Significance Conventional semiconductor lasers typically use gratings, such as distributed feedback (DFB), distributed Bragg reflector (DBR), and slotted surface, to select longitudinal modes and microstructures to select lateral modes, such as narrow ridge, chirped waveguide array, and angled cavity. Even though these technologies are mature, their practicality is limited by output power or complex fabrication processes. For example, a narrow ridge can suppress the high-order lateral modes of the edge-emitting semiconductor laser, thereby limiting the laser's output power due to the small area of current injection. Therefore, new physical effects should be explored to offer new insights into the designs of lasers. Recently, because of the similarity between quantum and optical systems, some physical terminologies of the former are introduced to the latter such as parity-time (PT) symmetry and supersymmetry (SUSY).

The PT symmetry can be used to control the laser's spectral and spatial characteristics. The optical system obeying PT symmetry requires that its complex refractive index satisfies the relation, n(x)=n^*(-x), which means that the distributions of the real and imaginary parts of the complex refractive index are even and odd functions, respectively. One specified pair of modes of the system can evolve from the PT-symmetric phase to the broken PT-symmetric phase by varying the gain/loss contrast of the PT-symmetric system [Figs. 1(b), (c)]. Especially when the modes stay in the broken phase, the mode field distribution of the amplified mode will be in the gain area and the lossy mode will be in the loss area [Fig. 1(d)], allowing the realization of a single-mode laser. SUSY can also control the optical modes of lasers, making it an excellent candidate for single lateral mode laser arrays. For a waveguide array, the superpartner of the array can be constructed by supersymmetric transformation to couple the high-order modes of the original array but do not influence the fundamental mode (Fig. 3), which can increase the lasing threshold difference between high-order and fundamental modes. Then, the SUSY laser array can exclusively achieve fundamental mode lasing, which improves the laser array's lateral beam quality. Therefore, it is critical to review recent works on the two new methods of optical mode control in lasers.

Progress PT symmetry can be realized in the lateral direction of the lasers (Figs. 4--6). Here, the lasing of a single lateral mode can be achieved due to the selective PT symmetric breaking of the fundamental mode, which results from the smaller coupling constant of the fundamental mode than that of high-order mode. When the optical system is PT symmetric, the increased gain threshold between the centered longitudinal modes in the gain spectrum and neighboring longitudinal modes aid the realization of a single longitudinal mode lasing. Furthermore, PT symmetry can be applied to the longitudinal direction (direction along the cavity length). The longitudinally PT-symmetric laser can also realize single-mode lasing because of the PT symmetric breaking of the specified modes (Fig. 7). In addition, coherent perfect absorber (CPA)-laser (Fig. 8) and orbital angular momentum (OAM) laser (Fig. 9) are realized on the basis of longitudinally PT-symmetric microstructures. The double mode spacing of the CPA-laser is observed compared with that of the common Fabry-Perot laser, showing that the neighboring lasing modes move in the opposite direction of the complex plane of frequency when the laser stays in the broken PT-symmetric phase [Fig. 2(f)]. The OAM laser can use the orbital angular momentum of light to transfer information, increase the density of data transmission, and pave the way to develop a multidimensional OAM-spin angular momentum (SAM)-wavelength division multiplexing.

Similarly, SUSY can control the optical modes of non-Hermitian systems. The SUSY transformation is used to determine the profile of the refractive index distribution of the SUSY laser array so that the modes are selectively confined in the original array. Simultaneously, the chirped energy pumping increases lasing threshold difference between the selectively confined modes and other modes. If the fundamental mode is confined in the original array and other modes extend to the lossy superpartners, single lateral mode lasing can be realized with higher output power than the single-ridge laser under the same energy pumping density [Figs. 10(a)--(h)]. Furthermore, the second-order SUSY micro-ring laser array is also reported [Figs. 10(i)--(k)], which greatly simplifies large-scale laser array engineering because the superpartner and original array possess identical elements. Also, the second-order SUSY micro-ring laser array emits light in a single lateral mode.

Conclusions and Prospect In summary, PT-symmetric lasers that can not only be pumped optically and electrically are realized. However, the methods to suppress the influences of nonlinear effects on the stability of PT-symmetric laser operation should be explored eagerly. Compared with the PT-symmetric lasers, SUSY lasers are still pumped optically. Electrically injected SUSY lasers with multiple coupling terminals are promising candidates for high output power single lateral mode lasers.