Information coding and decoding method based on concentric perfect vortex

Abstract

The invention discloses an information coding and decoding method based on a concentric perfect vortex. The method comprises the following steps: establishing a light field expression of a perfect vortex beam; a plurality of perfect vortex light beams are coaxially superposed, a light spot radius parameter is adjusted, a phase truncation factor is set, the perfect vortex light beams at different spatial positions are distinguished, and a concentric perfect vortex light field expression after the phase truncation factor is added is obtained; performing interference on the concentric perfect vortex and the spherical wave to obtain a light intensity expression after interference of the concentric perfect vortex and the spherical wave; the distribution condition of orbital angular momentum on each ring is obtained through a spherical wave and concentric perfect vortex interference light spot pattern, and then information decoding is achieved according to the mapping relation between different orbital angular momentum and numeric symbols. According to the method, coding is realized by integrating a plurality of independently regulated degrees of freedom of light spot radius / light spot position, orbital angular momentum mode and light spot number of the concentric perfect vortex, and the obtained light spots of the concentric perfect vortex are kept mutually independent.

Description

Technical Field

[0001] The invention belongs to the technical field of optical communication, and in particular relates to an information encoding and decoding method based on concentric perfect vortices. Background Art

[0002] Since Allen experimentally produced a vortex beam carrying orbital angular momentum in 1992 (Allen L, Beijersbergen MW, Spreeuw RJC, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes [J]. Physical Review A, 1992, 45 (11): 8185-8189.), the research on orbital angular momentum has shown an explosive growth trend in the scientific research community in recent decades. Especially in the field of optical communication technology, since orbital angular momentum can take an infinite number of modes and different orbital angular momentums have mutually orthogonal characteristics, it is possible to further reuse multiple orbital angular momentums on a communication link based on existing communication technology, thereby greatly expanding the spectrum efficiency and communication capacity of existing communication systems.

[0003] At present, most of the research on improving the performance of communication systems through orbital angular momentum multiplexing focuses on superimposing vortex beams of multiple modes of orbital angular momentum, and then completing the information encoding process by identifying the orbital angular momentum through coherent detection. However, in the traditional method, the spot size of the vortex beam will show a positive correlation with the value of the orbital angular momentum, which makes it difficult to avoid overlapping interference of the light spots after superposition, thereby affecting the accuracy of orbital angular momentum mode detection and increasing the communication bit error rate. Summary of the invention

[0004] The purpose of the present invention is to provide an information encoding and decoding method based on concentric perfect vortices, which solves the problem that it is difficult to avoid overlapping interference of light spots in the existing light field superposition, which in turn affects the accuracy of orbital angular momentum mode detection, thereby increasing the communication bit error rate.

[0005] The technical solution adopted by the present invention is: an information encoding and decoding method based on concentric perfect vortices, taking advantage of the natural advantage that the spot size of the perfect vortex beam is not affected by the value of the orbital angular momentum, by appropriately adjusting the spot radius parameter and setting the phase truncation factor, a coaxial superposition perfect vortex is proposed, and an information encoding and decoding method based on concentric perfect vortices is proposed. The method integrates the spot radius / spot position, orbital angular momentum mode, and spot number of the concentric perfect vortex to achieve encoding, and the concentric perfect vortex spots obtained are kept independent of each other; the specific operation steps are as follows

[0006] Step 1: Establish the light field expression of the perfect vortex beam;

[0007] Step 2: Superimpose multiple perfect vortex beams coaxially, adjust the spot radius parameter, set the phase truncation factor, distinguish the perfect vortex beams at different spatial positions, and obtain the concentric perfect vortex light field expression after adding the phase truncation factor;

[0008] Step 3: interfere the concentric perfect vortex with the spherical wave to obtain the light intensity expression after the interference of the concentric perfect vortex and the spherical wave;

[0009] Step 4: Obtain the distribution of orbital angular momentum on each ring through the spot pattern of interference between spherical waves and concentric perfect vortices, and then realize information decoding based on the mapping relationship between different orbital angular momentum and digital symbols.

[0010] The present invention is also characterized in that:

[0011] Step 1 The light field expression of the perfect vortex beam is:

[0012] In the cylindrical coordinate system, the light field expression of a perfect vortex beam is:

[0013]

[0014] Where (r, φ) represents polar coordinates, r and φ represent the polar diameter and polar angle respectively, i represents the imaginary unit, ω0 is the beam waist radius, ω is the width of the bright ring of the spot, R is the radius of the perfect vortex beam, and l represents the number of orbital angular momentum modes carried by the beam, that is, the topological charge;

[0015] In step 2, multiple perfect vortex beams are coaxially superimposed. Assuming that the beam parameters except l and R remain the same, the light field expression after superposition is:

[0016]

[0017] In the formula, l j represents the topological charge of the jth superimposed perfect vortex from the inside out, E j (r, φ) represents the light field of the jth superimposed perfect vortex, R j represents the radius of the jth superimposed perfect vortex, and N represents the number of superimposed perfect vortex beams.

[0018] In order to avoid mutual interference between multiple superimposed perfect vortex beams, a phase truncation factor is set based on the superimposed light field expression to distinguish the perfect vortex beams at different spatial positions. The additional phase truncation factor g is Rj The expression of the concentric perfect vortex light field after (r) is as follows:

[0019]

[0020] In the formula, R j and R s They respectively represent the radii of the j-th and s-th superimposed perfect vortices from the inside to the outside; N is the number of perfect vortices; r and φ represent the polar diameter and polar angle, respectively; thus, a concentric perfect vortex light field is obtained after the coaxial superposition of N perfect vortex beams.

[0021] Step 3 is as follows:

[0022] The concentric perfect vortex interferes with the spherical wave, and the expression of the spherical wave light field is:

[0023]

[0024] Where A′ is the amplitude constant, represents the finite beam width term of the spherical wave, d represents the distance from the spherical wave to the receiving screen. The light intensity expression after the interference of the concentric perfect vortex and the spherical wave is obtained as follows:

[0025] I=(U′+E sphere )·(U′+E sphere ) * (6)

[0026] In the formula, the symbol * Indicates the conjugate mode.

[0027] In step 2, the radius parameter R, orbital angular momentum mode number l, and perfect vortex number N of any perfect vortex light field that constitutes the concentric perfect vortex can be independently controlled to form a multi-dimensional information encoding degree of freedom; by setting N different radius parameter values, the perfect vortex light beam is distributed to N different spatial positions, and the orbital angular momentum mode value combination is {l1,l2,…,l M}, then there are M choices for the value of l on each ring, and each form represents log2(M N ) bits of information.

[0028] In step 4, a hexadecimal decoding table is designed to display the results of the interference between the perfect vortex beams of l=-8, l=-7, ..., l=1, ..., l=7, and l=8 and the spherical wave, and the hexadecimal numbers after the encoding and mapping of each orbital angular momentum mode are identified, where l=-8, l=-7, ..., l=1, ..., l=7, and l=8 represent the hexadecimal symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F respectively. According to the decoding table, the patterns on each ring after the interference between the concentric perfect vortex and the spherical wave are compared to obtain the overall distribution of the orbital angular momentum mode of the concentric perfect vortex, obtain the hexadecimal decoding sequence, and realize information restoration.

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

[0030] (1) By coaxially superimposing perfect vortex beams with different spot radii and designing the phase truncation factor, the concentric perfect vortex unit spots are independent of each other, effectively overcoming the current problem of spatial overlap of vortex beam multiplexing spots;

[0031] (2) The information encoding and decoding method based on the concentric perfect vortex proposed in the present invention comprehensively utilizes the concentric perfect vortex's multiple independently controllable degrees of freedom of the spot radius / spot position, orbital angular momentum mode, and spot number to encode information, and the encoding efficiency is high;

[0032] (3) The information encoding and decoding method based on concentric perfect vortices proposed in the present invention is compatible with existing communication technologies such as frequency division multiplexing, time division multiplexing, and wavelength division multiplexing, has good scalability, and is expected to further improve the performance of the communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Design concept diagram for concentric perfect vortex and two-dimensional light intensity distribution diagram of concentric perfect vortex;

[0034] Figure 2(a) shows the interference result of the perfect vortex and spherical wave in orbital angular momentum mode l = -8;

[0035] Figure 2(b) shows the interference result of the perfect vortex and spherical wave in orbital angular momentum mode l = 8;

[0036] Figure 3 Hexadecimal decoding diagram designed for the present invention;

[0037] Figure 4 Schematic diagram of information encoding and decoding based on concentric perfect vortices. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Example 1

[0040] The present invention is based on the information encoding and decoding method of concentric perfect vortex, and takes advantage of the fact that the spot size of the perfect vortex beam is not affected by the value of orbital angular momentum. By adjusting the spot radius parameter and setting the phase truncation factor, the perfect vortex is coaxially superimposed, and an information encoding and decoding method based on concentric perfect vortex is proposed. The method integrates the spot radius / spot position, orbital angular momentum mode, and spot number of multiple independently controlled degrees of freedom of the concentric perfect vortex to achieve encoding, and the concentric perfect vortex spots obtained are kept independent of each other.

[0041] Example 2

[0042] The information encoding and decoding method of the present invention is based on concentric perfect vortex, and the specific operation steps are as follows:

[0043] Step 1: Establish the light field expression of the perfect vortex beam;

[0044] Step 2: Superimpose multiple perfect vortex beams coaxially, adjust the spot radius parameter, set the phase truncation factor, distinguish the perfect vortex beams at different spatial positions, and obtain the concentric perfect vortex light field expression after adding the phase truncation factor;

[0045] Step 3: interfere the concentric perfect vortex with the spherical wave to obtain the light intensity expression after the interference of the concentric perfect vortex and the spherical wave;

[0046] Step 4: Obtain the distribution of orbital angular momentum on each ring through the spot pattern of interference between spherical waves and concentric perfect vortices, and then realize information decoding based on the mapping relationship between different orbital angular momentum and digital symbols.

[0047] Example 3

[0048] The information encoding and decoding method of the present invention is based on concentric perfect vortex, and the specific operation steps are as follows:

[0049] Step 1: Establish the light field expression of the perfect vortex beam;

[0050] In the cylindrical coordinate system, the light field expression of a perfect vortex beam is:

[0051]

[0052] Where (r, φ) represents polar coordinates, r and φ represent the polar diameter and polar angle respectively, i represents the imaginary unit, ω0 is the beam waist radius, ω is the width of the bright ring of the spot, R is the radius of the perfect vortex beam, and l represents the number of orbital angular momentum modes carried by the beam, that is, the topological charge number, and its value can be any integer.

[0053] Step 2: Superimpose multiple perfect vortex beams coaxially, adjust the spot radius parameter, set the phase truncation factor, distinguish the perfect vortex beams at different spatial positions, and obtain the concentric perfect vortex light field expression after adding the phase truncation factor;

[0054] Multiple perfect vortex beams are coaxially superimposed. Assuming that the beam parameters except l and R remain the same, the light field expression after superposition is:

[0055]

[0056] In the formula, l j represents the topological charge of the jth superimposed perfect vortex from the inside out, Ej (r, φ) represents the light field of the jth superimposed perfect vortex, R j represents the radius of the jth superimposed perfect vortex, and N represents the number of superimposed perfect vortex beams.

[0057] In order to avoid mutual interference between multiple superimposed perfect vortex beams, a phase truncation factor is set on the basis of formula (2) to distinguish the perfect vortex beams at different spatial positions. The additional phase truncation factor g is: Rj The expression of the concentric perfect vortex light field after (r) is as follows:

[0058]

[0059] At this point, a concentric perfect vortex light field is obtained after the coaxial superposition of N perfect vortex beams;

[0060] The radius parameter R, orbital angular momentum mode number l, and perfect vortex number N of any perfect vortex light field that constitutes the concentric perfect vortex can be independently controlled to form a multi-dimensional information encoding degree of freedom; by setting N different radius parameter values, the perfect vortex light beam is distributed to N different spatial positions, and the orbital angular momentum mode value combination is {l1,l2,…,l M}, then there are M choices for the value of l on each ring, and each form represents log2(M N ) bits of information;

[0061] Step 3: interfere the concentric perfect vortex with the spherical wave to obtain the light intensity expression after the interference of the concentric perfect vortex and the spherical wave;

[0062] The concentric perfect vortex interferes with the spherical wave, and the expression of the spherical wave light field is:

[0063]

[0064] Where A′ is the amplitude constant, represents the finite beam width term of the spherical wave, d represents the distance from the spherical wave to the receiving screen. The light intensity expression after the interference of the concentric perfect vortex and the spherical wave is obtained as follows:

[0065] I=(U′+E sphere )·(U′+E sphere ) * (6)

[0066] In the formula, the symbol * Indicates the conjugate mode.

[0067] Step 4: Obtain the distribution of orbital angular momentum on each ring through the spot pattern of interference between spherical waves and concentric perfect vortices, and then realize information decoding based on the mapping relationship between different orbital angular momentum and digital symbols;

[0068] In step 4, a hexadecimal decoding table is designed to display the results of the interference between the perfect vortex beams of l=-8, l=-7, ..., l=1, ..., l=7, and l=8 and the spherical wave, and the hexadecimal numbers after the encoding and mapping of each orbital angular momentum mode are marked, where l=-8, l=-7, ..., l=1, ..., l=7, and l=8 represent the hexadecimal symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F respectively. The digital sequence representing the information can eventually be mapped to a series of concentric perfect vortex spot patterns. According to the decoding table, the patterns on each ring after the interference between the concentric perfect vortex and the spherical wave are compared, so as to obtain the overall distribution of the concentric perfect vortex orbital angular momentum mode, obtain the hexadecimal decoding sequence, and realize information restoration. .

[0069] Example 4

[0070] On the basis of Example 3, Figure 1 As shown in Figure 1, the coaxial superposition process of concentric perfect vortices and the resulting two-dimensional light intensity distribution of concentric perfect vortices are shown. Assuming that the number of perfect vortices N = 8, the corresponding light field E j (r, φ), j = 1, 2, ..., 8 coaxial superposition, by giving each light field a different radius parameter R1 = 0.001m, R j =R1+0.005(j-1), we get Figure 1 As shown in (a), if the orbital angular momentum modes from inside to outside are l1 = -2, l2 = -1, l3 = -1, l4 = -3, l5 = -2, l6 = -6, l7 = -4, l8 = -7, the concentric perfect vortex two-dimensional light intensity distribution is obtained as follows Figure 1 (b) It can be clearly seen that the light spots of each unit are independent of each other in space.

[0071] The number of concentric perfect vortices is set to N=8, and the orbital angular momentum mode on each ring takes the value of l∈{-8,-7,…,7,8} and l≠0. Therefore, the number of possible values ​​of l on each ring is M=16. In this way, each orbital angular momentum mode is encoded in hexadecimal, where l=-8, l=-7,…, l=7, l=8 represent the hexadecimal symbols 0, 1,…, E, F respectively. Therefore, the digital sequence representing the information can eventually be mapped to a series of concentric perfect vortex spot patterns, realizing information encoding.

[0072] By adopting the orbital angular momentum mode selection of l∈{-8,-7,…,7,8} and l≠0 and setting the number of concentric perfect vortices N=8, the hexadecimal encoding of digital information is realized. Conversely, decoding can be achieved by obtaining the orbital angular momentum mode distribution of the concentric perfect vortices.

[0073] Example 5

[0074] Based on Example 4,

[0075] Consider interfering the concentric perfect vortex with the spherical wave to identify the orbital angular momentum modal information. The light field expression of the spherical wave is known to be:

[0076]

[0077] Where A′ is the amplitude constant, represents the finite beam width term of the spherical wave, d represents the distance from the spherical wave to the receiving screen. The light intensity expression after the interference of the concentric perfect vortex and the spherical wave is obtained as follows:

[0078] I=(U′+E sphere )·(U′+E sphere ) *

[0079] In the formula, the symbol "*" indicates the conjugated mode.

[0080] like Figure 2(a)-Figure 2(b) As shown, the two-dimensional distribution of light intensity after the interference of spherical waves and a single perfect vortex beam is shown. Figure 2(a) shows the interference result of the perfect vortex and spherical waves with l = -8. After observation, it is found that the interference pattern is transformed from the original bright ring to a rotating petal-shaped bright spot. The number of bright spots is equal to the size of the orbital angular momentum mode carried by the beam. Compared with the result of l = 8 in Figure 2(b), it is found that the rotation direction of the bright spot is related to the sign of the orbital angular momentum mode. In order to observe the rotation law more clearly, the interference result is partially enlarged. It is found that when l < 0, the rotation direction of the petal-shaped bright spot rotates counterclockwise from outside to inside, and when l > 0, the rotation direction of the petal-shaped bright spot rotates clockwise from outside to inside. Therefore, the orbital angular momentum mode sign information is obtained from the rotation direction of the bright spot rotation of the interference pattern.

[0081] like Figure 3 As shown, the hexadecimal decoding diagram designed by the present invention is given, showing the results of the interference of the perfect vortex beams of l=-8, l=-7, ..., l=7, l=8 with the spherical wave, and marking the hexadecimal numbers after the encoding and mapping of each orbital angular momentum mode. According to the decoding table, the pattern on each ring after the interference of the concentric perfect vortex and the spherical wave is compared, so as to obtain the overall distribution of the concentric perfect vortex orbital angular momentum mode, and obtain the hexadecimal decoding sequence table (as shown in Table 1) to achieve information restoration.

[0082] Table 1 Decoding sequence table

[0083]

[0084] Figure 3 The petals in the lower right corner represent the orbital angular momentum modulus (the absolute value of the mode) of the concentric perfect vortex. A clockwise distribution of the modulus from small to large indicates that the mode is positive, and a counterclockwise distribution of the modulus from small to large indicates that the mode is negative.

[0085] Example 6

[0086] The following is a detailed introduction combined with the image information encoding and decoding case.

[0087] Figure 4 The process of encoding and decoding 8-bit "Lena" image information based on concentric perfect vortices with N=8, l∈{-8,-7,…,7,8} and l≠0 is shown; the details are as follows:

[0088] First, read the gray value information of the "Lena" image. The four consecutive adjacent gray values ​​read are 103, 117, 98, and 65, respectively. The hexadecimal symbol sequence corresponding to the gray value is [6, 7, 7, 5, 6, 2, 4, 1], which is mapped to l = -8, l = -7, ..., l = 7, l = 8. The sixteen orbital angular momentum mode combinations are {-2, -1, -1, -3, -2, -6, -4, -7}, and the corresponding concentric perfect vortex is as follows: Figure 4 As shown on the far right of the first row, the encoding process is completed.

[0089] Interfering the concentric perfect vortex with the spherical wave, we get Figure 4 The pattern shown on the far right of the second row divides the interference result into 8 parts from the inside out with each ring as a unit, and obtains Figure 4 The results on the left side of the second row show that according to the number and direction of the rotating bright spots in the interference results, the orbital angular momentum modal information on each ring is obtained as {-2,-1,-1,-3,-2,-6,-4,-7}, which is then combined with Figure 3 The pattern comparison in the decoding table obtains the hexadecimal symbol sequence [6, 7, 7, 5, 6, 2, 4, 1], which is converted into the corresponding grayscale value information 103, 117, 98, 65 in groups of two hexadecimal numbers. That is, the grayscale values ​​of four adjacent pixels on the graphic are restored, and so on until the operation is completed for all pixels, thereby realizing the encoding and decoding transmission of image information.

[0090] It should be noted that the present invention is not limited to the above-mentioned specific embodiments. A person skilled in the art may make several improvements or substitutions based on the concept of the present invention, which should be regarded as falling within the scope of the present invention.

Claims

1. An information encoding and decoding method based on concentric perfect vortices, characterized in that: Taking advantage of the fact that the spot size of the perfect vortex beam is not affected by the value of the orbital angular momentum, by adjusting the spot radius parameter and setting the phase truncation factor, the perfect vortex is coaxially superimposed, and an information encoding and decoding method based on concentric perfect vortices is proposed.

2. The information encoding and decoding method based on concentric perfect vortices according to claim 1 is characterized in that: The specific steps are as follows: Step 1: Establish the light field expression of the perfect vortex beam; Step 2: Coaxially superimpose multiple perfect vortex beams, adjust the spot radius parameter, set the phase truncation factor, distinguish the perfect vortex beams at different spatial positions, and obtain the concentric perfect vortex light field expression after adding the phase truncation factor; Step 3: interfere the concentric perfect vortex with the spherical wave to obtain the light intensity expression after the interference of the concentric perfect vortex and the spherical wave; Step 4: Obtain the distribution of orbital angular momentum on each ring through the spot pattern of interference between spherical waves and concentric perfect vortices, and then realize information decoding based on the mapping relationship between different orbital angular momentum and digital symbols.

3. The information encoding and decoding method based on concentric perfect vortex according to claim 2 is characterized in that: The light field expression of the perfect vortex beam in step 1 is: In the cylindrical coordinate system, the light field expression of a perfect vortex beam is: Where (r, φ) represents polar coordinates, r and φ represent the polar diameter and polar angle respectively, i represents the imaginary unit, ω0 is the beam waist radius, ω is the width of the bright ring of the spot, R is the radius of the perfect vortex beam, and l represents the number of orbital angular momentum modes carried by the beam, that is, the topological charge.

4. The information encoding and decoding method based on concentric perfect vortices according to claim 3 is characterized in that: In step 2, multiple perfect vortex beams are coaxially superimposed. Assuming that the beam parameters except l and R remain the same, the light field expression after superposition is: In the formula, l j represents the topological charge of the jth superimposed perfect vortex from the inside out, E j (r, φ) represents the light field of the jth superimposed perfect vortex, R j represents the radius of the jth superimposed perfect vortex, and N represents the number of superimposed perfect vortex beams.

5. The information encoding and decoding method based on concentric perfect vortices according to claim 4 is characterized in that: In step 2, in order to avoid mutual interference between multiple superimposed perfect vortex beams, a phase truncation factor is set based on the superimposed light field expression to distinguish the perfect vortex beams at different spatial positions. The expression of the concentric perfect vortex light field is as follows: In the formula, R j and R s They respectively represent the radii of the j-th and s-th superimposed perfect vortices from the inside to the outside; N is the number of perfect vortices; r and φ represent the polar diameter and polar angle, respectively; thus, a concentric perfect vortex light field is obtained after the coaxial superposition of N perfect vortex beams.

6. The information encoding and decoding method based on concentric perfect vortices according to claim 1 is characterized in that: Step 3 is as follows: The concentric perfect vortex interferes with the spherical wave, and the expression of the spherical wave light field is: Where A′ is the amplitude constant, represents the finite beam width term of the spherical wave, d represents the distance from the spherical wave to the receiving screen. The light intensity expression after the interference of the concentric perfect vortex and the spherical wave is obtained as follows: I=(U′+E sphere )·(U′+E sphere ) * (6) In the formula, the symbol * Indicates the conjugate mode.

7. The information encoding and decoding method based on concentric perfect vortices according to claim 5 is characterized in that: In step 2, the radius parameter R, orbital angular momentum mode number l, and perfect vortex number N of any perfect vortex light field that constitutes the concentric perfect vortex can be independently controlled to form a multi-dimensional information encoding degree of freedom; by setting N different radius parameter values, the perfect vortex light beam is distributed to N different spatial positions, and the orbital angular momentum mode value combination is {l1,l2,…,l M }, then there are M choices for the value of l on each ring, and each form represents log2(M N ) bits of information.

8. The information encoding and decoding method based on concentric perfect vortices according to claim 7 is characterized in that: In step 4, a hexadecimal decoding table is designed to display the results of the interference between the perfect vortex light beams of l=-8, l=-7, ..., l=1, ..., l=7, and l=8 and the spherical wave, and the hexadecimal numbers after the encoding and mapping of each orbital angular momentum mode are identified, where l=-8, l=-7, ..., l=1, ..., l=7, and l=8 represent the hexadecimal symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F respectively, and the digital sequence representing the information can eventually be mapped to a series of concentric perfect vortex light spot patterns. According to the decoding table, the patterns on each ring after the interference between the concentric perfect vortex and the spherical wave are compared, so as to obtain the overall distribution of the concentric perfect vortex orbital angular momentum mode, obtain the hexadecimal decoding sequence, and realize information restoration.

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