Spiral spectrum optimization method for transmission of petal-shaped vortex in ocean turbulence

Abstract

The invention discloses a spiral spectrum optimization method for transmission of a petal-shaped vortex in ocean turbulence. The spiral spectrum optimization method comprises the following steps: step 1, establishing a petal-shaped vortex light field expression carrying orbital angular momentum; 2, according to the ocean turbulence refractive index power spectrum, a power spectrum inversion method is adopted to obtain a random phase screen, and according to the ocean turbulence phase screen, a light field expression after the petal-shaped vortex is transmitted through turbulence is calculated; and 3, expanding the petal-shaped vortex influenced by turbulence into superposition of a series of spiral spectrums, and calculating and optimizing the petal-shaped vortex spiral spectrum. According to the method, the identification accuracy of the petal-shaped vortex is improved, and a theoretical basis and a new solution are provided for researching the transmission characteristics of the petal-shaped vortex in a complex environment and overcoming the turbulence effect influence in vortex optical communication application.

Description

Technical Field

[0001] The invention belongs to the field of optical technology, and in particular relates to a spiral spectrum optimization method for a petal vortex transmitted in ocean turbulence. Background Art

[0002] Since the 1990s, the scientific community has proposed a light beam carrying orbital angular momentum (OAM). After decades of continuous research, this beam has been widely used in various fields such as super-resolution imaging, particle manipulation, remote sensing, and lithography, especially in the field of optical communications. Orbital angular momentum theoretically has an infinite number of eigenstates, so compared with beams with only horizontal and vertical polarization states, beams carrying orbital angular momentum have more modes. In addition, thanks to the orthogonal characteristics between orbital angular momentums of different modes, orbital angular momentum has good multiplexing characteristics. At the same time, it is compatible with existing communication means and can greatly expand the capacity and spectrum efficiency of communication systems. Orbital angular momentum has been listed as one of the important key technologies for building a 6G communication network. Research on orbital angular momentum has covered electromagnetic bands such as microwaves, terahertz, mid-infrared, near-infrared and visible light.

[0003] Since the wavefront of the light beam carrying orbital angular momentum is spiral-shaped, the academic community calls the light carrying orbital angular momentum a vortex beam. Unlike the solid bright spot presented by the traditional laser spot, the vortex beam appears as a dark hollow structure. To use vortex beams for communication, it is necessary to accurately identify the modal state of the orbital angular momentum carried. However, the dark hollow structure determines that it is impossible to directly complete the identification through the shape of the beam itself. It is necessary to use cylindrical lenses, holes and slits of specific structures to complete the modal identification of orbital angular momentum, which increases the complexity of the communication system, and the detection effect is affected by the transmission environment. In recent years, researchers have designed a petal-shaped vortex with a petal-shaped spot shape based on the vortex beam. The orbital angular momentum modal information can be directly obtained by observing the petal-shaped vortex spot, thereby effectively avoiding the complex pattern recognition link at the receiving end of the communication system (Li Yongxu, Optics Communication, Vol. 510, 127931). It is worth noting that although the petal-shaped vortex has better anti-turbulence ability than the vortex beam, the light intensity of the light spot will inevitably decay under the influence of the transmission environment, and the petal-shaped light spot shape will be destroyed, which will lead to inaccurate orbital angular momentum information. Therefore, it is urgent to carry out relevant research on this issue to provide useful ideas and references for the application of orbital angular momentum optical communication. Summary of the invention

[0004] The purpose of the present invention is to provide a spiral spectrum optimization method for the transmission of a lobe-shaped vortex in ocean turbulence, which solves the problem that the light spot intensity of the existing lobe-shaped vortex is attenuated and the light spot morphology is destroyed after being affected by the transmission environment, resulting in inaccurate acquisition of orbital angular momentum information.

[0005] The technical solution adopted by the present invention is: a spiral spectrum optimization method for the transmission of petal vortices in ocean turbulence, and the specific operating steps are as follows:

[0006] Step 1: Establish the expression of the lobed vortex light field carrying orbital angular momentum;

[0007] Step 2: According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method, and the light field expression of the lobe vortex after passing through turbulence is calculated according to the ocean turbulence phase screen;

[0008] Step 3: Expand the lobed vortex affected by turbulence into a superposition of a series of spiral spectra, and calculate and optimize the spiral spectrum of the lobed vortex.

[0009] The present invention is also characterized in that:

[0010] Step 1 is as follows:

[0011] In the cylindrical coordinate system, the expression of the vortex beam carrying orbital angular momentum transmitted from free space to a distance z is:

[0012]

[0013] Where (ρ, φ) is the polar coordinate, ω0 is the beam waist radius, It represents the beam waist size of the light spot at the distance z. is the Rayleigh distance, λ is the wavelength of the light wave, p and l are the radial coefficient and orbital angular momentum mode coefficient of the vortex beam, ξ=arctan(z / z R ), k = 2π / λ is the wave number, R = z[1+(z R / z) 2 ] represents the radius of curvature, i represents the imaginary unit, |·| represents the modulus value, represents the Laguerre polynomial;

[0014] Decompose the vortex beam expression into two parts: amplitude and phase.

[0015] The vortex beam amplitude expression is:

[0016]

[0017] The phase part of the vortex beam is expressed as:

[0018]

[0019] Take the conjugate mode of the vortex beam, that is, set the orbital angular momentum mode to the opposite number, then the amplitude part of the conjugate mode expression remains unchanged, and the phase part Ψ * The expression is:

[0020]

[0021] In the formula, * represents the conjugate operation;

[0022] The vortex beam and its conjugate mode are coaxially superimposed, and the expression of the superimposed light field V(ρ,φ,z) is obtained as follows:

[0023]

[0024] In the formula,

[0025] Thus, the light field expression of the petal vortex is obtained, and its light intensity I(ρ,φ,z) is obtained by the following formula:

[0026] I(ρ,φ,z)=|V(ρ,φ,z)| 2 =4A 2 cos 2 (lφ) (6)

[0027] Step 2 is as follows:

[0028] The power spectrum function of ocean turbulence refractive index fluctuation is expressed as follows:

[0029]

[0030] Where κ is the spatial frequency, η is the microscale of ocean turbulence, and A T =1.863×10 -2 , A s =1.9×10 -4 , A TS =9.41×10 -3 , ε represents the energy dissipation rate of ocean turbulence, and its value range is 10 -10 m 2 / s 3 ~10 -1 m 2 / s 3 , χ T It represents the temperature variance dissipation rate of turbulence, and its value range is 10 -10 K 2 / s~10 -4 K 2 / s, w is the ratio of ocean turbulence caused by seawater temperature and salinity, ranging from -5 to 0, is the equivalent turbulence intensity parameter, δ=8.284(κη) 4 / 3 +12.978(κη) 2 ;

[0031] According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method. The phase screen phase is expressed as:

[0032]

[0033] In the formula, H(κ x ,κ y ) is a complex Gaussian random matrix, is the inverse Fourier transform, Re(·) represents the real part, κ x and κ y is the spatial frequency in the x-direction and the y-direction;

[0034] After the lobed vortex passes through turbulence, an additional random phase θ is added due to the turbulence effect. The light field expression of the lobed vortex after passing through turbulence is calculated based on the ocean turbulence phase screen:

[0035] E(ρ,φ,z)=V(ρ,φ,z)exp(ilθ) (9)

[0036] Step 3 is as follows:

[0037] The petal-shaped vortex affected by turbulence is expanded into a superposition of a series of spiral harmonics and decomposed into multiple different orbital angular momentum mode coefficients l j Combination of:

[0038]

[0039] In the formula, is the normalized expansion coefficient, and its expression is:

[0040]

[0041] From this, we can get the decomposed orbital angular momentum mode coefficient l j The corresponding harmonic energy is Find the ratio of each mode to the total energy, and you will get the distribution of the petal-shaped vortex spiral spectrum:

[0042]

[0043] in, is the orbital angular momentum mode coefficient l j The corresponding harmonic energy.

[0044] Step 3 The method for optimizing the petal-shaped vortex spiral spectrum is:

[0045] After obtaining the spiral spectrum distribution of the petal-shaped vortex, the value of l is taken according to the orbital angular momentum mode coefficient j <0,l j =0, l j >0, the spiral spectrum distribution is divided into three parts accordingly; first,j After taking the opposite number of the mode coefficients <0, superimpose the corresponding spiral spectrum on the mode coefficient l j >0, and all mode coefficients l in the original spiral spectrum j <0, all spectral energies are reset to zero; then find the superimposed mode coefficient l j >0 part of the spiral spectrum energy maximum corresponding to the orbital angular momentum mode value; finally, l j = 0 and the found mode coefficient l j >0, and the maximum spectral energy of l j =0 corresponding to the spectral energy is set to zero; after the above steps, the optimization of the petal-shaped vortex spiral spectrum is achieved.

[0046] The beneficial effects of the present invention are:

[0047] The spiral spectrum based on the lobe-shaped vortex of the present invention has a special distribution form, and the spiral spectrum gradually decays from near to far with respect to the actual transmission orbital angular momentum mode coefficient and its conjugate mode energy; based on the turbulence random phase screen theory, the present invention constructs the light field expression of the lobe-shaped vortex in the ocean turbulence, calculates the spiral spectrum distribution of the lobe-shaped vortex through the ocean turbulence, and further designs a spiral spectrum optimization method, which improves the accuracy of lobe-shaped vortex identification, and provides a theoretical basis and a new solution for studying the transmission characteristics of the lobe-shaped vortex in a complex environment and overcoming the influence of turbulence effects in vortex optical communication applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a two-dimensional light intensity distribution diagram of the cross section of the vortex beam in Example 2;

[0049] Figure 2 is a two-dimensional light intensity distribution diagram of the cross section of the petal-shaped vortex in Example 2;

[0050] Figure 3 This is the spiral spectrum distribution diagram of the petal-shaped vortex (p=2, l=3) after being transmitted through the ocean turbulence in Example 3;

[0051] Figure 4 It is a flow chart of the method for optimizing the petal-shaped vortex spiral spectrum of the present invention;

[0052] Figure 5 This is the spiral spectrum distribution diagram of the ideal state of the petal-shaped vortex in Example 3 that is not affected by turbulence;

[0053] Figure 6 These are the spiral spectrum distribution diagrams before and after optimization of the petal-shaped vortex after transmission in ocean turbulence. DETAILED DESCRIPTION

[0054] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] Example 1

[0056] Step 1: Establish the expression of the lobed vortex light field carrying orbital angular momentum;

[0057] Step 2: According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method, and the light field expression of the lobe vortex after passing through turbulence is calculated according to the ocean turbulence phase screen;

[0058] Step 3: Expand the lobed vortex affected by turbulence into a superposition of a series of spiral spectra, and calculate and optimize the spiral spectrum of the lobed vortex.

[0059] Example 2

[0060] The spiral spectrum optimization method of the petal vortex transmitted in ocean turbulence of the present invention has the following specific operating steps:

[0061] Step 1: Establish the expression of the lobed vortex light field carrying orbital angular momentum;

[0062] In the cylindrical coordinate system, the expression for the free space transmission of the vortex beam carrying orbital angular momentum to a distance z is:

[0063]

[0064] Where (ρ, φ) is the polar coordinate, ω0 is the beam waist radius, It represents the beam waist size of the light spot at the distance z. is the Rayleigh distance, λ is the wavelength of the light wave, p and l are the radial coefficient and orbital angular momentum mode coefficient of the vortex beam, ξ=arctan(z / z R ), k = 2π / λ is the wave number, R = z[1+(z R / z) 2 ] represents the radius of curvature, i represents the imaginary unit, and the symbol “|·|” represents the modulus value. represents the Laguerre polynomial.

[0065] like Figure 1 As shown, the cross-sectional two-dimensional light intensity distribution of the vortex beam with a wavelength of λ=532nm and a waist radius of ω0=5mm after the transmission distance z=50m is shown when the radial coefficient is p=0 and p=2, and the orbital angular momentum mode coefficient is l=1,2,3,4. Figure 1 It can be seen that the vortex beam spot presents a dark hollow structure, and the number of bright rings in the spot is equal to p+1. Therefore, the radial parameters of the vortex beam can be obtained by directly observing the spot distribution. Although the spot size is positively correlated with the orbital angular momentum mode value, the orbital angular momentum mode coefficient cannot be directly obtained.

[0066] Decompose the vortex beam expression into two parts: amplitude and phase.

[0067] The vortex beam amplitude expression is:

[0068]

[0069] The phase part of the vortex beam is expressed as:

[0070]

[0071] Take the conjugate mode of the vortex beam, that is, set the orbital angular momentum mode to the opposite number, then the amplitude part of the conjugate mode expression remains unchanged, and the phase part Ψ * The expression is:

[0072]

[0073] In the formula, the symbol “*” represents a conjugate operation.

[0074] By coaxially superimposing the vortex beam and its conjugate mode, the expression V(ρ,φ,z) after superposition can be obtained as follows:

[0075]

[0076] In the formula

[0077] Thus, the light field expression of the petal vortex is obtained, and its light intensity I(ρ,φ,z) can be obtained by the following formula:

[0078] I(ρ,φ,z)=|V(ρ,φ,z)| 2 =4A 2 cos 2 (lφ) (6)

[0079] Based on the lobed vortex intensity I(ρ,φ,z), the parameter values ​​in the formula are Figure 1 Same, get Figure 2 The two-dimensional light intensity distribution diagram of the cross section of the petal-shaped vortex is shown in the figure. Obviously, unlike the dark hollow light spot of the vortex beam, the petal-shaped vortex light spot presents a "petal"-shaped bright spot morphology. When the radial coefficient p = 0, there is only one layer of petal-shaped structure. When p ≠ 0, the number of petal-shaped layers is equal to p + 1. Regardless of whether the number of petal-shaped layers is single or multi-layer, the number of petal-shaped bright spots on each layer is equal to twice the size of the orbital angular momentum mode coefficient 2|l|. Therefore, by observing the petal-shaped vortex light spot, the radial coefficient and orbital angular momentum mode coefficient information can be directly obtained at the same time.

[0080] Step 2: According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method, and the light field expression of the lobed vortex after passing through the turbulence is calculated according to the ocean turbulence phase screen;

[0081] The power spectrum function of ocean turbulence refractive index fluctuation is expressed as follows:

[0082]

[0083] Where κ is the spatial frequency (κ is the superposition of the spatial frequencies in the x-direction and the y-direction), η is the microscale of ocean turbulence, and A T =1.863×10 -2 , A s =1.9×10 -4 , A TS =9.41×10 -3 , ε represents the energy dissipation rate of ocean turbulence, and its value range is 10 -10 m 2 / s 3 ~10 -1 m 2 / s 3 , χ T It represents the temperature variance dissipation rate of turbulence, and its value range is 10 -10 K 2 / s~10 -4 K 2 / s, w is the ratio of ocean turbulence caused by seawater temperature and salinity, ranging from -5 to 0, is the equivalent turbulence intensity parameter, δ=8.284(κη) 4 / 3 +12.978(κη) 2 .

[0084] According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method. The phase screen phase is expressed as:

[0085]

[0086] In the formula, H(κ x ,κ y ) is a complex Gaussian random matrix, is the inverse Fourier transform, Re(·) represents the real part, κ x and κ y is the spatial frequency in the x and y directions.

[0087] After the lobed vortex passes through turbulence, an additional random phase θ is added due to the turbulence effect. The light field expression of the lobed vortex after passing through turbulence is calculated based on the ocean turbulence phase screen:

[0088] E(ρ,φ,z)=V(ρ,φ,z)exp(ilθ) (9)

[0089] Step 3: Expand the petal-shaped vortex affected by turbulence into a superposition of a series of spiral spectra, calculate and optimize the petal-shaped vortex spiral spectrum. The specific steps are as follows:

[0090] The petal-shaped vortex affected by turbulence is expanded into a superposition of a series of spiral harmonics and decomposed into multiple different orbital angular momentum mode coefficients l j Combination of:

[0091]

[0092] In the formula, is the normalized expansion coefficient, and its expression is:

[0093]

[0094] From this we can get the orbital angular momentum mode coefficient l j The corresponding harmonic energy is Find the ratio of each mode to the total energy, and you will get the spiral spectrum distribution of the beam:

[0095]

[0096] Example 3

[0097] Without loss of generality, Figure 3 The p=2, l=3 vortex lobe is shown in w=-3,η=10 -3 The spiral spectrum distribution obtained after the transmission of z = 50m in the ocean turbulence of l m. It can be clearly seen from the figure that, affected by the turbulent transmission environment, the lobe vortex produces the orbital angular momentum mode dispersion phenomenon, and the spiral spectrum energy changes from l j = -3 and l j =3The two modes gradually decay from near to far to other modes. We finally read the mode coefficient corresponding to the highest energy spectrum from the spiral spectrum distribution as the identification result. Figure 3 The distribution law of the spiral spectrum shows that the mode coefficient and its conjugate mode spectrum energy that we want to identify are higher than the other diffuse modes. However, as the turbulence intensity increases, the proportion of the diffuse mode spectrum energy will gradually increase. In order to improve the accuracy of the orbital angular momentum pattern recognition carried by the petal vortex, a design Figure 4 The spiral spectrum energy optimization algorithm is shown.

[0098] Figure 4 The spiral spectrum energy optimization algorithm process is given. The light field of the petal vortex after turbulent transmission is decomposed into spiral harmonics to obtain the spiral spectrum distribution P(l). The mode coefficient in the spiral spectrum is read as l j The spiral spectrum energy P(l j ), the discriminant mode coefficient l j Is it less than zero? If it meets the judgment condition, the mode coefficient is lj The spiral spectrum energy P(l j ) added to the model coefficient is -l j The corresponding spiral spectrum energy P(-l j ) on the surface, the added energy is l = -l j The spectral energy value is P(l=-l j )=P(l j )+P(-l j ), then P(l j ) is reset to zero; if it does not meet the discrimination condition, it enters the second discrimination condition, and the discrimination mode coefficient l j Is it equal to zero? If not, then l j The corresponding spectral energy P(l j ) is assigned to P(l=l j )=P(l j ), that is, the spectral energy remains unchanged; if the second judgment condition is met, the mode coefficient corresponding to the maximum spectral energy is first found and recorded as l0, and then l j = 0 spectral energy P(l j =0) is superimposed on the spectrum energy P(l0) of l0 to obtain P(l=l0), and P(l j =0) is reset to zero; after completing the above process, the complete optimized spiral spectrum P(l) is obtained.

[0099] In order to verify the effect of the optimized petal-shaped vortex spiral spectrum, Figure 5 The spiral spectrum distribution of the petal vortex in the ideal transmission state without the influence of turbulence is given. Figure 6 The spiral spectra before and after optimization in ocean turbulence are given for different radial coefficients and orbital angular momentum mode coefficients. Here, the orbital angular momentum mode coefficient l varies from -16 to 16, the radial coefficient p = 0 or p = 2, and the other parameter settings are consistent with the above. Figure 6 (a) and Figure 6 (c) The spiral spectrum distribution of the petal vortex with radial coefficient p = 0 before and after optimization in ocean turbulence, Figure 6 (b) and Figure 6 (d) is the spiral spectrum distribution of the petal vortex with radial coefficient p = 2 before and after optimization in ocean turbulence. Figure 5 As shown in the figure, ideally, the transmission mode coefficients and the receiving mode coefficients are exactly the same, that is, the spiral spectrum energy is completely concentrated on the diagonal line from the lower left to the upper right in the figure, but due to the influence of turbulence, the receiving mode diffuses toward the non-transmission mode. Figure 6 (a) and Figure 6 (b) Unoptimized spiral spectrum, the mode dispersion phenomenon is particularly obvious, and the transmission mode is almost unrecognizable, but Figure 6 (c) and Figure 6(d) shows the optimized spiral spectrum. The spectral energy is mainly concentrated on the diagonal line. The spiral spectrum is significantly improved, so it is easy to accurately identify the transmission mode coefficients.

[0100] The above content is only one embodiment of the present invention, and the present invention should not be considered to be limited to these descriptions. For those skilled in the art, several modifications and substitutions can be made without departing from the principle of the present invention, and these should all be included in the scope of protection of the present invention.

Claims

1. A spiral spectrum optimization method for the transmission of petal vortices in ocean turbulence, characterized in that: The specific steps are as follows: Step 1: Establish the expression of the lobed vortex light field carrying orbital angular momentum; Step 2: According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method, and the light field expression of the lobe vortex after passing through turbulence is calculated according to the ocean turbulence phase screen; Step 3: Expand the lobed vortex affected by turbulence into a superposition of a series of spiral spectra, and calculate and optimize the spiral spectrum of the lobed vortex.

2. The spiral spectrum optimization method for the transmission of petal-shaped vortices in ocean turbulence according to claim 1 is characterized in that: Step 1 is as follows: In the cylindrical coordinate system, the expression of the vortex beam carrying orbital angular momentum transmitted from free space to a distance z is: Where (ρ, φ) is the polar coordinate, ω0 is the beam waist radius, It represents the beam waist size of the light spot at the distance z. is the Rayleigh distance, λ is the wavelength of the light wave, p and l are the radial coefficient and orbital angular momentum mode coefficient of the vortex beam, ξ=arctan(z / z R ), k = 2π / λ is the wave number, R = z[1+(z R / z) 2 ] represents the radius of curvature, i represents the imaginary unit, |·| represents the modulus value, represents the Laguerre polynomial; Decompose the vortex beam expression into two parts: amplitude and phase. The vortex beam amplitude expression is: The phase part of the vortex beam is expressed as: Take the conjugate mode of the vortex beam, that is, set the orbital angular momentum mode to the opposite number, then the amplitude part of the conjugate mode expression remains unchanged, and the phase part Ψ * The expression is: In the formula, * represents the conjugate operation; The vortex beam and its conjugate mode are coaxially superimposed, and the expression of the superimposed light field V(ρ,φ,z) is obtained as follows: In the formula, Thus, the light field expression of the petal vortex is obtained, and its light intensity I(ρ,φ,z) is obtained by the following formula: I(ρ,φ,z)=|V(ρ,φ,z)| 2 =4A 2 cos 2 (lφ) (6).

3. The spiral spectrum optimization method for the transmission of petal-shaped vortices in ocean turbulence according to claim 1 is characterized in that: Step 2 is as follows: The power spectrum function of ocean turbulence refractive index fluctuation is expressed as follows: Where κ is the spatial frequency, η is the microscale of ocean turbulence, and A T =1.863×10 -2 , A s =1.9×10 -4 , A TS =9.41×10 -3 , ε represents the energy dissipation rate of ocean turbulence, and its value range is 10 -10 m 2 / s 3 ~10 -1 m 2 / s 3 , χ T It represents the temperature variance dissipation rate of turbulence, and its value range is 10 -10 K 2 / s~10 -4 K 2 / s, w is the ratio of ocean turbulence caused by seawater temperature and salinity, ranging from -5 to 0, is the equivalent turbulence intensity parameter, δ=8.284(κη) 4 / 3 +12.978(κη) 2 ; According to the power spectrum of ocean turbulence refractive index, the random phase screen is obtained by using the power spectrum inversion method. The phase screen phase is expressed as: In the formula, H(κ x ,κ y ) is a complex Gaussian random matrix, is the inverse Fourier transform, Re(·) represents the real part, κ x and κ y is the spatial frequency in the x and y directions; After the lobed vortex passes through turbulence, an additional random phase θ is added due to the turbulence effect. The light field expression of the lobed vortex after passing through turbulence is calculated based on the ocean turbulence phase screen: E(ρ,φ,z)=V(ρ,φ,z)exp(ilθ) (9).

4. The spiral spectrum optimization method for the transmission of petal-shaped vortices in ocean turbulence according to claim 1 is characterized in that: Step 3 is as follows: The petal-shaped vortex affected by turbulence is expanded into a superposition of a series of spiral harmonics and decomposed into multiple different orbital angular momentum mode coefficients l j Combination of: In the formula, is the normalized expansion coefficient, and its expression is: From this, we can get the decomposed orbital angular momentum mode coefficient l j The corresponding harmonic energy is Find the ratio of each mode to the total energy, and you will get the distribution of the petal-shaped vortex spiral spectrum: in, is the orbital angular momentum mode coefficient l j The corresponding harmonic energy.

5. The spiral spectrum optimization method for the transmission of petal-shaped vortices in ocean turbulence according to claim 1 is characterized in that: Step 3 The method for optimizing the petal-shaped vortex spiral spectrum is: After obtaining the spiral spectrum distribution of the petal-shaped vortex, the value of l is taken according to the orbital angular momentum mode coefficient j <0,l j =0, l j >0, the spiral spectrum distribution is divided into three parts accordingly; first, j After taking the opposite number of the mode coefficients <0, superimpose the corresponding spiral spectrum on the mode coefficient l j >0, and all mode coefficients l in the original spiral spectrum j <0, all spectral energies are reset to zero; then find the superimposed mode coefficient l j >0 part of the spiral spectrum energy maximum corresponding to the orbital angular momentum mode value; finally, l j = 0 and the found mode coefficient l j >0, and the maximum spectral energy of l j = 0 corresponding to the spectral energy is set to zero; After the above steps, the optimization of the petal-shaped vortex spiral spectrum is achieved.

Images