Fig. 1. (a) Schematic of the dual-element coupled PT stripe laser. (b) SEM image of the device.

Fig. 2. Ideal PT-symmetric laser model indicated by the solutions of Eqs. (1)–(3). (a) depicts the real part and the imaginary part of the complex propagation constants (β−β0) as a function of I1. In (b), the relative phase Δϕ and field amplitude ratio |E1|/|E2| are also given at different I1. In (c), (i) and (ii) are the temporal evolution of the field amplitude, carrier density, and relative phase, and they are before and after the exceptional point depicted in (a), respectively.

Fig. 3. Practical PT-symmetric laser model. (a) and (b) depict the real part and the imaginary part of the complex propagation constants (β−β0) as a function of current I1 from the theoretical model, respectively. It is a single-sided pumped structure with 2 μm spacing. Due to the synergistic interplay of gain contrast and frequency detuning, a distinct behavior arises, diverging from that depicted in Figs. 2(a) and 2(b). The position of the exceptional point is determined by both the gain contrast and frequency detuning parameters. In (c), the total output power of the two waveguides is depicted under different currents I1, while (d) illustrates the field amplitude |E1| in the gain waveguide and the field strength amplitude |E2| in the loss waveguide under different currents I1.

Fig. 4. LIV curves (a) and the spectra under different currents (b) for a single-sided pumped structure with 2 μm spacing. In the LIV curve, we emphasize the phase transition region around 180 mA. In this region, the appearance of a kink suggests the occurrence of mode hopping. From spectrum, when the current is low, the laser operates in a single longitudinal mode. As the pump intensity approaches the phase transition region, multimode lasing occurs. Upon surpassing the phase transition region threshold current, the system undergoes spontaneous symmetry breaking, maintaining single longitudinal mode emission.

Fig. 5. Horizontal far-field distribution (a) and near-field distribution (b) at specific currents for a single-sided pumped structure with 2 μm spacing. Before and after the exceptional point, both the near-field and far-field patterns transition from a double-lobed to a single-lobed profile, indicating the occurrence of PT symmetry breaking.

Fig. 6. In (a), the relative phase Δϕ and field amplitude ratio |E1|/|E2| under different currents I1 in gain waveguide and coupling coefficients κ are depicted. (b) and (c) are both single-sided pumped structures, and the distinction lies in the spacing distance between two ridges. In (b), the spacing distance corresponds to a 2 μm spacing, resulting in stronger coupling effects, whereas in (c), the spacing is 4 μm, leading to weaker coupling effects. (i) illustrates the theoretical calculations obtained through TCMT and RE, while (ii) depicts experimental measurements obtained from near-field and far-field data. Inset in (b, i) is derived from the FFT of the output electric field at a current I1 of 0.17 A. The black arrows indicate a significant field amplitude ratio in (ii), as the field strength within the loss waveguide cannot be measured under the testing precision.

Fig. 7. Relative phase Δϕ and field amplitude ratio |E1|/|E2| under different currents I1 in the gain waveguide and currents I2 in the loss waveguide are depicted. (a) 2 μm spacing, (d) 4 μm spacing. In (b) and (e), the loss waveguides are pumped with 15 mA current I2, whereas in (c) and (f), the pumping current I2 is 35 mA. (i) and (ii) present theoretical and experimental results, respectively. The relative phase and field amplitude ratio in the phase transition region are the density distribution maps under different initial settings in (c, i) and (f, ii).

Fig. 8. Distribution of the transverse (a) and lateral (b) carrier diffusion densities.

Fig. 9. Field amplitudes |E1,2| in (a) and carrier densities N1,2 in (b) versus the time t.