Objective Laser diodes have great demands in material processing and space communication because of their small size and high electro-optical conversion efficiency. However, due to the nonlinear effect, the traditional broad-area lasers are prone to filamentary emission and face the problems of large divergence angle and poor lateral beam quality, which limit their direct application. Angled cavity laser diodes have a unique oscillation optical path in which the fundamental lateral mode satisfies zigzag resonance, then the high-order lateral modes and filamentation effects in the broad-area lasers can be suppressed effectively. Presently, most of the angled cavity laser diodes are designed with a strong index guiding to total internal reflection of the fundamental lateral mode on the sidewalls, the non-radiative recombination loss is enhanced because the etching depth exceeds the active region. However, the resonance condition of the fundamental lateral mode is deviated as the etching depth decreases. Therefore, it is necessary to research angled cavity laser diodes with weak index guiding structure. For this purpose, the zigzag resonance conditions of angled cavity laser diodes in different etching depths are studied.

Methods Based on the stationary phase method, this paper gives a theoretical model containing the GH shift factor for strong and weak index guiding. The influence of the GH shift in the angled cavity laser diodes on the zigzag resonance condition of the fundamental mode is discussed theoretically (Fig.2), and the new fundamental lateral mode zigzag resonance conditions containing the GH factor are clarified. It is pointed out that the corresponding shallowest critical etching depth D_c,m exists for each order lateral mode, and the mode selection characteristics of the angled cavity under the fundamental lateral mode critical etching depth D_c,0 are analyzed.

Results and Discussions The GH shift factor in the angled cavity is studied based on the stationary phase method, and a theoretical model for strong and weak index guiding is given. Comparative analysis shows that the calculation results of the theoretical model are in good agreement with the simulation results under the two types of index guiding and can more accurately describe the resonance of the fundamental lateral mode in the angled cavity under the weak index guiding (Fig.3-Fig.4). The analysis of the theoretical model shows that there exists a corresponding critical etching depth D_c,m for the m-order lateral mode, when the etching depth of the angled cavity is less than D_c,m, the limiting effect of the waveguide on the m-order lateral mode decreases drastically, so the angled cavity exhibits a strong mode selective ability near the fundamental lateral mode critical etching depth D_c,0 (Fig.5).

Conclusions The theoretical model of the angled cavity for strong and weak index guiding is obtained through the theoretical analysis of the GH shift inside the angled cavity, and the critical etching depths D_c,m of lateral modes are given according to the effective refractive index method and the Snell's law. Combined with the software simulation, it shows that the GH shift is proportional to the ridge width W and inversely proportional to the waveguide tilt angle θ, which has a great influence on the zigzag resonance conditions of the fundamental mode under the weak refractive index. After the GH shift factor is introduced, the theoretical calculation results and simulation results are in good agreement in both strong and weak index guiding, which solves the problem of the zigzag resonance conditions deviation of the fundamental lateral mode under weak index guiding, and helps to improve the coupling efficiency of the fundamental lateral mode. In addition, the etching depth of the angled cavity laser diodes must be larger than or equal to the fundamental lateral mode critical etching depth D_c,0, selected the fundamental lateral mode critical etching depth D_c,0 reduces the non-radiative composite loss of the sidewalls and enhances the selectivity of high-order lateral modes at the same time compared with the strong index guiding.