Towards optimization of photonic-crystal surface-emitting lasers via quantum annealing

Novel real number representations in Ising machines and performance evaluation: Combinatorial random number sum and constant division

Quantum annealing machines are next-generation computers for solving combinatorial optimization problems. Although physical simulations are one of the most promising applications of quantum annealing machines, a method how to embed the target problem into the machines has not been developed except for certain simple examples. In this study, we focus on a method of representing real numbers using binary variables, or quantum bits. One of the most important problems for conducting physical simulation by quantum annealing machines is how to represent the real number with quantum bits. The variables in physical simulations are often represented by real numbers but real numbers must be represented by a combination of binary variables in quantum annealing, such as quadratic unconstrained binary optimization (QUBO). Conventionally, real numbers have been represented by assigning each digit of their binary number representation to a binary variable. Considering the classical annealing point of view, we noticed that when real numbers are represented in binary numbers, there are numbers that can only be reached by inverting several bits simultaneously under the restriction of not increasing a given Hamiltonian, which makes the optimization very difficult. In this work, we propose three new types of real number representation and compared these representations under the problem of solving linear equations. As a result, we found experimentally that the accuracy of the solution varies significantly depending on how the real numbers are represented. We also found that the most appropriate representation depends on the size and difficulty of the problem to be solved and that these differences show a consistent trend for two annealing solvers. Finally, we explain the reasons for these differences using simple models, the minimum required number of simultaneous bit flips, one-way probabilistic bit-flip energy minimization, and simulation of ideal quantum annealing machine.

Design of double-lattice GaN-PCSEL based on triangular and circular holes

We have theoretically designed a double-lattice photonic crystal surface-emitting laser (PCSEL) based on triangular and circular holes. In the design, porous-GaN which has the properties of lower refractive index and high quality stress-free homo-epitaxy with GaN, was first proposed to be the cladding layer for GaN-PCSEL. The finite difference-time domain (FDTD), the plane wave expansion (PWE), and the rigorous coupled-wave analysis (RCWA) method were employed in the investigation. Our simulations achieved a radiation constant of up to 50 cm-1 and a slope efficiency of more than 1 W/A while maintaining a low threshold gain. We conducted a systematic study on the effects of the filling factor, etching depth, and holes shift, on the performance of the PCSEL. The findings indicate that increasing the filling factor improves the radiation constant and slope efficiency. Asymmetric hole patterns and varying etching depths have a similar effect. The introduction of asymmetric patterns and a double lattice in the photonic crystal breaks the symmetry of electric fields in the plane, while different etching depths of the two holes break the symmetry in the vertical direction. Additionally, altering the shift of the double lattice modifies the optical feedback in the resonators, resulting in variations of cavity loss and confinement factor.

Design of low-threshold photonic-crystal surface-emitting lasers with confined gain regions by using selective area intermixing

Photonic-crystal surface-emitting lasers have many promising properties over traditional semiconductor lasers and are regarded as the next-generation laser sources. However, the minimum achievable lasing threshold of PCSELs is still several times larger than that of VCSELs, and limiting its applications especially if the required power is small. Here, we propose a new design that reduces the gain region in the lateral plane by using selective quantum-well intermixing to reduce the threshold current of PCSELs. By performing theoretical calculations, we confirmed that the threshold current can be lowered by a factor of two to three while keeping the PCSEL's advantage of small divergence angle.