CN111412983B - Method and system for measuring size, positive and negative of topological charge of partially coherent vortex light beam - Google Patents
Method and system for measuring size, positive and negative of topological charge of partially coherent vortex light beam Download PDFInfo
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Abstract
The invention discloses a method and a system for measuring the size, the positive and the negative of the topological charge number of a partially coherent vortex light beam, wherein the method comprises the following steps: the partially coherent vortex light beams are incident to the double slits and interfere with each other; focusing the interfered partial coherent vortex light beams onto a receiving screen of the pure phase spatial light modulator through a lens; introducing three disturbances of different phase assignments to the center of the upper part of the receiving screen by the pure phase spatial light modulator; carrying out Fourier transform on the disturbed partially coherent vortex light beam, and recording the light intensity of a Fourier plane under three different phase assignments; and calculating based on inverse Fourier transform according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments to obtain a cross spectral density function of the partially coherent vortex light beam after double-slit interference and focusing. The coherent singularity can be directly observed from the phase distribution diagram of the cross spectral density function, so that the topological charge number and the positive and negative information of the partially coherent vortex light beam can be obtained.
Description
Technical Field
The invention relates to the field of optical measurement, in particular to a method and a system for measuring the size, the positive and the negative of the topological charge number of a partially coherent vortex light beam.
Background
Vortex beam i.e. phase of
Each photon of which carries an orbital angular momentum
Wherein l is the topological charge number. The vortex beam has great application prospect in the aspects of laser particle capture, micromanipulation, information coding and optical information transmission. Therefore, measurement of the topological charge of the vortex beam is a very important task, which has unique advantages in laser processing, optical tweezers, atomic cooling and the like.
Singularities are points in the light field where certain parameters cannot be defined. Under the condition of complete coherence, the central light intensity of the vortex light beam is zero, the phase changes gradually in a spiral structure, and the phase of the cross midpoint is uncertain, namely the phase singularity. However, when the degree of coherence is reduced, the central light intensity of the vortex light beam is no longer zero and gradually becomes solid, and the originally defined phase singularity gradually disappears.
At present, we have a relatively comprehensive topological charge measurement technique for a fully coherent beam. However, as the degree of coherence decreases, the original method will gradually fail.
For vortex light beams with complete coherence or high coherence, methods for measuring topological charge mainly include three types: interferometry, diffractometry and light intensity analysis. Wherein the interference method comprises Mach-Zehnder interferometer, double slit interference (Liaokunshan, Chengzang, Typha) and multi-pin hole interference, the Young double slit interference experiment is used for detecting the topological charge number [ J ] of the vortex light beam, university of Chinese, 2009,30(6):623-, and obtaining a spatial frequency spectrum, wherein the number of dark rings in a distribution diagram of the spatial frequency spectrum is the topological charge number of the vortex light beam. However, when the degree of coherence is reduced, the interference and diffraction phenomena are no longer obvious, and the corresponding method is gradually aged; for light intensity analysis, the literature (Zhao C, Wang F, Dong Y, et al. effect of spatial coherence on determining the polarization charge of a vortex beam [ J ]. Applied Physics Letters,2012,101(26):261104.) states that as coherence decreases, the correspondence between the number of dark rings and the number of topological charges is disturbed, and the method also gradually fails.
For topological charge measurements of partially coherent vortex beams, the most experimentally used at present is to use the close relationship between cross-correlation function (CCF) and topological charge number (Yang Y, Chen M, Mazilu M, et al. Effect of the radial and asymmetric model indices of a partial coherent vortex field upper a partial correlation simple [ J ]. New Journal of Physics,2013,15(11):113053. the cross-correlation function of the radial and spatial model indices J ] Applied Physics, fibers, 108, 107) and the reduced cross-correlation function of the radial and transverse patterns of the radial lines 051 when compared to Liu R, Wang F, Chen D, et al. measuring model indices of a partial coherent vortex index with the radial cross-correlation property map of the radial and radial patterns of the light intensity of the cross-correlation property of the radial lines, 2016, and the cross-correlation function of the radial cross-correlation of the radial patterns of the light intensity of the radial patterns, and longitudinal patterns of the radial patterns of the light intensity of the radial patterns of the light intensity of the light beam, and radial patterns of the cross-correlation of the radial patterns of the light intensity of the radial patterns of the cross-correlation of the light intensity of the cross-correlation function of the radial patterns of the radial lines, 2016, 0, more stability exists (Palacios D M, Maleev I D, Marathay A S, et al.
In addition, the magnitude and sign of the topological charge of the partially coherent vortex beam are measured by using the phase distribution diagram of the complex coherence function of the partially coherent vortex beam (X Lu, C Zhao, Y Shao, J Zeng, appl. Phys. letter.114,201106 (2019)).
Aiming at three methods of vortex light beams with complete coherence or higher coherence, when the coherence is reduced, the interference and diffraction phenomena are no longer obvious, and the corresponding methods are gradually aged; for light intensity analysis, the literature (Zhao C, Wang F, Dong Y, et al. effect of spatial coherence on determining the polarization charge of a vortex beam [ J ]. Applied Physics Letters,2012,101(26):261104.) states that as coherence decreases, the correspondence between the number of dark rings and the number of topological charges is disturbed, and the method also gradually fails.
For the measurement of the topological charge of the partially coherent vortex light beam, only the magnitude of the topological charge can be measured by using the relation between a cross-correlation function (CCF) and the topological charge, and the positive and negative information of the topological charge cannot be obtained.
The size, the positive value and the negative value of the topological charge number can be obtained simultaneously by utilizing the measurement of the complex coherence function, but an appropriate off-axis reference point needs to be found in the experiment, and the experiment condition is harsh and complex.
In the patent of publication No. CN107764417B, in order to measure the positive, negative and magnitude of the topological charge, the reference point (disturbance point) loaded by the spatial light modulator needs to be offset from the center, and an example of a set of reference point coordinates is also given in the embodiment, only by taking proper reference point values, clear singular points can be seen from the correlation function phase distribution diagram to read the positive, negative and magnitude of the topological charge, and if the reference point is (0,0) point, or improper non-zero point, the magnitude and positive and negative values of the topological charge cannot be obtained. Particularly, when the reference point is (0,0), the phase distribution exhibits ring dislocation and no singular point can be seen. In the experiment, the selection condition of the off-axis reference point is very harsh, clear singular points can be seen only by finding a proper reference point, the selection of the reference point is related to factors such as the size of a light beam, and the like, and the proper reference point needs to be continuously debugged in the experiment, so that the experiment condition is very harsh and tedious, and the operation is very difficult. Meanwhile, positive and negative information of the topological load can be obtained only by calculating the complex phase dryness, so that the whole measuring process is more complicated.
Disclosure of Invention
In order to solve the above technical problems, an object of the present invention is to provide a method for accurately measuring the magnitude and positive and negative of the topological charge of a partially coherent vortex light beam under a low coherence condition, which is simple in operation, and adopts the following technical solutions:
a method for measuring the magnitude and the positive and negative of the topological charge of a partially coherent vortex beam comprises the following steps:
the partially coherent vortex light beams are incident to the double slits and interfere with each other;
focusing the interfered partial coherent vortex light beams on a receiving screen of the pure phase spatial light modulator;
introducing three disturbances of different phase assignments to the center of the upper part coherent vortex light beam of the receiving screen through the pure phase spatial light modulator;
carrying out Fourier transform on the disturbed partially coherent vortex light beam, and recording the light intensity of a Fourier plane under three different phase assignments;
obtaining a cross spectral density function of the interfered partially coherent vortex light beams through inverse Fourier transform according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments;
and drawing a phase distribution diagram of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution diagram is the topological charge number, and the positive and negative of the topological charge are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
As a further improvement of the invention, the partially coherent vortex light beam is incident to the double slit, and the cross spectral density expression is as follows:
wherein the double slit is located next to the source plane of the partially coherent vortex beam, W1(r1,r2) Representing the cross-spectral density expression, H (r), of a partially coherent vortex beam passing before the double slit, i.e. the source plane1)H*(r2) Representing a double slit function, x1,x2,y1,y2For the coordinates of the beam in the source plane, b is the slit width, 2a + b is the distance between the center points of the double slits, p is the radial index mode of the partially coherent vortex beam and takes 0, l is the Topological Charge (TC) of the partially coherent vortex beam, σgFor the transverse coherence width of the beam, ". is the complex conjugate,. omega."0Is the girdling of the waist, HxIs hermitian polynomial, q is the charge value, AmAnd BmAre coefficients of a function that models the double slit.
As a further improvement of the invention, b is 0.2mm, and 2a + b is 0.3 m.
As a further improvement of the present invention, the focusing the interfered partially coherent vortex light beam onto a receiving screen of a reflective phase-only spatial light modulator specifically includes:
and focusing the interfered partially coherent vortex light beams onto a receiving screen of the reflective phase-only spatial light modulator through a first lens.
As a further improvement of the present invention, the cross spectral density expression of the partially coherent vortex light beam after the interference is focused by the first lens is as follows:
wherein A, B, C, D are elements of a transmission matrix of the optical system, and when the light beams are transmitted through the first lens and focused,
B＝f；
d is 1. U ═ U, v is a vector coordinate, U1,v1,u2,v2Is the coordinates of the beam in the plane of the receiving screen of the spatial light modulator, f is the focal length of the first lens, and z is the distance of transmission, here equal to the focal length of the lens.
As a further improvement of the present invention, the obtaining of the cross spectral density function of the interfered partially coherent vortex light beam by inverse fourier transform according to the three different phase assignments and the light intensity of the fourier plane under the three different phase assignments specifically includes:
first, without introducing perturbations, the intensity of a partially coherent vortex beam in the fourier plane is expressed as:
I0(ρ)＝∫∫W(U1,U2)exp[-i2πρ(U1-U2)]dU1dU2
wherein W (U)1,U2) The cross spectral density is obtained by partially coherent vortex light beams entering a double slit to generate interference, passing through a lens and focusing on a spatial light modulator, wherein when the cross spectral density is equal to U0And (3) introducing disturbance, the light intensity expression becomes:
I(ρ)＝I0(ρ)+CC*W(U0,U0)++C∫W(U1,U0)exp[-i2πρ(U1-U0)]dU1+C*∫W(U0,U2)exp[-i2πρ(U0-U2)]dU2
where C is a complex number determined to characterize the disturbance, the inverse fourier transform of the intensity is obtained:
FT-1[I(ρ)](U)＝FT-1[I0(ρ)](U)+CC*W(U0,U0)δ(U)+CW(U0+U,U0)+C*W(U0,U0-U)
U0when the value is 0, namely the disturbance is taken at the central position of the light spot, three equations are obtained by changing the phase assignment of the disturbance three times, and the cross spectral density function W (U) is obtained by solving1,0)
As a further development of the invention, it is characterized in that the disturbance is circular.
As a further improvement of the invention, a second lens is used for Fourier transform of the disturbed partially coherent vortex light beam.
As a further improvement of the present invention, the intensity of the partially coherent vortex beam and the Fourier plane are recorded using a charge coupled device.
The invention also aims to provide a system which is simple to operate and can accurately measure the topological charge number and the positive and negative of a partially coherent vortex light beam under the condition of low coherence, and the technical scheme is as follows:
a system for measuring the magnitude and sign of the topological charge of a partially coherent vortex beam, comprising:
a double slit for receiving the partially coherent vortex beam and interfering;
the first lens is used for focusing the interfered partially coherent vortex light beams on a receiving screen of the pure-phase spatial light modulator;
the pure phase spatial light modulator is used for introducing three disturbances of different phase assignments to the center of the upper part coherent vortex light beam of the receiving screen;
the second lens is used for carrying out Fourier transform on the disturbed partially coherent vortex light beam;
the charge coupling element is used for recording the light intensity of the Fourier plane under three different phase assignments;
and the computer is used for obtaining a cross spectrum density function of the interfered partial coherent vortex light beams through inverse Fourier transform calculation according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments, drawing a phase distribution diagram of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution diagram is the number of topological charges, and the positive and negative of the topological charges are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
According to the method and the system for measuring the size, the positive and the negative of the topological charge of the partially coherent vortex light beam, the double slits are introduced, the partially coherent vortex light beam interferes after passing through the double slits, the ring dislocation of the phase structure is damaged, and each ring dislocation is divided into two singular points. Meanwhile, the harsh requirements on the measurement conditions are reduced, repeated debugging is not needed in the measurement, the measurement process is greatly simplified, and the success rate of the experiment is improved.
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 method for measuring the magnitude and the sign of the topological charge of a partially coherent vortex beam in an embodiment of the invention;
FIG. 2 is a schematic diagram of a system for measuring the magnitude and sign of the topological charge of a partially coherent vortex beam in an embodiment of the present invention;
FIG. 3 is a schematic structural view of a double seam in an embodiment of the present invention;
FIG. 4 is a phase distribution plot of a cross spectral density function modeled in an embodiment of the present invention;
FIG. 5 is a phase distribution plot of the cross spectral density function experimentally obtained in an embodiment of the present invention.
Description of the labeling: 1. double-sewing; 2. a first lens; 3. a phase-only spatial light modulator; 4. a second lens; 5. a charge-coupled element; 6. and (4) a computer.
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, a method for measuring the topological charge of a partially coherent vortex beam according to an embodiment of the present invention includes the following steps:
and step S110, enabling the partially coherent vortex light beams to be incident to the double slits and generate interference.
In one embodiment, the partially coherent vortex beam is generated by impinging the partially coherent beam on a phase-only spatial light modulator loaded with a vortex phase.
Wherein, the partially coherent vortex light beam is incident to the double slit, and the cross spectral density expression is as follows:
wherein the double slit is located next to the source plane of the partially coherent vortex beam, W1(r1,r2) Representing the cross-spectral density expression, H (r), of a partially coherent vortex beam passing before the double slit, i.e. the source plane1)H*(r2) Representing a double slit function, x1,x2,y1,y2For the coordinates of the beam in the source plane, b is the slit width, 2a + b is the distance between the center points of the double slits, p is the radial index mode of the partially coherent vortex beam and takes 0, l is the Topological Charge (TC) of the partially coherent vortex beam, σgFor the transverse coherence width of the beam, ". is the complex conjugate,. omega."0Is the girdling of the waist, HxIs HermitePolynomial q is the value of the charge, AmAnd BmAre coefficients of a function that models the double slit.
In one embodiment, b is 0.2mm and 2a + b is 0.3 mm.
And step S120, focusing the interfered partially coherent vortex light beams on a receiving screen of the pure-phase spatial light modulator.
Preferably, the interfered partially coherent vortex light beam is focused onto a receiving screen of the reflective phase-only spatial light modulator through a first lens.
The cross spectral density expression of the partially coherent vortex light beam after being focused and transmitted by the first lens is as follows:
wherein A, B, C, D are elements of a transmission matrix of the optical system, and when the light beams are transmitted through the first lens and focused,
B＝f；
d is 1. U ═ U, v is a vector coordinate, U1,v1,u2,v2Is the coordinates of the beam in the plane of the receiving screen of the spatial light modulator, f is the focal length of the first lens, and z is the distance of transmission, here equal to the focal length of the lens.
And step S130, introducing three disturbances of different phase assignments to the center of the upper part coherent vortex beam of the receiving screen through the pure phase spatial light modulator.
Preferably, the perturbation is circular, the radius of the perturbation being much smaller than the radius of the coherent vortex beam on the receiving screen. In other embodiments of the invention, the shape and size of the perturbations may be set as desired.
And S140, carrying out Fourier transform on the disturbed partially coherent vortex light beam, and recording the light intensity of a Fourier plane under three different phase assignments.
Preferably, the second lens is used to fourier transform the partially coherent vortex beam at the perturbed focal field.
Preferably, the intensity of the light at the fourier plane under three different phase assignments is recorded using a charge coupled device record.
And S150, calculating to obtain a cross spectral density function of the interfered partially coherent vortex light beam based on inverse Fourier transform according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments.
Specifically, the method comprises the following steps: first, without introducing perturbations, the intensity of a partially coherent vortex beam in the fourier plane is expressed as:
I0(ρ)＝∫∫W(U1,U2)exp[-i2πρ(U1-U2)]dU1dU2
wherein W (U)1,U2) The cross spectral density is obtained by making partial coherent vortex light beam incident on double slits to generate interference and focusing through a lens, when the cross spectral density is equal to U0And (3) introducing disturbance, the light intensity expression becomes:
I(ρ)＝I0(ρ)+CC*W(U0,U0)++C∫W(U1,U0)exp[-i2πρ(U1-U0)]dr1+C*∫W(U0,U2)exp[-i2πρ(U0-U2)]dr2
where C is a complex number determined to characterize the disturbance, the inverse fourier transform of the intensity is obtained:
FT-1[I(ρ)](U)＝FT-1[I0(ρ)](U)+CC*W(U0,U0)δ(U)+CW(U0+U,U0)+C*W(U0,U0-U)
U0when the value is 0, namely the disturbance is taken at the central position of the light spot, three equations are obtained by changing the phase assignment of the disturbance three times, and the cross spectral density function W (U) is obtained by solving1,0)
If the cubic phase assignment is: c0＝exp[0]And C±＝exp[±2iπ/3]The following can be solved:
and S160, drawing a phase distribution graph of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution graph is the topological charge number, and the positive and negative topological charges are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
As shown in FIG. 2, the system for measuring the topological charge magnitude and the positive and negative of the partially coherent vortex light beam comprises a double slit 1, a first lens 2, a phase-only spatial light modulator 3, a second lens 4, a charge-coupled device 5 and a computer 6.
The double slit 1 is used for receiving the partially coherent vortex light beam and generating interference; the first lens 2 is used for focusing the interfered partially coherent vortex light beams on a receiving screen of the phase-only spatial light modulator 3; the pure phase spatial light modulator 3 is used for receiving the focused partially coherent vortex light beams and introducing three disturbances of different phase assignments to the centers of the partially coherent vortex light beams on the receiving screen; the second lens 4 is used for carrying out Fourier transform on the disturbed partially coherent vortex light beam; the charge coupling element 5 is placed on a Fourier plane and used for recording the light intensity of the Fourier plane under three different phase assignments; and the computer 6 is used for obtaining a cross spectrum density function of the interfered partial coherent vortex light beams through inverse Fourier transform calculation according to the light intensity of the Fourier plane under three different phase assignments and three different phase assignments, drawing a phase distribution diagram of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution diagram is the number of topological charges, and the positive and negative of the topological charges are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
Wherein, the partially coherent vortex light beam is incident to the double slit 1, and the cross spectral density expression is as follows:
wherein the double slit 1 is located immediately adjacent to the source plane of the partially coherent vortex beam, W1(r1,r2) Representing the cross-spectral density expression, H (r), of a partially coherent vortex beam passing before the double slit, i.e. the source plane1)H*(r2) Representing a double slit function, x1,x2,y1,y2For the coordinates of the beam in the source plane, b is the slit width, 2a + b is the distance between the center points of the double slits, p is the radial index mode of the partially coherent vortex beam and takes 0, l is the Topological Charge (TC) of the partially coherent vortex beam, σgFor the transverse coherence width of the beam, ". is the complex conjugate,. omega."0Is the girdling of the waist, HxIs hermitian polynomial, q is the charge value, AmAnd BmAre coefficients of functions that model double slits, and specific data are found in the following article (J.J.Wen and M.A.Breazeale, "A differentiation beam field expressed as the preprocessing of Gaussian beams," J.Acoust.Soc.Am.83(5), 1752-1756 (1988)).
Fig. 3 is a schematic structural diagram of the double slit in this embodiment, in one embodiment, b is 0.2mm, and 2a + b is 0.3 mm.
And focusing the interfered partially coherent vortex light beams onto a receiving screen of the reflective phase-only spatial light modulator through a first lens.
Wherein, the cross spectral density expression of the partially coherent vortex light beam after being focused and transmitted by the lens is as follows:
wherein A, B, C, D are elements of a transmission matrix of the optical system, and when the light beams are transmitted through the first lens and focused,
B＝f；
d is 1. U ═ U, v is a vector coordinate, U1,v1,u2,v2Is the coordinates of the beam in the plane of the receiving screen of the spatial light modulator, f is the focal length of the first lens, and z is the distance of transmission, here equal to the focal length of the lens.
Wherein, pure phase spatial light modulator is reflective pure phase spatial light modulator: HOLOEYE GAEA, size 3840 × 2160 pixels, pixel size 3.74 μm. Is placed at the focal plane of the second lens 4. The pure phase spatial light modulator 3 is used for setting a measurement range, namely, a central region and an edge region are separated by loading a grating on the spatial light modulator, and the central region of a part of coherent vortex light beams is selected to recover the cross spectral density, so that stray light around the part of coherent vortex light beams is effectively eliminated, and the setting standard of the measurement range is as follows: only the interference information is removed, and the main information of the vortex light beam is in the measuring range and can not be intercepted and damaged.
In this embodiment, the measurement range set here is a circle, the center of the circle is located at the midpoint of the spatial light modulator 3, the radius is 0.5mm, and the partially coherent vortex beam at the focal field is irradiated in alignment with the measurement range. Simultaneously, disturbance is introduced, the disturbance is positioned at the center of a focal field light spot, namely the ordinate and the abscissa of the disturbance are both 0, the shape of the disturbance is circular, the radius is 0.05mm, and the three phase assignment of the disturbance is respectively as follows: c0＝exp[0]And C±＝exp[±2iπ/3]。
The computer 6 obtains the cross spectral density function of the interfered partially coherent vortex light beams through inverse Fourier transform calculation according to the three different phase assignments and the light intensity of the Fourier plane under the three different phase assignments. Specifically, the method comprises the following steps:
first, without introducing perturbations, the intensity of a partially coherent vortex beam in the fourier plane is expressed as:
I0(ρ)＝∫∫W(U1,U2)exp[-i2πρ(U1-U2)]dU1dU2
wherein W (U)1,U2) The cross spectral density is obtained by partially coherent vortex light beams entering a double slit to generate interference, passing through a lens and focusing on a spatial light modulator, wherein when the cross spectral density is equal to U0And (3) introducing disturbance, the light intensity expression becomes:
I(ρ)＝I0(ρ)+CC*W(U0,U0)++C∫W(U1,U0)exp[-i2πρ(U1-U0)]dU1+C*∫W(U0,U2)exp[-i2πρ(U0-U2)]dU2
where C is a complex number determined to characterize the disturbance, the inverse fourier transform of the intensity is obtained:
FT-1[I(ρ)](U)＝FT-1[I0(ρ)](U)+CC*W(U0,U0)δ(U)+CW(U0+U,U0)+C*W(U0,U0-U)
U0when the value is 0, namely the disturbance is taken at the central position of the light spot, three equations are obtained by changing the phase assignment of the disturbance three times, and the cross spectral density function W (U) is obtained by solving1,0)。
FIG. 4 shows the cross-spectral density function W (U) obtained in the simulation of the present invention10) phase profile. (the parameters for the simulation were beam waist of the beam of 1mm and coherence of 0.3 mm).
In the simulation, partial coherent vortex beams with topological charge of +1, +2, -2 and +3 are respectively tested, a phase diagram is obtained, black in the phase diagram represents-pi, white represents pi, the number of the topological charge is half of that of a coherent singularity and is respectively 2, 4 and 6 according to a phase distribution diagram, and the rotating direction of the phase change from-pi to + pi around the coherent singularity can be used for determining the positive and negative of the topological charge: positive counterclockwise and negative clockwise.
FIG. 5 shows the cross-spectral density function W (U) obtained in the experiment according to the present invention1,U2) The phase profile of (a). (the parameters in the experiment are that the beam waist of the light beam is 1mm, and the coherence is 0.3 mm).
Partial coherent vortex beams with topological charge of +1, +2 and-2 are respectively tested in experiments, a phase diagram is obtained, the number of the topological charge is half of that of a coherent singularity and is respectively 2, 4 and 4 according to a phase distribution diagram, and meanwhile, the rotating direction of phase change from-pi to + pi around the coherent singularity can be used for determining the positive and negative of the topological charge: positive counterclockwise and negative clockwise.
According to the method and the system for measuring the size, the positive and the negative of the topological charge of the partially coherent vortex light beam, the double slits are introduced, the partially coherent vortex light beam interferes after passing through the double slits, the ring dislocation of the phase structure is damaged, and each ring dislocation is divided into two singular points. Meanwhile, the harsh requirements on the measurement conditions are reduced, repeated debugging is not needed in the measurement, the measurement process is greatly simplified, and the success rate of the experiment is improved.
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 (9)
1. The method for measuring the size and the positive and negative of the topological charge number of the partially coherent vortex light beam is characterized by comprising the following steps of:
the partially coherent vortex light beams are incident to the double slits and interfere with each other;
focusing the interfered partial coherent vortex light beams on a receiving screen of the pure phase spatial light modulator;
introducing three disturbances of different phase assignments to the center of the upper part coherent vortex light beam of the receiving screen through the pure phase spatial light modulator;
carrying out Fourier transform on the disturbed partially coherent vortex light beam, and recording the light intensity of a Fourier plane under three different phase assignments;
calculating to obtain a cross spectral density function of the interfered focused partially coherent vortex light beams based on inverse Fourier transform according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments;
and drawing a phase distribution diagram of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution diagram is the topological charge number, and the positive and negative of the topological charge are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
2. The method for measuring the topological charge magnitude and the positive and negative of the partially coherent vortex light beam as claimed in claim 1, wherein the partially coherent vortex light beam is incident to the double slit, and the cross spectral density expression is as follows:
wherein the double slit is located next to the source plane of the partially coherent vortex beam, W1(r1,r2) Representing the cross-spectral density expression, H (r), of a partially coherent vortex beam passing before the double slit, i.e. the source plane1)H*(r2) Representing a double slit function, x1,x2,y1,y2For the coordinates of the beam in the source plane, b is the slit width, 2a + b is the distance between the center points of the double slits, p is the radial index mode of the partially coherent vortex beam and takes 0, l is the Topological Charge (TC) of the partially coherent vortex beam, σgFor the transverse coherence width of the beam, ". is the complex conjugate,. omega."0Is the girdling of the waist, HxIs hermitian polynomial, q is the charge value, AmAnd BmAre coefficients of a function that models the double slit.
3. The method for measuring the topological charge magnitude and the positive and negative of the partially coherent vortex light beam according to claim 1, wherein the step of focusing the interfered partially coherent vortex light beam onto a receiving screen of the phase-only spatial light modulator specifically comprises the steps of:
and focusing the interfered partially coherent vortex light beams onto a receiving screen of the reflective phase-only spatial light modulator through a first lens.
4. The method for measuring the topological charge magnitude and the positive and negative of the partially coherent vortex light beam as claimed in claim 3, wherein the cross spectral density expression of the partially coherent vortex light beam after the interfered partially coherent vortex light beam is focused by the first lens is as follows:
wherein A, B, C, D are elements of a transmission matrix of the optical system, and when the light beams are transmitted through the first lens and focused,
B＝f；
d is 1. U ═ U, v is a vector coordinate, U1,v1,u2,v2Is the coordinates of the beam in the plane of the receiving screen of the spatial light modulator, f is the focal length of the first lens, and z is the distance of transmission, here equal to the focal length of the lens.
5. The method for measuring the topological charge number and the positive and negative of the partially coherent vortex light beam according to claim 1, wherein the cross spectral density function of the partially coherent vortex light beam focused after interference is obtained through inverse fourier transform according to the light intensities of the fourier planes under three different phase assignments and three different phase assignments, specifically comprises:
first, without introducing perturbations, the intensity of a partially coherent vortex beam in the fourier plane is expressed as:
I0(ρ)＝∫∫W(U1,U2)exp[-i2πρ(U1-U2)]dU1dU2
wherein W (U)1,U2) The cross spectral density is obtained by partially coherent vortex light beams entering a double slit to generate interference, passing through a lens and focusing on a spatial light modulator, wherein when the cross spectral density is equal to U0And (3) introducing disturbance, the light intensity expression becomes:
I(ρ)＝I0(ρ)+CC*W(U0,U0)++C∫W(U1,U0)exp[-i2πρ(U1-U0)]dU1+C*∫W(U0,U2)exp[-i2πρ(U0-U2)]dU2
where C is a complex number determined to characterize the disturbance, the inverse fourier transform of the intensity is obtained:
FT-1[I(ρ)](U)＝FT-1[I0(ρ)](U)+CC*W(U0,U0)δ(U)+CW(U0+U,U0)+C*W(U0,U0-U)
U0when the value is 0, namely the disturbance is taken at the central position of the light spot, three equations are obtained by changing the phase assignment of the disturbance three times, and the cross spectral density function W (U) is obtained by solving1,0)。
6. The method of measuring the magnitude and sign of the topological charge of a partially coherent vortex beam according to claim 1, wherein said perturbation is circular.
7. The method of measuring the magnitude and sign of the topological charge of the partially coherent vortex beam according to claim 1, wherein the perturbed partially coherent vortex beam is fourier transformed using a second lens.
8. The method of measuring the magnitude and sign of the topological charge of the partially coherent vortex beam of claim 1, wherein the intensity of the partially coherent vortex beam and the fourier plane are recorded using a charge coupled device.
9. The system for measuring the size and the positive and negative of the topological charge number of the partially coherent vortex light beam is characterized by comprising the following components:
a double slit for receiving the partially coherent vortex beam and interfering;
the first lens is used for focusing the interfered partially coherent vortex light beams on a receiving screen of the pure-phase spatial light modulator;
the pure phase spatial light modulator is used for introducing three disturbances of different phase assignments to the center of the upper part coherent vortex light beam of the receiving screen;
the second lens is used for carrying out Fourier transform on the disturbed partially coherent vortex light beam;
the charge coupling element is used for recording the light intensity of the Fourier plane under three different phase assignments;
and the computer is used for obtaining a cross spectrum density function of the interfered partial coherent vortex light beams through inverse Fourier transform calculation according to the light intensity of the Fourier plane under the three different phase assignments and the three different phase assignments, drawing a phase distribution diagram of the cross spectrum density function, wherein half of the number of coherent singularities in the phase distribution diagram is the number of topological charges, and the positive and negative of the topological charges are determined according to the rotation direction of phase change around the coherent singularities, wherein the counterclockwise direction is positive, and the clockwise direction is negative.
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