Dynamic vector vortex beam generation method based on liquid crystal and metasurface regulation and control

Abstract

The invention discloses a dynamic vector vortex beam generation method based on liquid crystal and metasurface regulation and control, and belongs to the field of micro-nano optics. According to the dynamic vector vortex beam generation method based on liquid crystal and metasurface regulation and control, vortex light with spiral phase distribution is generated based on a metasurface, the metasurface and nematic phase liquid crystal are cascaded, an external electric field of the nematic phase liquid crystal is dynamically changed, then the deflection angle of a nematic phase liquid crystal molecule director is changed, and the dynamic vector vortex beam is generated. And obtaining the nematic-phase liquid crystal with corresponding turning direction. The light beam is jointly regulated and controlled through the metasurface and the nematic phase liquid crystal in the corresponding turning direction, and the dynamic vector vortex light beam is generated after regulation and control. By introducing the liquid crystal, flexible dynamic regulation and control of orbital angular momentum can be realized through an external electric field, the limitation of fixation of a traditional metasurface device is overcome, dynamic vector vortex light beams with spatial non-uniform polarization distribution such as radial polarization and angular polarization are generated, more complex light field control can be supported, and the method is suitable for large-scale popularization and application. And multi-scene requirements are met.

Description

Technical Field

[0001] The present invention relates to a method for generating dynamic vector vortex beams by modulating liquid crystal and metasurface, and belongs to the field of micro-nano optics. Background Art

[0002] A metasurface is an array of structural units with sub-wavelength dimensions. By designing the shape and size of the metasurface structural units, the polarization, phase, amplitude, and frequency of light can be flexibly modulated, thereby realizing some functions that cannot be achieved in traditional optical fields. However, metasurfaces are usually fixed structures and are difficult to dynamically adjust once fabricated. Liquid crystal is an organic compound that is in a transitional state between solid and liquid. It has both the orderliness of solid crystals and the fluidity of liquids. Liquid crystal has excellent dynamic modulation capabilities and can be dynamically modulated by applying an external electric field, temperature, or light field. Nematic liquid crystal molecules, as one of the phase structures, are anisotropic and sensitive to polarization. Usually, the long axis direction of a large number of nematic liquid crystal molecules is used as the director direction. The director of nematic liquid crystal can change the deflection angle under the drive of an electric field. The liquid crystal director is an important factor affecting the polarization modulation characteristics of liquid crystal. Utilizing its special polarization modulation ability and electro-optical properties, various optoelectronic devices based on liquid crystal materials have very wide applications in the field of dynamically modulating light fields.

[0003] A vortex beam is a beam with a special spatial structure. Its uniqueness lies in the distribution of the phase, amplitude, and orbital angular momentum of the light field. However, the polarization characteristics of vortex beams are relatively single and have fewer degrees of freedom. A vector vortex beam is a special type of vortex beam. In addition to having the helical phase and orbital angular momentum of the vortex beam, the vector vortex beam also has an anisotropic wavefront and polarization distribution. By designing the structure of the metasurface nanoantenna, the helical phase distribution of the incident light can be controlled to generate a vortex beam. Cascade the metasurface with the liquid crystal, and by controlling the external electric field of the liquid crystal, the polarization state of the vortex beam can be dynamically adjusted to generate different radially or azimuthally polarized vector vortex beams. From the realization of a single vortex beam to a vector vortex beam, due to its unique polarization distribution, it has shown great application potential in frontier fields such as optical trapping and manipulation, optical communication, super-resolution microscopy, and optical quantum information. Summary of the Invention

[0004] The present invention discloses a method for generating dynamic vector vortex beams by modulating liquid crystal and metasurface.

[0005] Generate vortex light with a helical phase distribution based on a metasurface. Cascade the metasurface and nematic liquid crystal, dynamically change the applied electric field of the nematic liquid crystal, and then change the deflection angle of the director of the nematic liquid crystal molecules to obtain a nematic liquid crystal corresponding to the deflection angle. The light beam is jointly regulated by the metasurface and the nematic liquid crystal with the corresponding steering, and a dynamic vector vortex beam is generated after regulation.

[0006] The object of the present invention is achieved by the following technical solutions.

[0007] Step 1, design the metasurface, and generate vortex light with a helical phase distribution based on the metasurface;

[0008] Step 2, cascade the metasurface and the nematic liquid crystal, that is, attach a thin layer of nematic liquid crystal to the metasurface, and then dynamically change the applied electric field of the nematic liquid crystal, and then change the deflection angle of the director of the nematic liquid crystal molecules to obtain a nematic liquid crystal with the corresponding steering;

[0009] Step 3, the light beam is jointly regulated by the metasurface and the nematic liquid crystal with the corresponding steering in Step 2, and a dynamic vector vortex beam is generated after regulation.

[0010] Further preferably, the implementation method of Step 1 is: controlling the helical phase distribution of the incident light by designing the structure of the nanoantennas on the metasurface to generate a vortex beam;

[0011] Obtain the electric field distribution of the vortex beam, expressed as:

[0012] E = E0e ilθ (1)

[0013] where E0 represents the amplitude, l (±1, ±2... ±n) represents the topological charge number of the vortex beam, θ represents the polar angle, and the phase of the vortex beam is e ilθ .

[0014] Design the metasurface, obtain the complex amplitude modulation characteristics of the nanoantenna columns on the metasurface, and obtain the corresponding amplitude and phase distributions. The metasurface is a reflective metasurface; specifically, it includes the following;

[0015] (1) By matching the phase distribution of the metasurface and the phase of the vortex beam, determine the geometric dimensions of the nanoantenna column array on the metasurface. The metasurface is composed of multiple nanoantenna column arrays with different geometric dimensions (length L, width W) and anisotropy. The geometric dimensions are determined based on the transmission phase principle of the metasurface. The amplitudes of the selected nanoantenna column arrays are approximately equal, and the phase distribution covers 0 - 2π;

[0016] (2) Arrange the nano - antenna pillar array of the metasurface, generate a processing file, and process it to obtain a solid metasurface structure.

[0017] Furthermore, obtaining the complex - amplitude modulation characteristics of the metasurface nano - antenna pillars and getting the corresponding amplitude and phase distributions also includes:

[0018] Preset the height H of the nano - antenna pillars and the period P of the structural unit. Scan the amplitude and phase distributions of the nano - antenna pillar array at different lengths L and widths W by the finite - difference time - domain method, so as to be able to regulate the phase within the range of 0 - 2π.

[0019] Preferably, in step two:

[0020] The amplitude and phase distributions included in the nematic liquid - crystal molecular director angle. Apply different electric fields to the nematic liquid crystal to obtain corresponding director angles; cascade the metasurface and the nematic liquid crystal to get the phase distribution after superposition of the cascaded metasurface and the nematic liquid crystal. Dynamically change the externally applied electric field of the nematic liquid crystal to obtain a nematic liquid crystal with a corresponding rotation.

[0021] The ways of dynamically changing the externally applied electric field of the nematic liquid crystal include but are not limited to changing the voltage of the externally applied electric field or controlling the externally applied electric field through a programmable logic gate array.

[0022] Optionally, the implementation method of step three is:

[0023] Step three: Superpose and regulate the y - direction phase distribution of the beam passing through the metasurface and the y - direction phase distribution of the nematic liquid crystal with a rotation corresponding to the applied electric field. After regulation, a dynamic vector vortex beam is generated. The dynamic vector vortex beam includes but is not limited to a radially polarized vector vortex beam or / and an azimuthally polarized vector vortex beam. The generated dynamic vector vortex beam has anisotropy and polarization distribution.

[0024] Apply the electric field to the nematic liquid crystal so that the nematic liquid crystal only modulates the vortex beam distributed in the y - direction, while the vortex beam distributed in the x - direction is not modulated. Different externally applied electric fields to the nematic liquid crystal obtain corresponding effects.

[0025] Beneficial effects:

[0026] 1. The method for generating a dynamic vector vortex beam based on the regulation of liquid crystal and metasurface of the present invention generates a vortex light with a helical phase distribution based on the metasurface, cascades the metasurface and nematic liquid crystal, dynamically changes the externally applied electric field of the nematic liquid crystal, and further changes the deflection angle of the director of the nematic liquid crystal molecules to obtain a nematic liquid crystal with a corresponding rotation direction. The light beam is jointly regulated by the metasurface and the nematic liquid crystal with a corresponding rotation direction, and a dynamic vector vortex beam is generated after regulation. By introducing liquid crystal, flexible dynamic regulation of orbital angular momentum can be achieved through an externally applied electric field, overcoming the limitations of traditional metasurface devices, and generating dynamic vector vortex beams with spatially non-uniform polarization distributions such as radial polarization and angular polarization, which can support more complex optical field manipulation and meet the requirements of multiple scenarios.

[0027] 2. The method for generating a dynamic vector vortex beam based on the regulation of liquid crystal and metasurface of the present invention can be applied to many fields such as high-resolution microscopic imaging, optical manipulation and optical tweezers, optical communication and quantum communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of the method for generating a dynamic vector vortex beam based on the regulation of liquid crystal and metasurface of the present invention.

[0029] Figure 2 is a schematic diagram of the method for generating a dynamic vector vortex beam based on the regulation of liquid crystal and metasurface of the present invention.

[0030] Figure 3 is the amplitude and phase distribution of nanocolumns with different geometric sizes in the present invention.

[0031] Figure 4 is the response distribution of light beams by nanoscale antennas with different geometric sizes and liquid crystals with different director directions in the present invention. Figure (a) shows the amplitude and phase distribution of nanoscale antenna columns with different geometric sizes under x-polarized incidence. Figure (b) shows the amplitude and phase distribution of nanoscale antenna columns with different geometric sizes under y-polarized incidence. Figure (c) shows the amplitude and phase distribution corresponding to liquid crystals with different director angles under y-direction polarized incidence. Figure (d) shows the phase distribution after superimposing liquid crystals with different director angles and nanoscale antenna columns with different geometric sizes under y-polarized incidence.

[0032] Figure 5 is the electric field distribution of the vector vortex beam generated by the present invention. (a) is the distribution of a radially polarized vector vortex beam with a topological charge number l = 1. (b) is the distribution of a vector polarized vortex beam with a topological charge number l = 2. (c) is the distribution of an angularly polarized vector vortex beam with a topological charge number l = 1. (d) is the distribution of a vector polarized vortex beam with a topological charge number l = 2.

[0033] Figure 6It is the optical field distribution of the radially polarized vector vortex beam with topological charge number l = 1 in the present invention at different polarization angles.

[0034] Figure 7 It is the optical field distribution of the vector polarized vortex beam with topological charge number l = 2 in the present invention at different polarization angles.

[0035] Figure 8 It is the optical field distribution of the azimuthally polarized vector vortex beam with topological charge number l = 1 in the present invention at different polarization angles.

[0036] Figure 9 It is the optical field distribution of the vector polarized vortex beam with topological charge number l = 2 in the present invention at different polarization angles. Detailed implementation manners

[0037] The following further elaborates on the method of the present invention in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0038] Embodiment 1 (Proving radial polarization)

[0039] The method for generating a dynamic appropriate vortex beam based on liquid crystal and metasurface regulation disclosed in Embodiment 1 is as follows. As shown in the accompanying Figure 1 figures, the phase of the outgoing beam is regulated under the irradiation of linearly polarized light, and its schematic diagram is as shown in the accompanying Figure 2 figures. The specific implementation method is as follows:

[0040] Step 1: The metasurface modulates the incident linearly polarized light to generate a vortex beam with a ilθ vortex phase distribution.

[0041] The electric field expression of the generated radially vector vortex beam is

[0042]

[0043] where E0 represents the amplitude, l = 1 represents the topological charge number, and θ represents the polar angle.

[0044] First, determine that the height H of the anisotropic nano - antenna pillar array of the metasurface is 600 nm, the period P is 500 nm, the wavelength λ of the incident light is 950 nm, and the material of the rectangular nano - antenna pillar used in the embodiment is silicon (Si). Based on the finite - difference time - domain method (FDTD), scan the length L (100 nm - 400 nm) and width W (100 nm - 400 nm) of the pillar, and the corresponding amplitude and phase distributions of the x - direction linearly polarized light passing through nano - antenna pillars of different sizes are as shown in the accompanying Figure 3As shown (the results in the y direction are consistent), the complex amplitude modulation characteristics of nano-antenna columns with different lengths L and widths W are obtained. Twelve groups of nano-antenna columns with different geometric sizes are selected, so that the phase can cover the range of 0 - 2π, and the intensity differences of the selected different nano-antenna columns are small, and the phase can cover the range of 0 - 2π. The amplitude and phase distributions corresponding to the x direction (attached Figure 4 a) and the y direction (attached Figure 4 b) of twelve groups of nano-antenna columns with different geometric sizes are obtained respectively. According to the determined geometric size and arrangement of the nano-antenna column array of the metasurface, a processing file is generated. Based on the processing file of the metasurface, a reflective metasurface is prepared by micro-nano processing methods such as silicon coating and electron beam lithography.

[0045] Step two:

[0046] Obtain the amplitude and phase distributions corresponding to the director angles of nematic liquid crystal molecules (liquid crystal parameters n e = 1.70, n o = 1.51) from 0° to 90°, as shown in attached Figure 4 c. Superimpose the y-direction phase distribution of the metasurface and the y-direction phase distributions of nematic liquid crystals with different orientations. The superimposed phase distribution is shown in attached Figure 4 d. Cascade the metasurface and the nematic liquid crystal, and apply an electric field to the nematic liquid crystal. In the Cartesian coordinate system, the light beam emitted from the metasurface propagates along the z-axis. An external electric field is applied to the nematic liquid crystal in the yz plane (the corresponding electric field is adjusted by using a voltage range of 0 - 6V, and then the corresponding electric field is determined). The long axis direction of the nematic liquid crystal turns in the yz plane, and the short axis direction is along the x-axis direction. Therefore, in the direction of the externally applied electric field to the nematic liquid crystal, the nematic liquid crystal only modulates the vortex beam distributed in the y direction, so that its phase distribution meets specific requirements, while the vortex beam distributed in the x direction is not modulated. The phase distribution in the x direction after the nematic liquid crystal after applying the electric field modulation is superimposed with the metasurface is The phase distribution in the y direction is Finally, the vortex beams of the phase distributions in the x direction and the y direction of the light beam emitted from the nematic liquid crystal are superimposed to generate a radially polarized vector vortex beam with an orbital angular momentum l = 1, as shown in attached Figure 5 a, and its optical field distribution is

[0047] When the orbital angular momentum l = 2 in step one, the vortex beams of the phase distributions in the x direction and the y direction of the light beam emitted from the nematic liquid crystal are superimposed to generate a vector polarized vortex beam distribution, as shown in attached Figure 5 b, and its optical field distribution is

[0048] The polarization states of the vector vortex beams generated when l = 1 and l = 2 are analyzed separately. After the radially polarized vector vortex beam with l = 1 is polarized at directions of 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, and 180°, its electric field distribution is as shown in Appendix Figure 6 shown. After the vector polarized vortex beam with l = 2 is polarized at the same directions, its electric field distribution is as shown in Appendix Figure 7 shown, and the obtained results indicate that the generated beams have vectorial properties.

[0049] Example 2 (Proving azimuthal polarization)

[0050] The method for generating a dynamic vector vortex beam based on liquid crystal and metasurface modulation disclosed in Example 2 has a process as shown in Appendix Figure 1 shown. Under the irradiation of linearly polarized light, the phase of the output beam is modulated. The specific implementation method is as follows:

[0051] Step 1: The metasurface modulates the incident linearly polarized light to generate a vortex beam with a vortex phase distribution of e ilθ .

[0052] The electric field expression of the generated azimuthal vector vortex beam is

[0053]

[0054] where E0 represents the amplitude, l = 1 represents the topological charge number, and θ represents the polar angle.

[0055] First, determine that the height H of the anisotropic nanoantenna columns of the metasurface is 600 nm, the period P is 500 nm, the wavelength λ of the incident light is 950 nm, and the material of the rectangular nanoantenna columns used in the example is silicon (Si). Based on the finite-difference time-domain (FDTD) method, scan the length L (100 nm - 400 nm) and width W (100 nm - 400 nm) of the columns, and the corresponding phase distributions and amplitudes of the x-direction linearly polarized light passing through nanoantenna columns of different sizes are as shown in Appendix Figure 3 shown (the results in the y direction are the same), and obtain the complex amplitude modulation characteristics of nanoantenna columns with different lengths L and widths W. Select 12 groups of nanoantenna columns with different geometric sizes so that the phase can cover the range of 0 - 2π, and the intensity differences of the selected different nanoantenna columns are small, and the phase can cover the range of 0 - 2π. Obtain the amplitude and phase distributions corresponding to the 12 groups of nanoantenna columns with different geometric sizes in the x direction (Appendix Figure 4 a) and the y direction (Appendix Figure 4 b) respectively. Generate a processing file according to the determined geometric sizes and arrangements of the nanoantenna column arrays of the metasurface. Based on the processing file of the metasurface, a reflective metasurface is fabricated by micro-nano processing methods such as silicon coating and electron beam lithography.

[0056] Step 2:

[0057] Obtain the amplitude and phase distributions corresponding to the director angles of the nematic liquid crystal molecules (the nematic liquid crystal molecules are the same as those in Embodiment 1, and the liquid crystal parameters are \(n = 1.70\), \(n = 1.51\)) ranging from \(0^{\circ}\) to \(90^{\circ}\), as shown in Appendix e \( = 1.70\), \(n\) o \( = 1.51\)), as shown in Appendix Figure 4 c. Superimpose the y - direction phase distribution of the metasurface and the y - direction phase distributions of the nematic liquid crystal with different rotations. The superimposed phase distribution is shown in Appendix Figure 4 d. Cascade the metasurface and the nematic liquid crystal, and apply an electric field to the nematic liquid crystal. In the Cartesian coordinate system, the light beam emitted from the metasurface propagates along the z - axis. An external electric field is applied to the nematic liquid crystal in the yz - plane. The long - axis direction of the nematic liquid crystal rotates in the yz - plane, and the short - axis direction is along the x - axis. Therefore, in the direction of the externally applied electric field to the nematic liquid crystal, the nematic liquid crystal only modulates the vortex beam with a y - direction distribution to make its phase distribution meet specific requirements, while the vortex beam with an x - direction distribution is not modulated. After applying the electric - field modulation, the x - direction phase distribution of the nematic liquid crystal superimposed with the metasurface is The y - direction phase distribution is Finally, superimpose the x - direction phase - distribution and y - direction phase - distribution vortex beams of the light beam emerging from the nematic liquid crystal to generate an azimuthally polarized vector vortex beam with an orbital angular momentum \(l = 1\), as shown in Appendix Figure 5 c, and its optical - field distribution is When the orbital angular momentum \(l = 2\), superimpose the x - direction phase - distribution and y - direction phase - distribution vortex beams of the light beam emerging from the nematic liquid crystal to generate a vector - polarized vortex - beam distribution, as shown in Appendix Figure 5 d, and its optical - field distribution is

[0058] Analyze the polarization of the optical fields of the vector vortex beams generated when \(l = 1\) and \(l = 2\) respectively. After the azimuthally polarized vector vortex beam with \(l = 1\) is analyzed by polarization at \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\), \(135^{\circ}\), \(150^{\circ}\), \(180^{\circ}\) directions, its electric - field distribution is shown in Appendix Figure 8 as shown. After the vector - polarized vortex beam with \(l = 2\) is analyzed by polarization in the same directions, its electric - field distribution is shown in Appendix Figure 9 as shown. The results obtained show that the generated light beam has vectorial properties.

[0059] Through the comprehensive analysis of Embodiment 1 and Embodiment 2 (the corresponding reflective metasurfaces in the two embodiments are the same, and the electric fields applied to the nematic liquid crystal molecules are the same), it can be obtained that generating dynamic vector vortex beams with spatially non - uniform polarization distributions such as radial polarization and azimuthal polarization can support more complex optical - field manipulation and meet the requirements of multiple scenarios.

[0060] So far, dynamic vector vortex beams are generated by liquid crystals and metasurfaces, so as to achieve the purpose of application in many fields such as high-resolution microscopic imaging, optical manipulation and optical tweezers, optical communication and quantum communication.

[0061] The specific descriptions above further elaborate on the purpose, technical solutions and beneficial effects of the invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for generating a dynamic vector vortex beam based on liquid crystal and metasurface regulation, characterized in that Generate vortex light with a helical phase distribution based on a metasurface, cascade the metasurface and nematic liquid crystal, dynamically change the external electric field of the nematic liquid crystal, and then change the deflection angle of the director of the nematic liquid crystal molecules to obtain a nematic liquid crystal corresponding to the deflection angle; the light beam is jointly regulated by the metasurface and the nematic liquid crystal with the corresponding steering, and a dynamic vector vortex beam is generated after regulation.

2. The method according to claim 1, characterized in that, Specifically, it includes the following steps: Step 1: Design the metasurface and generate vortex light with a helical phase distribution based on the metasurface; Step 2: Cascade the metasurface and nematic liquid crystal, that is, attach a thin layer of nematic liquid crystal to the metasurface, and then dynamically change the external electric field of the nematic liquid crystal, and then change the deflection angle of the director of the nematic liquid crystal molecules to obtain a nematic liquid crystal with the corresponding steering; Step 3: The light beam is jointly regulated by the metasurface and the nematic liquid crystal with the corresponding steering in Step 2, and a dynamic vector vortex beam is generated after regulation.

3. The method according to claim 2, wherein The implementation method of Step 1 is: control the helical phase distribution of the incident light by designing the structure of the metasurface nanoantennas to generate a vortex beam; Obtain the electric field distribution of the vortex beam, expressed as: E = E0e ilθ (1) where E0 represents the amplitude, l (±1, ±2…±n) represents the topological charge number of the vortex beam, θ represents the polar angle, and the phase of the vortex beam is e ilθ .

4. The method according to claim 2, characterized in that, In Step 1, design the metasurface, obtain the complex amplitude modulation characteristics of the metasurface nanoantenna columns, and obtain the corresponding amplitude and phase distributions. The metasurface is a reflective metasurface; specifically, it includes the following: (1) Determine the geometric dimensions of the nanoantenna column array of the metasurface by matching the phase distribution of the metasurface and the phase of the vortex beam. The metasurface is composed of multiple nanoantenna column arrays with different geometric dimensions (length L, width W) and anisotropy. The geometric dimensions are determined based on the transmission phase principle of the metasurface. The amplitudes of the selected nanoantenna column arrays are approximately equal, and the phase distribution covers 0-2π; (2) Arrange the nanoantenna column array of the metasurface, generate a processing file, and process it to obtain a solid metasurface structure.

5. The method according to claim 4, wherein In the above, obtaining the complex amplitude modulation characteristics of the metasurface nanoantenna columns and obtaining the corresponding amplitude and phase distributions also include: Preset the height H of the nanoantenna column and the period P of the structural unit, and scan the amplitude and phase distributions of the nanoantenna column array at different lengths L and widths W by the finite-difference time-domain method, so that the phase can be regulated within the range of 0-2π.

6. The method according to claim 2, characterized in that, The amplitude and phase distributions corresponding to the director angle of the nematic liquid crystal molecules in Step 2. Applying different electric fields to the nematic liquid crystal corresponds to different director angles; cascading the metasurface and the nematic liquid crystal to obtain the phase distribution superimposed after cascading the metasurface and the nematic liquid crystal, and dynamically changing the external electric field of the nematic liquid crystal to obtain a nematic liquid crystal with the corresponding steering.

7. The method according to claim 2, wherein The ways to dynamically change the external electric field of the nematic liquid crystal include but are not limited to changing the voltage of the external electric field or controlling the external electric field through a programmable logic gate array.

8. The method according to claim 2, wherein Step 3: Superpose and regulate the light beam through the y-direction phase distribution corresponding to the metasurface and the y-direction phase distribution of the nematic liquid crystal turned by the applied electric field. After regulation, a dynamic vector vortex beam is generated. The dynamic vector vortex beam includes, but is not limited to, a radially polarized vector vortex beam or / and an azimuthally polarized vector vortex beam. The generated dynamic vector vortex beam has anisotropy and polarization distribution.

9. The method according to claim 2, characterized in that, Apply the electric field to the nematic liquid crystal so that the nematic liquid crystal only modulates the vortex beam distributed in the y direction, and does not modulate the vortex beam distributed in the x direction. Different applied electric fields to different nematic liquid crystals yield corresponding effects.

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