Multi-Soliton Field Analysis in SiO2 Optical Microcavities with Thermal Effect
Objective Thermal effects in optical microcavities have an important influence on field evolution.Currently,the study on thermal effects in microcavities focuses on thermal oscillations.The thermal oscillations are caused by thermal expansion,thermo-optic effect,and Kerr effect,which lead to strong mode oscillations in microcavities.Self-stabilization of optical microcavities can be achieved by exploiting the resonance shift induced by the dynamic thermal effect.Through the thermo-optic(TO)effect,optical microcavities can be employed as temperature sensors with sensitivities up to 0.016％(RH)or higher.In addition,some studies on the thermal effect of microcavities focus on the influence of the optical field variation and thermal effect during the scanning process of the pump wavelength.However,there is a lack of discussion on the influence of thermal effects on the optical field in the microcavity,and existing studies fail to analyze how to maintain the solitons generated during the thermal effects.Therefore,in this paper,the effect of thermal response on the optical field in the enclosure is analyzed by taking the silica optical microcavity as an example,and a multi-soliton holding method is proposed.Methods In general,the variation of the optical field in the microcavity with time was described by the Lugiato-Lefever equation(LLE).On the basis of LLE,the thermal effect in the microcavity was taken into account,which consisted of the TO effect and the thermo-expansion(TE)effect.For the optical microcavity of SiO2 material discussed in this paper,since both the TO and TE effects were positive,and the coefficient of the TO effect was much larger than that of the TE effect,only the TO effect in the thermal effect was considered for the SiO2 optical microcavity.Generally speaking,during the microcavity operation,the thermal effect caused by the absorption of the optical field could change the resonant wavelength of the microcavity,which further led to the change of the detuning parameter.Therefore,the thermal effect would eventually cause a change in the microcavity operating state.In this paper,we combined the thermal effect with the LLE,and the field in SiO2 optical microcavities with thermal effects was investigated.Results and Discussions It is found that when the initial state is zero detuning,the resonant wavelength of the microcavity drifts in the positive direction under the thermal effect,and the resulting thermal detuning can excite the optical field in the form of multiple solitons inside the microcavity.However,with the accumulation of thermal effects,the thermal shift of the resonant wavelength increases,causing excessive detuning in the cavity,which leads to the gradual disappearance of the multi-soliton.In other words,under the influence of the thermal effect,the multi-soliton optical field can only exist briefly in the SiO2 optical microcavity.On this basis,we propose to utilize the regulating of the pump wavelength and power to maintain the multi-soliton in the microcavity.When the multi-soliton is generated in the microcavity,the pump wavelength is scanned at a suitable speed to compensate for the detuning caused by the thermal effect so that the total detuning in the microcavity remains constant.In this case,the multi-soliton state in the cavity can be maintained stably even if thermal effects exist.Since the tuning power and wavelength scanning speed of the pump lead to different results in the evolution of the original multi-soliton optical field,the effect of the pump tuning parameters on the multi-soliton optical field is also investigated.It is found that the number of regulated multi-soliton pulses is related to the regulating power of the pump.Higher regulating power of the pump indicates a more pronounced thermal effect in the microcavity and a larger resulting thermal shift of the resonant wavelength.When the pump wavelength is scanned at the same rate,a highly regulated pump power induces a larger detuning parameter,and the regulated multi-soliton optical field contains a larger number of pulses.Moreover,by keeping the regulated pump power constant,only a proper tuning speed of the pump wavelength can maintain the multi-soliton optical field in the microcavity.A small tuning speed of the pump wavelength leads to a gradual disappearance of the multi-soliton optical field.If the pump wavelength scanning is too fast,it will make the drift of the pump wavelength exceed that of the resonant wavelength,which makes the microcavity in a positive detuned state and ultimately leads to the evolution of the original multi-soliton optical field into a chaotic optical field.The results are of great significance for the generation of stable multi-soliton optical fields in SiO2 optical microcavities in practice.Conclusions The regulating process of SiO2 microcavity optical field under thermal effect is investigated.When the initial condition of the microcavity is zero detuning,the optical field in the form of multiple solitons can be generated inside the microcavity under the thermal effect.However,due to the increasing thermal detuning caused by the thermal effect,the multi-soliton will eventually disappear.In order to maintain the multi-soliton optical field in the microcavity,we propose to utilize the tuning of the pump wavelength and power to maintain the multi-soliton in the microcavity.After the generation of multi-soliton in the microcavity,the pump wavelength is scanned at a suitable speed to compensate for the detuning caused by thermal effects so that the total detuning in the microcavity remains constant.In this case,even if there is a thermal effect,the multi-soliton state in the cavity can be maintained stably.We also investigate the effect of the pump tuning parameters on the multi-soliton optical field.Higher tuning power of the pump indicates more obvious thermal effects in the cavity and larger thermal drift of the resonant wavelength,and the tuned multi-soliton light field contains more pulses.The small tuning speed of the pump wavelength will lead to the gradual disappearance of the multi-soliton optical field.The fast pump wavelength scanning will make the drift of the pump wavelength exceed the shift of the resonant wavelength,thus making the microcavity in a positive detuned state and ultimately leading to the evolution of the original multi-soliton optical field into a chaotic optical field.The study on the thermal effect of optical microcavities has important practical significance for the real application of optical microcavities.
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