Broadband Continuous Frequency Tuning in Non-Hermitian Laser Arrays Enabled by Mode-Switching Boundary Topology

Broadband and continuous frequency tuning is central to the versatility of semiconductor lasers, yet existing approaches typically rely on external moving components, limiting scalability and integration. Here we demonstrate broadband continuous frequency tuning in a non-Hermitian laser array achieved solely by controlling the pump currents. We show that in two coupled sub-lasers with frequency detuning ($Δω$) and relative loss ($Δα$), a mode-switching boundary emerges in the ($Δω$, $Δα$) parameter space, shaping the frequency landscape of the lower-loss supermode. The topology of this boundary comprises pseudo-symmetric (PS) and pseudo-symmetry-broken (PSB) branches connected at an exceptional point (EP). When tuning trajectories cross the PS branch, frequency tuning is discontinuous, whereas trajectories crossing the PSB branch enable continuous tuning; trajectories through the EP yield the maximum continuous tuning range. Experiments using two coupled terahertz quantum cascade lasers demonstrate continuous tuning over 10 GHz, enabled by arbitrarily many combinations of pump currents. Extending this approach to a multi-element array further expands the continuous tuning range to 163 GHz. These results establish a general route to broadband continuous tuning in moving-part-free semiconductor lasers and highlight the potential for dynamic eigenvalue engineering in non-Hermitian photonics and beyond.

💡 Research Summary

The authors present a novel, moving‑part‑free method for broadband continuous frequency tuning of semiconductor lasers by exploiting the topology of a mode‑switching boundary in a non‑Hermitian laser array. Starting from the well‑known challenge that conventional broadband tuning requires mechanically adjustable external cavities, the paper introduces a theoretical framework based on temporal coupled‑mode theory (TCMT) for two complexly coupled lasers. The key parameters are the frequency detuning Δω = (ω₁ – ω₂)/2 and the relative loss Δα = (α₁ – α₂)/2, while the mutual coupling is described by a complex coefficient κ. Solving the TCMT equations yields two complex eigenfrequencies ω₊ and ω₋ that form two Riemann sheets in the (Δω, Δα) plane. The real and imaginary parts of these eigenvalues intersect along two distinct curves: one where the real parts coalesce (pseudo‑symmetric, PS) and the imaginary parts split, and another where the imaginary parts coalesce (pseudo‑symmetry‑broken, PSB) while the real parts split. These two curves meet at an exceptional point (EP) where both eigenvalues and eigenvectors coalesce, creating a branch‑point singularity.

Lasing occurs in the supermode with the smaller imaginary part (lower loss). By varying the pump currents of the two sub‑lasers, Δα can be swept over a wide range while Δω remains fixed (set during fabrication). Consequently, the experimental tuning trajectory is essentially a line parallel to the Δα axis that inevitably crosses the mode‑switching boundary. If the trajectory crosses the PSB branch, the lower‑loss supermode’s real frequency changes smoothly, enabling continuous frequency tuning. If it crosses the PS branch, the real frequency jumps abruptly, producing a discontinuous “mode‑hop”. The EP represents the optimal crossing point: for a given Δα range, passing through the EP yields the maximal continuous tuning span.

To validate the theory, the authors design and fabricate terahertz quantum cascade lasers (THz QCLs) with second‑order distributed‑feedback gratings. By deliberately detuning the grating periods (Λ₁, Λ₂) they set Δω, and by engineering the gap between the two QCLs they control κ (both its magnitude and phase). Finite‑element electromagnetic simulations confirm that κ varies only weakly with Δω and Δα, justifying the constant‑κ assumption in the analytical model. Simulated eigenmode field profiles show the expected bonding/antibonding character of ω₊ and ω₋, and the calculated frequency landscape reproduces the PS and PSB branches and the EP.

Two experimental arrays are built. Array 1 has Δω ≈ 7 GHz < |Im κ|, placing its tuning trajectory below the EP; Array 2 has Δω ≈ 12 GHz > |Im κ|, placing it above the EP. By sweeping the pump currents (I₁, I₂) from (I₁max, 0) to (0, I₂max) the authors scan Δα from negative to positive values. In Array 1 the lasing frequency shifts continuously over ~10 GHz with smooth output power, confirming the PSB‑mediated continuous tuning. In Array 2 the frequency exhibits abrupt hops, confirming PS‑mediated discontinuous behavior. Mapping the entire (I₁, I₂) space shows a broad region of continuous tuning for the PSB case, illustrating the robustness of the approach.

Finally, the concept is extended to a multi‑element laser array (e.g., eight coupled QCLs). By arranging many sub‑lasers with varying Δω and Δα, the collective parameter space is vastly enlarged, allowing a continuous tuning range of 163 GHz—comparable to or exceeding that of traditional external‑cavity systems while retaining a compact, monolithic, and mechanically static architecture.

In summary, the work demonstrates that the topological features of non‑Hermitian coupled‑laser systems—specifically the mode‑switching boundary and its exceptional point—can be harnessed to achieve broadband, continuous frequency tuning using only electrical control. This strategy opens a pathway toward fully integrated, high‑speed, widely tunable laser sources across various spectral regions, with potential impact on spectroscopy, sensing, communications, and on‑chip photonic signal processing.