separate from the bulk spectra (see the evidence of wave function evolution in Fig. 2f). Consequently, two topological interface modes are created at arbitrary sites within the lattice when the gain exceeds at critical threshold (Γ > max(2 v,2w)), enabling topological lasing at these interface modes.

To verify the theoretical predictions of our model, we fabricated a photonic waveguide lattice based on the SSH model in a Nd:BaLaGa3O7 crystal using femtosecond laser direct writing. The fabricated SSH lattice, shown in Fig. 3a, b, consists of an odd number of identical waveguides, supporting a single topological zero-energy mode in the passive (non-gain) environment. The intracellular and intercellular spacings are 15 μm and 8 μm, respectively, corresponding to hopping coefficients of w = 0.208 and v = 0.95 (in units of 1/mm, more details in Supplementary Figs. 5, 6).

Fig. 3: Topological waveguide array design and laser performance.
Fig. 3: Topological waveguide array design and laser performance.
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a Schematic of the SSH-type waveguide array with alternating coupling strengths, as indicated by the single and double lines connecting consecutive sites. b End-face image of the fabricated SSH model waveguide array. The intra-cell (d1, w = 0.208) and inter-cell (d2, v = 0.95) spacings are 15 μm and 8 μm, respectively. c, d Measured output intensity profiles of the photonic lattice under passive (c) and active (d) conditions, with initial excitation at the topological defect site (Site 1), a trivial bulk site (Site 8), and a boundary site (Site 15). e End-face view of a conventional waveguide array (uniform spacing of 12 μm, coupling parameter of 0.399) and corresponding active laser output distribution. (f, g) Measured output laser power as a function of incident pump power (f) and emission spectra at 0.7 W pump power (g) for the SSH model waveguide array (Sites 1, 8, and 15 in b) and the conventional array (e). Scale bars in panels (a, e) are 20 μm.

Using the end-face coupling setup, we excited different sites within the waveguide array under a passive environment and examined the output light field distributions to assess the optical propagation characteristics. The experimental results closely match our simulation using the beam propagation method (BPM, see Supplementary Fig. 7). The normalized light field distribution after initial excitation at two edge sites (left and right), evolving over a propagation length of 1 cm, shown in Fig. 3c. When the non-trivial topological site is excited (upper inset of Fig. 3c, Site 1), the optical field remains highly localized at the boundary, consistent with the presence of a topologically protected edge mode. In contrast, excitation at a trivial bulk site (middle inset, Site 8) or the rightmost edge site (lower inset, Site 15) results in light gradually diffusing into the bulk, indicating the excitation of extended modes rather than localized ones. The propagation dynamics simulated via BPM (in Supplementary Fig. 8) further confirms the experimental observations.

As predicted by our theory, introducing strong non-Hermitian gain at a single site induces a complex PT phase transition in the edge/interface modes. This mechanism stands in stark contrast to previously reported topological lasers based on semiconductor microring resonators, which typically rely on periodically distributed gain and loss. In those semiconductor-based platforms, the limited damage threshold of the material imposes strict constraints on the allowable pump power density, resulting in relatively low net optical gain. Consequently, exploring topological lasing behaviours under high-gain or extreme pumping conditions remains a major challenge. In contrast, our solid-state waveguide laser system circumvents these limitations. Within our model framework, the pump light (at wavelength of 808 nm) also undergoes severe attenuation in the active system and is theoretically predicted to become spatially localized. However, owing to round-trip dissipation within the resonant cavity, these loss-induced localizations decay rapidly on sub-oscillation timescales, making them experimentally unobservable. As such, our investigation focuses exclusively on topological lasing behaviour in the gain regime above the lasing threshold. In practice, intrinsic pump loss and the nonlinear lasing threshold confine the effective gain to the spatially pumped region. In our experiment, multiple reflections of the laser within the parallel resonant cavity drive the evolution of the output mode-field distribution toward the intrinsic eigenmode profile of the lattice upon excitation. In Supplementary Note 8, we clearly demonstrate the threshold behavior of the laser—including spectral linewidth narrowing at the threshold, emergence of high-brightness localized lasing, polarization analysis, and log-log intensity plots—providing comprehensive evidence for the generation and output of topological lasers on a solid-state laser platform.

Under optical excitation of the conventional topological edge mode, laser emission is initiated via both direct pumping and nonlinear amplification, giving rise to a strongly localized output at the left boundary (Fig. 3d, upper inset). Remarkably, over 96% of the total output power is concentrated at the non-trivial site, highlighting the robustness and efficiency of topologically protected lasing. Notably, when the trivial edge or interface site is pumped, the resulting laser output does not diffuse into the bulk but instead forms a new localized mode, as shown in the middle inset or lower inset of Fig. 3d—a behaviour absent under conservative (passive) conditions. The resulting lasing mode is found to be a hybridized mode of two sites, in full agreement with our theoretical predictions. This observation underscores the power of local non-Hermitian perturbations in reshaping topological mode landscapes and enabling reconfigurable lasing.

In Fig. 3f, the conventional-topologically protected mode yields the highest active laser output power, reaching approximately 102.6 mW. The maximum output powers at the gain-induced topological interface mode and the right boundary mode are 72.7 mW and 82.2 mW, respectively. We note that the gain-induced topological interface mode (0.40 W) and right boundary mode (0.38 W) exhibit a relatively higher lasing threshold compared to the conventional topological edge mode (~0.34 W). This is attributed to the fact that these emergent topological modes only arise beyond a finite gain threshold, as discussed in Fig. 2. In contrast, the reference structure consisting of a uniform waveguide array without topological features (Fig. 3e) exhibits spatially delocalized lasing modes, leading to an obvious higher lasing threshold of 0.67 W. Moreover, the slope efficiency is lower, and the overall output power is limited to only 11.6 mW. Importantly, when benchmarked against previously reported topological laser systems based on semiconductor platforms24,33,34,35,36,37,38,39, the active topological lasers demonstrated here deliver markedly enhanced performance. They achieve output powers exceeding 100 mW and a power density surpassing 2.5 MW/cm2. Owing to the inherent advantages of the solid-state gain medium, the devices also exhibit superior beam quality, featuring well-defined single-mode emission, high ellipticity, and a narrow linewidth (~0.6 nm; see Fig. 3g and Supplementary Figs. 9–12), which make them highly promising for laser applications requiring high coherence and spectral purity.

To assess the robustness of the topological laser in our system, we investigated the laser output characteristics in a mildly disordered lattice structure. Specifically, we maintained an average lattice spacing of 18 μm and introduced positional disorder via the Fibonacci sequence modulation, which perturbs the lattice spacing quasi-periodically via a modulation parameter (modulation parameter Vn). This approach effectively simulates crystal defects or fabrication imperfections, as illustrated in Fig. 4a. In the passive regime, lasing at nontrivial topological sites remains well-confined and protected, whereas excitation at trivial sites results in delocalized output modes, as shown in Supplementary Fig. 13b. The near-field laser intensity distributions of the disordered waveguide array in active environment are shown in Fig.4b. Under this condition, when trivial sites (e.g., Sites8 and 15) are optically pumped, the resulting topological lasing remains robust against the disorder, maintaining strong spatial localization—demonstrating insensitivity to structural perturbations, as shown in Supplementary Fig. 13c. Additionally, we conducted studies by introducing a random position disorder scheme (in Supplementary Fig. 14, the maximum position offset ~2 μm), which similarly achieve stable localized laser output.

Fig. 4: Robustness of non-Hermitian topological laser.
Fig. 4: Robustness of non-Hermitian topological laser.
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a Cross-sectional images of waveguide arrays with slight disorder. The intercellular distance is fixed at d1 = 18 μm; The intracellular is d2 + Vn, with d2 = 9 μm; Vn = 3cos(2πβn); β = (√5-1)/2. b Intensity at the output of the photonic lattice in the active environments, with initial excitation at Site 1, Site 8, and Site 15. c, d Measured laser output power (c) and emission spectra at 0.7 W pump power (d), for the various input sites. Scale bar in panel a is 20 μm.

A quantitative analysis of the laser characteristics from the gain-induced topological modes in the disordered array is shown in Fig. 4c, d. The presence of disorder introduces no measurable spectral fluctuations, with the output laser linewidth consistently maintained around ~0.6 nm. Additionally, both the lasing thresholds and peak output powers exhibit minimal variation across different sites, further confirming the resilience of the gain-induced topological modes. These findings suggest that energy localization and extraction from the topological modes are preserved despite disorder, affirming that the gain profile inherits topological protection. In summary, the active topological laser demonstrates remarkable robustness under positional disorder, with stable lasing thresholds, narrow linewidths, and consistent output powers-highlighting its potential for practical applications in imperfect or scalable photonic systems.

In conclusion, we have successfully demonstrated active topological localized lasing in a SSH waveguide array based on an all-solid-state laser platform—a disordered Nd:BaLaGa3O7 crystal. By introducing optical gain, we observed merged topological lasing at a trivial end and arbitrarily positioned interface sites within the lattice. This work highlights the critical role of non-Hermitian gain or loss in driving topological phase transitions, offering a mechanism for realizing topological modes and lasing at configurable locations. Furthermore, the fabricated device demonstrates exceptional long-term stability—a critical requirement for practical applications. Remarkably, its key optical properties, including waveguiding transmission and lasing output, remain highly stable at room temperature over a three-year period without noticeable degradation. This unprecedented durability effectively overcomes a major obstacle to the practical implementation of topological lasers, establishing our architecture as a promising platform for stable device development. Beyond its immediate implications, our approach establishes a versatile platform and experimental framework for exploring high-dimensional and non-Hermitian physics in active photonics.

It is also worth noting that the recent work by Georgakilas et al.51 demonstrated selective polariton condensation in SSH lattices by tuning the excitation position and resonance, providing an important point of comparison. In their configuration, it appears that pumping near the centre results in condensation into trivial bulk modes. In contrast, our work establishes the local lasing of non-Hermitian interface modes, which is a distinct effect central to our findings.

Methods

Materials preparation

The disordered laser crystal Nd:BaLaGa3O7 used in this work belongs to a cubic system. It consists of layered GaO4 tetrahedra, with Ba2+ and La3+ randomly distributed between the layers in a 1:1 ratio at the corresponding lattice sites. Differences in the chemical valence of the two elements, particle radii, and crystallization properties result in the disordered structure of the crystals. The polycrystalline material synthesis was carried out according to the chemical equation, 0.005 Nd2O3 + BaCO3 + 0.495 La2O3 + 1.5 Ga2O3 = BaLa0.99Nd0.01Ga3O7 + CO2 ↑ . Before sintering, the raw materials were carefully weighed, ground, mixed, and pressed, followed by heating in a platinum crucible at temperature between 1050 °C and 1100 °C. The fully reacted polycrystalline material was subsequently subjected to crystal growth using a traditional pulling method in an iridium crucible. The initiation of crystal growth was achieved through the conventional pulling method. The crystal was then cut and polished to a size of 10 × 10 × 2 mm3 with a lattice orientation in the c-axis. 10 × 10 mm of the large surface was polished so that the processing laser could be incident on the inside of the material for waveguide writing. For the cross-section of the laser transmission, i.e. the parallel surface of the resonant cavity, we use a double-sided polishing method to ensure the parallelism and perpendicularity of the material. The perpendicularity of the material is kept below 15′ to ensure a low laser generation threshold, which is critical for high-performance laser output.

Fabrication of the SSH-model photonic lattices

The photonic lattice was fabricated in the Nd:BaLaGa₃O₇ crystal using a fiber chirped-pulse amplification laser (FemtoYLTM-25, YSL Photonics) with a central wavelength of 1030 nm, a pulse duration of 400 fs, and a tunable repetition rate (25 kHz–5 MHz). The femtosecond laser beam was focused inside the crystal via a 50×, NA = 0.45 objective lens (Sigma), while the sample was precisely positioned using a six-axis stage (Hybrid Hexapod, ALIO) with 100 nm spatial resolution. Single-mode Type I waveguides were inscribed via direct laser writing at a repetition rate of 25 kHz, a laser power of 12 mW, and a scanning speed of 1 mm/s. The cross sections of waveguides were imaged using a metallographic microscope (Zeiss) to verify waveguide positioning and detect any crystal damage. The refractive index contrast between the waveguide cores and the unmodified bulk crystal was measured to be Δn ≈ +3.6 × 10−3.

Measurements

To characterize the topological properties of the waveguide array in the passive regime, we employed a conventional end-coupled measurement system (Supplementary Fig. 5). The experimental setup utilized a 1064 nm laser source whose polarization was controlled by a half-wave plate. Laser coupling into the waveguide was achieved through a 20× objective lens (NA = 0.40), with an identical objective lens used to collect the output signal for power measurement. The output mode profile was simultaneously imaged using a CCD camera. For active topological lasing characterization (Supplementary Fig. 9), we implemented a pump-probe configuration using a tuneable CW Ti:Sapphire laser (Coherent MBR PE) as the excitation source. The pump polarization was similarly controlled by a half-wave plate, with beam focusing accomplished through a long working-distance plano-convex lens (f = 25 mm) to selectively excite individual sites within the waveguide array. The optical cavity was formed by two mirrors: a pump mirror (99.8% transmission at 808 nm and >99.9% reflectivity at 1060 nm) and an output coupler (total reflection at 808 nm with 40% ± 2% transmission at 1060 nm), arranged perpendicular to the waveguide propagation direction. The lasing output was collected using a 20× microscope objective and characterized through simultaneous power measurement and spatial profile imaging using powermeter, a CCD camera and a spectrometer (~0.1 nm resolution), respectively.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.