Objective   The external cavity spectral beam combining technology has two structures of open loop (without output coupler) and closed loop (with output coupler). The main difference between them is that the wavelength locked feedback beam of each light-emitting unit is different. Among them, the output coupler free external cavity spectral beam combining structure uses the beam returning from re-diffraction along the 0th-order and 1st-order diffraction direction as the feedback light, which avoids the waste of the beam and overcomes many problems of the feedback locking of the −1st order diffraction beam, and realizes the high-efficiency wavelength beam combination. For spectral beam combining technology, the feedback efficiency of the external cavity determines the stability of wavelength locking and even the success or failure of beam combination. Compared with the general closed-loop structure, the output coupler free external cavity spectral beam combining structure can only obtain enough feedback beams to achieve wavelength locking by controlling the parameters of the external cavity, and this external cavity structure is relatively complex, and the feedback efficiency variation caused by some factors in the external cavity are more obvious than the closed-loop structure. Therefore, for this structure, a simulation system is established to study the influencing factors of the external cavity feedback efficiency.

  Methods   The efficiency model of output coupler free external cavity spectral beam combining structure is constructed, and the expression of spectral beam combining efficiency is deduced. According to the expression, the length of the external cavity, the telescope filtering system and the "Smile" effect have great influence on the feedback efficiency of this structure. The output coupler free external cavity spectral beam combining structure in Zemax is established, and the level of the feedback quantity of the two diffraction cavities in this system and the change in feedback quantity caused by changing the cavity length, the influence of the 1st-order diffraction cavity added to the telescope system on the feedback efficiency and quality of the combined beam, and the influence of the "Smile" effect on the feedback beam intensity are studied respectively.

  Results and Discussions   According to the output coupler free external cavity spectral beam combining simulation system, the 1st-order diffraction light feedback power accounts for 2.73% of the output power, while the 0th-order diffraction light feedback power only accounts for 0.15% of the output power (Fig.3). As the distance of the external cavity increases from 27 mm to 558 mm, the feedback power decreases from 1.76 W to about 1.45 W (Fig.4), and the feedback beam crosstalk will occur (Fig.5); When different telescope filtering systems are inserted into the 1st-order diffraction cavity, the feedback power of the external cavity remains basically unchanged and the size of the slow-axis beam spot remains about 4 mm (Fig.8); The feedback power steadily diminishes and the combined spot size gradually increases as the degree of "Smile" effect rises from 0 μm to 1 μm. The feedback power of the 500-mm long focal length cylindrical lens inserted in the fast axis direction under the impact of the "Smile" effect at 1 μm is essentially the same as that without the "Smile" effect, which lessens the influence of the "Smile" effect on the feedback power.

  Conclusions   The factors impacting on the external cavity's feedback efficiency are analyzed using the output coupler free external cavity spectral beam combining efficiency model. The effects of the external cavity length, the filter structure of the telescope, and the "Smile" effect on the feedback efficiency of the 0th-order and 1st-order diffracted beams are studied, respectively, using the output coupler free external cavity spectral beam combining simulation system built in Zemax. The results show that: (1) The feedback beam is dominated by the 1st-order diffracted beam, and wavelength locking of the external cavity is essential. As the length of the external cavity rises, the feedback power falls and the beam crosstalk increases; (2) The telescope filter structure can effectively filter the stray beam with large deflection angle and accurately feed back the beam to the original light-emitting unit; (3) The degree of "Smile" effect has a particularly negative influence on feedback efficiency and output beam quality. Although the "Smile" effect can be lessened by inserting a long focal length cylindrical lens in the fast axis direction, the beam quality after beam combination won't be noticeably enhanced. The research on the feedback efficiency of the external cavity can be used as a guide when designing the parameters for the output coupler external cavity spectral beam combining structure.