Whispering gallery mode (WGM) optical resonator is a typical optical element. Due to low optical loss, small mode size, compact structure, and ability to store energy in a small volume for a long time, it has received extensive attention in recent years [1], [2], [3]. It can be used in many fields including optomechanics [4], [5], [6], [7], [8], [9], parametric oscillation [10], [11], [12], quantum information research [13], nonlinear optics [14], [15], high sensitivity sensor [16], [17]etc. In these applications, Pound–Drever–Hall (PDH) locking technology has to be mentioned, it locks the laser frequency of the fiber probe to the resonant frequency and the resonant detuning frequency by applying a feedback signal. It is widely used due to its high accuracy frequency locking. Compared with traditional Pound–Drever–Hall (PDH) locking, microsphere cavity thermal locking has the advantages of autonomous locking, simple structure, good flexibility and convenient operation. PDH locking loop requires a phase modulator, RF oscillator, mixer and PID controller [18]. While in the thermal locking loop, just the power amplifier is needed to adjust the pump optical power. In addition, the thermal locking of microsphere cavity is active locking with good stability. The microsphere cavity can quickly achieve the thermal balance by adjusting the thermal dissipation rate. In recent years, thermal nonlinear effects in the microspheres cavity have also been used for locking, which overcomes the difficulty of integration due to their simple device and small size.

Tal Carmon et al. proposed a power-stable locking method using coupled optical power as a feedback control parameter, which reduces the number of components used and facilitates some times when stable power operation is required and set-point power scanning is required to obtain data. However, thermal locking technique could only lock to the resonance slope of the blue detuning region, and external environmental disturbances may disrupt the thermal locking state, which makes it difficult to achieve long-term locking [19]. T. G. McRae et al. combined optical feedback locking with thermal feedback locking by exploiting the thermal bistability present in silicon microrings, they achieved over 12 h of thermo-optic locking between the laser and the cavity. However, in this locking device, optical feedback locking is dominant, and it is not fully explored from the perspective of improving the time of thermal locking [20]. Monica Agarwal et al. implemented a method for independent self-tuning by applying hotline width broadening to mode locking without using any feedback mechanism (In the experiment, the radius of the microsphere cavity R =150μm) [21]. Yang Lan et al. proposed an active thermal locking stabilization technique, their detector Whispering gallery mode (WGM) at 1450 nm exhibits a perfect Lorentz lineshape, however, there is not much in-depth study on the characteristics of locking itself [22]. Therefore, this paper focuses on the influence factors of thermal mode-locking and applies them to improve locking time and stability. Then, the thermodynamic model is modified to be related to the scanning speed, light intensity and the size of the microsphere cavity, it provides a new method to improve the hot locking time.