Construction,Propagation And Applications Of Structured Beams With Special Correlated Functions

Amplitude,frequency,phase and polarization are several controllable parameters which affect the propagation characteristics of the beam,while coherence is also a controllable parameter which is often easy to be ignored.One of the most important characteristics of laser is its high coherence.However,reducing the coherence of the laser properly,that is,it becomes partially coherent beams,and it shows unique advantages in many aspects.For example,partially coherent beams can increase the signal-to-noise ratio,reduce the bit error rate,reduce the scintillation and drift of light intensity caused by random media.However,the most studied beams are the Gaussian Schell mode beams.Until 2007,F.Gori et al.found the sufficient conditions for the construction of partially coherent beams with special correlation structure theoretically.A series of special correlation beams models with different correlation structures were proposed,and the propagation characteristics in various media were also widely studied.It was found that the special correlation beam has many unique propagation characteristics superior to the traditional correlation beam.When beams interact with nonlinear matter,many nonlinear optical effects can be produced,such as second harmonic,sum frequency,difference frequency,Kerr effect,four wave mixing and so on.Second harmonic generation is a convenient method to generate new frequency laser beams.Usually,the beams of these frequencies are not easy to obtain,but they have important applications in spectroscopy,optical communication,remote sensing,biomedicine and other fields.At present,the wave front control method is commonly used to control harmonics.Based on this,we mainly construct special correlated structure beams,and study the propagation characteristics and applications of special correlated structure beams in linear and nonlinear media in this paper.The beams with orbital angular momentum is considered to be the key to enhance optical communication in free space and atmospheric turbulence.It is well known that beams with vortex phase have orbital angular momentum.However,it is found that partially coherent beams with twist phase also have orbital angular momentum.In this paper,we construct one kind of partially coherent beams with twist phase,namely twisted Hermite Gaussian Schell mode beams,and study its propagation characteristics in free space and atmospheric turbulence.It is found that the twist factor of twisted Hermite Gaussian Schell mode beam exists not only in the twisted phase,but also in the correlation function.And the twist factor and the order of the beam have great influence on the coherence and spectral density distribution in the light source plane.It is different from the previous studies of Hermite Gaussian correlated beam with only one spot on the light source plane,the twisted Hermite Gaussian Schell mode beam can have more than one spot on the light source plane.The spectral intensity distribution has both self-splitting and self-rotation characteristics when it is propagating in the free space and in turbulence.The distribution of the orbital angular momentum of photons can be changed,the degradation of normalized orbital angular momentum of photons can be slowed down,and the ability to resist the negative effects of turbulence can be improved by adjusting the twist factor and the beam order.Therefore,the performance of this kind of beam is obviously better than that of other partially coherent beams,and it has many adjustable degrees of freedom,which provides a new method to control the orbital angular momentum flexibly and improve the ability to resist the negative effects of turbulence.We report the propagation properties of a new class of conjugate mode partially coherent beams called“Double-H”partially coherent beams in in free space and turbulent atmosphere.We investigate how the phase constant?₀ between the modes play a role in controlling the evolution of intensity distribution and resisting the degradation effects of the atmosphere.Our results indicate that these new class of structured beams provide a new degree of freedom for controlling the shape of the beams and improve turbulence resistance,which may be useful in free-space optical communications.The propagation characteristics of twisted Hermite Gaussian Schell mode beams and rectangular Hermite non-uniform correlated beams propagating in uniaxial crystals orthogonal to optical axis are studied.It is found that the normalized spectral intensity distribution and the coherence distribution are affected by the crystal parameters(such as the ratio of the refractive index of the ordinary light to that of the extraordinary light)and the beam parameters when the beam propagates in the uniaxial crystal.In addition,rectangular Hermite non-uniform correlated beams have independent self-focusing characteristics in x axial direction and y axial direction,and the focusing length in the crystal can be controlled by adjusting the order of the beam or the coherence length in both directions.Using this unique self-focusing propagation property,we first propose a method to measure the principal refractive index of uniaxial crystal by using rectangular Hermite non-uniform correlated beam,and give the specific implementation method.This method is widely used in many cases,and the experimental error caused by CCD detection accuracy can be reduced by increasing the beam order.The second harmonic generation in nonlinear crystals by multi Gaussian Schell mode beams is studied.It is found that for the multi Gaussian Schell mode fundamental beam,the correlation structure of the second harmonic is still multi Gaussian correlation,but the peak number of the coherence mode is twice that of the incident fundamental beam,and the intensity distribution of the second harmonic on the focal plane is the same as that of the fundamental beam,which is flat topped.Therefore,the coherent structure of the second harmonic can be adjusted by adjusting the coherent structure of the fundamental frequency beams,and it provides a new degree of freedom for the regulation of nonlinear harmonics.