Optical device based on a beam of flexural waves of metamaterial and method of implementation

Abstract

The application discloses an optical device based on a transformed material curved wave beam and an implementation method, and belongs to the technical field of transformed materials and optical signal processing technology.The optical device comprises an input surface, a two-dimensional straight-edge Eaton lens based on a transformed material curved wave beam and an output surface.The application adopts a transformed optical method to transform a traditional Eaton lens into a straight-edge lens, obtains a transformation relationship between the traditional Eaton lens through conformal transformation, and then obtains medium parameters by using a transformed material method.The incident angle and the exit angle of light on the transformed two-dimensional straight-edge Eaton lens remain unchanged, the light rays which are at the same angle with the normal line of each point of the input surface in the traditional Eaton lens are equivalent to parallel light rays after transformation, the incident angle of the light rays is equal to the exit angle, the propagation path of the wave beam is changed with the change of the incident angle, the wave beam path can reach a very wide curved angle, and variable-angle turning can be realized in a single device;the isotropy is ensured, and the preparation in engineering is facilitated.

Description

Technical Field

[0001] The present invention relates to an optical device for bending beams based on transformation materials and an implementation method thereof, belonging to the technical field of transformation materials and optical signal processing. Background Art

[0002] Controlling the propagation direction of a light beam is crucial for wave manipulation and is widely used in integrated optics, optical communications, laser processing, lidar, biomedicine and other fields.

[0003] Traditional beam steering uses a waveguide cavity with a specific spatial structure, but this approach has significant drawbacks. Waveguide cavities have a cutoff frequency, below which electromagnetic wave propagation is suppressed. Furthermore, the beam bending provided by waveguide cavities is insufficient for applications requiring large curvatures. Furthermore, their production is costly and complex, requiring high-precision manufacturing techniques.

[0004] Another way to bend the beam is to use a gradient refractive index (GRIN) medium to rotate the wavefront of the incident beam so that the propagation direction of the outgoing beam can be changed, overcoming the defects of the waveguide cavity. This is usually called a beam bender. The commonly used method to design GRIN beam benders is transformation optics (TO), but most of these beam benders are non-uniform and anisotropic, posing challenges to manufacturing and large bandwidth. More importantly, all previous beam benders can only bend the beam path at a fixed angle, which imposes some limitations on its flexibility. When the system requires different beam adjustment angles, the device must be replaced. Therefore, it is of great significance to use the same beam bender to achieve multi-angle and large-range beam steering.

[0005] Transformation optics is a method for solving the inverse problem of electromagnetic field distribution and electromagnetic parameters. Based on the form invariance of Maxwell's equations, the problem of solving the electromagnetic parameters corresponding to the wave field is converted into the problem of geometric shape design and coordinate transformation parameter calculation. The materials obtained by transformation optics are called transformation materials.

[0006] The traditional Eaton lens is a circular gradient refractive index lens with a special refractive index distribution. The refractive index increases radially from the outer surface to the center. It can turn a parallel light beam 180 degrees to achieve reverse reflection. It is a device that can return the incident wave to its source. Summary of the Invention

[0007] To address the problem that conventional beam benders can only bend a beam to a fixed angle regardless of the incident angle, the present invention aims to provide an optical device and implementation method for beam bending based on transformation materials. This device allows the beam propagation path to change with the incident angle, enabling multi-angle and wide-range beam bending without replacing the equipment. Based on the desired light field distribution, transformation optics is used to conformally transform a conventional Eaton lens. The light wave trajectory is controlled based on the properties of the transformation medium. Transformation optics methods are then used to determine the medium parameters of the optical device, guiding the light wave to propagate along a predetermined path within the optical device to achieve the desired light field distribution.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] The optical device for bending beams based on transformation materials disclosed in the present invention comprises an input surface, a two-dimensional straight-edge Eaton lens for bending beams based on transformation materials, and an output surface.

[0010] The input surface is the incident surface of the input signal entering the two-dimensional straight-edge Eaton lens based on the transformation material bending beam. The input surface is a plane. The input surface is obtained by conformal transformation of the input surface of a traditional Eaton lens with a radius R and a center (0,0) and a radially gradient refractive index. That is, the left semicircular arc of the traditional Eaton lens becomes the left boundary of the transformed two-dimensional straight-edge Eaton lens. The input surface is conformally transformed based on the input surface of the traditional Eaton lens, so that the shape of the input surface of the traditional Eaton lens is changed. Points on the input surface are in a one-to-one correspondence with points on the input surface of the traditional Eaton lens before the conformal transformation, and the refractive index of the input surface gradually decreases from the center point to both sides.

[0011] Compared to a traditional Eaton lens, the two-dimensional straight-edge Eaton lens based on a transformation material for beam bending has a shape changed from circular to rectangular. By using transformation optics, the radial gradient refractive index distribution of the traditional Eaton lens is altered, resulting in a conformal transformation in which the refractive index of the two-dimensional straight-edge Eaton lens is axially symmetrical about the lines x=0 and y=0, with the refractive index at the center being infinite. The middle portion of the conformal transformation lens is cut off to serve as the lens body of the two-dimensional straight-edge Eaton lens. The size of the cutoff portion is selected based on the steering angle range and the principle of material conservation, and the refractive index greater than a preset refractive index value is filled to the preset refractive index value. The refractive index distribution determines the propagation path of light in the lens. As long as the refractive index distribution is satisfied, the shape of the two-dimensional straight-edge Eaton lens based on a transformation material for beam bending is not restricted by the shape of the two-dimensional straight-edge Eaton lens. When a beam of parallel light is incident on the input surface of the two-dimensional straight-edge Eaton lens at an angle of θ with the positive axis of the x-axis, the light output is divided into two situations according to whether the light steering angle exceeds 180°. One is the steering of the light within the steering angle of 180°. At this time, the light incident surface and the light exit surface are two opposite surfaces. The light is emitted at an angle of θ on the output surface of the two-dimensional straight-edge Eaton lens, and the exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is 2θ; the other is the steering of the light with a steering angle exceeding 180°. The light incident surface and the light exit surface are the same surface. The light is emitted at an angle of θ on the output surface of the two-dimensional straight-edge Eaton lens, and the exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is π+2θ.

[0012] The preset refractive index value is selected based on the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, and takes into account the manufacturing difficulty. The larger the preset refractive index value, the more difficult it is to manufacture; the smaller the preset refractive index value, the larger the range of refractive index that needs to be intercepted, and the greater the impact on the light trajectory.

[0013] The output surface refers to the right boundary of the two-dimensional straight-edge Eaton lens transformed from the right semicircular arc of the traditional Eaton lens when the light beam turns within 180°. Compared with the input signal, the propagation direction of the light beam changes.

[0014] Through conformal transformation, the optical device maintains a one-to-one correspondence between the transformed two-dimensional straight-edge Eaton lens and the conventional Eaton lens before the transformation. Based on the desired light field distribution, the conventional Eaton lens is conformally transformed using transformation optics. The trajectory of the light wave is controlled based on the properties of the transformation medium, guiding the light wave to propagate along a preset path within the optical device to achieve the desired light field distribution. This one-to-one correspondence means that points on the conventional Eaton lens before the transformation correspond to points on the transformed two-dimensional straight-edge Eaton lens, the refractive index of the conventional Eaton lens before the transformation corresponds to the refractive index of the transformed two-dimensional straight-edge Eaton lens, and the shape of the conventional Eaton lens before the transformation is circular, while the shape of the transformed two-dimensional straight-edge Eaton lens is rectangular.

[0015] The present invention discloses a method for realizing an optical device for bending beams based on a transformation material, comprising the following steps:

[0016] Step 1: Perform a conformal transformation W = tan(Z) on the traditional Eaton lens to obtain an infinite two-dimensional straight-edge Eaton lens. Using transformation optics, determine the dielectric constant and magnetic permeability of the new lens after the transformation, and obtain the transformed refractive index.

[0017] The traditional Eaton lens corresponds to the original complex plane W = u + iv, which is a virtual space, where u is the real part of the original complex plane W, and v is the imaginary part of the original complex plane W;

[0018] The two-dimensional straight-edge Eaton lens corresponds to the transformed complex plane Z=x+iy, which is the physical space, where x is the real part of the transformed complex plane Z and y is the imaginary part of the transformed complex plane Z;

[0019] When the original complex plane W is conformally transformed into the transformed complex plane Z, according to the coordinate invariance of Maxwell's equations, the relationship between the physical space (x, y, Z) and the virtual space (u, v, W) is as shown in Equation (1):

[0020]

[0021] Where ε and μ are the dielectric constant and magnetic permeability of the virtual space W, ε′ and μ′ are the dielectric constant and magnetic permeability of the physical space Z, detA is the determinant of the matrix A, and A is the Jacobian matrix, as shown in formula (2):

[0022]

[0023] The spatial transformation relationship between virtual space W and physical space Z is shown in formula (3):

[0024]

[0025] in, represents partial differential;

[0026] According to Fermat's theorem, the relationship between the optical path of the physical space Z and the optical path of the virtual space W is shown in formula (4):

[0027]

[0028] According to formula (4),

[0029] Among them, d represents the differential, n w is the refractive index of the virtual space W, n z is the refractive index of physical space Z,

[0030]

[0031] After the virtual space W is conformally transformed into the physical space Z, the left semicircular arc boundary of the traditional Eaton lens before the transformation is the input surface, the right semicircular arc boundary of the traditional Eaton lens when turning within 180° is the output surface, and the left semicircular arc of the traditional Eaton lens when turning more than 180° is the output surface. The input surface and the output surface change from curved surfaces to straight surfaces before and after the transformation, are compressed at the midpoint, and are first compressed and then stretched to both sides.

[0032] Step 2: Cut the middle part of the infinite two-dimensional straight-edge Eaton lens obtained in step 1, select a preset refractive index value based on the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, and consider the manufacturing difficulty, fill the part with a refractive index greater than the preset refractive index value with the preset refractive index value, and obtain a two-dimensional straight-edge Eaton lens with a width of π / 2, a height of b, and a refractive index less than or equal to the preset refractive index value, thereby obtaining an optical device for bending beams based on transformation materials.

[0033] Beneficial effects:

[0034] 1. The optical device and implementation method for bending beams based on transformation materials disclosed in the present invention use transformation optics to unfold the input and output surfaces of a traditional Eaton lens into straight surfaces. Based on the properties of transformation optics, the incident and exit angles of light on the transformed two-dimensional straight-edge Eaton lens remain unchanged. In the traditional Eaton lens, light that is at the same angle to the normal of each point on the input surface is equivalent to a beam of parallel light after transformation, and is also a beam of parallel light when emitted, and the incident and exit angles of the light are equal, thereby changing the propagation path of the beam with different incident angles and achieving variable-angle steering within a single device.

[0035] 2. The optical device and implementation method based on the transformation material bending beam disclosed in the present invention assume that parallel light is horizontally incident on the left semicircular arc of the traditional Eaton lens. When expanded in the horizontal direction, the incident and outgoing light rays are on two different semicircular arcs of the traditional Eaton lens, corresponding to the light trajectory of the two-dimensional straight-edge Eaton lens after the transformation. At this time, the incident and outgoing light rays are on different surfaces of the two-dimensional straight-edge Eaton lens. When expanded in the vertical direction, the incident and outgoing light rays are on the same semicircular arc of the traditional Eaton lens, corresponding to the light trajectory of the two-dimensional straight-edge Eaton lens after the transformation. At this time, the incident and outgoing light rays are on the same surface of the two-dimensional straight-edge Eaton lens. In this way, both steering within 180° and large-angle steering exceeding 180° can be achieved.

[0036] 3. The method for realizing an optical device for bending beams based on transformation materials disclosed in the present invention, based on the beneficial effects 1 and 2, adopts conformal transformation to ensure the isotropy of a two-dimensional straight-edge Eaton lens, which is conducive to the manufacture of a two-dimensional straight-edge Eaton lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of the structure of the "optical device for bending beams based on transformation materials" of the present invention, i.e., a refractive index distribution diagram of the device;

[0038] Figure 2 Schematic diagram of the virtual space W and the physical space Z of the conformal transformation in the present invention "A method for realizing an optical device based on a transformation material bending beam", wherein Figure 2 (a) is the virtual space W, Figure 2 (b) is the physical space Z;

[0039] Figure 3 This is the geometric simulation result of the beam steering when the incident window is [-0.1, 0.1] for the present invention "An optical device for bending beams based on transformation materials", where Figure 3 (a) is oblique upward incidence, θ = 20°, Figure 3 (b) is oblique upward incidence, θ = 30°, Figure 3 (c) is oblique upward incidence, θ = 60°, Figure 3 (d) is oblique upward incidence, θ = 70°;

[0040] Figure 4 This is the geometric optics simulation result of the invention's "An optical device based on transformation material bending beam" when the incident window is [0.5, 0.8] and the light beam is turned within 180°. Figure 4 (a) is oblique downward incidence, θ = 30°, Figure 4 (b) is oblique downward incidence, θ = 50°, Figure 4 (c) is oblique downward incidence, θ = 60°, Figure 4 (d) is oblique downward incidence, θ = 70°;

[0041] Figure 5 This is the geometric optics simulation result of the invention's "An optical device for bending beams based on transformation materials" when the incident window is [0.5, 0.8] and the beam is turned more than 180°. Figure 5 (a) is oblique upward incidence, θ = 10°, Figure 5 (b) is oblique upward incidence, θ = 20°, Figure 5 (c) is oblique upward incidence, θ = 30°, Figure 5 (d) is oblique upward incidence, θ = 40°;

[0042] Figure 6 This is the wave optics simulation result of the invention "An optical device based on bending beams of transformation materials" when the incident window is [0.5, 0.8], where Figure 6 (a) is oblique downward incidence, θ = 40°, Figure 6 (b) is oblique upward incidence, θ = 20°. DETAILED DESCRIPTION

[0043] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0044] Example 1:

[0045] An optical device based on transforming material beam bending, wherein a transformed two-dimensional straight-edge Eaton lens maintains a one-to-one correspondence with a traditional Eaton lens through conformal transformation, comprising: an input surface, a two-dimensional straight-edge Eaton lens based on transforming material beam bending, and an output surface;

[0046] like Figure 1 As shown, ABCD is a composition diagram of an optical device for bending beams based on transformation materials. The left boundary AB is the input surface, and the right boundary CD is the output surface when the light beam is turned within 180°. When the light beam is turned more than 180°, the left boundary AB is both the input surface and the output surface.

[0047] The input surface is the incident surface of the input signal entering the two-dimensional straight-edge Eaton lens based on the transformation material bending beam. The input surface is a plane. The input surface is obtained by conformally transforming the input surface of a traditional Eaton lens with a radius R=1 and a center (0,0) with a radially gradient refractive index. That is, the left semicircular arc of the traditional Eaton lens is transformed into the left boundary of the transformed two-dimensional straight-edge Eaton lens. The left boundary corresponds to the line x=-π / 4, and the portion of the left boundary where -1≤y≤1 is intercepted. The input surface is conformally transformed based on the input surface of the traditional Eaton lens, so that the shape of the input surface of the traditional Eaton lens is changed. Points on the input surface are in a one-to-one correspondence with points on the input surface of the traditional Eaton lens before the conformal transformation, and the refractive index of the input surface gradually decreases from the center point to both sides.

[0048] Compared to a traditional Eaton lens, the two-dimensional straight-edge Eaton lens based on a transformation material for beam bending has a shape changed from circular to rectangular. By using transformation optics, the radial gradient refractive index distribution of the traditional Eaton lens is altered, resulting in a conformal transformation in which the refractive index of the two-dimensional straight-edge Eaton lens is axially symmetrical about the lines x=0 and y=0, with an infinite refractive index at the center. The portion of the lens with a value of -1≤y≤1 after the conformal transformation is taken as the lens body of the two-dimensional straight-edge Eaton lens, and the refractive index greater than a preset refractive index value is filled with the preset refractive index value. The refractive index distribution determines the propagation path of light in the lens. As long as the refractive index distribution is met, the shape of the two-dimensional straight-edge Eaton lens based on a transformation material for beam bending is not restricted by the shape of the two-dimensional straight-edge Eaton lens. When a beam of parallel light is incident on the input surface at an angle of θ with the positive axis of the x-axis, the two-dimensional straight-edge Eaton lens divides the light output into two situations according to whether the light steering angle exceeds 180°. One is the steering of the light within the steering angle of 180°. In this case, the light incident surface and the light exit surface are two opposite surfaces. The light is emitted at an angle of θ on the output surface of the two-dimensional straight-edge Eaton lens. The exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is 2θ. The other is the steering of the light with a steering angle exceeding 180°. In this case, the light incident surface and the light exit surface are the same surface. The light is emitted at an angle of θ on the output surface of the two-dimensional straight-edge Eaton lens. The exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is π+2θ.

[0049] The preset refractive index value is selected based on the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, and taking into account the manufacturing difficulty. The larger the preset refractive index value, the more difficult it is to manufacture; the smaller the preset refractive index value, the larger the range of refractive index that needs to be intercepted, and the greater the impact on the light trajectory. The preset refractive index value is selected to be 14.1.

[0050] The output surface refers to the right boundary of the two-dimensional straight-edge Eaton lens transformed from the right semicircular arc of the traditional Eaton lens when the light beam turns within 180°. The right boundary corresponds to the straight line x=π / 4. Compared with the input signal, the propagation direction of the light beam changes.

[0051] like Figure 2 As shown, a method for realizing an optical device for bending beams based on a transformation material comprises the following steps:

[0052] Step 1: Perform a conformal transformation W = tan(Z) on the traditional Eaton lens to obtain an infinite two-dimensional straight-edge Eaton lens. Using transformation optics, determine the dielectric constant and magnetic permeability of the new lens after the transformation, and obtain the transformed refractive index.

[0053] The traditional Eaton lens corresponds to the original complex plane W = u + iv, which is a virtual space, where u is the real part of the original complex plane W, and v is the imaginary part of the original complex plane W;

[0054] The two-dimensional straight-edge Eaton lens corresponds to the transformed complex plane Z=x+iy, which is the physical space, where x is the real part of the transformed complex plane Z and y is the imaginary part of the transformed complex plane Z;

[0055] like Figure 2 As shown in (a), in the two-dimensional coordinate system under the virtual space W, the radius of the traditional Eaton lens with radial refractive index gradient is R=1, the center is (0,0), the input surface is the left semicircular arc, the output surface is the right semicircular arc when the light beam is turned within 180°, and the output surface is the left semicircular arc when the light beam is turned more than 180°. Figure 2 The circular lens shown in (a) is transformed conformally to Figure 2 (b) The two-dimensional coordinate system in the physical space Z is transformed into Figure 2 The left semicircle arc of (a) becomes Figure 2 The straight line x = -π / 4 in (b); Figure 2 The right semicircle arc of (a) becomes Figure 2 The straight line x = π / 4 in (b);

[0056] When the original complex plane W is conformally transformed into the transformed complex plane Z, according to the coordinate invariance of Maxwell's equations, the relationship between the physical space (x, y, Z) and the virtual space (u, v, W) is as shown in Equation (1):

[0057]

[0058] Where ε and μ are the dielectric constant and magnetic permeability of the virtual space W, ε′ and μ′ are the dielectric constant and magnetic permeability of the physical space Z, detA is the determinant of the determinant of the matrix A, and A is the Jacobian matrix, as shown in Equation (2):

[0059]

[0060] The spatial transformation relationship between virtual space W and physical space Z is shown in formula (3):

[0061]

[0062] in, represents partial differential;

[0063] According to Fermat's theorem, the relationship between the optical path of the physical space Z and the optical path of the virtual space W is shown in formula (4):

[0064]

[0065] According to formula (4),

[0066] Among them, d represents the differential, n w is the refractive index of the virtual space W, n z is the refractive index of physical space Z,

[0067]

[0068] After the virtual space W is conformally transformed into the physical space Z, the left semicircular arc boundary of the traditional Eaton lens before the transformation is the input surface, the right semicircular arc boundary is the output surface when the rotation is within 180°, and the left semicircular arc is the output surface when the rotation exceeds 180°. The input and output surfaces are transformed from curved surfaces to straight surfaces before and after the transformation, and the midpoint is compressed, and the sides are first compressed and then stretched;

[0069] Step 2: Cut off the middle -1≤y≤1 part of the infinite two-dimensional straight-edge Eaton lens obtained in step 1, select a preset refractive index value according to the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, fill the part with a refractive index greater than the preset refractive index value with the preset refractive index value, and obtain a two-dimensional straight-edge Eaton lens with a width of π / 2, a height of 2, and a refractive index less than or equal to the preset refractive index value, thereby obtaining an optical device for bending beams based on transformation materials.

[0070] Example 2

[0071] This example illustrates the geometrical optical simulation results of the beam bending device described in the present invention's "Optical Device and Implementation Method for Transformation Material-Based Beam Bending" with an incident window of [-0.1, 0.1]. This example was simulated using COMSOL Multiphysics, using a normalized unit length, a wavelength of 0.07, and an incident light beam incident upward at an angle θ relative to the positive x-axis.

[0072] In the embodiment, the refractive index of the conventional Eaton lens before transformation is The refractive index of the optical device based on the transformation material bending beam of the present invention is n z =n w |dW / dZ|=n w / γ, the principal extension of the lens before and after the transformation γ=|dZ / dW|=|1 / (sec(Z)) 2 |=|1 / (1+W 2 )|, the input surface is the left boundary of the two-dimensional straight-edge Eaton lens;

[0073] like Figure 3 As shown, Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) The geometric optical simulation results of beam bending when θ = 20°, θ = 30°, θ = 60°, and θ = 70°, respectively. Figure 3 (a) and Figure 3 In (b), the incident angle and the outgoing angle of the light are equal, the incident light and the outgoing light are on the same plane, and the turning angle exceeds 180°. Figure 3 (a) The steering angle is 220°, Figure 3 (b) The steering angle is 240°, Figure 3 (c) and Figure 3 In (d), the incident angle and the outgoing angle of the light are equal. The incident light and the outgoing light are on different surfaces, and the turning angle is within 180°. Figure 3 (c) The steering angle is 120°, Figure 3 (d) The steering angle is 140°. The present invention can not only realize multi-angle steering, but also realize large-angle steering exceeding 180°.

[0074] Example 3

[0075] This example illustrates the geometric optical simulation results of the device described in the present invention, "Optical Device and Implementation Method for Transformation Material-Based Beam Bending," for a beam bending within 180° when the incident window is [0.5, 0.8]. This example was simulated using COMSOL Multiphysics, using a normalized unit length, a wavelength of 0.07, and an incident light beam incident obliquely downward at an angle θ to the positive x-axis.

[0076] like Figure 4 As shown, Figure 4 (a) Figure 4 (b) Figure 4 (c) Figure 4 (d) The geometric optical simulation results of beam bending when θ = 30°, θ = 50°, θ = 60°, and θ = 70° are shown. In the figure, the incident angle and the outgoing angle of the light are equal, the incident light and the outgoing light are on different planes, and the steering angle is within 180°. Figure 4 (a) The steering angle is 60°, Figure 4 (b) The steering angle is 100°, Figure 4 (c) The steering angle is 120°, Figure 4 (d) The steering angle is 140°. This demonstrates that the beam bending effect changes with the window position.

[0077] Example 4

[0078] This example illustrates the geometric optical simulation results of a beam bending device described in the present invention's "Optical Device and Implementation Method Based on Transformation Materials," where the incident window is [0.5, 0.8], resulting in a beam bending exceeding 180°. This example was simulated using COMSOL Multiphysics, using a normalized unit length, a wavelength of 0.07, and an incident light beam incident upward at an angle θ relative to the positive x-axis.

[0079] like Figure 5 As shown, Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) The geometric optical simulation results of beam bending when θ = 10°, θ = 20°, θ = 30°, and θ = 40°. In the figure, the incident angle and the outgoing angle of the light are equal, the incident light and the outgoing light are on the same plane, and the steering angle exceeds 180°. Figure 5 (a) The steering angle is 200°, Figure 5 (b) The steering angle is 220°, Figure 5 (c) The steering angle is 240°, Figure 5 (d) The steering angle is 260°. This demonstrates that the beam bending effect changes with the oblique incident direction.

[0080] Example 5

[0081] This example illustrates the wave optics simulation results of a curved beam in the device described in the present invention, "Optical Device and Implementation Method for Transformation-Based Beam Bending," with an incident window of [0.5, 0.8]. This example was simulated using COMSOL Multiphysics, using a normalized unit length and a wavelength of 0.07.

[0082] like Figure 6 As shown, Figure 6 (a) is the wave optics simulation result when the incident angle θ is 40°. The incident angle and the outgoing angle are equal, the incident light and the outgoing light are on different planes, and the steering angle is 80°. Figure 6 (b) is the wave optics simulation result when the incident angle θ = 20°. The incident light and the outgoing light are on the same plane, and the steering angle is 220°.

[0083] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An optical device for bending beams based on transformation materials, characterized in that: It includes an input surface, a two-dimensional straight-edge Eaton lens for bending beams based on transformation materials, and an output surface; The input surface is the incident surface of the input signal entering the two-dimensional straight-edge Eaton lens based on the transformation material bending beam, and the input surface is a plane; the input surface is obtained by conformal transformation of the input surface of a traditional Eaton lens with a radius of 1 and a center of (0,0) and a radial refractive index gradient, that is, the left semicircular arc of the traditional Eaton lens is transformed into the left boundary of the transformed two-dimensional straight-edge Eaton lens, the left boundary corresponds to the straight line x=-π / 4, and the part of the left boundary in the middle with -1≤y≤1 is intercepted; the input surface is conformally transformed on the basis of the input surface of the traditional Eaton lens, so that the shape of the input surface of the traditional Eaton lens is changed, and the points on the input surface are in a one-to-one correspondence with the points on the input surface of the traditional Eaton lens before the conformal transformation, and the refractive index of the input surface gradually decreases from the center point to both sides; Compared with the traditional Eaton lens, the shape of the two-dimensional straight-edge Eaton lens based on the transformation material bending beam is changed from circular to rectangular. By transforming the optical material, the dielectric constant and magnetic permeability of the new lens after the transformation are determined to obtain the transformed refractive index; the gradient refractive index distribution of the traditional Eaton lens along the radial direction is changed so that the refractive index of the two-dimensional straight-edge Eaton lens after the conformal transformation is axially symmetrical about the two lines x=0 and y=0, and the refractive index at the center point is infinite. The middle part of the lens after the conformal transformation, which is -1≤y≤1, is intercepted as the lens body of the two-dimensional straight-edge Eaton lens. The size of the intercepted part needs to be selected according to the steering angle range and the principle of saving materials, and the refractive index greater than the preset refractive index value is filled with the preset refractive index value; the refractive index distribution determines the propagation path of light in the lens. When the refractive index distribution is satisfied, the shape of the two-dimensional straight-edge Eaton lens based on the transformation material bending beam is not restricted by the shape of the two-dimensional straight-edge Eaton lens; The output surface refers to the right boundary of the two-dimensional straight-edge Eaton lens, which is transformed from the right semicircular arc of the traditional Eaton lens when the light beam is turned within 180°. The right boundary corresponds to the straight line x=π / 4. Compared with the input signal, the propagation direction of the light beam changes. The optical device undergoes conformal transformation, and the transformed two-dimensional straight-edge Eaton lens maintains a one-to-one correspondence with the traditional Eaton lens before the transformation. According to the expected light field distribution, the traditional Eaton lens is conformally transformed using transformation optics, and the trajectory of the light wave is controlled based on the properties of the transformation medium, and the light wave is guided to propagate in the optical device along a preset path to achieve the expected light field distribution. The one-to-one correspondence means that the points on the traditional Eaton lens before the transformation correspond to the points on the two-dimensional straight-edge Eaton lens after the transformation, the refractive index of the traditional Eaton lens before the transformation corresponds to the refractive index of the two-dimensional straight-edge Eaton lens after the transformation, the shape of the traditional Eaton lens before the transformation is circular, and the shape of the two-dimensional straight-edge Eaton lens after the transformation is rectangular.

2. The optical device for bending beams using a transformation material as claimed in claim 1, wherein: When a beam of parallel light is incident on the input surface of the two-dimensional straight-edge Eaton lens at an angle of θ to the positive axis of the x-axis, the light output is divided into two situations according to whether the light steering angle exceeds 180°. One is the steering of the light within the steering angle of 180°. At this time, the light incident surface and the light exit surface are two opposite surfaces. The light is emitted at an angle of θ from the output surface of the two-dimensional straight-edge Eaton lens, and the exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is 2θ; the other is the steering of the light with a steering angle exceeding 180°. The light incident surface and the light exit surface are the same surface. The light is emitted at an angle of θ from the output surface of the two-dimensional straight-edge Eaton lens, and the exit direction is symmetrical with the incident direction about the x-axis, realizing light beam steering, and the steering angle is π+2θ. The device can simply arrange the incident angle to control different directions of the beam path, guide the beam path to various very wide bending angles, and realize variable angle steering in a single device.

3. The optical device for bending beams using a transformation material as claimed in claim 2, wherein: The preset refractive index value is selected based on the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, and considering the manufacturing difficulty. The larger the preset refractive index value, the more difficult it is to manufacture. The smaller the preset refractive index value, the larger the range of refractive index that needs to be intercepted will be, and the greater the impact on the light trajectory.

4. The optical device for bending beams using a transformation material as claimed in claim 3, wherein: The preset refractive index value is selected as 14.

1.

5. A method for implementing an optical device for bending beams using a transformation material, the method being implemented based on the optical device for bending beams using a transformation material according to claim 1, 2, 3, or 4, characterized in that: The following steps are included: Step 1: Perform a conformal transformation W = tan(Z) on the traditional Eaton lens to obtain an infinite two-dimensional straight-edge Eaton lens. By transforming the optical material, the dielectric constant and magnetic permeability of the transformed new lens are determined to obtain the transformed refractive index. The traditional Eaton lens corresponds to the original complex plane W = u + iv, which is a virtual space, where u is the real part of the original complex plane W, and v is the imaginary part of the original complex plane W; The two-dimensional straight-edge Eaton lens corresponds to the transformed complex plane Z=x+iy, which is the physical space, where x is the real part of the transformed complex plane Z and y is the imaginary part of the transformed complex plane Z; When the original complex plane W is conformally transformed into the transformed complex plane Z, according to the coordinate invariance of Maxwell's equations, the relationship between the physical space (x, y, Z) and the virtual space (u, v, W) is as shown in Equation (1): Where ε and μ are the dielectric constant and magnetic permeability of the virtual space W, ε′ and μ′ are the dielectric constant and magnetic permeability of the physical space Z, detA is the determinant of the matrix A, and A is the Jacobian matrix, as shown in formula (2): The spatial transformation relationship between virtual space W and physical space Z is shown in formula (3): in, represents partial differential; According to Fermat's theorem, the relationship between the optical path of the physical space Z and the optical path of the virtual space W is shown in formula (4): According to formula (4), Among them, d represents the differential, n w is the refractive index of the virtual space W, n z is the refractive index of physical space Z, After the virtual space W is conformally transformed into the physical space Z, the left semicircular boundary of the traditional Eaton lens before the transformation is the input surface. When the lens is turned within 180°, the right semicircular boundary of the traditional Eaton lens is the output surface. When the lens is turned more than 180°, the left semicircular boundary of the traditional Eaton lens is the output surface. The input and output surfaces are transformed from curved surfaces to straight surfaces before and after the transformation. The midpoint is compressed, and the sides are first compressed and then stretched. Step 2: Cut off the middle part -1≤y≤1 of the infinite two-dimensional straight-edge Eaton lens obtained in step 1, select a preset refractive index value based on the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens, and consider the manufacturing difficulty, fill the part with a refractive index greater than the preset refractive index value with the preset refractive index value, and obtain a two-dimensional straight-edge Eaton lens with a width of π / 2, a height of 2, and a refractive index less than or equal to the preset refractive index value, thereby obtaining an optical device based on bending beams of transformation materials.

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