激光器内腔频差对双折射外腔激光回馈系统输出影响的理论及实验研究

玻璃材料的内应力关系及所在系统的稳定性、安全性和可靠性,是精密加工领域的重要问题.基于双折射外腔激光回馈效应的应力测量技术以其先进新颖的测量原理受到普遍关注.传统理论普遍认为双折射回馈系统中激光器的输出相位仅由外腔相位延迟决定,而将测量误差归因于外腔镜的非线性运动.本文结合正交偏振激光原理和三镜腔等效模型,测量了激光器的内腔双折射引起的频差大小,进行了频率调谐回馈实验,并根据结论计算了内腔频差对外腔相位延迟测量结果的影响,发现激光器的输出相位由外腔相位延迟、内腔频差、外腔长度共同决定.本文总结了内腔和外腔各向异性共同作用下激光器正交偏振态的相位特性,补充了激光回馈的物理内容,对于应力-双折射、位移、距离等重要参量的精确测量,都具有重要指导意义.     

External anisotropic feedback effects on the phase difference behavior of output intensities in microchip Nd:YAG lasers

We present the effects of optical feedback from an anisotropic external cavity on the characteristics of the output intensities in a single mode Nd:YAG laser. Due to the birefringence effect, the external cavity modulates laser intensities in the two orthogonal directions with a phase difference, which is twice as large as that of the birefringence element in the external cavity. Experimental results are presented, as well as a theoretical analysis. The potential applications of this phenomenon are also discussed. PACS 42.60.Jf; 42.62.Eh; 42.25.Lc; 42.60.By     

Single high-order round-trip feedback effects in orthogonally polarized dual frequency laser

We present the effects of single high-order round-trip feedback in orthogonally polarized dual frequency laser. The high quality intensity fringes of two orthogonally polarized lights are obtained, which are cosine-like. The fringe frequency of a single high-order round-trip feedback is five times that of the conventional optical feedback. Even higher frequencies are possible with this setup. Particularly, there is a phase difference between two orthogonal polarized lights in single high-order round-trip feedback and the phase difference is determined by the feedback order, the length of the external cavity, and the frequency difference of the two orthogonal polarized lights. A theoretical analysis based on a compound cavity model of a dual frequency laser agrees well with the experimental results. These results provide a potential application in precision measurement with both directional discrimination and high optical resolution.     

Laser Intensity Variation in Amplitude and Phase Induced by Elliptically Polarized Feedback

The laser output characteristics under elliptically polarized optical feedback effect are studied. Elliptically polarized light is generated by wave plate placed in the feedback cavity. By analyzing the amplitude and phase of the laser output in the orthogonal direction, some new phenomena are firstly discovered and explained theoretically.Elliptically polarized feedback light is amplified in the gain medium in the resonator, and the direction perpendicular to the original polarization direction is easiest to oscillate. The laser intensity variation in amplitude and phase are related to the amplified mode and the anisotropy of external cavity. The theoretical analysis and experimental results agree well. Because the output characteristic of the laser has a relationship with the anisotropy of the external cavity, the phenomenon also provides a method for measuring birefringence.     

Generation and Modulation of Phase Difference of Output Intensities in a Feedback Nd:YAG Laser with an Extracavity Waveplate Rotated

External anisotropic feedback effects on the phase difference behaviour of output intensities in a microchip Nd：YAG laser are presented. By rotating a quarter wave plate placed in the external cavity, the angle between laser initial polarization direction and o-axis of the wave plate is tuned from -45°to 45°, which results in variable extra-cavity birefringence along two orthogonal detection directions. With only one optical path and one wave plate, laser intensities of the two orthogonal directions, both modulated by the external cavity length, are output with a tunable phase difference, which can be continuously changed from zero to twice as large as that of the waveplate. Experimental results as well as a theoretical analysis based on Fabry-Perot cavity equivalent model and the refractive index ellipsoid, are presented. The potential applications of this phenomenon are also discussed.     

Self-mixing interference effects in orthogonally polarized dual-frequency Nd:YAG lasers at different feedback levels

The self-mixing interference effects are investigated in birefringence dual-frequency Nd:YAG lasers at different optical feedback levels. For weak feedback level, both of the intensities of the two modes are sinusoidally modulated by external cavity length with a feedback period of half laser wavelength. While these two modes can only coexist in a part of feedback period at moderate feedback level, i.e., one mode reaches its maximum intensity, the other one extinguishes. At high feedback level, complete polarization switching (one mode oscillating, the other one extinguishing) between two polarized modes is observed, and every switching corresponds to quarter-wavelength variation of external cavity length. Furthermore, two feedback schemes, i.e., isotropic optical feedback (IOF) and polarized optical feedback (POF) are taken into account. The theoretical analysis based on a model of two-mode-coupled laser is presented, which is in good agreement with experimental results. Our results can advance the research of self-mixing interferometer of orthogonally polarized dual-frequency lasers.     

A sensitive method of determining optic axis azimuth based on laser feedback

A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes with the angle between the optic axis of the birefringence element and laser original polarization. The phase difference is highly sensitive to the relative position of the optic axis and the laser original polarization. This method is used to highly precisely determine the optic axis azimuth, and is able to distinguish between the fast axis and the slow axis of the birefringence element. Theoretical analysis and experimental results are both demonstrated.     

双频氦氖激光回馈位移测量系统的实验与应用研究

研究了一种全新的纳米尺度位移测量系统。将双折射元件插入He-Ne激光器谐振腔内产生频率分裂效应，使原本单模谐振的激光器输出变成了频差可调的2个正交偏振频率（o光和e光），而形成双频激光器。在激光谐振腔外放置沿激光轴线位移的反射表面，将输出的激光束反射回腔内，以便对激光的光强进行调制，可实现高分辨率非接触式可判向位移测量。提出了一种细分方法，该方法突破了传统干涉系统的衍射极限（1/2波长）。对于633nm波长He-Ne激光，本系统的理想分辨率为1/8波长（约为79nm）。     

Output response in orthogonal directions of a He–Ne laser caused by birefringent-external-cavity feedback

The output responses of phase, amplitude, and polarization of light intensity of a He–Ne laser with the birefringent external cavity are presented. All phenomena are observed in two orthogonal directions related to the birefringent element’s orientation, and are studied under weak optical feedback. Experiments are carried out in five available detecting positions. It is found that laser intensities are modulated in the two orthogonal directions simultaneously, with a phase difference dominated by the phase retardation of the birefringence element. The modulation amplitudes are different in the two directions. A special polarization phenomenon is also observed and discussed. This research may provide a potential novel measuring principle for transparent birefringent materials.     

External optical feedback effects in a frequency locking dual frequency laser

We present a systematic study of external optical feedback effects on the output characteristics of the two orthogonally polarized modes in a frequency locking dual frequency laser. Accompanied by the change of the external cavity length, the length of the resonance cavity is changed very slowly to set the oscillating modes sweeping across the laser gain curve. Comprehensive results are obtained and a strong mode competition is observed. Particularly, when the laser runs in the middle region of the gain curve, which mode can oscillate is determined by the movement direction of the external feedback mirror. Based on the phenomenon, a displacement sensor with directional discrimination is proposed and its capability is also discussed.     

Strong optical feedback in birefringent dual frequency laser

Strong optical feedback in a birefringent dual frequency He--Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes are demonstrated in two different optical feedback cases: one is for both modes being fed back and the other is for only one of the modes being fed back. Strong mode competition can be observed between the two modes with strong optical feedback. And when one mode's intensity is near its maximum, the other mode is nearly extinguished. When both modes are fed back into the laser cavity, the mode competition is stronger than when only one mode is fed back. The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition, which has been experimentally and theoretically demonstrated.     

Orthogonally Linearly Polarized Dual Frequency Nd：YAG Lasers with Tunable Frequency Difference and Its Application in Precision Angle Measurement

The orthogonally linearly polarized dual frequency Nd： YA G lasers with two quarter wave plates in laser resonator are proposed. The intra-cavity variable birefringence, which is caused by relative rotation of these two wave plates in laser inner cavity, results in the frequency difference of the dual frequency laser also changeable. The theory model based on the Jones matrix is presented, as well as experimental results. The potential application of this phenomenon in precision roll-angle measurement is also discussed.     

Optical feedback in a Zeeman-birefringence HeNe laser and its application in ranging

The optical feedback characteristics in a Zeeman-birefringence HeNe laser have been studied systematically when the external cavity varies in a large range. The intensity variations of the two orthogonally polarized lights are observed during the laser cavity tuning in the dual frequency laser. When the external cavity length is an integral multiple of the laser cavity length, either polarized light's intensity modulation depth varies not obviously when the laser works in dual modes conditions or single mode condition. But when the external cavity length is far away from an integral multiple of the laser cavity length and the laser works in different dual modes conditions, polarized light's intensity modulation depth varies obviously. This characteristic can guide us to tune the laser to work in single mode condition to improve the sensitivity of the optical system when the system is used for a large displacement measurement. It can also be used for measuring the position of the target mirror. The theoretical analysis is in good agreement with experimental results.     

腔调谐过程中激光器中两垂直偏振光的回馈特性

腔调谐过程中同时对HeNe激光器进行光回馈，设定回馈镜驱动信号的周期远小于腔调谐信号的周期，此时便获得腔调谐过程中谐振腔中两垂直偏振光的回馈信号. 回馈的形式分为仅垂直光回馈、仅平行光回馈以及两光同时回馈三种情况. 当两光同时回馈时，两模式间的模竞争较弱，两光回馈曲线有一定的相位差，该相位差小于180°，两光总体波动幅度变化趋势相反. 当仅单偏振光回馈时，两模式间的模竞争较强，两光回馈曲线始终反相，而且两光波动幅度变化趋势相同，此时可以将两光强度信号相减以实现成倍提高回馈信号幅度，从而提高系统灵敏度. 尤其仅垂直光回馈时，两光各自光强波动幅值都较大，并且在较大的增益曲线范围内保持光强波动幅值无明显变化，该特性可用于提高回馈系统的抗干扰能力，减少因激光功率漂移而引起的错误计数. 关键词： 自混合干涉 光回馈 模竞争 位移测量     

Anisotropic optical feedback of single frequency intra-cavity He--Ne laser

This paper presents the anisotropic optical feedback of a single frequency intra-cavity He--Ne laser. A novel phenomenon was discovered that the laser output an elliptical polarized frequency instead of the initial linear polarized one. Two intensities with a phase difference were detected, both of which were modulated in the form of cosine wave and a fringe shift corresponds to a λ/2 movement of the feedback mirror. The phase difference can be continuously modulated by the wave plate in the external cavity. Frequency stabilization was used to stabilize the laser frequency so as to enlarge the measuring range and improve the measurement precision. This anisotropic optical feedback system offers a potential displacement measurement technology with the function of subdivision of λ/2 and in-time direction judgment. The three-mirror Fabry--Perot cavity model is used to present the experimental results. Given the lack of need of lasing adjustment, this full intra-cavity laser can significantly improve the simplicity and stability of the optical feedback system.     

Optical feedback characteristics in a helium neon laser with a birefringent internal cavity

The output characteristics of optical feedback in a helium neon laser with a birefringent internal cavity are studied systematically in five different regions of the gain curve for the two orthogonally polarized modes. When the laser operates in the two end regions of the laser gain curve, one of the two orthogonally polarized modes will be a leading one in optical feedback. Strong mode competition can be observed. However, when the laser operates in the middle region of the laser gain curve, the two modes can oscillate equally with optical feedback. Besides the intensity of the two polarized lights, the total light intensity is also studied at the same time. M-shaped optical feedback curves are found. Particularly, when the average intensities of the two lights are comparable, the intensity modulation curve of the total light is doubled, which can be used to improve the resolution of an optical feedback system.[第一段]     

微片Ｎｄ∶ＹＡＧ 双频激光器腔调谐现象研究

 基于微片Ｎｄ∶ＹＡＧ 正交偏振双频激光器,研究了若干重要的双频激光器腔调谐现象, 包括光强调谐、频差调谐、子谐振腔效应及频差闭锁等,给出了实验结果和数据。腔调谐下,正交双频的频差调谐量约为３５０ ｋＨｚ;存在子谐振腔效应时,频差调谐量最大可达到２ ＭＨｚ;未发现明显频差闭锁现象,频差最小值可达到１４ ＭＨｚ。     

Observation of a superposition of orthogonally polarized geometric beams with a <Emphasis Type="Italic">c</Emphasis>-cut Nd:YVO<Subscript>4</Subscript> crystal

We investigate a superposition of orthogonally polarized geometric beams generated from a c-cut Nd:YVO₄ laser. Experimental results reveal that a geometric mode possesses a linearly polarized state and circularly polarized states in opposite directions at the same time and the superposition of orthogonally polarized geometric beams can be generated systematically by controlling the pump offset. We use the birefringence theory to analyze the data, and the numerical results have a good agreement with the experimental results.     

半外腔微片Nd∶YAG正交偏振激光器及其在精密测角中的应用

设计了一种半外腔微片Nd∶YAG正交偏振双频激光器。把2个1/4波片置于激光谐振腔内,一个静止,一个作360°旋转,旋转引起2个1/4波片快轴之间的角度变化被激光器转化成激光2个频率之差的变化,从而输出可调谐的双频激光。采用琼斯矩阵对光在腔内的本征模进行分析,给出了双频频差的理论解释。讨论了一种体积小、分辨率高和可整周测量的新型Nd∶YAG激光测角仪的潜在前景。     

Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate

Simultaneous generation of helical beams with linear and radial polarization is demonstrated by use of a segmented half-wave plate in a Ti:sapphire laser cavity. A linearly polarized Laguerre-Gaussian beam is converted to a radially polarized beam with a spiral phase shift and vice versa. In addition, these two beams coexist in the cavity, and the cavity emits one of these two beams from an output coupler.