CN117394914A - Method for improving transmitting efficiency of maca antenna by utilizing perfect vortex beam - Google Patents

Abstract

The invention discloses a method for improving the transmitting efficiency of a maca antenna by utilizing perfect vortex beams, which comprises the following steps: step 1: establishing a perfect vortex light beam diffraction light field model through the Marca antenna according to a Collins formula and an ABCD transmission matrix of the Marca antenna; step 2: utilizing the diffraction model established in the step 1 to theoretically deduce a diffraction light field expression of the POV light beam after passing through the maca antenna; step 3: and calculating the emission efficiency of the maca antenna according to the geometrical optical analysis method. The method is used for solving the problem of energy loss caused by shielding of the secondary reflector of the maca antenna.

Description

Method to improve the emission efficiency of Maca antenna by using perfect vortex beam

Technical field

The invention belongs to the technical field of wireless optical communication, and specifically relates to a method for improving the emission efficiency of a Maca antenna by utilizing a perfect vortex beam.

Background technique

With the rapid development of wireless communication technology, modern communications have gradually put forward higher and higher requirements for free space optical communication (FSO) technology. Optical antennas play an important role as an essential component in FSO systems. In the FSO system, the optical antenna plays the role of collimation and focusing respectively in the transmission and reception of optical signals. Therefore, the emission efficiency of the optical antenna will directly determine the communication quality of the FSO system.

In the selection of optical antennas for the FSO system, the Cassegrain system is a typical double-reflecting telephoto objective lens, and the entire system has no chromatic aberration. The primary reflection is generally a paraboloid, and the secondary reflector is generally a convex hyperboloid mirror. The Maksutov-Cassegrain telescope (referred to as the Maksutov-Cassegrain antenna) is a telephoto objective lens improved on the structure of the Cassegrain system. It is based on a spherical reflector and adds refraction for correcting aberrations. The original piece becomes a fold-back structure. Compared with the Cassegrain system, since each component in the Maca antenna is spherical, the manufacturing cost can be reduced. Based on the advantages of the Maca antenna, relevant research has analyzed and explored the emission efficiency of different types of light sources through the Maca antenna. Some studies have found that for uniformly distributed light sources, the energy loss caused by the sub-reflector of the Maca antenna is more than 30%; for Gaussian distributed laser light sources, the energy loss can reach 50% or more. The light spots emitted by the Maca antenna are distributed in a ring, which is a serious problem for wireless optical communications.

In recent years, perfect optical vortex (POV) beams have the advantage that the bright ring radius does not change with the topological charge. They have important application value in fields such as particle manipulation and quantum communications. Therefore, from the physical structure The perfect vortex beam can match the Marka antenna because its light intensity is distributed in a ring shape, but there is no research to explore and analyze the diffraction characteristics and emission efficiency of the perfect vortex beam after passing through the Marka antenna.

Contents of the invention

The purpose of the present invention is to provide a technical method for improving the transmission efficiency of the Maca antenna by using a perfect vortex beam, so as to solve the problem of energy loss caused by the obstruction of the Maca antenna's sub-reflector.

The technical solution adopted by the present invention is to use a perfect vortex beam to improve the emission efficiency of the Maca antenna, specifically:

Step 1: Establish the light field model of the perfect vortex beam diffracted by the Marka antenna based on the Collins formula and the ABCD transmission matrix of the Marka antenna;

Step 2: Using the diffraction model established in step 1, theoretically derive the expression of the diffraction light field of the POV beam after passing through the Maca antenna;

Step 3: Calculate the emission efficiency of the Maca antenna according to the geometric optics analysis method.

The present invention is also characterized in that,

The specific process of step 1 is as follows:

Step 1.1. Give the light field expression of the light source at the emission end, that is, the expression of the light field E(r,θ,0) of the POV beam on the distance z=0 plane is:

where E ₀ is the amplitude constant, m is the topological charge, i is an imaginary number, I _m is the first m-order modified Bessel function; ω ₀ is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively Equal to 2ω ₀ and R, r and θ variables are the radial and azimuthal coordinates of the cylindrical coordinate system;

Step 1.2. According to the Collins formula, after the perfect vortex beam passes through the Macca antenna, the diffraction light field on the observation plane for:

Among them, z is the transmission distance, k=2π/λ is the wave number, and λ is the wavelength; H(r) is the transmittance function of the Maca antenna; Represents the two-dimensional vector on the plane at z>0 in the cylindrical coordinate system. The parameters A, B, C, and D are the ABCD transmission matrices of the Maca antenna optical system;

Step 1.3. The Maca antenna is mainly composed of the second barrier, the first barrier, the primary reflector, the secondary reflector and the meniscus correction mirror. The catadioptric structure makes the Maca antenna compact, and a lens system with a large aperture and long focal length can be formed through a smaller size. The working principle of the Maca antenna as a transmitting antenna is: the secondary reflector reflects the beam emitted by the light source for the first time. The reflected beam is incident on the surface of the primary reflector, and then the beam reflected by the primary reflector is processed by the correction mirror. Correct and transmit the Maca antenna system to achieve directional emission. When studying the beam passing through the Maca antenna, the Maca antenna is equivalent to a lens system; the ABCD transmission matrix and transmittance function H(r) of this lens system are:

H(r)＝H ₁ (r)-H ₂ (r) (4)

In formula (4), the expressions of H ₁ (r) and H ₂ (r) are as follows:

Among them, f is the focal length of the equivalent lens, Δz = (zf)/f; D ₀ is the diameter of the meniscus correction mirror of the Maca antenna optical system, d ₀ is the diameter of the sub-reflector of the Maca antenna optical system, A _α , B _α is the coefficient, T=10;

Substituting equations (1), (4), (5), and (6) into equation (2), we can get the diffracted light field on the observation plane at distance z for:

In step 1.3, A _α and B _α are coefficient values as shown in Table 1:

Table 1A _α , B _α are coefficient values

The specific process of step 2 is as follows:

Step 2.1, with the help of formula:

Substituting the parameters in the diffraction light field on the observation plane at distance z obtained in formula (7), we can get:

Step 2.2, use the integral formula:

Integrate the parameter θ in equation (9) and sort it out:

Step 2.3, from the formula

J _-α (x)＝(-1) ^α J _α (x) (12)

Transform (11) into:

Step 2.4, use the integral formula:

Integrating r in equation (13), the diffraction light field on the observation plane can be obtained as:

in,

The specific process of step 3 is as follows: According to the analysis method of geometric optics, the emission efficiency of the Maca antenna is defined as:

Among them, P ₀ is the total optical power incident on the end face of the Maca antenna, P is the total optical power on the detection plane; I ₀ (x ₀ , y ₀ , 0) is the light intensity of the initial POV beam, I (x, y ,z) is the light intensity of the diffracted light field on the observation plane; the light intensity I ₀ of the initial POV beam can be obtained from the POV beam light field expression in formula (1), that is:

I ₀ =<E(r,θ,0)·E ^* (r,θ,0)> (18)

The light intensity I of the diffracted light field on the observation plane can be determined by the light field at distance z in formula (15) Obtain, that is:

The beneficial effects of the present invention are:

The present invention utilizes the dark hollow spatial distribution structure of the perfect vortex beam and the characteristic that the bright ring radius does not change with the topological charge. It can perfectly match the Maka antenna structure in terms of spatial distribution and select the appropriate parameters for the perfect vortex beam radius. In the case of any topological charge, a perfect vortex beam can directly avoid the blocking problem of the Marka antenna's sub-reflector and achieve the purpose of improving the Marka antenna's emission efficiency.

Description of the drawings

Figure 1 is an application scenario of the method of using a perfect vortex beam to improve the transmission efficiency of the Maca antenna according to the present invention;

Figure 2 is a histogram of the corresponding emission power of POV beams with different topological charges.

Detailed ways

The present invention will be described in detail below with reference to the drawings and specific embodiments.

The present invention proposes a method for improving the emission efficiency of the Maca antenna by using a perfect vortex beam, specifically as follows:

Step 1: Establish the light field model of the perfect vortex beam diffracted by the Marka antenna based on the Collins formula and the ABCD transmission matrix of the Marka antenna;

The specific process of step 1 is as follows:

Step 1.1. Give the light field expression of the light source at the emission end, that is, the expression of the light field E(r,θ,0) of the POV beam on the distance z=0 plane is:

where E ₀ is the amplitude constant, m is the topological charge, i is an imaginary number, I _m is the first m-order modified Bessel function; ω ₀ is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively Equal to 2ω ₀ and R, r and θ variables are the radial and azimuthal coordinates of the cylindrical coordinate system;

Step 1.2. According to the Collins formula, after the perfect vortex beam passes through the Macca antenna, the diffraction light field on the observation plane for:

Among them, z is the transmission distance, k=2π/λ is the wave number, and λ is the wavelength; H(r) is the transmittance function of the Maca antenna; Represents the two-dimensional vector on the plane at z>0 in the cylindrical coordinate system. The parameters A, B, C, and D are the ABCD transmission matrices of the Maca antenna optical system;

Step 1.3. The Maca antenna is mainly composed of the second barrier, the first barrier, the primary reflector, the secondary reflector and the meniscus correction mirror. The catadioptric structure makes the Maca antenna compact, and a lens system with a large aperture and long focal length can be formed through a smaller size. The working principle of the Maca antenna as a transmitting antenna is: the secondary reflector reflects the beam emitted by the light source for the first time. The reflected beam is incident on the surface of the primary reflector, and then the beam reflected by the primary reflector is processed by the correction mirror. Correct and transmit the Maca antenna system to achieve directional emission. When studying the light beam passing through the Maca antenna, the Maca antenna is generally equivalent to a lens system. The ABCD transmission matrix and transmittance function H(r) of this lens system are respectively:

H(r)＝H ₁ (r)-H ₂ (r) (4)

In formula (4), the expressions of H ₁ (r) and H ₂ (r) are as follows:

Among them, f is the focal length of the equivalent lens, Δz = (zf)/f; D ₀ is the diameter of the meniscus correction mirror of the Maca antenna optical system, d ₀ is the diameter of the sub-reflector of the Maca antenna optical system, A _α , B _α is the coefficient, the value is shown in Table 1; T=10;

Table 1A _α , B _α are coefficient values

Substituting equations (1), (4), (5), and (6) into equation (2), we can get the diffracted light field on the observation plane at distance z for:

Step 2: Use the diffraction model established in step 1 (that is, the diffracted light field on the observation plane at distance z ), the expression of the diffraction light field of the POV beam after passing through the Maca antenna is theoretically derived;

The specific process of step 2 is as follows:

Step 2.1, with the help of formula:

Substituting the parameters in the diffraction light field on the observation plane at distance z obtained in formula (7), we can get:

Step 2.2, use the integral formula:

Integrate the parameter θ in equation (9) and sort it out:

Step 2.3, from the formula

J _-α (x)＝(-1) ^α J _α (x) (12)

Transform (11) into:

Step 2.4, use the integral formula:

Integrating r in equation (13), the diffraction light field on the observation plane can be obtained as:

in,

Step 3: Calculate the emission efficiency of the Maca antenna according to the geometric optics analysis method;

Step 3 is implemented according to the following specific steps:

According to the analysis method of geometric optics, the emission efficiency of the Maca antenna is defined as:

Among them, P ₀ is the total optical power incident on the end face of the Maca antenna, P is the total optical power on the detection plane; I ₀ (x ₀ , y ₀ , 0) is the light intensity of the initial POV beam, I (x, y ,z) is the light intensity of the diffracted light field on the observation plane; the light intensity I ₀ of the initial POV beam can be obtained from the POV beam light field expression in formula (1), that is:

I ₀ =<E(r,θ,0)·E ^* (r,θ,0)> (18)

The light intensity I of the diffracted light field on the observation plane can be determined by the light field at distance z in formula (15) Obtain, that is:

Example 1:

Combined with formulas (17), (18) and (19) in step 3, calculate the emission efficiency of the Maca antenna. Unless otherwise specified, set the Matlab simulation parameters as follows: wavelength λ = 1.06 μm, beam waist radius ω ₀ = 5cm, transmission distance z = 1km, equivalent lens diameter D ₀ = 0.03m, equivalent lens focal length f = 0.5m . Figure 2 is a comparison diagram of the emission efficiency of the Marka antenna and the emission efficiency of the Gaussian beam passing through the Marka antenna when the blocking ratio b=d ₀ /D ₀ =0.2 and the topological charge m=1, 2, 3, 5, and 8. Observing Figure 2, we can see that the emission efficiency of Gaussian light passing through the Marka antenna is 0.79, and the emission efficiency of POV passing through the Marka antenna reaches more than 0.88. The results prove that the use of perfect vortex beams can indeed improve the emission efficiency of the Marka antenna.

The present invention is a method of using a perfect vortex beam to avoid the obstruction of the Marka antenna sub-reflector and improve the radiation efficiency of the Marka antenna. The system to which it can be applied is shown in Figure 1. The free space optical communication system is mainly divided into the transmitting end. and two signal processing units at the receiving end, specifically including: encoder, modulator, transmitting optical system, receiving optical system, optical receiver, and decoder. The data information carried by the source is encoded by the source, modulated onto the optical carrier, and then sent out through the channel using the atmosphere as the medium. The present invention uses a perfect vortex beam as an optical carrier and a Marka antenna as a transmitting optical system. It analyzes the emission efficiency of the perfect vortex beam passing through the Marka antenna and compares the emission efficiency of a Gaussian beam passing through the Marka antenna. The results prove that the perfect vortex beam passes through the Marka antenna. It indeed improves the transmission efficiency of the Maca antenna.

Example 2

The method of using perfect vortex beam to improve the emission efficiency of Maca antenna is as follows:

Step 1: Establish the light field model of the perfect vortex beam diffracted by the Marka antenna based on the Collins formula and the ABCD transmission matrix of the Marka antenna;

Step 2: Using the diffraction model established in step 1, theoretically derive the expression of the diffraction light field of the POV beam after passing through the Maca antenna;

Step 3: Calculate the emission efficiency of the Maca antenna according to the geometric optics analysis method.

Example 3

The method of using perfect vortex beam to improve the emission efficiency of Maca antenna is as follows:

Step 1: Establish the light field model of the perfect vortex beam diffracted by the Marka antenna based on the Collins formula and the ABCD transmission matrix of the Marka antenna;

The specific process of step 1 is as follows:

Step 1.1. Give the light field expression of the light source at the emission end, that is, the expression of the light field E(r,θ,0) of the POV beam on the distance z=0 plane is:

where E ₀ is the amplitude constant, m is the topological charge, i is an imaginary number, I _m is the first m-order modified Bessel function; ω ₀ is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively Equal to 2ω ₀ and R, r and θ variables are the radial and azimuthal coordinates of the cylindrical coordinate system;

Step 1.2. According to the Collins formula, after the perfect vortex beam passes through the Macca antenna, the diffraction light field on the observation plane for:

Among them, z is the transmission distance, k=2π/λ is the wave number, and λ is the wavelength; H(r) is the transmittance function of the Maca antenna; Represents the two-dimensional vector on the plane at z>0 in the cylindrical coordinate system. The parameters A, B, C, and D are the ABCD transmission matrices of the Maca antenna optical system;

Step 1.3. The Maca antenna is mainly composed of the second barrier, the first barrier, the primary reflector, the secondary reflector and the meniscus correction mirror. The catadioptric structure makes the Maca antenna compact, and a lens system with a large aperture and long focal length can be formed through a smaller size. The working principle of the Maca antenna as a transmitting antenna is: the secondary reflector reflects the beam emitted by the light source for the first time. The reflected beam is incident on the surface of the primary reflector, and then the beam reflected by the primary reflector is processed by the correction mirror. Correct and transmit the Maca antenna system to achieve directional emission. When studying the beam passing through the Maca antenna, the Maca antenna is equivalent to a lens system; the ABCD transmission matrix and transmittance function H(r) of this lens system are:

H(r)＝H ₁ (r)-H ₂ (r) (4)

In formula (4), the expressions of H ₁ (r) and H ₂ (r) are as follows:

Among them, f is the focal length of the equivalent lens, Δz = (zf)/f; D ₀ is the diameter of the meniscus correction mirror of the Maca antenna optical system, d ₀ is the diameter of the sub-reflector of the Maca antenna optical system, A _α , B _α is the coefficient, T=10;

Substituting equations (1), (4), (5), and (6) into equation (2), we can get the diffracted light field on the observation plane at distance z for:

Step 2: Using the diffraction model established in step 1, theoretically derive the expression of the diffraction light field of the POV beam after passing through the Maca antenna;

Step 3: Calculate the emission efficiency of the Maca antenna according to the geometric optics analysis method.

Claims (5)

1. The method of using perfect vortex beam to improve the emission efficiency of Maca antenna is characterized by: Step 1: Establish the light field model of the perfect vortex beam diffracted by the Marka antenna based on the Collins formula and the ABCD transmission matrix of the Marka antenna; Step 2: Using the diffraction model established in step 1, theoretically derive the expression of the diffraction light field of the POV beam after passing through the Maca antenna; Step 3: Calculate the emission efficiency of the Maca antenna according to the geometric optics analysis method. 2. The method for improving the emission efficiency of the Maca antenna by utilizing a perfect vortex beam according to claim 1, characterized in that the specific process of step 1 is as follows: Step 1.1. Give the light field expression of the light source at the emission end, that is, the expression of the light field E(r,θ,0) of the POV beam on the distance z=0 plane is: where E ₀ is the amplitude constant, m is the topological charge, i is an imaginary number, I _m is the first m-order modified Bessel function; ω ₀ is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively Equal to 2ω ₀ and R, r and θ variables are the radial and azimuthal coordinates of the cylindrical coordinate system; Step 1.2. According to the Collins formula, after the perfect vortex beam passes through the Macca antenna, the diffraction light field on the observation plane for: Among them, z is the transmission distance, k=2π/λ is the wave number, and λ is the wavelength; H(r) is the transmittance function of the Maca antenna; Represents the two-dimensional vector on the plane at z>0 in the cylindrical coordinate system. The parameters A, B, C, and D are the ABCD transmission matrices of the Maca antenna optical system; Step 1.3. When studying the light beam passing through the Maca antenna, the Maca antenna is equivalent to a lens system; the ABCD transmission matrix and transmittance function H(r) of this lens system are: H(r)＝H ₁ (r)-H ₂ (r) (4) In formula (4), the expressions of H ₁ (r) and H ₂ (r) are as follows: Among them, f is the focal length of the equivalent lens, Δz = (zf)/f; D ₀ is the diameter of the meniscus correction mirror of the Maca antenna optical system, d ₀ is the diameter of the sub-reflector of the Maca antenna optical system, A _α , B _α is the coefficient, T=10; Substituting equations (1), (4), (5), and (6) into equation (2), we can get the diffracted light field on the observation plane at distance z for: 3. The method for improving the emission efficiency of the Maca antenna by utilizing a perfect vortex beam according to claim 2, characterized in that in step 1.3, A _α and B _α are coefficient values as shown in Table 1: Table 1 A _α , B _α are coefficient values . 4. The method for improving the emission efficiency of the Maca antenna by utilizing a perfect vortex beam according to claim 2, characterized in that the specific process of step 2 is as follows: Step 2.1, with the help of formula: Substituting the parameters in the diffraction light field on the observation plane at distance z obtained in formula (7), we can get: Step 2.2, use the integral formula: Integrate the parameter θ in equation (9) and sort it out: Step 2.3, from the formula J _-α (x)＝(-1) ^α J _α (x) (12) Transform (11) into: Step 2.4, use the integral formula: Integrating r in equation (13), the diffraction light field on the observation plane can be obtained as: in, 5. The method for improving the emission efficiency of the Maca antenna by utilizing a perfect vortex beam according to claim 3, characterized in that the specific process of step 3 is as follows: According to the analysis method of geometric optics, the emission efficiency of the Maca antenna is defined as: Among them, P ₀ is the total optical power incident on the end face of the Maca antenna, P is the total optical power on the detection plane; I ₀ (x ₀ , y ₀ , 0) is the light intensity of the initial POV beam, I (x, y ,z) is the light intensity of the diffracted light field on the observation plane; the light intensity I ₀ of the initial POV beam can be obtained from the POV beam light field expression in formula (1), that is: I ₀ =<E(r,θ,0)•E ^* (r,θ,0)> (18) The light intensity I of the diffracted light field on the observation plane can be determined by the light field at distance z in formula (15) Obtain, that is: