Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbu...Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.展开更多
The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （...The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （PIB） are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity/max and the PIB decrease and w（z） increases as the refraction index structure constant Cn^2 increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance Xd and beam number M is less affected by the turbulence than that with a larger value of y and smaller values of Xd and M. The main results obtained in this paper are explained physically.展开更多
Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model corre...Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.展开更多
The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a gen...The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian-Schell model （GSM） beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence （DOC） and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens-Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field. A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.展开更多
This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model （GSM） beams with edge dislocation propagating through atmospheric turbulence along a slan...This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model （GSM） beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope ｜p｜ and the smaller the off-axis distance ｜d｜ are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The CSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.展开更多
Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A...Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A flow diagram is presented to illustrate the procedure of phase optimization by the SA algorithm. Numerical examples demonstrate the advantages of the SA algorithm in shaping partially coherent beams. An uniform flat-topped beam profile with maximum reconstruction error RE 〈 1.74% is achieved. A further extension of the approach is discussed.展开更多
Based on the paraxial wave equation,this study extends the theory of small-scale self-focusing(SSSF)from coherent beams to spatially partially coherent beams(PCBs)and derives a general theoretical equation that reveal...Based on the paraxial wave equation,this study extends the theory of small-scale self-focusing(SSSF)from coherent beams to spatially partially coherent beams(PCBs)and derives a general theoretical equation that reveals the underlying physics of the reduction in the B-integral of spatially PCBs.From the analysis of the simulations,the formula for the modulational instability(MI)gain coefficient of the SSSF of spatially PCBs is obtained by introducing a decrease factor into the formula of the MI gain coefficient of the SSSF of coherent beams.This decrease can be equated to a drop in the injected light intensity or an increase in the critical power.According to this formula,the reference value of the spatial coherence of spatially PCBs is given,offering guidance to overcome the output power limitation of the high-power laser driver due to SSSF.展开更多
The self-focusing phenomenon of partially coherent beams(PCBs)was simulated using the complex screen method combined with the split-step Fourier method to solve the nonlinear Schrödinger equation.Considering the ...The self-focusing phenomenon of partially coherent beams(PCBs)was simulated using the complex screen method combined with the split-step Fourier method to solve the nonlinear Schrödinger equation.Considering the propagation of Gaussian Schell-model beams in a nonlinear medium as an example,the suppression effects of intensity,propagation distance,and spatial coherence on small-scale self-focusing were demonstrated.Simulations of overall and small-scale self-focusing using this method were compared with the existing literature to demonstrate the validity of the method.This method can numerically analyze the degree of self-focusing in PCBs and advance the study of their nonlinearity.展开更多
A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture...A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then,the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.展开更多
Based on the modified Rytov theory and the international telecommunication union-radio （ITU-R） slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian-Schell model ...Based on the modified Rytov theory and the international telecommunication union-radio （ITU-R） slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian-Schell model （GSM） beam propa- gation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Compar- ison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.展开更多
On the basis of the extended Huygens-Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication S...On the basis of the extended Huygens-Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector,the characteristics of the partially coherent Gaussian Schell-model（GSM） beams propagating in slanted atmospheric turbulence are studied.Using the cross-spectral density function（CSDF）,we derive the expressions for the effective beam radius,the spreading angle,and the average intensity.The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically.The influences of the coherence degree,the propagation distance,the propagation height,and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.展开更多
The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is establi...The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is established. The influence of a collimating system and thermal blooming is considered together with atmospheric turbulence and me- chanical jitter. The laser energy concentration of partially coherent beams in the far field is calculated and analysed based on the theoretical model. It is shown that the propagation performance of partially coherent beams depends on the collimating system, atmospheric turbulence, mechanical jitter and thermal blooming. The propagation performance of partially coherent beams and fully coherent beams is studied and the results show that partially coherent beams are less sensitive to the influence of thermal blooming, which results in that the energy degeneration for partially coherent beams is only 50% of that for fully coherent beams. Both partially coherent beams and fully coherent beams become less sensitive to thermal blooming when the average structural constant of the refraction index fluctuations increases to 1.7×10^-14 m^-2/3. The investigation presents a reference for applications of a high-power fibre laser system.展开更多
Coherence is one of the most salient features of a laser beam,and laser beams which are not completely coherent,the so-called partially coherent beams,are preferred in many applications.The degrees of coherence of con...Coherence is one of the most salient features of a laser beam,and laser beams which are not completely coherent,the so-called partially coherent beams,are preferred in many applications.The degrees of coherence of conventional spatial partially coherent beams can be described by Gaussian distributions.Currently,more and more attention is being paid to partially coherent beams with prescribed degrees of coherence due to their extraordinary optical properties,such as self-focusing,self-shaping,selfsplitting,periodicity reciprocity,and super-strong reconstruction. Manipulating the structure of the degree of a partially coherent beam provides a novel way for modulating and controlling its propagation properties and is useful in beam shaping,free-space optical communications,optical trapping,optical encryption and image or information transfer through adverse inhomogeneous environments.In this paper,we present a review on the recent advances in partially coherent beams with prescribed degrees of coherence.展开更多
The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intens...The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negiigibl% while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.展开更多
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
Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollo...Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained.It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.展开更多
Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for ma...Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for maximum irradiance on-axis and the relative focal shift are evaluated by the analytical propagation formulas. Our numerical results show that both the relative focal shift and the effective beam width of focused partially coherent CDHBs are mainly determined by the initial transverse coherence width 6g and the Fresnel number Nw, which are also affected by the changes of both the dark-size adjusting parameter p and the order N of CDHBs.展开更多
The concept of partially coherent nonparaxial modified Bessel Gauss （MBG） beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG...The concept of partially coherent nonparaxial modified Bessel Gauss （MBG） beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, ζ and f parameters, and to compare the difference between the paraxial and nonparaxial results.展开更多
Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially cohere...Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.展开更多
Taking partially coherent cosh-Gaussian （ChG） beams as an example of more general partially coherent beams, we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is sh...Taking partially coherent cosh-Gaussian （ChG） beams as an example of more general partially coherent beams, we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is shown that, unlike Gaussian Schell-model （GSM） beams, in the strict sense there do not exist two partially coherent ChG beams which can generate far fields with the same spectral degree of coherence. However, under certain conditions it is possible to find two partially coherent ChG beams with the same spectral degree of coherence in the far field.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 60778048)
文摘Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.
基金supported by the National Natural Science Foundation of China (Grant No 60778048)
文摘The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （PIB） are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity/max and the PIB decrease and w（z） increases as the refraction index structure constant Cn^2 increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance Xd and beam number M is less affected by the turbulence than that with a larger value of y and smaller values of Xd and M. The main results obtained in this paper are explained physically.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574097）.
文摘Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.
基金supported by the Fundamental Research Funds for the Central Universities of China(Grant No.K5051207001)the National Natural Science Foundation of China(Grant Nos.61172031 and 61271110)
文摘The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian-Schell model （GSM） beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence （DOC） and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens-Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field. A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.
基金supported by the National Natural Science Foundation of China (Grant No.10874125)
文摘This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model （GSM） beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope ｜p｜ and the smaller the off-axis distance ｜d｜ are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The CSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.
基金supported by the National Natural Science Foundation of China (Grant No 10574097)
文摘Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A flow diagram is presented to illustrate the procedure of phase optimization by the SA algorithm. Numerical examples demonstrate the advantages of the SA algorithm in shaping partially coherent beams. An uniform flat-topped beam profile with maximum reconstruction error RE 〈 1.74% is achieved. A further extension of the approach is discussed.
文摘Based on the paraxial wave equation,this study extends the theory of small-scale self-focusing(SSSF)from coherent beams to spatially partially coherent beams(PCBs)and derives a general theoretical equation that reveals the underlying physics of the reduction in the B-integral of spatially PCBs.From the analysis of the simulations,the formula for the modulational instability(MI)gain coefficient of the SSSF of spatially PCBs is obtained by introducing a decrease factor into the formula of the MI gain coefficient of the SSSF of coherent beams.This decrease can be equated to a drop in the injected light intensity or an increase in the critical power.According to this formula,the reference value of the spatial coherence of spatially PCBs is given,offering guidance to overcome the output power limitation of the high-power laser driver due to SSSF.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Nos.XDA25020203 and 25020301)the Innovation Fund of the Key Laboratory of the Chinese Academy of Sciences(No.CXJJ-21S015)。
文摘The self-focusing phenomenon of partially coherent beams(PCBs)was simulated using the complex screen method combined with the split-step Fourier method to solve the nonlinear Schrödinger equation.Considering the propagation of Gaussian Schell-model beams in a nonlinear medium as an example,the suppression effects of intensity,propagation distance,and spatial coherence on small-scale self-focusing were demonstrated.Simulations of overall and small-scale self-focusing using this method were compared with the existing literature to demonstrate the validity of the method.This method can numerically analyze the degree of self-focusing in PCBs and advance the study of their nonlinearity.
基金supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20190953)。
文摘A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then,the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.
基金supported by the National Natural Science Foundation of China(Grant Nos.61172031 and 61271110)
文摘Based on the modified Rytov theory and the international telecommunication union-radio （ITU-R） slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian-Schell model （GSM） beam propa- gation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Compar- ison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61172031)
文摘On the basis of the extended Huygens-Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector,the characteristics of the partially coherent Gaussian Schell-model（GSM） beams propagating in slanted atmospheric turbulence are studied.Using the cross-spectral density function（CSDF）,we derive the expressions for the effective beam radius,the spreading angle,and the average intensity.The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically.The influences of the coherence degree,the propagation distance,the propagation height,and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.
文摘The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is established. The influence of a collimating system and thermal blooming is considered together with atmospheric turbulence and me- chanical jitter. The laser energy concentration of partially coherent beams in the far field is calculated and analysed based on the theoretical model. It is shown that the propagation performance of partially coherent beams depends on the collimating system, atmospheric turbulence, mechanical jitter and thermal blooming. The propagation performance of partially coherent beams and fully coherent beams is studied and the results show that partially coherent beams are less sensitive to the influence of thermal blooming, which results in that the energy degeneration for partially coherent beams is only 50% of that for fully coherent beams. Both partially coherent beams and fully coherent beams become less sensitive to thermal blooming when the average structural constant of the refraction index fluctuations increases to 1.7×10^-14 m^-2/3. The investigation presents a reference for applications of a high-power fibre laser system.
基金supported by the National Natural Science Fund for Distinguished Young Scholar(11525418)the National Natural Science Foundation of China(11274005&11474213)+1 种基金the Project of the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutionsthe Innovation Plan for Graduate Students in the Universities of Jiangsu Province(KYZZ16_0079)
文摘Coherence is one of the most salient features of a laser beam,and laser beams which are not completely coherent,the so-called partially coherent beams,are preferred in many applications.The degrees of coherence of conventional spatial partially coherent beams can be described by Gaussian distributions.Currently,more and more attention is being paid to partially coherent beams with prescribed degrees of coherence due to their extraordinary optical properties,such as self-focusing,self-shaping,selfsplitting,periodicity reciprocity,and super-strong reconstruction. Manipulating the structure of the degree of a partially coherent beam provides a novel way for modulating and controlling its propagation properties and is useful in beam shaping,free-space optical communications,optical trapping,optical encryption and image or information transfer through adverse inhomogeneous environments.In this paper,we present a review on the recent advances in partially coherent beams with prescribed degrees of coherence.
基金Project supported by the National Natural Science Foundation of China (Grant No.10874125)
文摘The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negiigibl% while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.
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 Major Research Plan of the National Natural Science Foundation of China(Grant No.61405205)
文摘Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained.It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.
基金Supported by the National Natural Science Foundation of China under Grant No 61201193
文摘Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for maximum irradiance on-axis and the relative focal shift are evaluated by the analytical propagation formulas. Our numerical results show that both the relative focal shift and the effective beam width of focused partially coherent CDHBs are mainly determined by the initial transverse coherence width 6g and the Fresnel number Nw, which are also affected by the changes of both the dark-size adjusting parameter p and the order N of CDHBs.
基金Project supported by the National High Technology Development Program of China （Grant No 823070） and the National Natural Science Foundation of China （Grant No 10574097）.
文摘The concept of partially coherent nonparaxial modified Bessel Gauss （MBG） beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, ζ and f parameters, and to compare the difference between the paraxial and nonparaxial results.
文摘Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.
基金supported by the National Natural Science Foundation of China (Grant Nos 10574097 and 10874125)
文摘Taking partially coherent cosh-Gaussian （ChG） beams as an example of more general partially coherent beams, we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is shown that, unlike Gaussian Schell-model （GSM） beams, in the strict sense there do not exist two partially coherent ChG beams which can generate far fields with the same spectral degree of coherence. However, under certain conditions it is possible to find two partially coherent ChG beams with the same spectral degree of coherence in the far field.
