Method for measuring topological charge of fractional order vortex beam by using spinning beam phase

Abstract

A method for measuring the topological charge of a fractional order vortex light beam by using a spin light beam phase comprises the following steps: modulating the fractional order vortex light beam by using the spin light beam phase, modulating the electric field distribution of the light beam, and obtaining the far-field light intensity distribution of the fractional order vortex light beam modulated by the spin light beam phase through two-dimensional fast Fourier transform; and performing cross-correlation calculation on far-field light intensity distribution of the fractional order vortex light beam subjected to phase modulation of the spinning light beam and the adjacent integer order vortex light beam. Along with the increase of the topological charge, the central light intensity of the fractional order vortex light beam subjected to spin light beam phase modulation is linearly changed, and finally, the central light intensity has the characteristic of linear change along with the increase of the fractional topological charge, so that the accurate measurement of the fractional order topological charge is realized. According to the method, the quantitative relation between the fractional topological charge and the far-field light intensity distribution is established by using the spin beam phase, the fractional order vortex beam topological charge can be measured with the resolution of 0.1, and the method is suitable for the fields of optical control, communication, imaging and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of fractional-order vortex beam topological charge measurement, and in particular to a method for accurately measuring the topological charge of a fractional-order vortex beam by utilizing the phase of a spin beam. Background Art

[0002] The topological charge of a vortex beam represents the number of times the light wavefront rotates around a phase singularity and is a key parameter describing its wavefront phase spiral structure, orbital angular momentum quantization, and topological invariance. When the value of the topological charge is fractional, the corresponding vortex beam is called a fractional-order vortex beam. Compared with integer-order vortex beams, fractional-order vortex beams have different mode distributions and show broad application prospects in fields such as particle manipulation, optical communications, optical imaging, and optical encryption. In these applications, accurately measuring the fractional topological charge is crucial, especially in the fields of optical communications and optical encryption.

[0003] To measure the fractional topological charge, several methods have been proposed. One basic measurement method involves interfering a fractional vortex beam with its conjugate beam [Opt. Commun. 334, 235-239 (2015)], and identifying the fractional topological charge by the ratio of the peak light intensities after interference. However, the measurement accuracy of this method depends on the interferometer, and adjusting the interferometer to achieve high-precision measurement is very difficult. In addition, the topological charge of a fractional vortex beam can also be measured by the change in light intensity after the mutual conversion between the Hermite-Gaussian mode and the Laguerre-Gaussian mode [Appl. Phys. Lett. 108, 111108 (2016)]. However, the mode converter has strict matching requirements for the input beam waist, and its stability depends on high-precision mechanical assembly. In addition to these methods, the fractional topological charge can be measured by diffracting the fractional vortex beam through an angle grating and finally analyzing its orbital angular momentum spectrum [Opt. Express 33, 553-561 (2025)]. However, this method requires a complex experimental setup (two spatial light modulators), which limits its application. The aforementioned measurement methods suffer from insufficient resolution, reliance on precision mechanical assembly, and the need for a complex experimental setup, making it impossible to accurately measure the topological charge of fractional vortex beams.

[0004] In summary, there is currently a lack of a simple and effective method to accurately measure the topological charge of fractional vortex beams. Summary of the Invention

[0005] To address these technical issues, the present invention provides a simple, stable, and precise method for measuring the topological charge of a fractional vortex beam. This method uses the phase of the spinning beam to establish a quantitative relationship between the fractional topological charge and the far-field intensity distribution. This method can measure the topological charge of a fractional vortex beam with a resolution of 0.1, making it suitable for applications in optical manipulation, communications, and imaging.

[0006] The technical solution adopted in the present invention is: A method for measuring the topological charge of a fractional vortex beam using a spin beam phase, comprising the following steps: S1. First, generate the spin beam phase, which can be expressed as: Where ρ is the radial coordinate, is the azimuth angle, ρ0 is the normalization factor of the radial coordinate, a is the phase modulation amplitude, n is the spin sign parameter, and b is the spin morphology index. a, n, and b are used to adjust the phase distribution of the spin beam phase; S2. Then, the fractional vortex beam is phase-modulated using the spin beam. The electric field distribution of the modulated beam can be expressed as: Where l represents the topological charge of the fractional vortex beam, A0 and w represent the amplitude and beam waist width of the fractional vortex beam, respectively. Then, the far-field intensity distribution of the fractional vortex beam modulated by the spin beam phase is obtained through two-dimensional fast Fourier transform. S3. The transmittance function of the digital hologram of the fractional vortex beam phase-modulated by the spin beam can be expressed as: Among them, i is the imaginary unit, angle() is the phase function, exp{} is the exponential function, is the Fourier transform function, is the fractional vortex beam phase-modulated by the spin beam, is the phase of the blazed grating, where d is the period of the blazed grating. The blazed grating is selected to maximize the diffraction efficiency of the +1 order image reconstructed by the hologram; In this step, when parallel light is irradiated on the hologram of the spin beam phase modulated fractional vortex beam, after passing through the lens, the far-field light intensity distribution of the spin beam phase modulated fractional vortex beam can be obtained at its focal plane. S4. Perform cross-correlation calculation on the far-field light intensity distribution of the fractional-order vortex beam phase-modulated by the spin beam and the adjacent integer-order vortex beam to complete the measurement process. In step S4 of this scheme, it can be found that as the topological charge increases, the central intensity of the fractional vortex beam modulated by the spin beam phase modulates a linear change. Finally, the central intensity exhibits a linear change with increasing fractional topological charge, thus enabling accurate measurement of the fractional topological charge.

[0007] Technical effects of the present invention: This paper proposes a method for measuring the topological charge of a fractional vortex beam using spin beam phase modulation. A fractional vortex beam with the topological charge to be measured is subjected to spin beam phase modulation to establish a quantitative relationship between the fractional topological charge and the far-field light intensity distribution, enabling a simple and accurate measurement of the fractional topological charge. Specifically, a cross-correlation calculation is performed on the far-field light intensity distribution of the spin beam phase-modulated fractional vortex beam and the adjacent integer-order vortex beam, thereby achieving accurate measurement of the fractional topological charge with a resolution of 0.1. The proposed method stands out for its simplicity, requiring no complex experimental setup or precision mechanical assembly, while maintaining high accuracy and high measurement efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 The figure shows a hologram of a fractional-order vortex beam with spin beam phase modulation generated by the method of the present invention, with a topological charge l=3.1-3.4 and a step size of 0.1. Figure 2 is Figure 1 The hologram corresponds to the far-field intensity map of the fractional vortex beam generated by phase modulation of the spin beam. DETAILED DESCRIPTION

[0009] This method utilizes the principles of computational holography to generate a hologram of a fractional vortex beam modulated by the phase of a spin beam through computer encoding. The hologram is then reconstructed by diffraction, and its far-field intensity distribution is analyzed through cross-correlation to measure the topological charge of the fractional vortex beam. This method offers the advantages of high precision, simplified equipment, and strong interference resistance.

[0010] A method for measuring the topological charge of a fractional vortex beam using a spin beam phase is provided. The steps are as follows: First, a spin beam phase is generated, which can be expressed as: Where ρ is the radial coordinate, is the azimuth angle, ρ0 is the normalization factor of the radial coordinate, a is the phase modulation amplitude, n is the spin sign parameter, and b is the spin morphology index. a, n, and b are used to adjust the phase distribution of the spin beam phase. In this embodiment, a = 200, n = -1, and b = 2. Then, the fractional vortex beam is phase-modulated by the spin beam, and the electric field distribution of the modulated beam can be expressed as: Where l represents the topological charge of the fractional vortex beam, A0 and w represent the amplitude and beam waist width of the fractional vortex beam, respectively. In this embodiment, the beam amplitude A0 = 1, and the beam waist radius w = 3 mm. The far-field intensity distribution of the fractional vortex beam phase-modulated by the spinning beam is then obtained through a two-dimensional fast Fourier transform. The transmittance function of the digital hologram of the fractional-order vortex beam modulated by the spin beam phase can be expressed as: Among them, i is the imaginary unit, angle() is the phase function, exp{} is the exponential function, is the Fourier transform function, is the fractional vortex beam phase-modulated by the spin beam, is the phase of the blazed grating, where d is the period of the blazed grating. In this embodiment, the grating period d = 25.6 μm. The blazed grating is selected to maximize the diffraction efficiency of the +1-order image reproduced by the hologram. When parallel light is irradiated on the hologram of the fractional-order vortex beam modulated by the spin beam phase, after passing through the lens (in this embodiment, the lens focal length f = 150 mm), the far-field light intensity distribution of the fractional-order vortex beam modulated by the spin beam phase can be obtained at its focal plane. The far-field intensity distributions of the fractional-order vortex beam modulated by the spin beam phase modulation and the adjacent integer-order vortex beam were then cross-correlated. It was found that the central intensity of the fractional-order vortex beam modulated by the spin beam phase modulation changes linearly with increasing topological charge. Finally, the central intensity exhibits a linear variation with increasing fractional topological charge, enabling precise measurement of fractional topological charge.

[0011] The hologram of the fractional vortex beam with phase modulation of the spin beam generated by the method of the present invention is as follows: Figure 1 As shown by Figure 1 The far-field intensity distribution of the light beam generated by the hologram is as follows: Figure 2 As shown in Figure 3, the far-field intensity distribution changes linearly with the increase of fractional topological charge. Quantifying this linear change based on the cross-correlation operation can measure the topological charge of the fractional vortex beam. Example

[0012] In this embodiment, the selected continuous wave solid-state laser has a wavelength of 532 nm and a power of 50 mW. The spatial light modulator is a reflective spatial light modulator: HOLOEYE PLUTO-VIS-016, with a size of 1902 pixels × 1080 pixels, a pixel size of 8 μm × 8 μm, and a fill factor of 93%. The hologram of the fractional vortex beam generated by the phase modulation of the spin beam is input into the spatial light modulator via a personal computer. The hologram is as follows: Figure 1As shown, the size is 1080 pixels × 1080 pixels, the phase distribution parameter is n = -1, the topological charge l = 3.1-3.4, and the step size is 0.1. The camera is a professional CCD camera Basler acA1600-60gc with a pixel size of 4.5μm × 4.5μm. The CCD camera records the far-field luminosity distribution of the fractional-order vortex beam modulated by the spin beam phase, as shown in Figure 2 As shown in Figure 2, the fractional vortex beam with the topological charge to be measured undergoes spin beam phase modulation, is reconstructed by diffraction of a hologram loaded by a spatial light modulator, and is then Fourier transformed using a lens. The far-field intensity distribution of the spin beam phase-modulated fractional vortex beam is then recorded using a CCD camera. Finally, the topological charge of the fractional vortex beam is measured by performing cross-correlation calculation on the far-field intensity distribution.

[0013] In summary, the present invention proposes a specific design and implementation scheme for accurately measuring the topological charge of a fractional vortex beam. This method utilizes a spinning beam to phase-modulate the fractional vortex beam to be measured, performs cross-correlation calculations on its far-field intensity distribution, and accurately measures the fractional topological charge by measuring the linear variation of the central light intensity. This method establishes a quantitative relationship between the fractional topological charge and the far-field intensity distribution, enabling the measurement of the topological charge of a fractional vortex beam with a resolution of 0.1, without the need for complex experimental setup or precision mechanical assembly, while maintaining high accuracy and measurement efficiency.

[0014] The above-described method for generating fractional vortex beam holograms using spin beam phase modulation and for measuring fractional topological charge represents only one specific embodiment of the present invention and should not be construed as limiting the scope of protection of the present invention. It should be noted that, without departing from the basic concept of the present invention, a person skilled in the art may make various variations and improvements to the specific implementation details proposed in this patent, all of which fall within the scope of protection of the present invention.

Claims

1. A method for measuring the topological charge of a fractional vortex beam using the phase of a spin beam, characterized by: Here are the steps: S1. First, generate the spin beam phase, which is expressed as: Where ρ is the radial coordinate, is the azimuth angle, ρ0 is the normalization factor of the radial coordinate, a is the phase modulation amplitude, n is the spin sign parameter, and b is the spin morphology index; S2. Then, the fractional vortex beam is phase-modulated using the spin beam. The electric field distribution expression of the modulated beam is: Where l represents the topological charge of the fractional vortex beam, A0 and w represent the amplitude and beam waist width of the fractional vortex beam, respectively; S3, the transmittance function of the digital hologram of the fractional vortex beam phase-modulated by the spin beam is expressed as: Among them, i is the imaginary unit, angle() is the phase function, exp{} is the exponential function, is the Fourier transform function, is a fractional vortex beam with phase modulation of the spin beam; S4. Perform cross-correlation calculation on the far-field light intensity distribution of the fractional-order vortex beam phase-modulated by the spin beam and the adjacent integer-order vortex beam to complete the measurement process.

2. The method for measuring the topological charge of a fractional vortex beam using a spin beam phase according to claim 1, characterized in that: In step S3, the phase expression of the blazed grating is: where d is the period of the blazed grating.

3. The method for measuring the topological charge of a fractional vortex beam using a spin beam phase according to claim 1, characterized in that: In step S3, when parallel light is irradiated on the hologram of the spin beam phase modulated fractional vortex beam, after passing through the lens, the far-field light intensity distribution of the spin beam phase modulated fractional vortex beam can be obtained at its focal plane.

4. The method for measuring the topological charge of a fractional vortex beam using a spin beam phase according to claim 1, characterized in that: In step S4, as the topological charge increases, the central light intensity of the fractional-order vortex beam modulated by the spin beam phase changes linearly. Finally, the central light intensity has the characteristic of linear change as the fractional topological charge increases, thereby realizing the accurate measurement of the fractional topological charge.

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