CN113504656A - System and method for generating polygonal partially coherent vortex light beam - Google Patents
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Abstract
The invention relates to the technical field of optics, and discloses a system and a method for generating polygonal partially coherent vortex beams. The invention can flexibly regulate the geometric structure of the partially coherent vortex light beam in real time, and can simply and conveniently generate the polygonal partially coherent vortex light beam, thereby having important application value in the field of particle manipulation. Further, the light intensity distribution of an ellipse, a triangle, a quadrangle and a pentagram can be realized by regulating and controlling the numerical values of the power exponent factor and the spiral factor. Compared with the traditional partially coherent vortex light beam, the light intensity distribution has higher regulation and control freedom degree and reserves higher energy.
Description
Technical Field
The invention relates to the technical field of optics, in particular to a system and a method for generating a polygonal partially coherent vortex light beam.
Background
The vortex light beam is a special light beam with a dark hollow structure, and has important application value in the fields of particle manipulation, optical tweezers, optical communication, optical measurement, super-resolution imaging and the like in recent years due to the fact that the vortex light beam carries orbital angular momentum. And thus gradually attract the attention of researchers. With the increasing development of science and technology, researchers need to construct various vortex light beams to meet the special requirements of the application fields. The manipulated variables of the vortex beam are mainly amplitude, phase, polarization, frequency and coherence. One of the great features of laser is its high coherence, but the coherence of the beam is somewhat reduced after passing through atmospheric turbulence, random phase, or rotating scatterers, and we refer to this beam with a low coherence as a partially coherent beam. The partially coherent beam is more ubiquitous than the fully coherent beam and has some unique advantages in practical applications. For example, the partially coherent light beam can improve transmission efficiency in a nonlinear optical process, enhance signal-to-noise ratio, reduce bit error rate, achieve particle capture, ghost imaging, and other applications.
Partially coherent vortex beams were first proposed by Gori et al and can be represented by the incoherent superposition of a series of coherent laguerre gaussian modes. Thereafter, the study of vortex beams has been expanded from the fully coherent domain to the partially coherent domain. Unlike a fully coherent vortex beam having a phase singularity at its center resulting in a central intensity of zero, for a partially coherent vortex beam, the intensity distribution evolves to a gaussian distribution as the coherence decreases. Furthermore, the partially coherent vortex beam has no visible phase singularity due to the disappearance of the intensity null point, but it has a coherent singularity, i.e. a point where the cross spectral density is zero. And by regulating the coherence size, the phase singularity in the completely coherent vortex optical beam and the coherent singularity in the partially coherent vortex optical beam can be mutually converted, and the position of the coherent singularity is determined by the value of the reference point in the cross spectral density function. The partially coherent vortex light beam has some advantages compared with the completely coherent vortex light beam, for example, the light intensity distribution can be shaped from hollow to solid by regulating the coherence, so that low-refractive-index particles can be captured by utilizing the hollow light intensity, high-refractive-index particles can be captured by utilizing the solid light intensity, the light intensity flicker and light beam expansion effect caused by transmission can be overcome in the free space optical communication field of the partially coherent vortex light beam, and the specific correlation function of the partially coherent vortex light beam has strong self-repairing capability. Therefore, constructing a new type of partially coherent vortex beam is very important in basic scientific research and practical applications.
Two methods are currently used to construct a novel Partially coherent vortex beam, the first method of modulating the phase of the vortex beam to generate a fractional order Partially coherent vortex beam (Zeng, J., et al (2018). "partial coherent fractional vortex beam." Optics Express26(21):26830), and the second method of modulating the spatial correlation function of the partial coherent vortex beam to construct a specially correlated Partially coherent vortex beam, such as a Laguerre-Gaussian correlated Shell-model vortex beam ("Optics 22(5): 5838).
First, for a conventional integer order partially coherent vortex beam with a gaussian correlation function structure, the change amount of the spiral phase within one period is an integer multiple of 2 pi, i.e. the topological charge number is an integer, and the generated light intensity distribution is a circular ring under the condition of high coherence and becomes a gaussian spot with the decrease of the coherence. When the topological charge number is not an integer, a partially coherent fractional order vortex light beam with a gap can be generated, and the shaping of the light intensity distribution of the light beam is realized. Secondly, when the correlation function of the partially coherent vortex light beam is Laguerre-Gaussian correlation, the light intensity distribution is determined by joint regulation and control of the vortex phase, the initial coherence and the correlation structure function. When the degree of coherence is very low, the light beam is mainly regulated and controlled by the correlation function, so that the light intensity has dark hollow light intensity distribution; with the increase of the degree of coherence, the regulation and control effect of the correlation function is reduced, and the light intensity gradually changes into Gaussian distribution; when the coherence increases to a large extent, the correlation function no longer acts as a modulation, which is mainly controlled by the vortex phase, so that the light intensity returns to the dark hollow structure.
In summary, the existing fractional order vortex phase scheme can only realize the partially coherent vortex light beam with the notch, and the degree of freedom of regulation and control of the light intensity distribution is not high. The method for regulating the correlation structure needs to utilize a spatial light modulator to regulate the correlation function in front of the dynamic scatterer, so that the energy loss is overlarge, and the method is difficult to be applied to the fields of optical tweezers and the like which need higher energy of light beams.
Disclosure of Invention
The invention aims to provide a polygonal partially coherent vortex light beam generating system which is simple in structure and good in stability.
In order to solve the above problems, the present invention provides a system for generating a polygonal partially coherent vortex light beam, comprising a computer, and a laser, a collimating and beam expanding element, a first lens, a light beam scattering element, a second lens, a gaussian filter, a spatial light modulator, and a third lens, which are sequentially arranged along a light path, wherein the spatial light modulator is connected to the computer, and the computer is configured to load a hologram of an abnormal power index vortex light beam to the spatial light modulator;
the laser instrument produces the complete coherent light beam, the collimation expands the component and carries out the collimation to the complete coherent light beam and expand, the complete coherent light beam focus after the collimation expands is broken up on the component to the light beam by first lens, the component is broken up to the light beam and is broken up and generate complete incoherent light beam, the second lens carries out Fourier transform to complete incoherent light beam, the Gaussian filter piece filters the complete incoherent light beam after Fourier transform and obtains the partial coherent light beam that has Gaussian light intensity distribution, spatial light modulator modulates partial coherent light beam, the light beam after the third lens will modulate focuses on and obtains the partial coherent vortex light beam that has polygonal structure.
As a further improvement of the invention, the complex transmittance function of the hologram of the abnormal power exponential vortex beam is expressed as:
t＝exp[i·(angle(E(r,θ))+P)]
wherein, angle (eta) is a function for solving the phase of the abnormal power index vortex, P is a phase expression of a blazed grating, and a hologram for generating the abnormal power index vortex beam can be obtained by squaring the mode of the complex transmittance function t;
wherein the expression of P is:
P＝2πx/D
where D denotes the phase period of the blazed grating used to separate the generated polygonal partially coherent vortex beam from the zero-order spot and x denotes the x-axis coordinate of the cartesian coordinate system.
As a further improvement of the present invention, the cross spectral density function of the partially coherent vortex beam with polygonal structure is expressed as:
W(r1,θ1,r2,θ2)＝<E*(r1,θ1)E(r2,θ2)> (1)
where < > denotes an ensemble averaging operation, and "+" denotes a complex conjugate operation. E (r, θ) represents the electric field of the anomalous power exponential vortex beam when fully coherent, r represents the radial factor, θ represents the azimuthal factor, and the electric field can be expressed as:
wherein, w0Representing the initial beam waist radius of the light beam, wherein i is an imaginary number unit, rem (right) is a complementation function, m is a spiral factor, n is a power exponent factor, and the light intensity distribution of the partially coherent vortex light beam can be regulated and controlled by regulating and controlling the sizes of the spiral factor m and the power exponent factor n; substituting the formula (2) into the formula (1) to obtain the cross spectrum density expression of the polygonal partially coherent vortex light beam in the space-frequency domain:
where σ represents the initial coherence length of the beam, and the second term in the equation is the conventional gaussian correlation function.
As a further development of the invention, a camera is also included, which images the generated partially coherent vortex beam with a polygonal structure.
As a further improvement of the invention, the beam breaking element is a rotating ground glass, and the surface of the rotating ground glass is provided with tiny particles which are subject to Gaussian statistical distribution.
As a further improvement of the present invention, the collimated beam expanding element is a beam expander.
The invention also provides a method for generating the polygonal partially coherent vortex light beam, which comprises the following steps:
generating a completely coherent light beam;
collimating and expanding the fully coherent light beam;
breaking up the fully coherent beam and generating a fully incoherent beam;
fourier transforming the completely incoherent light beam;
filtering the completely incoherent light beam after Fourier transform to obtain a partially coherent light beam with Gaussian light intensity distribution;
modulating the partially coherent light beam with a spatial light modulator loaded with a hologram of an abnormal power index vortex light beam;
and focusing the modulated light beam to obtain a partially coherent vortex light beam with a polygonal structure.
As a further improvement of the present invention, a rotating ground glass is used to break up the fully coherent beam and generate a fully incoherent beam.
As a further development of the invention, the completely incoherent light beam is fourier-transformed by means of a second lens.
As a further improvement of the invention, a Gaussian filter is used for filtering the completely incoherent light beam after Fourier transform.
The invention has the beneficial effects that:
the system and the method for generating the polygonal partially coherent vortex light beam can flexibly regulate and control the geometric structure of the partially coherent vortex light beam in real time, and can simply and conveniently generate the polygonal partially coherent vortex light beam, so that the system and the method have important application value in the field of particle manipulation. Further, the light intensity distribution of an ellipse, a triangle, a quadrangle and a pentagram can be realized by regulating and controlling the numerical values of the power exponent factor and the spiral factor. Compared with the traditional partially coherent vortex light beam, the light intensity distribution has higher regulation and control freedom degree and reserves higher energy.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of a polygonal partially coherent vortex beam generation system in a preferred embodiment of the present invention;
FIG. 2 is a hologram of an abnormal power exponential vortex beam in a preferred embodiment of the invention;
FIG. 3 is a graph of the intensity distribution of a partially coherent vortex beam having a polygonal configuration at the focal plane of a third lens according to a preferred embodiment of the present invention.
Description of the labeling: 1. a laser; 2. a collimated beam expanding element; 3. a first lens; 4. a beam break-up element; 5. a second lens; 6. a Gaussian filter; 7. a spatial light modulator; 8. a third lens; 9. a camera.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
As shown in fig. 1, the system for generating a polygonal partially coherent vortex beam in a preferred embodiment of the present invention includes a computer, and a laser 1, a collimating beam expanding element 2, a first lens 3, a beam breaking element 4, a second lens 5, a gaussian filter 6, a spatial light modulator 7, and a third lens 8, which are sequentially disposed along an optical path, wherein the spatial light modulator 7 is connected to the computer, and the computer is configured to load a hologram of an abnormal power index vortex beam to the spatial light modulator 7. Optionally, the computer obtains the required hologram through MATLAB calculation.
The laser device 1 generates a completely coherent light beam, the collimation and beam expanding element 2 performs collimation and beam expansion on the completely coherent light beam, the first lens 3 focuses the completely coherent light beam after the collimation and beam expansion on the light beam scattering element 4, the light beam scattering element 4 scatters the completely coherent light beam and generates a completely incoherent light beam, the second lens 5 performs Fourier transformation on the completely incoherent light beam, the Gaussian filter 6 filters the completely incoherent light beam after the Fourier transformation to obtain a partially coherent light beam with Gaussian light intensity distribution, the spatial light modulator 7 modulates the partially coherent light beam, and the third lens 8 focuses the modulated light beam and obtains a partially coherent vortex light beam with a polygonal structure.
In the present invention, the cross spectral density function of a partially coherent vortex beam with a polygonal structure can be expressed as:
W(r1,θ1,r2,θ2)＝<E*(r1,θ1)E(r2,θ2)> (1)
where < > denotes an ensemble averaging operation, and "+" denotes a complex conjugate operation. E (r, θ) represents the electric field of the anomalous power exponential vortex beam when fully coherent, r represents the radial factor, θ represents the azimuthal factor, and the electric field can be expressed as:
wherein, w0The initial beam waist radius of the light beam is represented, i is an imaginary number unit, rem (right) is a complementation function, m is a spiral factor, n is a power exponent factor, and the light intensity distribution of the partially coherent vortex light beam can be regulated and controlled by regulating and controlling the sizes of the spiral factor m and the power exponent factor n; substituting the formula (2) into the formula (1) to obtain the cross spectrum density expression of the polygonal partially coherent vortex light beam in the space-frequency domain:
where σ represents the initial coherence length of the beam, and the second term in the equation is the conventional gaussian correlation function.
In this embodiment, the system further comprises a camera 9, said camera 9 imaging the generated partially coherent vortex beam having a polygonal structure.
Optionally, the beam breaking element 4 is a rotating ground glass, and the surface of the rotating ground glass has fine particles subject to gaussian statistical distribution.
Optionally, the collimated beam expanding element 2 is a beam expander.
In the present invention, the complex transmittance function of the hologram of the abnormal power exponent vortex beam can be expressed as:
t＝exp[i·(angle(E(r,θ))+P)] (4)
wherein, angle (eta) is a function for solving the phase of the abnormal power index vortex, P is a phase expression of a blazed grating, and a hologram for generating the abnormal power index vortex beam can be obtained by squaring the mode of the complex transmittance function t;
wherein the expression of P is:
P＝2πx/D (5)
where D denotes the phase period of the blazed grating used to separate the generated polygonal partially coherent vortex beam from the zero-order spot and x denotes the x-axis coordinate of the cartesian coordinate system.
The preferred embodiment of the invention also discloses a method for generating the polygonal partially coherent vortex light beam, which comprises the following steps:
A. generating a completely coherent light beam;
B. collimating and expanding the fully coherent light beam;
C. breaking up the fully coherent beam and generating a fully incoherent beam;
D. fourier transforming the completely incoherent light beam;
E. filtering the completely incoherent light beam after Fourier transform to obtain a partially coherent light beam with Gaussian light intensity distribution;
F. modulating the partially coherent light beam with a spatial light modulator loaded with a hologram of an abnormal power index vortex light beam;
G. and focusing the modulated light beam to obtain a partially coherent vortex light beam with a polygonal structure.
Optionally, the completely coherent light beam is scattered by the rotating ground glass and a completely incoherent light beam is generated; fourier transforming the completely incoherent light beam with a second lens; and filtering the completely incoherent light beam subjected to Fourier transform by using a Gaussian filter. The devices and principles involved in the method are the same as those in the above system embodiment, and are not described herein again.
In the experiment, the selected laser is a continuous wave solid laser with the wavelength of 532nm and the power is 300 mW. The focal lengths of the lens 1 and the lens 2 are 100mm, the focal length of the lens 3 is 300mm, the roughness of the rotating ground glass is 400, and the rotating speed of the rotating ground glass is controlled by a 3-volt stabilized voltage supply. The rotating ground glass needs to be placed in the back focal plane of lens 1 and the front focal plane of lens 2. The spatial light modulator is a transmissive spatial light modulator: the HOLOEYELC2012, having a size of 1024 x 768 pixels and a pixel size of 36 μm, inputs the generated hologram into the spatial light modulator through a personal computer. The camera is a professional CCD camera ECO655MVGE, and the specific parameters are 2448 × 2050 pixels in size and 3.45 μm in pixel size.
FIG. 2 is a hologram of an abnormal power exponential vortex beam used in the experiment. And selecting a power exponent factor n as 2, selecting spiral factors m as 2, 3, 4 and 5 respectively, and obtaining the hologram of the abnormal power exponent vortex light beam according to the hologram transmittance function. A hologram of such an anomalous power exponential vortex beam can be generated by the above-described HOLOEYELC2012 spatial light modulator.
Fig. 3 is an experimental light intensity distribution diagram of a partially coherent vortex light beam with a polygonal structure on the focal plane of the lens 3. The initial beam waist radius of the beam in the experiment was 1mm and the coherence length was 0.5 mm. It can be seen from the figure that when the power exponent factor n is equal to 2, by changing the value of the spiral factor m, elliptical, triangular, quadrilateral, pentagon-shaped light intensity distributions can be produced. It can be seen that the present invention enables versatile shaping of partially coherent vortex beams, which would provide potential applications for the field of particle manipulation.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. A polygonal partially coherent vortex light beam generation system is characterized by comprising a computer, a laser, a collimation and beam expansion element, a first lens, a light beam scattering element, a second lens, a Gaussian filter, a spatial light modulator and a third lens, wherein the laser, the collimation and beam expansion element, the first lens, the light beam scattering element, the second lens, the Gaussian filter, the spatial light modulator and the third lens are sequentially arranged along a light path;
the laser instrument produces the complete coherent light beam, the collimation expands the component and carries out the collimation to the complete coherent light beam and expand, the complete coherent light beam focus after the collimation expands is broken up on the component to the light beam by first lens, the component is broken up to the light beam and is broken up and generate complete incoherent light beam, the second lens carries out Fourier transform to complete incoherent light beam, the Gaussian filter piece filters the complete incoherent light beam after Fourier transform and obtains the partial coherent light beam that has Gaussian light intensity distribution, spatial light modulator modulates partial coherent light beam, the light beam after the third lens will modulate focuses on and obtains the partial coherent vortex light beam that has polygonal structure.
2. The polygonal partially coherent vortex beam generating system of claim 1 wherein the complex transmittance function of the hologram of the anomalous power exponent vortex beam is expressed as:
t＝exp[i·(angle(E(r,θ))+P)]
wherein, angle (eta) is a function for solving the phase of the abnormal power index vortex, P is a phase expression of a blazed grating, and a hologram for generating the abnormal power index vortex beam can be obtained by squaring the mode of the complex transmittance function t;
wherein the expression of P is:
P＝2πx/D
where D denotes the phase period of the blazed grating used to separate the generated polygonal partially coherent vortex beam from the zero-order spot and x denotes the x-axis coordinate of the cartesian coordinate system.
3. The polygonal partially coherent vortex beam generation system of claim 1 wherein the cross spectral density function of the polygonal-structured partially coherent vortex beam is expressed as:
W(r1,θ1,r2,θ2)＝<E*(r1,θ1)E(r2,θ2)> (1)
where < > denotes an ensemble averaging operation, and "+" denotes a complex conjugate operation. E (r, θ) represents the electric field of the anomalous power exponential vortex beam when fully coherent, r represents the radial factor, θ represents the azimuthal factor, and the electric field can be expressed as:
wherein, w0The initial beam waist radius of the light beam is represented, i is an imaginary number unit, rem (right) is a complementation function, m is a spiral factor, n is a power exponent factor, and the light intensity distribution of the partially coherent vortex light beam can be regulated and controlled by regulating and controlling the sizes of the spiral factor m and the power exponent factor n; substituting the formula (2) into the formula (1) to obtain the cross spectrum density expression of the polygonal partially coherent vortex light beam in the space-frequency domain:
where σ represents the initial coherence length of the beam, and the second term in the equation is the conventional gaussian correlation function.
4. The polygonal partially coherent vortex beam generation system of claim 1 further comprising a camera that images the generated partially coherent vortex beam having a polygonal structure.
5. The polygonal partially coherent vortex beam generating system of claim 1 wherein said beam breaking element is a rotating ground glass having a surface with fine particles subject to a gaussian statistical distribution.
6. The polygonal partially coherent vortex beam generation system of claim 1 wherein the collimated beam expanding element is a beam expander.
7. A method of generating a polygonal partially coherent vortex beam, comprising:
generating a completely coherent light beam;
collimating and expanding the fully coherent light beam;
breaking up the fully coherent beam and generating a fully incoherent beam;
fourier transforming the completely incoherent light beam;
filtering the completely incoherent light beam after Fourier transform to obtain a partially coherent light beam with Gaussian light intensity distribution;
modulating the partially coherent light beam with a spatial light modulator loaded with a hologram of an abnormal power index vortex light beam;
and focusing the modulated light beam to obtain a partially coherent vortex light beam with a polygonal structure.
8. The method of claim 7, wherein the substantially coherent light beam is broken up and a substantially incoherent light beam is generated by rotating ground glass.
9. The method of generating a polygonal partially coherent vortex beam of claim 7 wherein the completely incoherent beam is fourier transformed using a second lens.
10. The method of claim 7, wherein the Fourier transformed substantially incoherent light beam is filtered using a Gaussian filter.
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