弱耦合互注入锁定半导体激光器的线宽研究

Linewidth of Mutually Injection-Locked Semiconductor Lasers in Weak Coupling Regime

高速光通信、高分辨率光传感等领域的发展迫切需要窄线宽激光器,半导体激光器凭借其高可靠性、高转化效率以及易于集成等优点得到广泛应用。当前,虽然实验已发现在弱耦合条件下,互注入锁定激光器可以显著改善半导体激光器的线宽,但缺乏稳定性分析的有效手段以及关键参数对线宽影响的深入分析。本文使用基于传输矩阵理论的阈值增益分析模型定性分析了互注入锁定激光器的稳定性,并应用基于噪声相关性的迭代噪声模型深入分析了线宽的主要影响参数,为窄线宽互注入锁定半导体激光器的应用提供参考。

Objective Narrow linewidth lasers are required in sectors such as high data rate optical communication,high-resolution optical sensing,precision spectroscopy,and atomic clocks.Semiconductor lasers are widely used in the above fields,because of their excellent reliability,high efficiency,and ease of integration.Recently,significant effort has gone into increasing the linewidth characteristics of semiconductor lasers,which can be divided into the following three techniques:1)increase the semiconductor laser's output power while retaining a single-mode operation.At increasing output power,however,spatial hole-burning and thermally induced nonlinearities restrict the line width.2)need external cavity laser.To avoid multimode operation caused by the lengthy exterior cavity,critical control for single-mode operation is required.3)require unidirectional injection locking.However,the requirement of a master laser with a narrow linewidth limits its application.To address the issues above,a new method known as mutual injection locking in a weak coupling regime was recently proposed.The simulation and experimental results have shown the excellent ability of linewidth suppression,and a unique model was used to investigate the process.However,further research is required on the stability of mutually injection-locked semiconductor lasers and the primary parameters that determine line width.This study addressed the issues above and proposed the foundations for the application of mutually injection-locked semiconductor lasers.Methods Two theoretical models used in this study are as follows:1)A threshold gain analysis based on the transfer matrix was proposed to qualitatively explain mutual injection locking stability with index coupled distributed feedback(DFB)lasers.Systematic transfer functions were established to analyze the threshold gains of laser modes in a steady state.The stability of mutual injection-locked semiconductor lasers was determined by the difference between adjacent threshold gains near the minimum.The bigger the difference,the stronger the interference,and hence the higher the stability.2)To demonstrate the stability and noise characteristics,an iterative noise correlation model is used.The typical roundtrip time of photons in semiconductor lasers is only a few picoseconds,whereas the coupling time of the coupled lasers in our study is more significant.Thus,the process of creating stable mutual injection locking can be regarded as quasi-static.The process of mutual injection locking can be decomposed into two unidirectional injections locking simultaneously in each sub-process,because of the weak coupling strength,which results in the negligible effect of external feedback.The Wiener-Khinchin theorem and five noise sources were used to create iterative relationships between noise correlations in the adjacent three sub-processes.Finally,two commercial 1550 nm multiple quanta well(MQW)DFB lasers without built-in isolators were used for experimental verification.To facilitate injection locking,the wavelength difference between the coupled lasers is less than 0.1 nm in a free-running state,and a variable optical attenuator was used to adjust the coupling strength.Results and Discussions According to the theoretical model in section 2.1,the threshold gain analysis is implemented with suitable parameters.To analyze the influence of the coupling delay,the situations of different fiber lengths are simulated.The simulation results show that the envelope of the threshold gain distribution is independent of the fiber length(or coupling delay).However,the more potential lasing modes there are,the lower the threshold gain difference at the minimum,resulting in reduced stability as the fiber length(or coupling delay)increases(Fig.5).To determine the influence of the coupling strength,the cases of different optical attenuation are simulated.The findings reveal that high coupling strength can reduce the lasing mode,which results in strong stability(Fig.6).According to the model in section 2.2,we carefully choose eight stable points(Table 1)of mutual injection locking in a weak coupling regime.We discovered that long coupling delay(Fig.7)and strong coupling strength(Fig.8)can reduce linewidth on the magnitude by comparing their simulated frequency noise.However,the phase difference has a minor effect and needs to be evaluated.To verify the theoretical results,we extract the parameters of the DFB lasers and measure the linewidth experimentally,and found that the simulation result(97 Hz)is in good agreement with the experiment result(100 Hz).Conclusions A novel method of stability analysis was proposed by threshold gain analysis based on a transfer matrix theory in this study.The results reveal that long coupling delays need weak coupling strength,whereas short coupling delays need strong coupling strength.To analyze the linewidth of mutually injection-locked semiconductor lasers under weak coupling,an analytical method based on noise correlation analysis is used.The results show that the coupling delay and coupling strength are the main factors affecting the linewidth;however,the phase difference has less influence on the linewidth,which can be used for fine adjustment.