CN117394914A - Method for improving transmitting efficiency of maca antenna by utilizing perfect vortex beam - Google Patents
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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
Technical Field
The invention belongs to the technical field of wireless optical communication, and particularly relates to a method for improving the transmitting efficiency of a maca antenna by using perfect vortex beams.
Background
With the rapid development of wireless communication technology, modern communication is increasingly placing higher demands on spatial optical communication (Free space optical communication, FSO) technology. Optical antennas are important as an integral part of FSO systems. In FSO systems, the optical antennas function as collimation and focusing, respectively, on the transmission and reception of optical signals. Therefore, the magnitude of the optical antenna transmission efficiency will directly determine the communication quality of the FSO system.
In the selection of an optical antenna of an FSO system, the Cassegrain system is a typical dual reflection telescope objective, and the whole system has no chromatic aberration. The primary reflection is a hyperbolic mirror, typically parabolic, and the secondary mirror is typically convex. A mactuff-cassegrain telescope (called a macadam antenna for short) is an objective lens for telescope, which is improved on the basis of the structure of a cassegrain system, is based on a spherical reflector, and is added with a refraction element for correcting aberration to be changed into a foldback structure. Compared with the cassegrain Lin Jitong, the manufacturing cost can be reduced because each component in the maca antenna is spherical. Based on the advantages of the maca antenna, related researches analyze and explore the emission efficiency of different types of light sources through the maca antenna. There are studies found that: for uniformly distributed light sources, the energy loss caused by shielding of the secondary reflector of the maca antenna is more than 30%; for gaussian distributed laser sources, the energy loss can reach 50% or more. The light spots emitted by the maca antennas are distributed in a ring shape, which is a serious problem for wireless optical communication.
In recent years, the perfect vortex (Perfect optical vortex, POV) light beam has important application value in the fields of particle manipulation, quantum communication and the like because the light beam has the advantage that the radius of a bright ring is not changed along with the topological charge number, so that the perfect vortex light beam can be matched with a maca antenna due to the fact that the light intensity distribution of the perfect vortex light beam is annular in physical structure, but no research and analysis on diffraction characteristics and emission efficiency of the perfect vortex light beam after passing through the maca antenna are performed.
Disclosure of Invention
The invention aims to provide a technical method for improving the transmitting efficiency of a maca antenna by utilizing perfect vortex beams, which is used for solving the problem of energy loss caused by shielding of a secondary reflector of the maca antenna.
The technical scheme adopted by the invention is that the method for improving the transmitting efficiency of the maca antenna by utilizing perfect vortex beams 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 present invention is also characterized in that,
the specific process of the step 1 is as follows:
step 1.1, the light field expression of the light source at the transmitting end is given, namely, the expression of the light field E (r, θ, 0) of the POV light beam on the plane with the distance z=0 is as follows:
wherein E is 0 Is an amplitude constant, m is a topological charge number, I is an imaginary number, I m Is a first class of m-order modified Bessel functions; omega 0 Is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively equal to 2 omega 0 And the R, R and theta variables are the radial and azimuthal coordinates of the cylindrical coordinate system;
step 1.2, as known from Collins formula, after the perfect vortex beam passes through the Maka antenna, the diffraction light field on the observation planeThe method comprises the following steps:
wherein z is a transmission distance, k=2pi/λ is a wave number, and λ is a wavelength; h (r) is the transmittance function of the maca antenna;representing z in a cylindrical coordinate system>The two-dimensional vector on the plane at the position 0, and parameters A, B, C and D are ABCD transmission matrixes of the optical system of the maca antenna;
step 1.3, the maca antenna mainly comprises a second obscuration, a first obscuration, a primary mirror, a secondary mirror and a meniscus correction mirror. The catadioptric structure enables the maca antenna to be compact in structure, and a lens group system with large caliber and long focal length can be formed through a small size. The working principle when the maca antenna is used as a transmitting antenna is as follows: the secondary reflector reflects the light beam emitted by the light source for the first time, the reflected light beam is incident on the surface of the main reflector, and the light beam reflected by the main reflector is corrected by the correction mirror and transmitted out of the maca antenna system, so that directional emission is realized. When the research light beam passes 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 respectively:
H(r)＝H 1 (r)-H 2 (r) (4)
in the formula (4), H 1 (r) and H 2 The expression of (r) is as follows:
wherein f is the focal length of the equivalent lens, Δz= (z-f)/f; d (D) 0 The diameter of the meniscus correcting mirror, d, for a maca antenna optical system 0 Is the diameter of a secondary reflector of a Marca antenna optical system, A α ，B α T=10 for the coefficient;
substituting the equations (1), (4), (5) and (6) into the equation (2) can obtain the diffraction light field on the observation plane at the distance zThe method comprises the following steps:
in step 1.3, A α ，B α The values for the coefficients are shown in table 1:
TABLE 1A α ，B α Take the value of the coefficient
The specific process of the step 2 is as follows:
step 2.1, by means of the formula:
the parameters in the diffraction light field on the observation plane at the distance z obtained in the formula (7) are replaced, and the method can be obtained:
step 2.2, utilizing an integral formula:
integrating the parameter theta in the formula (9), and finishing to obtain:
step 2.3, from the formula
J -α (x)＝(-1) α J α (x) (12)
Equation (11) is:
step 2.4, utilizing an integral formula:
integrating r in the formula (13) to obtain the diffraction light field on the observation plane as follows:
wherein,
the specific process of the step 3 is as follows: according to the analysis method of geometrical optics, the emission efficiency of the maca antenna is defined as follows:
wherein P is 0 The total optical power incident to the end face of the maca antenna is P, and the total optical power on the detection plane is P; i 0 (x 0 ,y 0 0) is the initial POV lightThe intensity of the beam, I (x, y, z) is the intensity of the diffracted light field on the observation plane; intensity I of initial POV Beam 0 Can be obtained from the POV beam light field expression in equation (1), namely:
I 0 ＝<E(r,θ,0)·E * (r,θ,0)> (18)
the intensity I of the diffracted light field at the observation plane can be determined by the light field at the distance z in equation (15)The preparation method comprises the following steps:
the beneficial effects of the invention are as follows:
the invention can perfectly match with the maca antenna structure in space distribution by utilizing the hollow space distribution structure of the perfect vortex beam and the characteristic that the radius of the bright ring is not changed along with the topological charge number, and can directly avoid the shielding problem of the secondary reflector of the maca antenna by the perfect vortex beam with any topological charge number under the condition of proper selection of the radius parameter of the perfect vortex beam, thereby achieving the purpose of improving the emission efficiency of the maca antenna.
Drawings
FIG. 1 is an application scenario of the method of the present invention for improving the efficiency of a Marka antenna using a perfectly vortex beam;
fig. 2 is a bar graph of the corresponding transmit power of POV beams of different topological charges.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention provides 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;
the specific process of the step 1 is as follows:
step 1.1, the light field expression of the light source at the transmitting end is given, namely, the expression of the light field E (r, θ, 0) of the POV light beam on the plane with the distance z=0 is as follows:
wherein E is 0 Is an amplitude constant, m is a topological charge number, I is an imaginary number, I m Is a first class of m-order modified Bessel functions; omega 0 Is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively equal to 2 omega 0 And the R, R and theta variables are the radial and azimuthal coordinates of the cylindrical coordinate system;
step 1.2, as known from Collins formula, after the perfect vortex beam passes through the Maka antenna, the diffraction light field on the observation planeThe method comprises the following steps:
wherein z is a transmission distance, k=2pi/λ is a wave number, and λ is a wavelength; h (r) is the transmittance function of the maca antenna;representing z in a cylindrical coordinate system>The two-dimensional vector on the plane at the position 0, and parameters A, B, C and D are ABCD transmission matrixes of the optical system of the maca antenna;
step 1.3, the maca antenna mainly comprises a second obscuration, a first obscuration, a primary mirror, a secondary mirror and a meniscus correction mirror. The catadioptric structure enables the maca antenna to be compact in structure, and a lens group system with large caliber and long focal length can be formed through a small size. The working principle when the maca antenna is used as a transmitting antenna is as follows: the secondary reflector reflects the light beam emitted by the light source for the first time, the reflected light beam is incident on the surface of the main reflector, and the light beam reflected by the main reflector is corrected by the correction mirror and transmitted out of the maca antenna system, so that directional emission is realized. In studying the beam passing through a 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 the formula (4), H 1 (r) and H 2 The expression of (r) is as follows:
wherein f is the focal length of the equivalent lens, Δz= (z-f)/f; d (D) 0 The diameter of the meniscus correcting mirror, d, for a maca antenna optical system 0 Is the diameter of a secondary reflector of a Marca antenna optical system, A α ，B α The values of the coefficients are shown in table 1; t=10;
TABLE 1A α ，B α Take the value of the coefficient
Substituting the equations (1), (4), (5) and (6) into the equation (2) can obtain the diffraction light field on the observation plane at the distance zThe method comprises the following steps:
step 2: using diffraction built up in step 1Model (i.e. diffracting the light field in the observation plane at distance z) Theoretically deducing a diffraction light field expression of the POV light beam after passing through the maca antenna;
the specific process of the step 2 is as follows:
step 2.1, by means of the formula:
the parameters in the diffraction light field on the observation plane at the distance z obtained in the formula (7) are replaced, and the method can be obtained:
step 2.2, utilizing an integral formula:
integrating the parameter theta in the formula (9), and finishing to obtain:
step 2.3, from the formula
J -α (x)＝(-1) α J α (x) (12)
Equation (11) is:
step 2.4, utilizing an integral formula:
integrating r in the formula (13) to obtain the diffraction light field on the observation plane as follows:
wherein,
step 3: calculating the emission efficiency of the maca antenna according to a geometric optical analysis method;
step 3 is implemented according to the following specific steps:
according to the analysis method of geometrical optics, the emission efficiency of the maca antenna is defined as follows:
wherein P is 0 The total optical power incident to the end face of the maca antenna is P, and the total optical power on the detection plane is P; i 0 (x 0 ,y 0 0) is the intensity of the initial POV beam, and I (x, y, z) is the intensity of the diffracted light field on the observation plane; intensity I of initial POV Beam 0 Can be obtained from the POV beam light field expression in equation (1), namely:
I 0 ＝<E(r,θ,0)·E * (r,θ,0)> (18)
the intensity I of the diffracted light field at the observation plane can be determined by the light field at the distance z in equation (15)The preparation method comprises the following steps:
example 1:
and (3) combining the formulas (17), (18) and (19) in the step 3, and calculating the emission efficiency of the maca antenna. When not specifically described, matlab simulation parameters were set as follows: wavelength λ=1.06 μm, beam waist radius ω 0 Transmission distance z=1 km, equivalent lens diameter D =5 cm 0 =0.03 m, equivalent lens focal length f=0.5 m. Fig. 2 is a mask ratio b=d 0 /D 0 When the topological charge number m=1, 2, 3, 5 and 8, the emission efficiency of the maca antenna and the emission efficiency of the Gaussian beam passing through the maca antenna are compared. As can be seen from the observation of fig. 2, the emission efficiency of gaussian light passing through the maca antenna is 0.79, and the emission efficiency of pov passing through the maca antenna is more than 0.88, and the result proves that the emission efficiency of the maca antenna can be improved by using perfect vortex light beams.
The invention relates to a method for avoiding shielding of a secondary reflector of a maca antenna by utilizing perfect vortex beams and improving the transmitting efficiency of the maca antenna, wherein an applicable system is shown in a figure 1, and a free space optical communication system is mainly divided into two signal processing units of a transmitting end and a receiving end, and specifically comprises the following steps: encoder, modulator, transmitting optical system, receiving optical system, optical receiver, decoder. After source coding, the data information carried by the information source is modulated onto an optical carrier wave and then sent out through a channel taking the atmosphere as a medium. According to the invention, the perfect vortex beam is taken as an optical carrier wave, the maca antenna is taken as an emission optical system, the emission efficiency of the perfect vortex beam passing through the maca antenna is analyzed, and compared with the emission efficiency of the Gaussian beam passing through the maca antenna, the result proves that the emission efficiency of the maca antenna is improved by the perfect vortex beam.
Example 2
The method for improving the transmitting efficiency of the maca antenna by utilizing the perfect vortex beam comprises the following specific 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.
Example 3
The method for improving the transmitting efficiency of the maca antenna by utilizing the perfect vortex beam comprises the following specific 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;
the specific process of the step 1 is as follows:
step 1.1, the light field expression of the light source at the transmitting end is given, namely, the expression of the light field E (r, θ, 0) of the POV light beam on the plane with the distance z=0 is as follows:
wherein E is 0 Is an amplitude constant, m is a topological charge number, I is an imaginary number, I m Is a first class of m-order modified Bessel functions; omega 0 Is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively equal to 2 omega 0 And the R, R and theta variables are the radial and azimuthal coordinates of the cylindrical coordinate system;
step 1.2, as known from Collins formula, after the perfect vortex beam passes through the Maka antenna, the diffraction light field on the observation planeThe method comprises the following steps:
wherein z is a transmission distance, k=2pi/λ is a wave number, and λ is a wavelength; h (r) is the transmittance function of the maca antenna;representing z in a cylindrical coordinate system>The two-dimensional vector on the plane at the position 0, and parameters A, B, C and D are ABCD transmission matrixes of the optical system of the maca antenna;
step 1.3, the maca antenna mainly comprises a second obscuration, a first obscuration, a primary mirror, a secondary mirror and a meniscus correction mirror. The catadioptric structure enables the maca antenna to be compact in structure, and a lens group system with large caliber and long focal length can be formed through a small size. The working principle when the maca antenna is used as a transmitting antenna is as follows: the secondary reflector reflects the light beam emitted by the light source for the first time, the reflected light beam is incident on the surface of the main reflector, and the light beam reflected by the main reflector is corrected by the correction mirror and transmitted out of the maca antenna system, so that directional emission is realized. When the research light beam passes 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 respectively:
H(r)＝H 1 (r)-H 2 (r) (4)
in the formula (4), H 1 (r) and H 2 The expression of (r) is as follows:
wherein f is the focal length of the equivalent lens, Δz= (z-f)/f; d (D) 0 The diameter of the meniscus correcting mirror, d, for a maca antenna optical system 0 Is the diameter of a secondary reflector of a Marca antenna optical system, A α ，B α T=10 for the coefficient;
substituting the equations (1), (4), (5) and (6) into the equation (2) can obtain the diffraction light field on the observation plane at the distance zThe method comprises the following steps:
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.
Claims (5)
1. The method for improving the transmitting efficiency of the maca antenna by utilizing the perfect vortex beam is characterized by comprising the following steps of:
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.
2. The method for improving the radiation efficiency of a maca antenna by utilizing a perfect vortex beam according to claim 1, wherein the specific process of the step 1 is as follows:
step 1.1, the light field expression of the light source at the transmitting end is given, namely, the expression of the light field E (r, θ, 0) of the POV light beam on the plane with the distance z=0 is as follows:
wherein E is 0 Is an amplitude constant, m is a topological charge number, I is an imaginary number, I m Is a first class of m-order modified Bessel functions; omega 0 Is the Gaussian beam waist radius at the focus, and the ring width and radius of the bright ring are respectively equal to 2 omega 0 And the R, R and theta variables are the radial and azimuthal coordinates of the cylindrical coordinate system;
step 1.2, as known from Collins formula, after the perfect vortex beam passes through the Maka antenna, the diffraction light field on the observation planeThe method comprises the following steps:
wherein z is a transmission distance, k=2pi/λ is a wave number, and λ is a wavelength; h (r) is the transmittance function of the maca antenna;representing z in a cylindrical coordinate system>The two-dimensional vector on the plane at the position 0, and parameters A, B, C and D are ABCD transmission matrixes of the optical system of the maca antenna;
step 1.3, when the research light beam passes 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 respectively:
H(r)＝H 1 (r)-H 2 (r) (4)
in the formula (4), H 1 (r) and H 2 The expression of (r) is as follows:
wherein f is the focal length of the equivalent lens, Δz= (z-f)/f; d (D) 0 The diameter of the meniscus correcting mirror, d, for a maca antenna optical system 0 Is the diameter of a secondary reflector of a Marca antenna optical system, A α ，B α T=10 for the coefficient;
substituting the equations (1), (4), (5) and (6) into the equation (2) can obtain the diffraction light field on the observation plane at the distance zThe method comprises the following steps:
3. the method for improving the radiation efficiency of a maca antenna by using a perfectly vortex beam according to claim 2, wherein in step 1.3, a α ，B α The values for the coefficients are shown in table 1:
table 1A α ，B α Take the value of the coefficient
。
4. The method for improving the radiation efficiency of a maca antenna by utilizing a perfect vortex beam according to claim 2, wherein the specific process of the step 2 is as follows:
step 2.1, by means of the formula:
the parameters in the diffraction light field on the observation plane at the distance z obtained in the formula (7) are replaced, and the method can be obtained:
step 2.2, utilizing an integral formula:
integrating the parameter theta in the formula (9), and finishing to obtain:
step 2.3, from the formula
J -α (x)＝(-1) α J α (x) (12)
Equation (11) is:
step 2.4, utilizing an integral formula:
integrating r in the formula (13) to obtain the diffraction light field on the observation plane as follows:
wherein,
5. the method for improving the radiation efficiency of a maca antenna by using a perfect vortex beam according to claim 3, wherein the specific process of the step 3 is as follows: according to the analysis method of geometrical optics, the emission efficiency of the maca antenna is defined as follows:
wherein P is 0 The total optical power incident to the end face of the maca antenna is P, and the total optical power on the detection plane is P; i 0 (x 0 ,y 0 0) is the intensity of the initial POV beam, and I (x, y, z) is the intensity of the diffracted light field on the observation plane; intensity I of initial POV Beam 0 Can be obtained from the POV beam light field expression in equation (1), namely:
I 0 ＝<E(r,θ,0)•E * (r,θ,0)> (18)
the intensity I of the diffracted light field at the observation plane can be determined by the light field at the distance z in equation (15)The preparation method comprises the following steps:
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Citations (3)
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|---|---|---|---|---|
| US20130225089A1 (en) * | 2012-02-28 | 2013-08-29 | Fujitsu Limited | Radio communication apparatus, system, and method |
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| CN111355530A (en) * | 2020-03-13 | 2020-06-30 | 山东师范大学 | Method and device for improving performance of wireless optical communication system |
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