Optical device based on transformation material bending beam and implementation method

Abstract

The invention discloses an optical device based on a transformation material bending beam and an implementation method, and belongs to the technical field of transformation materials and optical signal processing. The optical device includes an input surface, a two-dimensional straight-sided Eaton lens based on a transformation material curved beam, and an output surface. A traditional Eaton lens is converted into a straight-sided lens through an optical conversion method, the conversion relation between the straight-sided lens and the traditional Eaton lens is obtained through conformal conversion, and then medium parameters are obtained through a material conversion method. The incident angle and the emergent angle of the light on the transformed two-dimensional straight-edge Eaton lens are kept unchanged, the light, which has the same angle with the normal of each point of the input surface, in the traditional Eaton lens is equivalent to a beam of parallel light after transformation, and the incident angle and the emergent angle of the light are equal in size, so that the propagation path of a wave beam is changed along with the difference of the incident angle; a beam path can be guided to reach various very wide bending angles, and variable-angle steering is realized in single equipment; isotropy is ensured, and engineering preparation is facilitated.

Description

Technical Field

[0001] The invention relates to an optical device and an implementation method for bending beams based on transformation materials, 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 method has significant drawbacks. The waveguide cavity has a cutoff frequency, below which the propagation of electromagnetic waves is suppressed. And the beam bending of the waveguide cavity is not sufficiently curved for applications that require large curvature. In addition, its production cost is high and complex, requiring high-precision manufacturing technology.

[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, which poses 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-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 a problem of geometric shape design and coordinate transformation parameter calculation. The material obtained by transformation optics is called transformation material.

[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] In view of the problem that conventional beam benders can only bend beams at fixed angles regardless of the incident angle, the purpose of the present invention is to provide an optical device and implementation method for bending beams based on transformation materials, so that the beam propagation path changes with the incident angle, and multi-angle and wide-range beam bending can be achieved without changing the equipment. According to the expected light field distribution, the traditional Eaton lens is conformally transformed using transformation optics, the trajectory of the light wave is controlled based on the properties of the transformation medium, and the medium parameters of the optical device are determined using the method of transformation optics, and the light wave is guided to propagate in the optical device along a preset path to achieve the expected light field distribution.

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

[0009] The optical device based on transforming material for bending beams disclosed by the present invention comprises an input surface, a two-dimensional straight-edge Eaton lens based on transforming material for bending beams, 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, 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 R and a center of (0,0) with a radial refractive index gradient, 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 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 changes, 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.

[0011] 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 a circle to a rectangle. By using the transformation optical method, 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 respectively axially symmetrically distributed 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 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 limited 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 steering angle within 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. The exit direction is symmetrical with the incident direction about the x-axis to achieve light beam steering, and the steering angle is 2θ. The other is the steering of the light 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. The exit direction is symmetrical with the incident direction about the x-axis to achieve 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 will be, 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] The optical device is transformed by 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 by 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 point on the traditional Eaton lens before the transformation corresponds to the point 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.

[0015] The present invention discloses a method for realizing an optical device based on a transformation material to bend a beam, 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. Determine the dielectric constant and magnetic permeability of the new lens after the transformation through the method of transformation optics to 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 the virtual space W and the 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 equation (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 is the output surface when turning more than 180°. 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 according to the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens and considering 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 adopt 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 angle and the exit angle of light on the transformed two-dimensional straight-edge Eaton lens remain unchanged. In the traditional Eaton lens, the 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 angle and the exit angle of the light are equal, so that the propagation path of the beam can be changed with the different incident angles, and variable angle steering can be achieved in a single device.

[0035] 2. The optical device and implementation method based on transforming material bending beam disclosed in the present invention assume that parallel light is horizontally incident on the left semicircular arc of a 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, thereby achieving both steering within 180° and large-angle steering exceeding 180°.

[0036] 3. The method for realizing an optical device based on a transformation material bending beam 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 It is a schematic diagram of the structure of "an optical device for bending beams based on transformation materials" of the present invention, that is, 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 a geometric simulation result diagram of the beam steering of the present invention "An optical device for bending beams based on transformation materials" when the incident window is [-0.1, 0.1], 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 a geometric optical simulation result diagram of the light beam turning within 180° when the incident window is [0.5, 0.8] for the present invention's "An optical device for bending beams based on transformation materials", where 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 a geometric optical simulation result diagram of the light beam turning more than 180° when the incident window is [0.5, 0.8] for the present invention "An optical device for bending beams based on transformation materials", where 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 transformation material bending beam" 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] Embodiment 1:

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

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

[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, and the input surface is a plane. The input surface is obtained by conformal transformation of the input surface of the traditional Eaton lens with a radius R=1 and a center (0,0) with a radial refractive index gradient, that is, the left semicircular arc of the traditional Eaton lens is changed to the left boundary of the transformed two-dimensional straight-edge Eaton lens, and the left boundary corresponds to the straight line x=-π / 4, and the part of the left boundary in the middle -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.

[0048] 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 a circle to a rectangle. By using the transformation optical method, 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 respectively axially symmetrically distributed about the two lines x=0 and y=0, and the refractive index at the center point is infinite. The part of the middle of the lens after the conformal transformation -1≤y≤1 is intercepted as the lens body of the two-dimensional straight-edge Eaton lens, 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 limited 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 steering angle within 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. The emission direction is symmetrical with the incident direction about the x-axis to achieve light beam steering, and the steering angle is 2θ. The other is the steering of the light steering angle exceeding 180°. At this time, 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. The emission direction is symmetrical with the incident direction about the x-axis to achieve 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 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. 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 a beam 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. Determine the dielectric constant and magnetic permeability of the new lens after the transformation through the method of transformation optics to 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) shows the two-dimensional coordinate system in the physical space Z. After transformation, Figure 2 The left semicircle of (a) becomes Figure 2 The straight line x = -π / 4 in (b); Figure 2 The right semicircle 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 matrix A, and A is the Jacobian matrix, as shown in formula (2):

[0059]

[0060] The spatial transformation relationship between the virtual space W and the 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 equation (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 surface and the output surface change 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 embodiment describes the geometric optical simulation results of the bending beam of the device in the invention "Optical device and implementation method for bending beam based on transformation material" when the incident window is [-0.1, 0.1]. This embodiment uses COMSOL Multiphysics for computer simulation, uses a normalized unit length, takes a wavelength of 0.07, and the incident light is incident obliquely upward at an angle of θ 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 bending beam of the transformation material of the present invention is n z =n w |dW / dZ|=n w / γ, the main 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 planes, 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 embodiment describes the geometric optical simulation results of the device in the present invention "Optical device and implementation method for bending beams based on transformation materials" when the incident window is [0.5, 0.8], and the light beam is turned within 180°. This embodiment uses COMSOL Multiphysics for computer simulation, 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°, respectively. 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 proves that the beam bending effect will change with different window positions.

[0077] Example 4

[0078] This embodiment describes the geometric optical simulation results of the bending beam of the device in the present invention "Optical device and implementation method based on transformation material bending beam" when the incident window is [0.5, 0.8], and the light beam is turned more than 180°. This embodiment uses COMSOL Multiphysics for computer simulation, using a normalized unit length, a wavelength of 0.07, and an incident light beam incident upward at an angle θ 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 proves that the beam bending effect will change with different oblique incident directions.

[0080] Example 5

[0081] This example describes the wave optics simulation results of the bending beam of the device in the invention "Optical device and implementation method based on transformation material bending beam" when the incident window is [0.5, 0.8]. This example uses COMSOL Multiphysics for computer simulation, using normalized unit length and wavelength of 0.07.

[0082] like Figure 6 As shown, Figure 6 (a) is the wave optics simulation result diagram when the incident angle θ=40°, the incident angle is equal to the outgoing angle, 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 diagram 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 specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 R and a center of (0,0) and a radial refractive index gradient, that is, the left semicircular arc of the traditional Eaton lens becomes the left boundary of the two-dimensional straight-edge Eaton lens after transformation; 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 a circle to a rectangle. The gradient refractive index distribution of the traditional Eaton lens along the radial direction is changed by the transformation optical method, so that the refractive index of the two-dimensional straight-edge Eaton lens after the conformal transformation is respectively axially symmetrically distributed 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 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 limited 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 transformed from the right semicircular arc of the traditional Eaton lens when the light beam turns within 180°, and the propagation direction of the light beam changes compared with the input signal; The optical device is transformed conformally, 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 by 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 point on the traditional Eaton lens before the transformation corresponds to the point 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 based on transformation materials as claimed in claim 1, characterized in that: 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 steering angle within 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. The exit direction is symmetrical with the incident direction about the x-axis to achieve beam steering. The steering angle is 2θ. The other is the steering of the light 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. The exit direction is symmetrical with the incident direction about the x-axis to achieve beam steering. 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 achieve variable angle steering in a single device.

3. The optical device for bending beams based on transformation materials as claimed in claim 2, characterized in that: 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 the manufacturing difficulty is taken into consideration. The larger the preset refractive index value, the more difficult it is to manufacture. The smaller the preset refractive index value is, the larger the range of refractive index that needs to be intercepted will be, and the greater the impact on the light trajectory will be.

4. The optical device based on bending beams using transformation materials as claimed in claim 3, characterized in that: The preset refractive index value is selected as 14.

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5. A method for realizing an optical device based on transformation material for bending beams, which is realized based on the optical device based on transformation material for bending beams as claimed in 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. Determine the dielectric constant and magnetic permeability of the new lens after the transformation through the method of transformation optics 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 the virtual space W and the physical space Z is shown in formula (3): Among them, θ· represents the 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 equation (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 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 it is turned within 180° is the output surface, and the left semicircular arc of the traditional Eaton lens when it is turned over 180° is the output surface. The input surface and the output surface are changed 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; 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 according to the refractive index distribution and light trajectory of the two-dimensional straight-edge Eaton lens and considering 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.

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