摘要
精确的简并范围是运用横模频率简并原理产生结构光场的重要条件。本文基于激光频谱研究了共焦腔处于1/2简并态时激光横模频率简并的现象,并提出一种更准确的简并范围测量方法。实验中详细观测输出激光频谱信号随腔长的变化。利用频谱信息,实现了对腔内不同阶横模在发生简并时动力学行为变化的监测。研究结果表明,当腔内不同阶横模发生频率简并时,不同简并族的横模未因模式竞争被抑制,而是共存于腔内。同时,利用激光频谱随腔长的变化,实现了对简并范围更准确的测量。简并过程中重点监测的两个频率信号随着腔进入简并态合并成一个频率信号,该状态在一段腔长范围内稳定存在。据此测得更精确的简并范围,对应腔长约为0.20 mm。此外,对实验中测得的频谱信号进行理论对比,频谱信号的实验值与理论值基本吻合。
Objective Structured light has been exploited in several fields in the past two decades,such as optical tweezers,spiral interferometers,and phase-contrast microscopes.The generation of structured light is generally achieved by utilizing optical elements such as spatial light modulators or spiral phase plates.Because of the limit on output power when utilizing these optical elements to generate structured light,a direct generation of structured light is proposed in the laser cavity.Intracavity generation of structured light could be achieved based on the theory of transverse mode degeneracy.The degenerate range (or lock range),which means a special short range of cavity length,is an important condition for exploiting transverse mode degeneracy to generate structured light.When the cavity length is adjusted to the degenerate range,the degeneracy condition is met.When the cavity meets the degeneracy condition,resonant frequencies of specific transverse modes become equal.In this situation,these specific modes will coherently superpose each other and generate a light field that may exhibit spatial structure.Therefore,the accurate degenerate range plays an important role in utilizing this method to generate structured light.Thus,to the approach of measuring the accurate degenerate range becomes a significant issue,which is what we mainly consider in this research.Methods The degenerate range is determined by the variation of output power or threshold of pump power in some articles.However,the widths of the degenerate range determined using these methods are somewhat approximate;their precision could be improved using other measurement methods.To more accurately measure the degenerate range,we try to exploit the frequency spectra of laser beams to characterize the degenerate range in this paper.As the cavity length is tuned slowly in the experiment,the frequency spectra of laser beams are detected in detail.Two peaks in the spectra that particularly considered in this study to show an obvious process of merging as the confocal resonator approaches the degenerate position.In this paper,the range of cavity length in which the two peaks become superposed is defined as the degenerate range.This type of measurement method is more accurate than the methods that utilize the variation of output power or threshold of pump power to determine the degenerate range because it directly monitors the variation of frequency spectra.We use the frequency spectra measured in experiment to analyze the change of dynamic behavior of transverse modes with different orders.Results and Discussions The frequency data measured in the experiment are shown in Fig.3.As the cavity length changes,each of these frequencies(Δf;,2Δf;,Δf;-Δf;,Δf;,andΔf;-2Δf;)show a variation tendency consistent with the theoretical variation tendency.Variations of these detected frequencies indicate the change of dynamic behavior of transverse modes with different orders.By analyzing these frequency spectra,we find that even though competition between modes exists,transverse modes that belong to different degenerate families are not suppressed when degeneracy occurs.The frequency difference of modes with the same order is clearly detected in the vicinity of the degeneration point,and it is not observed away from the degeneration point.From the beam patterns(Fig.4),we can observe that higher-order transverse modes are generated when the confocal resonator is tuned in the vicinity of the degeneration point.This phenomenon implies that as the resonant frequency of the high-order mode becomes equal to that of the low-order mode,the high-order mode becomes easier to generate in the cavity.The detailed frequency spectra are presented in Fig.5,using which we determine the degenerate range.As the confocal resonator is tuned to the degeneration point,the two peaks(Δf;-Δf;andΔf;)become closer to each other and finally superpose.The state in which these two peaks are superposed sustains for a short range of cavity lengths.Accordingly,we could obtain the width of the degenerate range,which is approximately 0.20mm in this experiment.The degenerate range defined in this way ought to be more accurate because it is directly determined from frequency spectra.Conclusions In this paper,the phenomenon of transverse mode degeneracy is researched based on the variation of frequency spectra,and a more accurate method for measuring the degenerate range(or lock range)is proposed.As the cavity length varies in the experiment,frequency spectra of laser beams are recorded in detail.The variation of dynamic behavior of transverse modes before and after the degeneracy is analyzed based on the frequency spectra.When the cavity satisfies the degeneracy condition,the two degenerate families of transverse modes (in 1/2degeneracy)coexist in the cavity,neither of them is suppressed because of the competition between them.Meanwhile,the beam patterns measured in the experiment show that higher-order transverse modes are generated when degeneracy occurs.As the resonant frequency of the high-order transverse mode becomes degenerate with that of the low-order mode,the high-order mode becomes easier to generate,thus resonating with the low-order mode in the cavity.We achieve a more accurate measurement of the degenerate range with the frequency spectra measured in the experiment.The degenerate range is approximately 0.20mm in this experiment.It exhibits a higher precision and is more accurate than the degenerate range determined using other methods.The results of this paper may provide some reference value for the application of transverse mode degeneracy.
作者
林达
王晶
李丙轩
廖文斌
林长浪
汤凯飞
李柯
张戈
Lin Da;Wang Jing;Li Bingxuan;Liao Wenbin;Lin Zhanglang;Tang Kaifei;Li Ke;Zhang Ge(Key Laboratory of Optoelectronic Materials Chemistry and Physics,Fujian Institute of Research on the Structure of Matter,Chinese Academy of Sciences,Fuzhou,Fujian 350002,China;University of Chinese Academy of Sciences,Beijing 100049,China;College of Chemistry,Fuzhou University,Fuzhou,Fujian 350108,China)
出处
《中国激光》
EI
CAS
CSCD
北大核心
2021年第20期41-46,共6页
Chinese Journal of Lasers
基金
国家自然科学基金(61875199,61975208,51761135115)
中国科学院战略重点研究计划(XDB20000000)
福建省科学基金(2019J02015)。
关键词
激光器
横模
频谱
简并
简并范围
lasers
transverse modes
frequency spectra
degeneracy
degenerate range
