Fig. 1. Mode energy distribution induced by beam misalignment

Fig. 2. Relationship between logarithmic energy of optical modes and misalignment

Fig. 3. Finding the maximum of n-th order mode energy utilizing gradient ascent method

Fig. 4. Angle combination strategies for dual-mirror systems. (a) Lateral offset; (b) tilt

Fig. 5. Resonant mode data acquisition device

Fig. 6. Examples of the resonant mode dataset

Fig. 7. Accuracy and loss curves of training on the dataset using EfficientNet

Fig. 8. Confusion matrix of the mode picture recognition on the test dataset by EfficientNet

Fig. 9. Intensity maps under different modes. (a) HG00; (b) HG01; (c) HG02; (d) LG01

Fig. 10. Block diagram of the experimental set-up

Fig. 11. Experimental set-up

Fig. 12. Relationship between the tilt angles and logarithmic intensity of the fundamental mode

Fig. 13. Cavity recoupling based on mode energy gradient ascent

Fig. 14. Laser frequency locking on different optical modes