An orbital angular momentum generator based on helically twisted photonic crystal fiber

Abstract

Invention Name: An orbital angular momentum generator based on a helically twisted photonic crystal fiber Abstract: The present invention discloses an orbital angular momentum generator based on a helically twisted photonic crystal fiber. A method of simplifying the analysis using the principle of optical transformation is proposed, and it is found that under the action of helical twisting, a specially designed photonic crystal fiber can generate higher-order orbital angular momentum modes. The specially designed photonic crystal fiber consists of three real fiber cores and a double cladding. The three real fiber cores are distributed in a regular triangle, and the air holes in the double cladding are distributed in a hexagonal pattern. The air holes in the inner and outer claddings are of different sizes. The diameter of the air holes in the inner cladding is smaller than that of the air holes in the outer cladding. The hole spacing between the two claddings is equal, and there is a certain distance between the double claddings to form a ring core. The orbital angular momentum generator of this application invention generates a large number of orbital angular momentums with a higher order and lower loss, which can be better compatible with the optical fiber communication system and reduce unnecessary losses.

Description

Technical Field

[0001] The present invention relates to the field of optical fiber technology, and in particular to an orbital angular momentum generator based on helical twisted photonic crystal fiber. Background Art

[0002] Orbital Angular Momentum (OAM) is a new dimension independent of traditional physical dimensions, carrying orbital angular momentum of The light is also called vortex beam, which has a wavefront phase factor exp(ilφ), where i is the imaginary unit, is the reduced Planck constant, l is the topological charge, and φ is the azimuthal coordinate of the spatial angular direction. Currently, optical orbital angular momentum has been applied in many fields, including optical tweezers, sensing, image processing, and communications. Since the OAM topological charge value is theoretically infinite and different OAM modes are orthogonal to each other, orbital angular momentum can be used for multiplexed communication. Among them, optical fiber-based orbital angular momentum multiplexing communication can solve the bottleneck problem of communication capacity, greatly improving the communication capacity and rate, and is a current research hotspot. Studying the generation of high-quality vortex beams is a key issue in improving the application of orbital angular momentum. However, general orbital angular momentum generators have low compatibility with optical fiber communication systems. Therefore, designing an orbital angular momentum generator with high optical fiber compatibility, high order, and high quality is an urgent problem to be solved.

[0003] Currently, there are two main methods for generating beams carrying orbital angular momentum. One is the spatial method, such as spiral phase plates, mode converters, and silicon integrated devices. The other is the fiber method, such as fiber couplers, special fiber Bragg gratings, and helically twisted fibers. Among them, the use of fiber methods to generate orbital angular momentum can be coupled with fiber systems to improve compatibility, thereby reducing unnecessary losses. The relatively simple and low-cost production of helically twisted fibers has attracted the attention of experts at home and abroad. The order of orbital angular momentum currently generated by helically twisted fibers is relatively low, and it is necessary to design new optical fibers to generate high-order orbital angular momentum through helically twisting. Summary of the Invention

[0004] The purpose of the present invention is to provide an orbital angular momentum generator based on a helically twisted photonic crystal fiber, so as to achieve better coupling of the generated orbital angular momentum into a fiber orbital angular momentum multiplexing communication system, while reducing the generated orbital angular momentum mode loss and improving the generated orbital angular momentum quality.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] Step 1: A photonic crystal fiber that can be used for orbital angular momentum transmission is designed. The characteristics are: the photonic crystal fiber consists of three real fiber cores and a double cladding. The air holes in the double cladding are circular and distributed in a hexagonal pattern. The three air holes distributed at a 120-degree angle around the middle air hole in the inner cladding are removed to form three real fiber cores distributed in a regular triangle. There is a certain distance between the two claddings to form a ring core. In this case, the ring core can support intrinsic modes. The same-order intrinsic odd and even modes with a phase difference of π / 2 can be superimposed to form an OAM mode, so that the fiber supports orbital angular momentum transmission. The specific superposition formula is:

[0007] Where l is the orbital angular momentum order, m is the radial mode order, and j is the π / 2 phase difference.

[0008] Furthermore, the base material of the optical fiber is silica.

[0009] Step 2: Helical twisting of the photonic crystal fiber designed in step 1 forms an orbital angular momentum generator with a twist period of Λ L , the distortion rate is α=2π / Λ L , and then the three-dimensional problem is converted into a two-dimensional problem through optical transformation for research. Under the action of the helical twisting force, the eigenmode supported by the ring core will carry orbital angular momentum. For a specific twist rate and wavelength, the core supermode and the ring core mode will resonate and couple to form a hybrid mode state. At this time, the hybrid mode carries orbital angular momentum and can be called an orbital angular momentum mode. By observing the loss peak in the loss spectrum of the core supermode at different twist rates, the wavelength where the resonant coupling occurs can be found, and then the conditions for generating orbital angular momentum can be determined. The calculation formula for mode loss is:

[0010] Where L is the mode loss value, λ is the wavelength, Im(n eff ) is the imaginary part of the effective refractive index of the core supermode, n eff is the effective refractive index, in dB·m -1 .

[0011] Step 3: Analyze the mode electromagnetic field of the orbital angular momentum generator based on the helically twisted photonic crystal fiber in step 2 to obtain the effective refractive index and electromagnetic field distribution of the core supermode, ring core mode and orbital angular momentum mode, and then know the influence of helical twist on the effective refractive index of the fiber mode; analyze the phase of the orbital angular momentum mode to determine the corresponding generated orbital angular momentum order; study the changes in the effective refractive index of the core supermode and ring core mode to know the matching conditions for resonant coupling.

[0012] The present invention designs an orbital angular momentum generator based on a helical twisted photonic crystal fiber. Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0013] When α = 7853.982 rad / m, the generated OAM modes include "OAM -4,1 , OAM +9,1 , OAM +10,1 , OAM +11,1 , OAM +13,1 ", where "OAM+13,1" is the highest-order OAM mode with the lowest loss that can be generated using helically twisted optical fiber. When α ≥ 8377.58 rad / m, the number of generated OAM modes is no less than 10.

[0014] The generated OAM mode loss is low. When α = 7853.982 rad / m, the loss of all modes is less than 1.64×10 -3 dB / m, which is at least two orders of magnitude lower than the OAM mode loss generated by existing helically twisted optical fibers, improving the practical application value of orbital angular momentum generators.

[0015] The generated OAM mode has a high purity. When α = 7391.983 rad / m, α = 7853.982 rad / m and α = 8377.58 rad / m, the OAM mode purity is greater than 93%. The generated orbital angular momentum has high quality and low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a schematic cross-sectional view of an orbital angular momentum generator based on a helically twisted photonic crystal fiber, according to a specific embodiment. In the figure: 1 - inner cladding air holes, 2 - outer cladding air holes, 3 - background silica material, 4 - three solid fiber cores, d1 - inner cladding air hole diameter, Λ1 - inner cladding air hole spacing, d2 - outer cladding air hole diameter, Λ2 - outer cladding air hole spacing. H - annular core width, R2 - overall fiber cross-sectional radius.

[0017] Figure 2 5 is a three-dimensional schematic diagram of an orbital angular momentum generator based on a helical twisted photonic crystal fiber in a specific embodiment. 5 is a cross section of the orbital angular momentum generator, i.e., Figure 1 .

[0018] Figure 3 The figure shows the circular birefringence of the core supermode in an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment.

[0019] Figure 4 In a specific embodiment, a ring core of an orbital angular momentum generator based on a helical twisted photonic crystal fiber is supported Mode phase distribution diagram.

[0020] Figure 5 In a specific embodiment, a ring core of an orbital angular momentum generator based on a helical twisted photonic crystal fiber is supported Mode phase distribution diagram.

[0021] Figure 6 FIG1 is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 7853.982 rad / m, showing a loss peak at a wavelength λ=1360 nm.

[0022] Figure 7 FIG1 is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 7853.982 rad / m, showing loss peaks at wavelengths λ=1820 nm and λ=1900 nm.

[0023] Figure 8 This is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 7853.982 rad / m, showing a loss peak at a wavelength λ=1940 nm.

[0024] Figure 9 This is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 7853.982 rad / m, showing loss peaks at wavelengths λ=2000 nm and λ=2530 nm.

[0025] Figure 10 In a specific embodiment, an orbital angular momentum generator based on a helical twisted photonic crystal fiber has a twist rate of α = 7853.982 rad / m, and the core supermodes "M1, M2, M4, M5" and the ring core mode "OAM 10,1 , OAM 11,1 , OAM 13,1 ,” changes with wavelength.

[0026] Figure 11 In a specific embodiment, an orbital angular momentum generator based on a helical twisted photonic crystal fiber has a twist rate of α = 7853.982 rad / m, and the core supermodes "M1, M2, M3, M5, M6" and the ring core mode "OAM 4,1 , OAM 9,1 , OAM 10,1 ” changes with wavelength.

[0027] Figure 121 is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 7391.983 rad / m.

[0028] Figure 13 1 is a loss spectrum of a core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rate α is 8377.58 rad / m.

[0029] Figure 14 Schematic diagram of the orbital angular momentum mode purity of an orbital angular momentum generator based on a helically twisted photonic crystal fiber in a specific embodiment when the twist rates are α=7391.983 rad / m, α=7853.982 rad / m and α=8377.58 rad / m respectively. DETAILED DESCRIPTION

[0030] The present invention will be further described in detail below with reference to the accompanying drawings and through examples. The following examples are intended to explain the present invention but the present invention is not limited to the following examples.

[0031] Figure 1 The figure shows a cross-sectional schematic diagram of an orbital angular momentum generator based on a helically twisted photonic crystal fiber according to the present invention. The orbital angular momentum generator mainly includes two parts, namely three solid fiber cores and a double cladding structure, wherein a certain distance exists between the double claddings to form a ring core. The background material of the optical fiber is silica, and the rest is air holes. The radius of the entire optical fiber cross section is R2. The diameter of the inner cladding air hole is d1, the diameter of the outer cladding air hole is d2, and d2>d1. The hole spacing of the inner cladding air hole is Λ1, the hole spacing of the outer cladding air hole is Λ2, and Λ1=Λ2. The twist period of the optical fiber is Λ L , the distortion rate is α.

[0032] In this embodiment, the parameters of an orbital angular momentum generator based on a helically twisted photonic crystal fiber are as follows: the inner and outer cladding air hole diameters d1 and d2 are 1 μm and 1.6 μm, respectively. The inter-cladding air hole spacings Λ1 and Λ2 are 2.2 μm and 2.2 μm, respectively. The annular core width H between the double claddings is 3.1 μm. The radius R2 of the entire fiber cross section is 19.14 μm. The twist rate α is the variable of interest, with values ​​ranging from α = 7391.983 rad / m, α = 7853.982 rad / m, and α = 8377.58 rad / m.

[0033] During the analysis, the present invention simplifies the three-dimensional problem into a two-dimensional problem through the principle of optical transformation. The finite element method is used in combination with the perfect matching layer boundary absorption condition to perform theoretical calculations to obtain the modes supported by the fiber core and the ring core of the present invention. The effective refractive index of the mode, the thin supermode loss spectrum and the generated OAM mode purity are calculated. The specific principles of optical transformation are as follows:

[0034] The spiral coordinate system for three-dimensional problems is (ξ1, ξ2, ξ3), and the Cartesian coordinate system for two-dimensional problems is (x, y, z). The parameter conversion relationship between the two coordinate systems is:

[0035]

[0036] The Jacobian matrix of the conversion relationship between three-dimensional coordinates and two-dimensional coordinates is:

[0037]

[0038] The transformation of the coordinate system is equivalent to replacing the isotropic material with an inhomogeneous anisotropic equivalent material. In this case, the dielectric tensor ε' in the spiral coordinate system is εT -1 and the magnetic permeability tensor μ'=μT -1 are all tensors, and ε=n 2 and μ = 1 are the dielectric constant and magnetic permeability in Cartesian coordinates, respectively, and both are real numbers, n is the refractive index of the material, T is the transformation matrix between the two coordinates, and its inverse matrix is ​​T -1 :

[0039]

[0040]

[0041] When the helical twisted perfectly matched layer is formed, the rectangular coordinate system is first converted to the cylindrical coordinate system (ρ, θ, z), and the complex constant s is introduced. ρ ,use represents the complex stretched form of ρ. Then the cylindrical coordinate system is converted to the spiral coordinate system, and the spiral torsion angle is introduced The transformation matrix and inverse matrix of the two coordinate transformations are T PML and At this time, the dielectric tensor of the replaced material is The magnetic permeability tensor is

[0042]

[0043] in

[0044] In this embodiment, an orbital angular momentum generator based on a helically twisted photonic crystal fiber has three real fiber cores supporting six supermodes, namely, modes "M1, M2, M3, M4, M5, M6". According to the polarization direction of the supermode, it can be divided into left-handed (LP) polarization modes (M1, M2 and M4) and right-handed (RC) polarization modes (M3, M4 and M5). Since the effective refractive index values ​​are approximately equal when α = 0, the six supermodes can be divided into three module groups, namely, module 1 "M2 and M3", module 2 "M5 and M6", and module 3 "M1 and M4". When the α value increases, the three modules will experience circular birefringence, such as Figure 3 As shown, observe Figure 3 It can be seen that:

[0045] The orbital angular momentum generator based on a helically twisted photonic crystal fiber described in the present invention exhibits circular birefringence in the three modules as the twist rate increases. This means that the effective refractive index of the left-handed and right-handed polarization modes in the three modules splits, and the splitting changes in a symmetrical "<" pattern as the twist rate increases. Specifically, one of the two supermodes in each module increases with the twist rate, while the other decreases. The specific relationship between the effective refractive index changes is:

[0046]

[0047] Among them, n eff ' is the effective refractive index of the mode after optical fiber twisting, n eff is the effective refractive index of the untwisted fiber mode, k is the total order of the mode (k = l + s), s is the spin angular momentum, λ is the wavelength, and Λ L is the twist period, and α is the twist rate.

[0048] The orbital angular momentum generator ring core based on helical twisted photonic crystal fiber described in the present invention can support intrinsic modes (EH mode and HE mode). Figure 4 and Figure 5 Ring core supported and Mode phase diagram, observation Figure 4 and Figure 5 It can be seen that the phase diagram has a spiral phase wavefront for the following reasons:

[0049] When the photonic crystal fiber described in the present invention is free of helical twist, the Poynting vector of the fiber mode precisely points in the direction of the fiber axis. However, when the photonic crystal fiber is helically twisted, a helical channel is induced, forcing light in the annular core to propagate along a helical path. This forces some of the light energy to point transversely to the fiber. This means that the Poynting vector of the fiber mode partially points transversely to the fiber plane, causing the mode to carry orbital angular momentum. At this point, the intrinsic HE and EH modes can be considered weak OAM modes.

[0050]

[0051] Where l is the fiber mode order, m is the radial mode order, which is generally set to 1, and even and odd are the even and odd modes of HE and EH modes, respectively. The superscript "±" represents the left and right circular polarization directions, and the subscript "±" represents the direction of the spiral wavefront. Figure 4 and Figure 5 If the spiral wavefront rotates counterclockwise, its orbital angular momentum order l>0; if the spiral wavefront rotates clockwise, its orbital angular momentum order l<0; when the polarization direction rotates counterclockwise, it is the RC polarization state, and its spin angular momentum s=-1; when the polarization direction rotates clockwise, it is the LC polarization state, and its spin angular momentum s=+1.

[0052] When the twist rate of the orbital angular momentum generator based on the helical twisted photonic crystal fiber of the present invention is α=7853.982rad / m, the loss spectrum of the core supermode is as follows: Figure 6-Figure 9 As shown, observe Figure 6-Figure 9 It can be seen that:

[0053] The core supermode of an orbital angular momentum generator based on a helically twisted photonic crystal fiber described in the present invention exhibits a loss peak at a specific wavelength. This is because at this wavelength, the core supermode and the ring core mode undergo resonant coupling, which increases the loss of the core supermode. At this point, the fiber is in a hybrid mode state, and both the core supermode and the ring core mode carry orbital angular momentum. Therefore, the hybrid mode is also called the orbital angular momentum mode, and the loss value of the orbital angular momentum mode is relatively ideal, less than 1.64×10 -3 dB / m. Combining formula (9), we can know:

[0054] The invention discloses an orbital angular momentum generator based on a helical twisted photonic crystal fiber, which can generate "OAM" when the twist rate is α = 7853.982 rad / m. -4,1 , OAM +9,1 , OAM +10,1 , OAM +11,1 , OAM +13,1 "Orbital angular momentum mode, a total of 9 loss peaks.

[0055] When the twist rate of the orbital angular momentum generator based on the helical twisted photonic crystal fiber of the present invention is α=7853.982rad / m, the relationship between the effective refractive index of the core supermode and the ring core mode and the wavelength is as follows: Figure 10 and Figure 11 As shown, observe Figure 10 and Figure 11 It can be seen that:

[0056] The resonant coupling between the core supermode and the ring core mode in the orbital angular momentum generator based on the helical twisted photonic crystal fiber described in the present invention needs to meet the matching conditions:

[0057] n co =n rc (10)

[0058] where n co and n rc are the effective refractive index of the supermode and the ring core mode after the optical fiber is twisted.

[0059] When the twist rates of the orbital angular momentum generator based on the helical twisted photonic crystal fiber of the present invention are α=7391.983rad / m and α=8377.58rad / m, the loss spectra of the core supermode are as follows: Figure 12 and Figure 13 As shown, observe Figure 12 and Figure 13 It can be seen that:

[0060] The orbital angular momentum generator based on helical twisted photonic crystal fiber described in the present invention can generate "OAM" after the structure is determined. -4,1 , OAM +9,1 , OAM +10,1 , OAM +11,1 , OAM +13,1 " modes, but the number varies. That is, the theoretically possible OAM modes are definite, but the actual possible OAM modes are related to the twist rate. When α = 7391.983 rad / m, there are 7 loss peaks in total. When the twist rate α ≥ 8377.58 rad / m, at least 10 loss peaks are generated.

[0061] When the twist rate of the orbital angular momentum generator based on the helical twisted photonic crystal fiber of the present invention is different,

[0062] The OAM mode purity changes as Figure 14 As shown, observe Figure 14 It can be seen that:

[0063] The orbital angular momentum generator based on helically twisted photonic crystal fiber described in the present invention has excellent characteristics, and the purity of the generated OAM mode is greater than 93%.

[0064] The above is only one embodiment of the present invention, not all or the only embodiment. Any equivalent transformation of the technical solution of the present invention made by ordinary technicians in this field after reading the specification of the present invention is covered by the claims of the present invention.

Claims

1. An orbital angular momentum generator based on a helical twisted photonic crystal fiber, which applies helical twist to a specially designed photonic crystal fiber to achieve the generation of higher-order orbital angular momentum, characterized in that: The following steps are involved: Step 1: A photonic crystal fiber that can be used for orbital angular momentum transmission is designed, characterized in that: the photonic crystal fiber consists of three real fiber cores and a double cladding, small air holes close to the fiber core constitute the inner cladding, and large air holes away from the fiber core constitute the outer cladding, the distance between two adjacent air holes is the hole spacing, and the hole spacings are equal, the air holes in the double cladding are circular and distributed in a hexagonal pattern as a whole, removing the inner cladding and surrounding the middle air hole at an angle of 120 degrees to form three real fiber cores distributed in a regular triangle, and a certain distance between the two claddings forms a ring core. At this time, the ring core can support intrinsic modes, and the same-order intrinsic odd and even modes with a phase difference of π / 2 can be superimposed into OAM modes, so that the fiber supports orbital angular momentum transmission. The specific superposition formula is: Where l is the orbital angular momentum order, m is the radial mode order, and j is the π / 2 phase difference; Step 2: Helical twisting of the photonic crystal fiber designed in step 1 forms an orbital angular momentum generator with a twist period of Λ L , the distortion rate is α=2π / Λ L , and then the three-dimensional problem is converted into a two-dimensional problem through the principle of optical transformation for research. Under the action of spiral twisting, the intrinsic mode supported by the ring core will carry orbital angular momentum. For specific twist rates and wavelengths, the core supermode and the ring core mode resonate and couple to form a hybrid mode state. At this time, the hybrid mode carries orbital angular momentum and can be called orbital angular momentum mode. By observing the loss peak in the core supermode loss spectrum at different twist rates, the specific wavelength where resonant coupling occurs can be found, and then the conditions for generating orbital angular momentum can be determined. The calculation formula for mode loss is: Where L is the mode loss value, λ is the wavelength, Im(n eff ) is the imaginary part of the effective refractive index of the core supermode, n eff is the effective refractive index, in dB·m -1 ; Step 3: Analyze the mode electromagnetic field of the orbital angular momentum generator based on the helically twisted photonic crystal fiber in step 2 to obtain the effective refractive index and electromagnetic field distribution of the core supermode, ring core mode and orbital angular momentum mode, and then know the influence of helical twist on the effective refractive index of the fiber mode; analyze the phase of the orbital angular momentum mode to determine the corresponding generated orbital angular momentum order; study the changes in the effective refractive index of the core supermode and ring core mode to know the matching conditions when resonant coupling occurs.

2. An orbital angular momentum generator based on a helically twisted photonic crystal fiber according to claim 1, characterized in that: The base material of the optical fiber in step 1 is silicon dioxide.

3. The orbital angular momentum generator based on a helically twisted photonic crystal fiber according to claim 1, characterized in that: In step 2, the three-dimensional problem is converted into a two-dimensional problem through optical transformation, and then the fiber mode is analyzed. Optical changes can reduce the complexity of research. The specific principle formula is: The spiral coordinate system for three-dimensional problems is (ξ1, ξ2, ξ3), and the Cartesian coordinate system for two-dimensional problems is (x, y, z). The parameter conversion relationship between the two coordinate systems is: where α = 2π / Λ L is the twist rate, in rad·m -1 , the Jacobian matrix reflecting the transformation relationship between the two coordinates is: The transformation of the coordinate system is equivalent to replacing the isotropic material with an inhomogeneous anisotropic equivalent material. In this case, the dielectric tensor ε' in the spiral coordinate system is εT -1 and the magnetic permeability tensor μ'=μT -1 are all tensors, and ε=n 2 and μ = 1 are the dielectric constant and magnetic permeability in Cartesian coordinates, respectively, and are both real numbers. n is the refractive index of the material. T is the transformation matrix between the two coordinates, which depends only on ξ1 and ξ2. Its inverse matrix is ​​T -1 : 。 .

4. The orbital angular momentum generator based on a helically twisted photonic crystal fiber according to claim 1, characterized in that: a. The eigenmode supported by the ring core after the fiber helical twist carries orbital angular momentum. In this case, the eigenmode can be directly regarded as a discrete weak OAM mode. b. When α ≥ 8377.58 rad / m, the core supermode and the ring core mode resonate and couple to generate at least 10 OAM modes, of which the +13th order is the highest-order and lowest-loss orbital angular momentum mode currently generated by the helically twisted fiber method. The resonant coupling needs to meet the matching conditions: n co =n rc (8) Where n co and n rc are the effective refractive index of the supermode and the ring core mode after the optical fiber is twisted; c. The effective refractive index change relationship of the twisted fiber mode is: Among them, n eff ' is the effective refractive index of the mode when the optical fiber is twisted, n eff is the effective refractive index of the fiber mode when it is not twisted, k is the total order of the mode (k = l + s), s is the order of spin angular momentum, λ is the wavelength, Λ L is the twist period, and α is the twist rate.

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