Approximate diffraction-free polarization Mobius ring generation method based on Bessel beam

Abstract

The invention belongs to the technical field of photon spin-orbital angular momentum coupling of a metasurface, and particularly relates to an approximately diffraction-free polarization Mobius ring generation method based on a Bessel beam, and the method comprises the following steps: 1, completing the generation of a Poincare beam through the comprehensive regulation and control of a propagation phase and a geometric phase; 2, introducing a Bessel beam phase to replace an aggregation phase, and designing different unit sizes according to the requirements of the Bessel beam phase on unit positions in a unit structure to realize that emergent light is an approximately diffraction-free light beam with an invariable light beam radius; furthermore, a stable polarization Mobius ring structure is generated in a long-distance light path; based on the photon spin-orbital angular momentum coupling theory and the characteristics of the Bessel beam, the generation position of the three-dimensional polarization topology is regulated and controlled. According to the invention, stable generation of a three-dimensional polarization structure at any position is realized, and stable polarization Mobius rings can be generated and observed at different positions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of photonic spin-orbit angular momentum coupling of super-structured surfaces, and particularly relates to a method for generating a polarization Mobius ring based on a Bessel beam. BACKGROUND

[0002] Polarization is a basic degree of freedom of light. In a common paraxial optical field, a two-dimensional polarization topology is usually generated. The two-dimensional polarization topology is arranged by rotating the primary and secondary axes on a closed circular path around a phase singularity. If the major and minor axes of the polarization ellipse are tilted out of the horizontal plane, an additional component in the z direction will be generated, which will produce a three-dimensional polarization topology on the closed circular path. The core of the three-dimensional polarization topology is to study the topology structure exhibited by the distribution and evolution of the polarization state in three-dimensional real space or momentum space. According to the parity of the half-twist number, the three-dimensional polarization topology structure can be divided into two basic structures, namely, a Mobius band and a twisted band. The polarization Mobius ring is a three-dimensional polarization structure with arbitrary odd half-twist number and special topology characteristics of single-sided single-face. The polarization twisted band does not have such special topology characteristics of single-sided single-face, and is a three-dimensional geometric structure with arbitrary even half-twist number.

[0003] At present, there are several main methods to generate a three-dimensional polarization topology structure. For example, a q-plate liquid crystal device or a subwavelength super-structured surface is used. The q-plate can convert circularly polarized light into circularly polarized light carrying opposite chirality and orbital angular momentum l=±2q, and through the selection of q value and incident light, an appropriate amount of vortex beam with special topological charge can be efficiently generated. The super-structured surface is a two-dimensional planar array composed of subwavelength artificial units. By designing the geometric shape, orientation and arrangement of the units, the polarization response can be flexibly controlled on the macro or local scale, so that a controllable polarization topology can be realized.

[0004] The traditional method of generating a three-dimensional polarization topology using a super-structured surface is limited to the focal depth range of the converging beam. The stable polarization Mobius band can only be observed at a specific position such as the focal plane. As the observation point moves, if the observation distance is too close or too far, the light field distribution of the observation plane will be distorted, and it is difficult to observe a stable three-dimensional polarization structure. Therefore, this method is limited to the focal depth range, and it is difficult to continuously observe the polarization Mobius ring or the polarization twisted band in long-distance propagation.

[0005] In view of the problem that the observation of the polarization Mobius ring by the super-structured surface focusing Pogalay beam is limited to the focal depth range, the application provides a method for designing a super-structured surface for generating a three-dimensional polarization topology based on a Bessel beam. SUMMARY

[0006] The application aims to provide a Bessel beam-based approximate non-diffraction polarization Mobius ring generation method, which realizes stable generation of three-dimensional polarization structures at any position by combining transmission phase, geometric phase and axicon phase control principles.

[0007] The technical solutions adopted by the application are as follows:

[0008] The Bessel beam-based approximate non-diffraction polarization Mobius ring generation method comprises the following steps:

[0009] Step 1: First, generate a Poincare beam through comprehensive control of propagation phase and geometric phase;

[0010] The step 1 comprises the following steps: step 101: adjust the unit size to control the propagation phase to generate a co-polarization component of transmitted light.

[0011] Step 102: adjust the unit rotation angle to control the geometric phase to add an arbitrary desired orbital angular momentum to the cross-polarization component of the transmitted light.

[0012] The step 1 further comprises the following step: step 103: superimpose the co-polarization component and the orbital angular momentum and tightly focus them, so that a specific electric field distribution and three-dimensional polarization topology are generated at the focal plane.

[0013] Step 2: introduce a Bessel beam phase to replace the focusing phase, design different unit sizes according to the requirements of the Bessel beam phase for the unit position in the unit structure, so that the outgoing light is a beam with a constant radius and approximate non-diffraction; further generate stable polarization Mobius ring structures in a long-distance optical path without specially controlling the position of the focal point and the focal plane; based on the photon spin-orbital angular momentum coupling theory and the characteristics of the Bessel beam, the generation position of the three-dimensional polarization topology is flexibly controlled, and finally by introducing an axicon phase, the Bessel beam is applied to the Poincare beam to design an approximate non-diffraction superstructure surface for generating polarization Mobius rings and polarization twist bands, which can avoid the influence of the focal depth range of the tightly focused beam and generate stable three-dimensional polarization topologies at any observation point.

[0014] Based on the photon spin-orbit angular momentum coupling theory and the comprehensive regulation of propagation phase and geometric phase, it is used for two different independent Poincare beams; left-handed circularly polarized light LCP and right-handed circularly polarized light RCP are incident on the superstructure surface respectively, the left-handed circularly polarized light is represented by |L>, and the right-handed circularly polarized light is represented by R>, for the Gaussian beam in the left-handed circularly polarized light and the right-handed circularly polarized light state propagating along the z direction, the optical element should perform basic beam conversion:

[0015]

[0016] Wherein, δ and χ represent amplitude coefficient and relative phase respectively, m (n) is an arbitrary integer, Is the azimuth angle.

[0017] In the calculation, the core phase of the Bessel beam is introduced, that is, the axicon phase; the axicon is a special optical element, and the core function of the axicon is to convert the incident parallel Gaussian beam into an approximately non-diffractive Bessel beam, to produce a long focal depth gathering line instead of a point; the required axicon phase formula is:

[0018]

[0019] Wherein, r represents the radial distance of each point of the array to the origin, λ is the wavelength, and α is the cone angle parameter.

[0020] Finally, the Jones matrix of the superstructure surface performing the transformation function is obtained:

[0021]

[0022] Based on the calculation formula of the propagation phase, the geometric phase and the axicon phase, according to the distance r and the azimuth angle Different, a superstructure surface phase distribution with Bessel beam characteristics is designed, wherein the propagation phase and the axicon phase are regulated by the unit size, and the geometric phase is regulated by the unit rotation angle, so that the long-distance stable generation of the polarization Mobius ring is realized.

[0023] The technical effects obtained by the present application are:

[0024] In the present application, by combining the transmission phase, the geometric phase and the axicon phase regulation principle, the stable generation of the three-dimensional polarization structure at any position is realized. The present application breaks through the limitation of the focal depth of the traditional superstructure surface, can generate and observe the stable polarization Mobius ring at different positions, and realizes the long-distance generation and observation of the three-dimensional polarization topological structure through the non-diffractive characteristics of the Bessel beam.

[0025] In the application, by introducing the axicon phase, the Poincare beam is subjected to the constraint of the Bessel beam, an approximately non-diffracting superstructure surface for generating polarization Mobius ring and polarization twisted band is designed, which can avoid the influence of the focal depth range of tightly focused beam, and generate stable three-dimensional polarization topology at any observation point. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a flowchart of the application based on the Bessel beam approximately non-diffracting polarization Mobius ring generation method.

[0027] Figure 2 is a schematic diagram showing the change of polarization Mobius ring with distance when left-handed circularly polarized light (m=1) is incident at every 10mm in the z=100mm-150mm interval respectively in the application;

[0028] Figure 3 is a schematic diagram showing the change of polarization Mobius ring with distance when left-handed circularly polarized light (m=1) is incident at every 10mm in the z=160mm-210mm interval respectively in the application;

[0029] Figure 4 is a schematic diagram showing the change of polarization Mobius ring with distance when right-handed circularly polarized light (n=-2) is incident at every 10mm in the z=100mm-150mm interval respectively in the application;

[0030] Figure 5 is a schematic diagram showing the change of polarization Mobius ring with distance when right-handed circularly polarized light (n=-2) is incident at every 10mm in the z=160mm-210mm interval respectively in the application. DETAILED DESCRIPTION

[0031] In order to make the purpose and advantages of the application more clear and apparent, the application will be specifically described below in combination with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the application, and does not strictly limit the specific protection scope requested by the application.

[0032] As shown in Figure 1 , the Bessel beam based approximately non-diffracting polarization Mobius ring generation method includes the following steps:

[0033] Step 1: First, the generation of Poincare beam is completed by comprehensive control of propagation phase and geometric phase;

[0034] The step 1 includes: step 101: adjusting the unit size to control the copolarization component of the transmitted light generated by the propagation phase.

[0035] Step 102: The cross-polarization component of the transmitted light is added to any desired orbital angular momentum by adjusting the corner of the unit to control the geometric phase.

[0036] The step 1 further comprises: step 103: superimposing the co-polarization component and the orbital angular momentum and tightly focusing, then generating a specific electric field distribution and three-dimensional polarization topology at the focal plane.

[0037] Step 2: Introducing the Bessel beam phase to replace the focusing phase, by designing different unit sizes according to the requirements of Bessel beam phase on unit position in the unit structure, the exit light is a beam with constant radius and approximate non-diffraction; Further generate stable polarization Mobius ring structure in long distance optical path without special control of focusing point and focal plane position; Based on the theory of photon spin-orbit angular momentum coupling and the characteristics of Bessel beam, the generation position of three-dimensional polarization topology is flexibly regulated, and finally by introducing the axicon phase, a kind of superstructure surface for generating polarization Mobius ring and polarization twisted band with approximate non-diffraction is designed, which can avoid the influence of focal depth range of tightly focused beam, and generate stable three-dimensional polarization topology at any observation point.

[0038] Based on the theory of photon spin-orbit angular momentum coupling and the comprehensive regulation of propagation phase and geometric phase, it is used for two different Poincare beams; Let the left-handed circularly polarized light LCP and the right-handed circularly polarized light RCP be incident on the superstructure surface respectively, the left-handed circularly polarized light is represented by |L> and the right-handed circularly polarized light is represented by R>, for the Gaussian beam propagating along the z direction in the state of left-handed circularly polarized light and right-handed circularly polarized light respectively, the optical element should perform the basic beam conversion:

[0039]

[0040] Where δ and χ represent amplitude coefficient and relative phase respectively, m(n) is any integer, is the azimuth angle.

[0041] The core phase of Bessel beam is introduced in the calculation, which is the axicon phase; Axicon is a special optical element, the core function of axicon is to convert the incident parallel Gaussian beam into approximate non-diffraction Bessel beam, which produces a long focal depth aggregation line instead of a point; The required axicon phase formula is:

[0042]

[0043] Where r represents the radial distance of each point on the array to the origin, λ is the wavelength (λ=30mm in this design), and α is the cone angle parameter.

[0044] The Jones matrix of the super-structured surface for performing the transformation function is finally obtained:

[0045]

[0046] Based on the calculation formula of the propagation phase, the geometric phase and the axicon phase, according to the different distances r and azimuth angles φ of different units, a super-structured surface phase distribution with Bessel beam characteristics is designed, wherein the propagation phase and the axicon phase are controlled by the unit size, and the geometric phase is controlled by the unit corner, so that the long-distance stable generation of the polarization Mobius ring is realized.

[0047] In actual use, for example, the present application generates an electric field distribution with special symmetry and a three-dimensional polarization topological structure at each 10 mm in the z=100 mm-210 mm interval with the super-structured surface as the reference plane z=0. Figure 2 and Figure 3 It is shown that under the condition of left-handed circularly polarized light (topological charge number m=1) incidence, a right-handed polarization Mobius ring with three half-twists is generated, and the opening flips appear with the evolution of the polarization ellipse, which conforms to the single-edge single-surface characteristics of the Mobius ring. Figure 4 and Figure 5 It is shown that under the condition of left-handed circularly polarized light (topological charge number m=1) incidence, a right-handed polarization Mobius ring with three half-twists is generated, and the opening flips appear with the evolution of the polarization ellipse, which conforms to the single-edge single-surface characteristics of the Mobius ring.

[0048] In the present application, the stable generation of three-dimensional polarization structures at any position is realized by combining the transmission phase, the geometric phase and the axicon phase control principle.

[0049] In the present application, by introducing the axicon phase, the super-structured surface for generating polarization Mobius ring and polarization twisted band with approximate non-diffraction is designed, which can avoid the influence of the focal depth range of the tightly focused beam and generate stable three-dimensional polarization topologies at any observation point.

[0050] The above description is only the preferred embodiment of the present application, it should be pointed out that for the ordinary skilled in the art, without departing from the principles of the present application, can also make several improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application. The structure, device and operation method not specifically described and explained in the present application, if no special description and limitation, are implemented according to the conventional means in the art.

Claims

1. A method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam, characterized by: The following steps are involved: Step 1: First, the Poincare beam is generated by comprehensively controlling the propagation phase and the geometric phase; Step 2: Introduce the Bessel beam phase to replace the focusing phase. By designing different unit sizes in the unit structure according to the requirements of the Bessel beam phase on the unit position, the outgoing light is a beam with a constant beam radius and approximately no diffraction. Then, a stable polarization Möbius ring structure is generated in the long-distance optical path. Based on the photon spin-orbital angular momentum coupling theory and the characteristics of the Bessel beam, the generation position of the three-dimensional polarization topology is controlled. Finally, by introducing the axicon phase, the Poincare beam is constrained by the Bessel beam, and a metasurface that generates polarization Möbius rings and polarization twisted bands with approximately no diffraction is designed. This can avoid the influence of the focal depth range of a tightly focused beam and generate a stable three-dimensional polarization topology at any observation point.

2. The method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam according to claim 1, wherein: The step 1 includes: step 101: regulating the propagation phase by adjusting the unit size to generate a co-polarization component of the transmitted light.

3. The method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam according to claim 2, wherein: The step 1 further includes: step 102: controlling the geometric phase by adjusting the unit rotation angle to achieve adding any desired orbital angular momentum to the cross-polarization component of the transmitted light.

4. The method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam according to claim 3, wherein: The step 1 further includes: step 103: superimposing the co-polarization component and the orbital angular momentum and tightly focusing them, thereby generating a specific electric field distribution and a three-dimensional polarization topological structure at the focal plane.

5. The method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam according to claim 4, wherein: Based on the theory of photon spin-orbital angular momentum coupling and the comprehensive control of propagation phase and geometric phase, it is used for two different independent Poincare beams. Assume that left-handed circularly polarized light LCP and right-handed circularly polarized light RCP are incident on the metasurface respectively. The left-handed circularly polarized light is represented by |L> and the right-handed circularly polarized light is represented by R>. For Gaussian beams propagating along the z direction in the left-handed circularly polarized light and right-handed circularly polarized light states, respectively, the optical element should perform the basic beam conversion: Where δ and χ represent the amplitude coefficient and relative phase respectively, m(n) is an arbitrary integer, is the azimuth.

6. The method for generating a nearly non-diffraction polarization Möbius strip based on a Bessel beam according to claim 5, wherein: The core phase of the Bessel beam is introduced into the calculation. The core phase is also the axicon phase. The axicon is a special optical element. Its core function is to convert the incident parallel Gaussian beam into a nearly non-diffracting Bessel beam, generating a converging line with a long focal depth rather than a point. The required axicon phase formula is: Among them, r represents the radial distance from each point on the array to the origin, λ is the wavelength, and α is the cone angle parameter.

7. The method for generating a nearly diffraction-free polarization Möbius strip based on a Bessel beam according to claim 3, wherein: The Jones matrix of the metasurface that performs the transformation function is finally obtained as: Based on the calculation formulas of propagation phase, geometric phase and axicon phase, and according to the different distances r and azimuth angles φ of different units, a metasurface phase distribution with Bessel beam characteristics is designed. The propagation phase and axicon phase are controlled by the unit size, and the geometric phase is controlled by the unit rotation angle, thereby realizing the long-distance and stable generation of polarized Möbius rings.

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