Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electrom...Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov's phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.展开更多
Using two typical types of polarization controller, this paper analyses theoretically and experimentally the fact that it is necessary to adjust at least three instead of two waveplates in order to transform any state...Using two typical types of polarization controller, this paper analyses theoretically and experimentally the fact that it is necessary to adjust at least three instead of two waveplates in order to transform any state of polarization to any other output covering the entire Poincar6 sphere. The experimental results are exactly in accordance with the theory discussed in this paper. It has corrected the conventional and inaccurate point of view that two waveplates of a polarization controller are adequate to complete the transformation of state of polarization.展开更多
An expression of degree of polarization(DOP) for metallic material is presented based on the three-component polarized bidirectional reflectance distribution function(p BRDF) model with considering specular reflec...An expression of degree of polarization(DOP) for metallic material is presented based on the three-component polarized bidirectional reflectance distribution function(p BRDF) model with considering specular reflection, directional diffuse reflection and ideal diffuse reflection. The three-component p BRDF model with a detailed reflection assumption is validated by comparing simulations with measurements. The DOP expression presented in this paper is related to surface roughness, which makes it more reasonable in physics. Test results for two metallic samples show that the DOP based on the three-component p BRDF model accords well with the measurement and the error of existing DOP expression is significantly reduced by introducing the diffuse reflection. It indicates that our DOP expression describes the polarized reflection properties of metallic surfaces more accurately.展开更多
With spin-polarized-dependent band gap renormalization effect taken into account, the energy-dependent evolu- tion of electron spin polarization in GaAs is calculated at room temperature and at a low temperature of 1O...With spin-polarized-dependent band gap renormalization effect taken into account, the energy-dependent evolu- tion of electron spin polarization in GaAs is calculated at room temperature and at a low temperature of 1OK. We consider the exciting light with right-handed circular polarization, and the calculation results show that the degree of electron spin polarization is dependent strongly on the quasi-Fermi levels of |1/2) and |- 1/2) spin conduction bands. At room temperature, the degree of electron spin polarization decreases sharply from 1 near the bottom of the conduction band, and then increases to a stable value above the quasi-Fermi level of the |- 1/2) band. The greater the quasi-Fermi level is, the higher the degree of electron spin polarization with excessive en- ergy above the quasi-Fermi level of the |- 1/2) band can be achieved. At low temperature, the degree of electron spin polarization decreases from 1 sharply near the bottom of the conduction band, and then increases with the excessive energy, and in particular, up to a maximum of i above the quasi-Fermi level of the |1/2) band.展开更多
Polarization upconversion luminescence(PUCL)of lanthanide ions(Ln^(3+))has been widely used in single particle tracking,microfluidics detection,three-dimensional displays,and so on.However,no effective strategy has be...Polarization upconversion luminescence(PUCL)of lanthanide ions(Ln^(3+))has been widely used in single particle tracking,microfluidics detection,three-dimensional displays,and so on.However,no effective strategy has been developed for modulating PUCL.Here we report a strategy to regulate PUCL in Ho^(3+)-doped NaYF4single nanorods based on the number of upconversion photons.By constructing a multiphoton upconversion system for Ho^(3+),we regulate the degree of polarization(DOP)of PUCL from 0.590 for two-photon luminescence to 0.929 for three-photon upconversion luminescence(UCL).Furthermore,our strategy is verified from cross-relaxation between Ho^(3+)and Yb^(3+),excitation wavelength,excitation power density,and local site symmetry.And this regulation strategy of PUCL has also been achieved in Tm^(3+),with the DOP ranging from 0.233 for two-photon luminescence to 0.925 for four-photon UCL Besides,multi-dimensional anti-counterfeiting display has been explored with PUCL.This work provides an effective strategy for regulating PUCL and also provides more opportunities for the development of polarization display optical encoding,anti-counterfeiting,and integrated optical devices.展开更多
Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Rouje...Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Roujean model was used to quantitatively describe different fruits intensity components (<i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;">) and polarization phase angle (Orient), and the simulation results were analyzed and compared using statistical analysis and comparison methods to realize the prediction from the regular model to the outdoor fruit tree canopy to the canopy of outdoor fruit tree canopy random distribution. The experimental results showed that: 1) when the phase angle of jujube was 52.19<span style="white-space:nowrap;">°</span>, 66.51<span style="white-space:nowrap;">°</span></span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">and 88.26<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model are 0.9982, 0.9963, 0.9912 and 3.80%, 4.17%, 6.40%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">a</span><span style="font-family:Verdana;font-size:12px;">nd the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9056,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9223,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9260 and 6.23%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">3.32%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">8.05%, respectively;It can be seen that roujean model can quantitatively describe the Orient parameter of jujube</span><span style="font-family:Verdana;font-size:12px;">;</span><span style="font-family:Verdana;font-size:12px;">2) When the phase angle of apricot was 70.99<span style="white-space:nowrap;">°</span>, 71.28<span style="white-space:nowrap;">°</span> and 67.91<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model </span><span style="font-family:Verdana;font-size:12px;">is</span><span style="font-family:Verdana;font-size:12px;"> 0.9862, 0.9823, 0.9792 and 3.40%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">4.82%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">5.19%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">And the R</span><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9382, 0.8947, 0.8849 and 7.19%, 9.28%, 9.47%, respectively.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">Roujean model can also quantitatively describe the Orient parameter of white apricot. In summary, the Roujean model can provide a good quantitative description of </span><i><span style="font-family:Verdana;font-size:12px;">f</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> and a good quantitative description of Orient, which in turn can predict the pBRDF parameter for more fruits with different incidence and detection directions.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">It can correct the influence of angle factor in the nondestructive testing of outdoor fruits.</span>展开更多
The theoretical and experimental analyses of widening the differential group delay (DGD) dynamic range of degree of polarization(DOP)-based polarization mode dispersion monitor using a band-pass filter are presented. ...The theoretical and experimental analyses of widening the differential group delay (DGD) dynamic range of degree of polarization(DOP)-based polarization mode dispersion monitor using a band-pass filter are presented. The experiment shows that the maximum DGD same time, DOP sensitivity has a little change. The experimental results are in accordance with the numerical ones.展开更多
In this paper,a spectral beam combining(SBC)structure of multi-single emitters laser diode based on a polarization full feedback(PFF)external cavity is proposed and demonstrated.The maximum combining efficiency is 75....In this paper,a spectral beam combining(SBC)structure of multi-single emitters laser diode based on a polarization full feedback(PFF)external cavity is proposed and demonstrated.The maximum combining efficiency is 75.6%,which leads to an output power of 38.48 W,a degree of polarization(DOP)of 99.42%,and electro-optical conversion efficiency of 35.63%under continuous wave operation at a current of 8 A.Compared to the conventional SBC,the output power,the combining efficiency,the electro-optical conversion efficiency,and the DOP of the PFF-SBC structure present improvements of 5.73 W,11.26 percentage points,5.3 percentage points,and 7.26 percentage points,respectively.The results show that this SBC method can achieve a high efficiency and linearly polarized laser output of SBC,thereby making the subsequent polarization beam-combining efficiency approach the limit.展开更多
为提高天空偏振模式探测的稳定性,该文通过分析天空偏振光分布模式和Stokes矢量解析模型,设计了一种基于三目偏振相机的天空偏振模式探测试验装置。该装置克服了传统的天空偏振模式探测装置低效和密封性差的问题,适用于雨天和海面的偏...为提高天空偏振模式探测的稳定性,该文通过分析天空偏振光分布模式和Stokes矢量解析模型,设计了一种基于三目偏振相机的天空偏振模式探测试验装置。该装置克服了传统的天空偏振模式探测装置低效和密封性差的问题,适用于雨天和海面的偏振光探测工作。三目偏振相机的偏振角度为0°、60°、120°,通过求解Stokes矢量解可求出目标观测点处的偏振度(degree of polarization,DOP)和偏振方位角(angle of polarized elevation,AOE),分析了天空偏振模式图中AOE和DOP的分布规律。实验结果表明DOP和AOE关于中性点呈有规律的对称分布,该装置能有效探测天空偏振模式,为偏振导航技术提供有力的技术支持。展开更多
Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical e...Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 60778048)
文摘Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov's phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.
基金supported by the National Natural Science Foundation of China (Grant No 60577046)the Corporative Building Project of Beijing Educational Committee of China (Grant No XK100130737) Shandong High Technology Project of China (Grant No 2006GG2201002)
文摘Using two typical types of polarization controller, this paper analyses theoretically and experimentally the fact that it is necessary to adjust at least three instead of two waveplates in order to transform any state of polarization to any other output covering the entire Poincar6 sphere. The experimental results are exactly in accordance with the theory discussed in this paper. It has corrected the conventional and inaccurate point of view that two waveplates of a polarization controller are adequate to complete the transformation of state of polarization.
文摘An expression of degree of polarization(DOP) for metallic material is presented based on the three-component polarized bidirectional reflectance distribution function(p BRDF) model with considering specular reflection, directional diffuse reflection and ideal diffuse reflection. The three-component p BRDF model with a detailed reflection assumption is validated by comparing simulations with measurements. The DOP expression presented in this paper is related to surface roughness, which makes it more reasonable in physics. Test results for two metallic samples show that the DOP based on the three-component p BRDF model accords well with the measurement and the error of existing DOP expression is significantly reduced by introducing the diffuse reflection. It indicates that our DOP expression describes the polarized reflection properties of metallic surfaces more accurately.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11504194 and 11274189the Project of Shandong-Provincial Higher Educational Science and Technology Program under Grant No J14LJ06the Application Foundation Research Program of Qingdao under Grant No 14-2-4-101-jch
文摘With spin-polarized-dependent band gap renormalization effect taken into account, the energy-dependent evolu- tion of electron spin polarization in GaAs is calculated at room temperature and at a low temperature of 1OK. We consider the exciting light with right-handed circular polarization, and the calculation results show that the degree of electron spin polarization is dependent strongly on the quasi-Fermi levels of |1/2) and |- 1/2) spin conduction bands. At room temperature, the degree of electron spin polarization decreases sharply from 1 near the bottom of the conduction band, and then increases to a stable value above the quasi-Fermi level of the |- 1/2) band. The greater the quasi-Fermi level is, the higher the degree of electron spin polarization with excessive en- ergy above the quasi-Fermi level of the |- 1/2) band can be achieved. At low temperature, the degree of electron spin polarization decreases from 1 sharply near the bottom of the conduction band, and then increases with the excessive energy, and in particular, up to a maximum of i above the quasi-Fermi level of the |1/2) band.
基金financially supported by the National Natural Science Foundation of China(Nos.11704081,52125205,52250398,U20A20166,52192614 and 52003101)Guangxi Natural Science Foundation(Nos.2020GXNSFAA297182,2020GXNSFAA297041 and 2017GXNSFBA19-8229)+5 种基金the special fund for Guangxi Bagui ScholarsNational Science and Technology Innovation Talent Cultivation Program(No.2023BZRC016)National Key R&D Program of China(Nos.2021YFB3200302 and2021YFB3200304)the Natural Science Foundation of Beijing Municipality(No.2222088)Shenzhen Science and Technology Innovation Program(No.KQTD20170810105439418)the Fundamental Research Funds for the Central Universities。
文摘Polarization upconversion luminescence(PUCL)of lanthanide ions(Ln^(3+))has been widely used in single particle tracking,microfluidics detection,three-dimensional displays,and so on.However,no effective strategy has been developed for modulating PUCL.Here we report a strategy to regulate PUCL in Ho^(3+)-doped NaYF4single nanorods based on the number of upconversion photons.By constructing a multiphoton upconversion system for Ho^(3+),we regulate the degree of polarization(DOP)of PUCL from 0.590 for two-photon luminescence to 0.929 for three-photon upconversion luminescence(UCL).Furthermore,our strategy is verified from cross-relaxation between Ho^(3+)and Yb^(3+),excitation wavelength,excitation power density,and local site symmetry.And this regulation strategy of PUCL has also been achieved in Tm^(3+),with the DOP ranging from 0.233 for two-photon luminescence to 0.925 for four-photon UCL Besides,multi-dimensional anti-counterfeiting display has been explored with PUCL.This work provides an effective strategy for regulating PUCL and also provides more opportunities for the development of polarization display optical encoding,anti-counterfeiting,and integrated optical devices.
文摘Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Roujean model was used to quantitatively describe different fruits intensity components (<i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;">) and polarization phase angle (Orient), and the simulation results were analyzed and compared using statistical analysis and comparison methods to realize the prediction from the regular model to the outdoor fruit tree canopy to the canopy of outdoor fruit tree canopy random distribution. The experimental results showed that: 1) when the phase angle of jujube was 52.19<span style="white-space:nowrap;">°</span>, 66.51<span style="white-space:nowrap;">°</span></span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">and 88.26<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model are 0.9982, 0.9963, 0.9912 and 3.80%, 4.17%, 6.40%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">a</span><span style="font-family:Verdana;font-size:12px;">nd the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9056,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9223,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9260 and 6.23%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">3.32%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">8.05%, respectively;It can be seen that roujean model can quantitatively describe the Orient parameter of jujube</span><span style="font-family:Verdana;font-size:12px;">;</span><span style="font-family:Verdana;font-size:12px;">2) When the phase angle of apricot was 70.99<span style="white-space:nowrap;">°</span>, 71.28<span style="white-space:nowrap;">°</span> and 67.91<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model </span><span style="font-family:Verdana;font-size:12px;">is</span><span style="font-family:Verdana;font-size:12px;"> 0.9862, 0.9823, 0.9792 and 3.40%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">4.82%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">5.19%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">And the R</span><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9382, 0.8947, 0.8849 and 7.19%, 9.28%, 9.47%, respectively.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">Roujean model can also quantitatively describe the Orient parameter of white apricot. In summary, the Roujean model can provide a good quantitative description of </span><i><span style="font-family:Verdana;font-size:12px;">f</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> and a good quantitative description of Orient, which in turn can predict the pBRDF parameter for more fruits with different incidence and detection directions.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">It can correct the influence of angle factor in the nondestructive testing of outdoor fruits.</span>
基金National Natural Science Foundation of China(60377026)
文摘The theoretical and experimental analyses of widening the differential group delay (DGD) dynamic range of degree of polarization(DOP)-based polarization mode dispersion monitor using a band-pass filter are presented. The experiment shows that the maximum DGD same time, DOP sensitivity has a little change. The experimental results are in accordance with the numerical ones.
基金This work was supported by the Key Technology Research and Development Program of Shandong(Nos.2022CXGC020104 and 2023ZLYS03)the Key-Area Research and Development Program of Guangdong Province(No.2020B090922003).
文摘In this paper,a spectral beam combining(SBC)structure of multi-single emitters laser diode based on a polarization full feedback(PFF)external cavity is proposed and demonstrated.The maximum combining efficiency is 75.6%,which leads to an output power of 38.48 W,a degree of polarization(DOP)of 99.42%,and electro-optical conversion efficiency of 35.63%under continuous wave operation at a current of 8 A.Compared to the conventional SBC,the output power,the combining efficiency,the electro-optical conversion efficiency,and the DOP of the PFF-SBC structure present improvements of 5.73 W,11.26 percentage points,5.3 percentage points,and 7.26 percentage points,respectively.The results show that this SBC method can achieve a high efficiency and linearly polarized laser output of SBC,thereby making the subsequent polarization beam-combining efficiency approach the limit.
文摘为提高天空偏振模式探测的稳定性,该文通过分析天空偏振光分布模式和Stokes矢量解析模型,设计了一种基于三目偏振相机的天空偏振模式探测试验装置。该装置克服了传统的天空偏振模式探测装置低效和密封性差的问题,适用于雨天和海面的偏振光探测工作。三目偏振相机的偏振角度为0°、60°、120°,通过求解Stokes矢量解可求出目标观测点处的偏振度(degree of polarization,DOP)和偏振方位角(angle of polarized elevation,AOE),分析了天空偏振模式图中AOE和DOP的分布规律。实验结果表明DOP和AOE关于中性点呈有规律的对称分布,该装置能有效探测天空偏振模式,为偏振导航技术提供有力的技术支持。
基金Project supported by the National Natural Science Foundation of China (Grant No. 10874125)
文摘Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.