Fig. 1. Spectral beam combination systems. (a) Traditional spectral beam combination system; (b) compact spectral beam combining system

Fig. 2. Schematics of light path of the nth subbeam in cases of different deviations. (a) Without deviation; (b) x-axis displacement deviation; (c) z-axis displacement deviation; (d) horizontal pointing deviation

Fig. 3. Intensity distribution of beams at different planes (I₀ is the maximum intensity of central subbeam in the source plane). (a) Intensity distribution of each subbeam in source plane; (b) intensity distribution of combined laser at focal plane of lens

Fig. 4. Beam quality factor curve of combined laser when only central fiber is in different deviations. (a) In x-axis displacement deviation; (b)in z-axis displacement deviation; (c) in horizontal pointing deviation

Fig. 5. Beam quality factor curve of combined laser when entire optical fiber array is in different deviations. (a) In x-axis displacement deviation; (b) in z-axis displacement deviation; (c) in horizontal pointing deviation

Fig. 6. Random horizontal pointing deviation in the nth subbeam

Fig. 7. Statistical results of beam quality factor M² of combined laser when all fiber array in random deviations. (a) In x-axis deviation ${\sigma }_x$; (b) in z-axis deviation ${\sigma }_z$; (c) in horizontal pointing deviation ${\sigma }_{\theta }$

Fig. 8. Statistical results of beam quality factor M² of combined laser when all fiber array in random deviations. (a) Random x-axis displacement deviation ${\sigma }_x$ and z-axis displacement deviation ${\sigma }_z$; (b) random x-axis displacement deviation ${\sigma }_x$ and horizontal pointing deviation ${\sigma }_{\theta }$; (c) z-axis displacement deviation ${\sigma }_z$ and horizontal pointing deviation ${\sigma }_{\theta }$

Fig. 9. Variation of statistical results of beam quality factor M² of combined laser with fiber array scale under standard deviations of different random deviations. (a) ${\sigma }_x$=5 μm; (b) ${\sigma }_z$=150 μm; (c) ${\sigma }_{\theta }$=10 mrad

Table 1. Optical parameters of beam combining system

Table 2. Beam quality factor M² of combined laser affected by central disturbance

Table 3. Beam quality factor M² of combined laser affected by disturbance of whole fiber array