Measurement Device and Method for Single-Mode Perfect Vortex Light with Large Topological Charge Value

Abstract

A measuring device and method for perfect vortex light with a large topological charge value. The device includes a laser, and successively along the laser output direction of the laser are a beam expander, a linear polarizer, a first reflector, a second reflector, a reflective pure-phase liquid crystal spatial light modulator, a plano-convex cylindrical lens, a Fourier lens, a diaphragm, and a CCD camera. The control end of the reflective pure-phase liquid crystal spatial light modulator is connected to a first PC control end, the control end of the CCD camera is connected to a second PC control end, the CCD camera is placed at the focal plane of the Fourier lens, and the plano-convex cylindrical lens is located at any position between the reflective pure-phase liquid crystal spatial light modulator and the Fourier lens. The present invention can measure the topological charge value range of perfect vortex light to be relatively large, and can measure perfect vortex light with different base angle parameters. The optical path of the present invention is simple and has strong flexibility. The position and angle of the plano-convex cylindrical lens are both adjustable, and the operation is extremely convenient, and it can be applied to the detection of perfect vortex light with a large topological charge number.

Description

Technical Field

[0001] The present invention relates to the field of vortex optics technology, and particularly to a measuring device and method for perfect vortex light with a large topological charge value. Background Technique

[0002] A vortex beam is a beam with vortex characteristics. The phase or wavefront of this kind of light is spiral, and the complex amplitude contains a spiral phase term, which can be expressed as where l is the topological charge, is the angular coordinate. Each photon in the vortex beam carries orbital angular momentum (OAM), and has orthogonality, that is, any two vortex lights of different orders are orthogonal to each other, and vortex beams of different orders can be separated from each other. Due to these properties, vortex beams have great potential value in the fields of optical communication, detection, quantum information processing, etc.

[0003] In order to pursue better performance, vortex light with a large topological charge is often required. However, the ring radius of traditional vortex light increases with the increase of the topological charge. In 2013, Ostrovsky et al. first proposed the concept of perfect vortex light, and their ring diameter is independent of the topological charge value [Opt Lett 38, 534 - 536 (2013)].

[0004] The existing measurement methods for the topological charge value of vortex light can be generally divided into two categories: the interference method and the diffraction method. However, due to the characteristics of perfect vortex light, such as existing only within a limited distance near the focal plane, the beam size being independent of the angular quantum number, and the Bessel mode generating perfect vortex light having non-diffraction properties, the methods for measuring vortex light are not fully applicable to perfect vortex light. For perfect vortex light, the most commonly used method is the coaxial interference method with Gaussian light [Opt Let 40, 597 - 600 (2015)]. The topological charge value is judged by the spiral petal-shaped interference pattern, and the sign of the topological charge value can be judged by the rotation direction of the pattern. However, this method uses a double-path interference, requires adjusting the vortex light and Gaussian light to coaxial interference, which is difficult to implement, has a complex optical path, and when the topological charge value is large, the spiral patterns are too dense to distinguish. Therefore, this method is also difficult to be used in the measurement of perfect vortex light with large topological charge values. In addition, among the diffraction methods for measuring the topological charge value of vortex light, there are also gratings applicable to measuring perfect vortex light: compound fork gratings, standard Dammann gratings [Opt Let 35, 3495 - 3497 (2010)] and integrated Dammann gratings [Appl Opt 55, 1514 - 7 (2016)]. These gratings need to be simulated using a spatial light modulator, which is costly, the detectable orders are fixed and limited by the resolution of the spatial light modulator. Even the integrated Dammann grating with the largest range can only measure orders in (-24, +24), and it is difficult to measure larger topological charge values. Thus, the existing methods for measuring the topological charge value of perfect vortex light face problems such as complex optical paths and a small detection range of topological charge values. Summary of the Invention

[0005] Aiming at the problem of difficult measurement of perfect vortex light with large topological charge values at present, the present invention proposes a measurement device and method for perfect vortex light with large topological charge values. The principle of this method is simple and the optical path is concise, and it can realize the detection of the topological charge value of a perfect vortex beam with any bottom angle parameter γ and large topological charge value l.

[0006] The technical solution of the present invention is as follows:

[0007] A measurement device for perfect vortex light with large topological charge values, characterized in that the device includes a laser, and in the laser output direction of the laser are successively a beam expander, a linear polarizer, a first reflector, a second reflector, a reflective pure-phase liquid crystal spatial light modulator, a plano-convex cylindrical lens, a Fourier lens, a diaphragm and a CCD camera. The control end of the reflective pure-phase liquid crystal spatial light modulator is connected to a first PC control end, the control end of the CCD camera is connected to a second PC control end, the second PC control end is used to display the light intensity distribution received by the CCD camera, the CCD camera is placed at the focal plane of the Fourier lens, and the plano-convex cylindrical lens is located at any position between the reflective pure-phase liquid crystal spatial light modulator and the Fourier lens.

[0008] A method for measuring a perfect vortex beam with a large topological charge value by using the above measurement device for a perfect vortex beam with a large topological charge value, the method comprising the following steps:

[0009] 1) Start the laser. The laser beam emitted by the laser is collimated and expanded by a beam expander and then incident on a polarizer to generate linearly polarized light. After the Bessel-Gaussian light field output by the reflective pure-phase liquid crystal spatial light modulator passes through the plano-convex cylindrical lens, the complex amplitude of the Bessel-Gaussian light field is:

[0010]

[0011] where A l is a constant term, k r is the radial wave number, k z is the wave number in the propagation direction, and the ratio γ = k r / k z is the base angle parameter, J l is the Bessel function of the first kind of order l, is the cylindrical coordinate of the light field, l is the topological charge value of the perfect vortex beam, ω g is the beam waist radius of the Gaussian light;

[0012] The symmetry axis of the plano-convex cylindrical lens coincides with the y-axis, and its transmittance function is:

[0013]

[0014] where k = 2π / λ is the wave number of the incident light, λ is the wavelength of the incident light, and f is the focal length of the plano-convex cylindrical lens;

[0015] After the Bessel-Gaussian light passes through the plano-convex cylindrical lens, it is focused on its focal region by the Fourier lens; the light spot in the focal region is imaged on the detection surface of the CCD camera,

[0016] 2) The light spot observed on the detection surface of the CCD camera is distributed in an inclined stripe shape, and the number of dark stripes between the two brightest points is equal to the magnitude of the topological charge l; observe the inclination direction of the light spot on the CCD camera to obtain the sign of the topological charge value l of the perfect vortex beam to be measured: the sign of the topological charge value is judged according to the inclination direction of the stripes. If the line connecting the two brightest points is in the second and fourth quadrants, it is positive, and if it is in the first and third quadrants, it is negative.

[0017] In the ratio k r / k zWhen it is relatively large, that is, when the bottom angle parameter γ of the perfect vortex light is relatively large, by rotating the plano-convex cylindrical lens around the non-functional axis, the interval between the light spots on the CCD camera can be increased, thereby improving the clarity of the measured light spot results and making the results more accurate; when the aperture of the plano-convex cylindrical lens is large enough, the plano-convex cylindrical lens can be rotated around the non-functional axis to measure the topological charge value of the perfect vortex light with any bottom angle parameter.

[0018] Advantages of the present invention:

[0019] The device and method for measuring the topological charge value of the perfect vortex light using a plano-convex cylindrical lens in the present invention, compared with the existing technologies for measuring the perfect vortex light, have the advantages that the optical path of the present invention has a simple structure, low alignment requirements, convenient implementation, low requirements for the position and angle of the plano-convex cylindrical lens, a large range for measuring the topological charge value l, and is applicable to the perfect vortex light with any bottom angle parameter γ. The size and sign of the topological charge value of the to-be-measured perfect vortex light can be directly determined by the number and direction of the fringes received by the CCD. Description of the drawings

[0020] Figure 1 is the schematic diagram of the optical path of the detection device for the perfect vortex light with a large topological charge value of the present invention.

[0021] Among them, 1 - laser; 2 - beam expander; 3 - linear polarizer; 4 - first mirror; 5 - second mirror; 6 - reflective pure-phase liquid crystal spatial light modulator (SLM); 7 - first PC control terminal; 8 - plano-convex cylindrical lens; 9 - Fourier lens; 10 - aperture; 11 - CCD camera; 12 - second PC control terminal.

[0022] Figure 2 : (a) In this embodiment, without a plano-convex cylindrical lens, the perfect vortex light with different topological charge values; (b) In this embodiment, with a plano-convex cylindrical lens, the measurement results of the perfect vortex light with different topological charge values; (c) In this embodiment, the measurement results of the topological charge value of the perfect vortex light obtained by simulation.

[0023] Figure 3 : (a) In this embodiment, when the topological charge value of the to-be-measured perfect vortex light is relatively large, being 40, the measurement result; (b) In this embodiment, the measurement result of the perfect vortex light with a topological charge value of 40 obtained by simulation.

[0024] Figure 4 : (a) In this embodiment, when the bottom angle parameter of the perfect vortex light is increased to 0.6 and the plano-convex cylindrical lens 8 is perpendicular to the optical axis, the measurement result; (b) In this embodiment, with a bottom angle parameter of 0.6 and after rotating the plano-convex cylindrical lens 30° around its non-functional axis direction, the measurement result.

[0025] Figure 5:(a) In this example, the plano-convex cylindrical lens is placed 0.15 m away from the SLM, and the measurement results when the Fourier lens 9 is placed 0.4 m away from the SLM; (b) Keeping the position of the Fourier lens 9 unchanged, the measurement results when the plano-convex cylindrical lens is moved to a position 0.37 m away from the SLM and closer to the Fourier lens. Detailed implementation manners

[0026] The present invention will be further described in combination with embodiments and the accompanying drawings. The following examples are only for explaining the present invention and do not limit its content. If the specific experimental conditions are not specified in the examples, they are usually in accordance with conventional conditions or the conditions recommended by the sales company.

[0027] Please refer to Figure 1 , Figure 1 is a schematic optical path diagram of the detection device for large topological charge value perfect vortex light of the present invention. As can be seen from the figure, the measurement device for large topological charge value perfect vortex light of the present invention is characterized in that the device includes a laser 1, and in the laser output direction of the laser 1 are successively a beam expander 2, a linear polarizer 3, a first mirror 4, a second mirror 5, a reflective pure-phase liquid crystal spatial light modulator 6, a plano-convex cylindrical lens 8, a Fourier lens 9, a diaphragm 10 and a CCD camera 11. The control end of the reflective pure-phase liquid crystal spatial light modulator 6 is connected to the first PC control end 7, the control end of the CCD camera 11 is connected to the second PC control end 12, the light intensity distribution received by the CCD camera 11 is displayed on the second PC control end 12, the CCD camera 11 is placed at the rear focal plane of the Fourier lens 9, and the plano-convex cylindrical lens 8 is located at any position between the reflective pure-phase liquid crystal spatial light modulator 6 and the Fourier lens 9.

[0028] A method for measuring large topological charge value perfect vortex light by using the above measurement device for large topological charge value perfect vortex light, the method comprising the following steps:

[0029] 1) Start the laser 1, the laser beam emitted by the laser 1 is collimated and expanded by the beam expander 2, and is incident on the polarizer 3 to generate linearly polarized light; after the Bessel-Gaussian light field output by the reflective pure-phase liquid crystal spatial light modulator 6 passes through the plano-convex cylindrical lens 8, the complex amplitude of the Bessel-Gaussian light field is:

[0030]

[0031] where A l is a constant term, k r is the radial wave number, k z is the wave number in the propagation direction, and the ratio γ = k r / k z is the base angle parameter, J lis the first kind of Bessel function of order l, is the cylindrical coordinate of the optical field, l is the topological charge value of the perfect vortex light, ω g is the waist radius of the Gaussian light; the axis of symmetry of the plano-convex cylindrical mirror 8 coincides with the y-axis, and its transmittance function is:

[0032]

[0033] where k = 2π / λ is the wave number of the incident light, λ is the wavelength of the incident light, and f is the focal length of the plano-convex cylindrical mirror 8; after the Bessel-Gaussian light passes through the plano-convex cylindrical mirror 8, it is focused on its focal region by the Fourier lens 9; the light spot in the focal region is imaged on the detection surface of the CCD camera 11;

[0034] 2) The light spot observed from the detection surface of the CCD camera 11 is distributed in an inclined stripe shape, and the number of dark stripes between the two brightest points is equal to the magnitude of the topological charge l; observe the inclination direction of the light spot on the CCD camera 11 to obtain the sign of the topological charge value l of the perfect vortex beam to be measured: the sign of the topological charge value is judged according to the inclination direction of the stripes. If the connection line between the two brightest points is in the second and fourth quadrants, it is positive, and if it is in the first and third quadrants, it is negative.

[0035] When the ratio k r / k z of the radial wave number to the propagation direction wave number of the perfect vortex light to be measured is large, that is, when the bottom angle parameter γ of the perfect vortex light is large, the plano-convex cylindrical mirror 8 can be rotated around the non-functional axis to increase the interval of the light spot on the CCD camera 11, thereby improving the clarity of the measured light spot result and making the result more accurate; when the aperture of the plano-convex cylindrical mirror 8 is large enough, the plano-convex cylindrical mirror 8 can be rotated around the non-functional axis to measure the topological charge value of the perfect vortex light with any bottom angle parameter.

[0036] Embodiment

[0037] The linearly polarized light is reflected by the first mirror 4 and the second mirror 5 and then irradiates on the reflective pure-phase liquid crystal spatial light modulator (SLM) 6. The first PC control terminal 7 is used to control the reflective pure-phase liquid crystal spatial light modulator 6 to perform phase modulation on the incident light, and the modulation function is:

[0038]

[0039] where l is the topological charge value of the perfect vortex light, atan2(y, x) is the four-quadrant arctangent of the coordinates, k = 2π / λ is the wave number of the incident light, λ is the wavelength of the incident light 1064 nm, γ is the bottom angle parameter of the perfect vortex light, which affects the ring diameter of the perfect vortex light, n is the refractive index parameter, g x and gy are the number of periods of the blazed grating in the x and y directions within the screen range, respectively, which are limited by the resolution of the SLM. After the linearly polarized light is phase modulated by the SLM, multiple diffraction orders are formed, and the +1 diffraction order is a Bessel-Gaussian light field that can produce perfect vortex light;

[0040] After the Bessel-Gaussian light field propagates for a certain distance, it is irradiated onto a plano-convex cylindrical mirror 8 with a focal length of 0.8 m and a non-functional direction perpendicular to the table. The transmittance function of the plano-convex cylindrical mirror 8 is:

[0041]

[0042] After passing through the plano-convex cylindrical mirror 8, the Bessel-Gaussian light field propagates for a distance again, is focused by a Fourier lens 9 with a focal length of 0.1 m, and uses an aperture 10 to filter out diffraction orders other than the +1 order, and finally forms an image on the focal plane of the Fourier lens 9;

[0043] The CCD camera 11 is placed on the focal plane of the Fourier lens 9 to detect the final diffraction light intensity distribution.

[0044] Experimental verification of the method for detecting the topological charge of perfect vortex light of the present invention: a plano-convex cylindrical mirror 8 with a focal length of 0.8 m is placed at a distance of 0.15 m from the SLM, a Fourier lens 9 with a focal length of 0.1 m is placed at a distance of 0.4 m from the SLM, and a CCD camera 11 is placed on the back focal plane of the Fourier lens 9.

[0045] First, the base angle parameter of the perfect vortex light is selected as 0.4, and the topological charge value l is selected as 1, 5, 10, and 15 respectively. If the plano-convex cylindrical mirror 8 is not added, then Figure 2 As shown in (a), the back focal plane at this time is a series of perfect vortex light ring diameters that are not affected by the topological charge value. The plane-convex cylindrical mirror 8 is placed at a specified position, and the plane of the plane-convex cylindrical mirror 8 is perpendicular to the optical axis, and the non-functional direction of the plane-convex cylindrical mirror 8 is perpendicular to the desktop, then a series of diffraction fringes will be obtained on the receiving surface, such as Figure 2 (b) As shown. By observing its intensity distribution, the absolute value and sign of the topological charge l of the incident light beam can be quickly distinguished: the absolute value l of the topological charge is equal to the number of dark fringes between the two brightest points in the diffraction fringes. The sign of the topological charge is determined by the inclination direction of the fringes. If the line connecting the two brightest points is in the second and fourth quadrants, it is positive, and if it is in the first and third quadrants, it is negative. The corresponding simulation results are shown in Figure 2 (c) as shown.

[0046] In order to further illustrate that this method is still applicable under large topological charge values, the topological charge value is set to 40. The experimental and simulation results are shown in Figure 3 As shown, the stripes are still clearly discernible, and the number of dark stripes is equal to the absolute value of the topological charge l.

[0047] To further illustrate that the method is applicable to the measurement of perfect vortex light with different bottom angle parameters, the bottom angle parameter is increased from 0.4 to 0.6. Figure 3 (a) shows the result when the plane of the plano-convex cylindrical lens 8 is perpendicular to the optical path. The bottom angle parameter affects the distance between the diffraction fringes. By rotating the plano-convex cylindrical lens 8 around the non-functional axis, the width of the overall fringes can be increased, thereby increasing the distance between the diffraction fringes, as Figure 3 (b) shows the result after a 15° rotation, and the fringes are clear again. Therefore, in this method, the influence of the increase in the bottom angle parameter γ on the fringe clarity can be compensated by rotating the plano-convex cylindrical lens 8.

[0048] For comparison, the plano-convex cylindrical lens 8 is moved from a position 0.15 m away from the SLM to a position 0.35 m away from the SLM, while keeping the positions of other components unchanged. Figure 4 (a) and (b) respectively represent the light intensity distribution diagrams of the receiving surface before and after the movement. Figure 5 : (a) In this example, the measurement result when the plano-convex cylindrical lens 8 is placed 0.15 m away from the SLM and the Fourier lens 9 is placed 0.4 m away from the SLM; (b) The measurement result when the position of the Fourier lens 9 is kept unchanged and the plano-convex cylindrical lens 8 is moved to a position 0.37 m away from the SLM, closer to the Fourier lens.

[0049] As can be seen from the figure, during this process, the diffraction light intensity distribution does not change significantly, and moving the plano-convex cylindrical lens 8 between the SLM 6 and the Fourier lens 9 will not affect the detection result.

[0050] In summary, the above are only preferred examples of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, etc. made within the principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A measuring device for perfect vortex light with a large topological charge value, characterized in that, the device includes a laser (1), and along the laser output direction of the laser (1) are successively a beam expander (2), a linear polarizer (3), a first reflector (4), a second reflector (5), a reflective pure-phase liquid crystal spatial light modulator (6), a plano-convex cylindrical lens (8), a Fourier lens (9), a diaphragm (10) and a CCD camera (11). The control end of the reflective pure-phase liquid crystal spatial light modulator (6) is connected to a first PC control end (7), and the first PC control end (7) is used to control the reflective pure-phase liquid crystal spatial light modulator (6) to perform phase modulation on the incident light to generate a Bessel-Gaussian light field. The control end of the CCD camera (11) is connected to a second PC control end (12), and the second PC control end (12) is used to display the light intensity distribution received by the CCD camera (11). The CCD camera (11) is placed at the focal plane of the Fourier lens (9). The plano-convex cylindrical lens (8) is located at any position between the reflective pure-phase liquid crystal spatial light modulator (6) and the Fourier lens (9). The diaphragm (10) is used to filter out light fields of other orders except the +1 order diffraction order. The symmetry axis of the plano-convex cylindrical lens (8) coincides with the y-axis, and the transmittance function of the plano-convex cylindrical lens (8) is: where k = 2π / λ is the wave number of the incident light, λ is the wavelength of the incident light, and f is the focal length of the plano-convex cylindrical lens (8); after the Bessel-Gaussian light field passes through the plano-convex cylindrical lens (8), it is focused by the Fourier lens (9) to its focal region; the light spot in the focal region is imaged on the detection surface of the CCD camera (11).

2. A method for measuring perfect vortex light with a large topological charge value by using the measuring device for perfect vortex light with a large topological charge value according to claim 1, characterized in that the method includes the following steps: 1) Start the laser (1). The laser beam emitted by the laser (1) is collimated and expanded by the beam expander (2) and then incident on the polarizer (3) to generate linearly polarized light; after the Bessel-Gaussian light field output by the linearly polarized light passing through the reflective pure-phase liquid crystal spatial light modulator (6) passes through the plano-convex cylindrical lens (8), the complex amplitude of the Bessel-Gaussian light field is: Among them, A l is a constant term, k r is the radial wave number, k z is the wave number in the propagation direction, and the ratio γ = k r / k z is the base angle parameter, J l is the Bessel function of the first kind of order l, is the cylindrical coordinate of the optical field, l is the topological charge value of the perfect vortex light, ω g is the beam waist radius of the Gaussian light; the symmetry axis of the plano-convex cylindrical mirror (8) coincides with the y-axis, and the transmittance function of the plano-convex cylindrical mirror (8) is: where k = 2π / λ is the wave number of the incident light, λ is the wavelength of the incident light, and f is the focal length of the plano-convex cylindrical lens (8); after the Bessel-Gaussian light passes through the plano-convex cylindrical lens (8), it is focused by the Fourier lens (9) to its focal region; the light spot in the focal region is imaged on the detection surface of the CCD camera (11); 2) The light spots observed on the detection surface of the CCD camera (11) are distributed in an inclined stripe shape, and the number of dark stripes between the two brightest spots is equal to the magnitude of the topological charge l; the sign of the topological charge value l of the perfect vortex beam to be measured is obtained by observing the inclination direction of the light spot on the CCD camera (11): the sign of the topological charge value is judged according to the inclination direction of the stripes. If the connection line between the two brightest spots is in the second and fourth quadrants, it is positive; if it is in the first and third quadrants, it is negative.

3. The method for measuring the topological charge value of a perfect vortex beam according to claim 2, characterized in that When the ratio k of the radial wave number to the propagation direction wave number of the perfect vortex light to be measured r / k z is relatively large, that is, when the bottom angle parameter γ of the perfect vortex light is relatively large, by rotating the plano-convex cylindrical lens (8) around the non-functional axis, the interval of the light spots on the CCD camera (11) can be increased, thereby improving the clarity of the measured light spot results and making the results more accurate; when the aperture of the plano-convex cylindrical lens (8) is large enough, the plano-convex cylindrical lens (8) can be rotated around the non-functional axis, so as to measure the topological charge value of the perfect vortex light with any bottom angle parameter.

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