Spiral elliptic lens and preparation method thereof

Abstract

The invention discloses a spiral elliptical lens and a preparation method thereof, and relates to the field of vortex beams, and the spiral elliptical lens is obtained by modifying a hyperbolic lens phase through an elliptical polar coordinate equation and then superposing a spiral phase. The preparation method comprises the following steps: step 1, determining polar coordinate equation parameters of an ellipse; 2, the focal length and the wave number of the modified hyperbolic lens are designed; 3, designing a spiral phase function; step 4, superposing the phase of the modified hyperbolic lens and the spiral phase to obtain the height morphology of the processing material; and 5, carrying out selective polymerization on the processed material according to the height morphology. The spiral elliptic lens designed by the invention can efficiently generate an elliptic perfect vortex beam at any designed focal length; and meanwhile, the miniaturization of the spiral elliptic lens is realized by utilizing the high-precision processing capability of the femtosecond laser direct writing technology, so that the application of the device in a micro-optical system and integrated optics is facilitated.

Description

Technical Field

[0001] The present invention relates to the field of vortex beams, and in particular to a spiral elliptical lens and a preparation method thereof. Background Art

[0002] Perfect vortex beams have the characteristic that the intensity distribution does not change with the topological charge value. They solve the problem of simultaneous coupling of multiple orbital angular momentum in fiber-optic communication applications and the problem of obtaining large orbital angular momentum while keeping the size of the intensity distribution unchanged during optical capture. Despite this, traditional perfect vortex beams are still limited to circular intensity distributions. In order to further expand its application areas, researchers have explored elliptical perfect vortex beams with greater adjustment freedom. Therefore, the traditional circular perfect vortex beam can be regarded as a special case of an elliptic perfect vortex beam with an ellipticity of 1.

[0003] Typically, the generation of an elliptical perfect vortex beam requires first generating an elliptical Bessel beam on a spatial light modulator and then passing it through a Fourier lens. This generation method requires heavy optical components and precise optical path alignment, which is not conducive to its application in integrated optics and systems. Using the same generation principle, an integrated phase plate prepared by laser direct writing has also successfully generated an elliptical perfect vortex beam, but there are large intensity side lobes near the beam, resulting in low theoretical and experimental efficiency. In recent years, by utilizing the geometric phase or (and) dynamic phase characteristics of the metasurface, the elliptical spiral cone phase and the Fourier lens phase of the light beam are modulated, and elliptical perfect vortex beams can also be generated on the micron scale. Although the metasurface has a wide spectrum adjustment capability, its polarization characteristics, complex processing technology and high cost are still important factors limiting its widespread application.

[0004] Therefore, in order to achieve high-efficiency, low-cost, polarization-insensitive, and micrometer-scale elliptical perfect vortex beam generation, technicians in this field have been committed to developing a spiral elliptical lens. By modifying the phase of a traditional hyperbolic lens and combining it with a spiral phase, an elliptical perfect vortex beam with a very small size change with the topological charge value can be generated on the designed focal plane. At the same time, a method for preparing a micrometer-scale spiral elliptical lens based on femtosecond laser direct writing technology has been proposed, which is expected to further expand the application field of perfect vortex beams. Summary of the Invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to design and prepare a spiral elliptical lens that can generate an elliptical perfect vortex beam at any designed focal length.

[0006] To achieve the above object, the present invention provides a spiral elliptical lens, characterized in that the phase of the spiral elliptical lens is obtained by modifying the phase of a hyperbolic lens through the polar coordinate equation of the ellipse and then superimposing the spiral phase.

[0007] Furthermore, the spiral elliptical lens obtained by modifying the phase of the hyperbolic lens by the polar coordinate equation of the ellipse satisfies the following formula:

[0008]

[0009] in, is the modified hyperbolic lens phase, (r,θ) are polar coordinates, k and f are wave number and focal length respectively, ρ(θ) is the polar coordinate equation of the ellipse, a and b are the minor and major semi-axes of the ellipse respectively, and θ0 is the initial phase.

[0010] Furthermore, the spiral phase is expressed by the following formula:

[0011]

[0012] Where l is the topological charge.

[0013] Furthermore, the spiral elliptical lens is used to modulate the incident light beam to generate an elliptical perfect vortex light beam on the focal plane.

[0014] A method for preparing a spiral elliptical lens, characterized by comprising the following steps:

[0015] Step 1, determine the polar coordinate equation parameters of the ellipse;

[0016] Step 2, designing the focal length and wave number of the modified hyperbolic lens;

[0017] Step 3, design the spiral phase function;

[0018] Step 4: superimposing the modified hyperbolic lens phase and the spiral phase to obtain a spiral elliptical lens phase, and converting the spiral elliptical lens phase into a height morphology of the processed material;

[0019] Step 5: selectively polymerizing the processed material according to the height morphology to obtain a processed sample;

[0020] Step 6: Develop and dry the sample to obtain the spiral elliptical lens.

[0021] Furthermore, in step 3, the topological charge value of the spiral phase function is any integer.

[0022] Furthermore, in step 4, the height profile of the processed material is expressed by the following formula:

[0023]

[0024] Among them, n p and n c are the refractive index of the material of the spiral elliptical lens and the refractive index of its environment respectively.

[0025] Furthermore, in step 4, the processing material is photoresist.

[0026] Furthermore, step 5 also includes: drying the processed material to obtain a pre-processed sample of solid photoresist, placing the pre-processed sample on a nano-displacement stage of a femtosecond laser direct writing system, and performing selective polymerization through a focused femtosecond laser beam.

[0027] Furthermore, in step 6, the unpolymerized photoresist is dissolved by placing the sample into a developing solution of the photoresist.

[0028] Traditional perfect vortex beams usually have a circular intensity distribution, which limits its application scenarios, and the previous generation methods of elliptical perfect vortex beams have the problems of heavy optical components, low generation efficiency and polarization. The present invention proposes a spiral elliptical lens. By performing elliptical modification on the phase of the traditional hyperbolic lens and combining the spiral phase, an elliptical perfect vortex beam with a size that varies very little with the topological charge value can be generated on the designed focal plane; and a preparation method of a micron-scale spiral elliptical lens based on femtosecond laser direct writing technology is proposed. The spiral elliptical lens designed by the present invention utilizes the phase center that changes along the ellipse to converge the light beam into an elliptical shape, and utilizes the loaded spiral phase to give the light beam orbital angular momentum. The designed spiral elliptical lens can efficiently generate an elliptical perfect vortex beam at any designed focal length; at the same time, the high-precision processing capability of the femtosecond laser direct writing technology is utilized to realize the preparation of structures on the micron scale, which can realize the miniaturization of the spiral elliptical lens, which is conducive to promoting the application of the device in micro-optical systems and integrated optics.

[0029] The beneficial technical effects of the present invention are as follows:

[0030] 1. Highly efficient generation of elliptical perfect vortex beams. The modified hyperbolic lens phase pair of the present invention has a strong ability to bind the light beam, resulting in an elliptical vortex beam with minimal size variation with topological charge and perfect characteristics. Furthermore, compared to the elliptical perfect vortex beam obtained by Fourier transforming a Bessel beam in an elliptical coordinate system, the beam generated by the present invention has smaller sidelobes and more concentrated energy, resulting in higher generation efficiency.

[0031] 2. It can fabricate spiral elliptical lenses at any operating wavelength at the micron scale. Femtosecond laser direct writing technology offers high precision and maskless operation. It selectively polymerizes the processed material according to the designed path, resulting in a micron-scale polymerized structure with the desired height morphology. During the design process, the lens' operating wavelength (i.e., wave number) can be changed as needed, thereby altering the lens' height morphology. Using femtosecond laser direct writing technology, it is possible to fabricate spiral elliptical lenses at any operating wavelength.

[0032] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of a spiral elliptical lens generating an elliptical perfect vortex beam according to a preferred embodiment of the present invention;

[0034] Figure 2 This is a phase generation process of a spiral elliptical lens in a preferred embodiment of the present invention;

[0035] Figure 3 This is the preparation result of a spiral elliptical lens of a preferred embodiment of the present invention, wherein the topological charges of the spiral elliptical lens are 1, 2 and 3 respectively. DETAILED DESCRIPTION

[0036] The following describes several preferred embodiments of the present invention with reference to the accompanying drawings to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0037] The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[0038] The present invention realizes a spiral elliptical lens capable of generating an elliptical perfect vortex beam. The polar coordinate equation of the ellipse is used to modify the phase of a conventional hyperbolic lens. The spiral phase is then superimposed to modulate the incident light beam, generating an elliptical perfect vortex beam on the focal plane. The relationship between optical path and phase is utilized to convert the phase of the spiral elliptical lens into a height variation in the processed material. Femtosecond laser direct writing technology is then used to fabricate the spiral elliptical lens at the micrometer scale. The specific implementation method includes the following:

[0039] First, the polar coordinate equation of the ellipse is used to modify the phase of the traditional hyperbolic lens. The resulting spiral elliptical lens satisfies the following formula:

[0040]

[0041] in, is the modified hyperbolic lens phase, (r,θ) is the polar coordinate, k and f are the wave number and focal length respectively, ρ(θ) is the polar coordinate equation of the ellipse, a and b are the minor and major axes of the ellipse respectively, θ0 is the initial phase, and the rotation angle of the ellipse can be controlled.

[0042] Secondly, determine the superimposed spiral phase, which can be expressed as follows:

[0043]

[0044] Where l is the topological charge. By superimposing the modified hyperbolic lens phase and the spiral phase, a spiral elliptical lens phase can be obtained. The transmittance function of this phase is the designed spiral elliptical lens. The designed spiral elliptical lens can be regarded as a combination of a converging lens and a diverging lens. By limiting the incident light beam to an intensity distribution that satisfies the designed elliptical equation, an elliptical perfect vortex beam carrying orbital angular momentum can be generated on the focal plane, such as Figure 1 shown.

[0045] Before preparing the spiral elliptical lens, it is necessary to use the relationship between optical path and phase to convert the phase morphology of the lens into the height morphology of the processed material:

[0046]

[0047] Among them, n p and n c The refractive indexes of the material and the surrounding environment of the spiral elliptical lens are respectively. The continuously varying height is discretized and converted into processing file data suitable for a femtosecond laser direct writing system. Under optimized processing parameters, a spiral elliptical lens at the micrometer scale is fabricated. Specific embodiment:

[0049] Step 1: Determine the parameters of the polar coordinate equation of the ellipse, and set the minor and major axes to 9 μm and 10.8 μm, respectively.

[0050] Step 2: Design the focal length and wave number of the modified hyperbolic lens. The focal length is set to 80 microns and the wave number is set to 2π / 532nm-1.

[0051] Step 3: Design the spiral phase function, where the topological charge values ​​are set to 1, 2, and 3 respectively.

[0052] Step 4: Superimpose the modified hyperbolic lens phase and the spiral phase to obtain the spiral elliptical lens phase. Figure 2The process of phase superposition with a topological charge of 1 is demonstrated. The superimposed phases are converted into corresponding height profiles. The processing material used here is SZ2080 photoresist, with a refractive index of approximately 1.5, so the maximum height corresponding to the 2π phase is approximately 1064nm. The continuously varying height profile data is discretized into 11 height levels at a rate of 100nm per layer.

[0053] Step 5: Drop SZ2080 photoresist onto a coverslip cleaned with acetone, ethanol, and deionized water. The solvent was dried on a 100°C hot plate for 1 hour to obtain a pre-processed sample of solid-state photoresist. The processed sample was placed on the nanopositioning stage of a femtosecond laser direct writing system. The processing power and single-point exposure time were set to 6 mW and 600 μs, respectively. The focused femtosecond laser beam selectively polymerized the photoresist according to the beam scanning path predefined in step 4.

[0054] Step 6: Place the processed sample in n-propanol solution for 1 hour. The polymerized part is retained and the unpolymerized photoresist is dissolved. After drying in air, the desired spiral elliptical lens is obtained, as shown in FIG. Figure 3 shown.

[0055] The preferred embodiments of the present invention have been described in detail above. It should be understood that numerous modifications and variations based on the concepts of the present invention are possible without inventive effort by those skilled in the art. Therefore, any technical solution that can be derived by one skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A spiral elliptical lens, characterized in that: The phase of the spiral elliptical lens is obtained by modifying the phase of the hyperbolic lens through the polar coordinate equation of the ellipse and then superimposing the spiral phase.

2. The spiral elliptical lens according to claim 1, wherein: The spiral elliptical lens obtained by modifying the phase of the hyperbolic lens by the polar coordinate equation of the ellipse satisfies the following formula: in, is the modified hyperbolic lens phase, (r,θ) are polar coordinates, k and f are wave number and focal length respectively, ρ(θ) is the polar coordinate equation of the ellipse, a and b are the minor and major semi-axes of the ellipse respectively, and θ0 is the initial phase.

3. The spiral elliptical lens according to claim 1, wherein: The spiral phase is expressed by the following formula: Where l is the topological charge.

4. The spiral elliptical lens according to claim 1, wherein: The spiral elliptical lens is used to modulate the incident light beam and generate an elliptical perfect vortex light beam on the focal plane.

5. The method for preparing a spiral elliptical lens according to any one of claims 1 to 4, characterized in that: The following steps are involved: Step 1, determine the polar coordinate equation parameters of the ellipse; Step 2, designing the focal length and wave number of the modified hyperbolic lens; Step 3, design the spiral phase function; Step 4: superimposing the modified hyperbolic lens phase and the spiral phase to obtain a spiral elliptical lens phase, and converting the spiral elliptical lens phase into a height morphology of the processed material; Step 5: selectively polymerizing the processed material according to the height morphology to obtain a processed sample; Step 6: Develop and dry the sample to obtain the spiral elliptical lens.

6. The method for preparing a spiral elliptical lens according to claim 5, wherein: In step 3, the topological charge value of the spiral phase function is any integer.

7. The method for preparing a spiral elliptical lens according to claim 5, wherein: In step 4, the height profile of the processed material is expressed by the following formula: Among them, n p and n c are the refractive index of the material of the spiral elliptical lens and the refractive index of its environment respectively.

8. The method for preparing a spiral elliptical lens according to claim 5, wherein: In step 4, the processing material is photoresist.

9. The method for preparing a spiral elliptical lens according to claim 8, wherein: The step 5 further includes: drying the processed material to obtain a pre-processed sample of solid photoresist, placing the pre-processed sample on a nano-displacement stage of a femtosecond laser direct writing system, and performing selective polymerization through a focused femtosecond laser beam.

10. The method for preparing a spiral elliptical lens according to claim 8, wherein: In step 6, the unpolymerized photoresist is dissolved by placing the sample into a developing solution of the photoresist.

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