Antenna structure, light emitting device, and method of designing antenna structure

Abstract

This invention relates to the field of antennas, and one example of the invention relates to an antenna structure (10) for guiding the directional radiation of light. The antenna structure (10) includes a reflector (12) having a reflective surface (12a), an annular dielectric grating (14) arranged on the reflective surface (12a) and extending concentrically along a central axis (100) perpendicular to the reflective surface, and an omnidirectional reflector formed by a low-refractive-index central region (18) surrounded by the annular dielectric grating (14). The antenna structure (10) allows light emitted from the low-refractive-index central region (18) along the central axis (100) onto the dielectric grating (14) to achieve a projection efficiency η relative to a Gaussian beam of at least 65%. Other examples of the invention also relate to a light-emitting device (22) and a method for designing the antenna structure (10).

Description

Technical Field

[0001] Examples of this invention include an antenna structure, a light-emitting device, and a method for designing the antenna structure. Therefore, this invention relates to the field of antennas for guiding and collecting radiation, particularly radiation in the optical frequency range. Background Technology

[0002] In most cases, the availability of a light-emitting device depends on the spatial distribution of the optical field of the light emitted from the device. In particular, when the emitted light needs to be coupled into a waveguide, a suitable and reliable spatial distribution of the optical field is required to increase the coupling efficiency of the emitted light.

[0003] Single-photon sources are considered among the most promising instruments for single-photon-based quantum technologies. However, practical applications often require the bright and quasi-definite emission of single-photon radiation into a specific spatial mode. Traditional methods for guiding light radiation into a suitable spatial distribution mostly rely on coupling the single-photon source with nanowires or microcavity modes. However, fabricating such structures requires sophisticated etching techniques, leading to high manufacturing costs.

[0004] If a solution allows light to couple out with a suitable optical field distribution, thereby further improving the utilization of the emitted light, then both single-photon emitters and other conventional light-emitting devices can benefit from such a reliable and low-cost solution.

[0005] While the use of dielectric gratings to collect emitted light from quantum light sources has been reported (Optics Express, Vol. 25, Issue 26, pp. 32420-32435 (2017)), some other objective technical problems remain, such as how to effectively couple the light emitted by the light-emitting device to a usable spatial light field distribution, such as a Gaussian mode. Summary of the Invention

[0006] Examples of the present invention can solve the various technical problems mentioned above. Optional embodiments are specified in the following description.

[0007] In one embodiment, the invention relates to an antenna structure for guiding the directional radiation of light. The antenna structure includes a reflector with a reflective surface, an annular dielectric grating arranged on the reflective surface and extending concentrically along a central axis perpendicular to the reflective surface, and an omnidirectional reflector formed by a low-refractive-index central region surrounded by the annular dielectric grating. The antenna structure allows light emitted from the low-refractive-index central region along the central axis above the dielectric grating to achieve a projection efficiency η of at least 65% relative to a Gaussian beam.

[0008] In another example, the present invention relates to a light-emitting device comprising an antenna structure according to any one of the foregoing claims and one or more light sources arranged in a low-refractive-index central region of the antenna structure, wherein light emitted from the low-refractive-index central region is emitted by the one or more light sources.

[0009] The present invention also relates to a method for designing an antenna structure in a light-emitting device having a predetermined emission wavelength. The method includes determining the thicknesses of a first layer and a second layer of an annular dielectric grating and adding additional components along a direction perpendicular to the central axis of the reflecting surface to form an omnidirectional reflector surrounding a low-refractive-index central region. The thicknesses of the first and second layers are determined by comparing the optical thickness of each layer to a quarter of the predetermined emission wavelength. The method further includes optimizing the thicknesses of the first and second layers, the height of the dielectric grating, the position of the light source in the low-refractive-index central region, and the diameter of the low-refractive-index central region through numerical simulation, thereby maximizing the projection efficiency η of light emitted from the light source to the outside of the instrument relative to Gaussian light.

[0010] The advantage of these examples is that the light energy emitted from the low-refractive-index central region along the central axis of the antenna structure is effectively collected and coupled into a suitable optical field spatial distribution, thus allowing for efficient use in further applications. For example, if the emitted light highly coincides with the optical field spatial distribution of a Gaussian beam, it can be ensured that the emitted light can be effectively focused and / or coupled into a waveguide, such as a single-mode fiber.

[0011] These examples also have other advantages, namely that the manufacturing process of the antenna structure is simple and requires little work, thus allowing for the provision of suitable antenna structures and light-emitting devices to meet the high versatility of emitted light.

[0012] The ring of the dielectric grating is not necessarily a perfect circle. According to an alternative example, the ring can be a perfect circle, while according to other examples, the ring can deviate from a perfect circle, such as an ellipse.

[0013] The low-refractive-index central region is part of the antenna structure located at the center of the ring structure, and its refractive index is lower than that of the ring dielectric grating. According to examples, the low-refractive-index central region can be empty or filled with a gas, such as air or nitrogen. According to other examples, the low-refractive-index central region can be filled with a liquid or solid material with a refractive index lower than that of the ring dielectric grating.

[0014] One or more light sources disposed in the low-refractive-index central region of the antenna structure may be disposed within a cavity of the low-refractive-index central region and / or may be embedded in a material with a lower refractive index than the ring having a dielectric grating. According to other examples, one or more light sources may fill part or all of the low-refractive-index central region.

[0015] Light emitted by a transmitter and / or directed by an antenna structure. Optionally, it can be in the ultraviolet, visible, and / or infrared spectral range. Optionally, the center wavelength of the light is in the range of 100 nanometers to 3 micrometers.

[0016] Numerical optimization to maximize the projection efficiency of a beam includes, but is not limited to, simulating the antenna structure and examining the electric field distribution within the antenna structure, particularly in the low-refractive-index central region. Numerical optimization can simulate the emitted light for various parameters dependent on the antenna structure, such as spatial dimensions and / or material properties, or the location of one or more light sources within the low-refractive-index central region, and optimize these parameters by calculating the projection efficiency of the emitted light.

[0017] By way of example, the Gaussian beam projection efficiency η represents a measure of the degree of overlap between the spatial optical field distribution of the outgoing beam and the Gaussian beam. In other words, the Gaussian beam projection efficiency η of the outgoing beam represents a parameter that defines the degree of overlap between the outgoing beam and the Gaussian beam. The greater the overlap, the greater the projection efficiency η. By way of example, the projection efficiency of the outgoing beam is in the range of 0 to 1 (0 to 100%). A Gaussian beam represents the transverse mode TEM. 00 Here, the Gaussian projection efficiency η is defined as the output light field distribution relative to the TEM with a suitable beam waist. 00 The square of the overlap integral of the field distribution. A suitable waist is achieved by maximizing the TEM with different waists. 00 The projection efficiency η is determined. In other words, determining the projection efficiency η of a Gaussian beam may include, but is not limited to, determining the degree of overlap between the actual outgoing light field distribution and the Gaussian beam field distribution with a corresponding initial beam waist, and changing the beam waist size until the projection efficiency reaches its maximum value. The range of beam waist variation is 0.1 to 2.0 wavelengths.

[0018] According to examples, the Gaussian beam projection efficiency η of the antenna structure is at least 70%, optionally at least 75%, optionally at least 80%, and optionally at least 90%. Theoretically, Gaussian beam projection efficiency is of higher priority; however, in some future applications, Gaussian beam projection efficiency may (decline) to 65%. For manufacturing process considerations, it may even be necessary to have an antenna structure with 65% Gaussian beam projection efficiency, as lower projection efficiency means lower requirements for manufacturing precision.

[0019] According to an example, the low-refractive-index central region extends in at least one direction perpendicular to the central axis, with an extension length of D. The low-refractive-index central region may have a circular cross-sectional shape in at least one plane perpendicular to the central axis, and the diameter of this circle corresponds to the extension length D. According to a specific embodiment, the low-refractive-index central region may have a polygonal cross-sectional shape, such as a rectangle, hexagon, or octagon. The extension length D represents the distance between opposite sides (diagonals) of the polygon.

[0020] The length D of the extra component can optionally be no greater than 1 mm, no greater than 100 μm, no greater than 10 μm, or no greater than 1 μm. These small extra components allow for the confinement of one or more light sources within a low-refractive-index central region. Since the manufacturing workload increases with size, small extensions can reduce the workload of antenna structure fabrication. For a small light source, such as fluorescent or phosphorescent molecules, quantum dots, or nanoparticles, a small extra component length D is suitable.

[0021] According to the example, the additional component length D is at least 100 nanometers, and optionally at least 200 nanometers, to provide sufficient space to place one or more light sources.

[0022] According to the example, the height of the annular dielectric grating along the central axis is no greater than D, and optionally no more than D / 2. In other words, the height of the annular dielectric grating may depend on the spatial dimensions of the low-refractive-index central portion in a plane parallel to the reflector's reflecting surface, with its optional height not exceeding the extension length D, and optionally no more than half of the extension length D. This is advantageous for the emitted light to have high Gaussian beam projection efficiency. Numerical simulations of the antenna structure and emitter, based on the optional example where the height does not exceed the additional component length D of the low-refractive-index central region, show that a Gaussian beam projection efficiency η greater than 85% can be achieved, with settings greater than 90%. Therefore, choosing a height of the dielectric grating along the central axis no greater than the additional component length D of the low-refractive-index central region may be beneficial for achieving an antenna structure with very high Gaussian beam projection efficiency η. Furthermore, limiting the additional component length D further limits the workload required to manufacture the dielectric grating.

[0023] According to the example, the height of the annular dielectric grating along its central axis is no more than 10 mm, optionally no more than 5 mm, optionally no more than 1 mm, optionally no more than 100 micrometers, optionally no more than 10 micrometers, optionally no more than 1 micrometer, optionally no more than 0.5 micrometers, optionally no more than 0.1 micrometers. This ensures good coupling efficiency. Furthermore, the limited height of the dielectric grating also helps to maintain low manufacturing workload.

[0024] According to an example, the annular dielectric grating is composed of two alternating layers: a first layer with a refractive index n1 and a second layer with a refractive index n2, wherein the refractive index n2 is greater than the refractive index n1, and the refractive index of the low-refractive-index central region is less than the refractive index n1. This structure can effectively form an omnidirectional reflector in the low-refractive-index central region. No other layers with refractive indices different from the first and second layers are placed between the first and second layers.

[0025] In this example, the second layer with a refractive index n2 forms the innermost layer that confines the low-refractive-index central region. In other words, the layer with a higher refractive index forms the innermost layer that surrounds and confines the low-refractive-index central region. This ensures good reflectivity of the omnidirectional reflector, resulting in high collection and projection efficiency of the antenna structure.

[0026] According to the examples, the value of refractive index n2 is greater than 1.75 and / or the value of refractive index n1 is between 1.1 and 1.75. Such values ​​are beneficial for the dielectric grating to form an omnidirectional reflector. The dielectric layer with refractive index n1 can be composed of at least one of the following materials: magnesium difluoride, silicon dioxide, polymethyl methacrylate, diamond, cubic zirconia, gallium arsenide, indium gallium phosphide, indium gallium arsenide, and aluminum gallium arsenide. The dielectric layer with refractive index n2 can be composed of at least one of the following materials: titanium dioxide, gallium arsenide, diamond, and indium gallium arsenide. These materials allow for the fabrication of annular dielectric gratings via epitaxial growth.

[0027] As an example, each layer can have its own optical thickness to match one-quarter of the expected emitted light wavelength, where optical thickness represents the thickness multiplied by the refractive index. Therefore, the antenna structure can be designed for emitting light at a specific wavelength. And for wavelengths deviating from the design wavelength, the antenna structure can still exhibit near-optimal performance.

[0028] A ring-shaped dielectric grating comprises at least two layers of two different types: two first layers and two second layers. Optionally, each type of layer has at least three layers, and optionally at least ten layers of each type. The more layers of each type, the better the omnidirectional reflection effect. However, with more layers, the manufacturing workload of the antenna structure may increase. Furthermore, different layers can have different optical thicknesses, thus adapting to various wavelengths of light, and even being designed as omnidirectional reflection devices with bandwidth.

[0029] According to the example, the low-refractive-index central region is empty or at least partially filled with a material whose refractive index is lower than refractive index n1, and the low-refractive-index central region is at least partially filled with air or nitrogen. The refractive index of the filling material needs to be lower than that of the materials of the first and second layers of the annular dielectric grating. Optionally, the refractive index of the low-refractive-index central region ranges from 1 to 1.1. This makes the difference between the refractive index of the low-refractive-index central region and the refractive index of the second layer surrounding the low-refractive-index central region particularly large. The greater the difference in value between the refractive index of the low-refractive-index central region, the refractive index n1 of the first layer, and the refractive index n2 of the second layer, the better the omnidirectional reflection performance of the annular dielectric grating.

[0030] Based on the example, the low-refractive-index central region causes the light emitted from within it to establish an electric field intensity distribution along the central axis similar to a standing wave, and the standing wave has at least two points of maximum electric field intensity along the central axis. The electric field intensity distribution within the low-refractive-index central region can be obtained from numerical simulations of the antenna structure, the ring-shaped dielectric grating, or the emitter. Furthermore, the electric field intensity distribution within the low-refractive-index central region can be numerically optimized. For example, by numerically optimizing the spatial dimensions of the dielectric grating, such as its in-plane dimensions and height, as well as the layer thickness and refractive index, and the spatial dimensions and refractive index of the low-refractive-index central region, an ideal electric field intensity distribution of the emitted light can be achieved within the low-refractive-index central region.

[0031] According to the example, the height of the annular dielectric grating needs to be such that the upper end of the dielectric grating is between 0.3 and 0.8 times the maximum electric field intensity. In other words, the light field exhibits a standing wave distribution along the central axis in the low-refractive-index central region, where the several maxima of the electric field intensity distribution are arranged periodically or aperiodically along the central axis. The location of the maxima can be used to select the height of the dielectric grating such that the Gaussian beam projection efficiency is at least 65%. Optionally, the precise height of the truncated dielectric grating can be numerically optimized. However, numerical simulations show that, at least for some instances, truncating between 0.3 and 0.8 times the maximum electric field intensity will result in a Gaussian beam projection efficiency η of at least 65%.

[0032] According to the example, at least one light source may be placed in the low-refractive-index central region. The light source may include, but is not limited to, a single-photon light source, a quantum light source, a fluorescent light source, and / or a phosphorescent light source.

[0033] According to one example, the antenna structure also includes a top element above the annular dielectric grating. This top element can be used to further influence the collection and projection efficiency of the emitted light. Furthermore, this top element can prevent fluids or solids from entering the low-refractive-index central region, thus avoiding oxidation or degradation of some materials and causing contamination. According to another example, the top element has a hemispherical shape and may optionally be a solid-immersion lens. Attached Figure Description

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Figures 1A-1E Cross-sectional views of various examples of antenna structures;

[0036] Figure 2 This is a cross-sectional view of a light emitter corresponding to an antenna structure.

[0037] Figures 3A-3C The image shows an example of a light emitter, along with a cross-sectional view of the internal and external electric field intensity distribution.

[0038] Figures 4A-4D This shows another example of a light emitter, along with a cross-sectional view of the internal and external electric field intensity distribution.

[0039] Figures 5A-5D The images shown are cross-sectional views of examples of emitters for different light sources.

[0040] Figures 6A-6C It displays various spectral information of the light emitter.

[0041] Figures 7A-7E The diagram shows the electric field distribution of a truncated annular dielectric grating, as well as the relationship between the projection efficiency, collection efficiency, and total efficiency and the truncated height of the annular dielectric grating.

[0042] Symbol explanation: 10 represents antenna structure, 12 represents reflector, 12a represents reflective surface, 14 represents ring dielectric grating, 16 represents double-layer dielectric structure, 16a represents first layer dielectric, 16b represents second layer dielectric, 18 represents low refractive index central region, 18a represents a certain solid material, 20 represents top element, 22 represents emitter, 24 represents light source, and 100 is the central axis. Detailed Implementation

[0043] To more clearly illustrate the purpose, principles, technical solutions, and advantages of this invention, the following description, in conjunction with the accompanying drawings and specific embodiments, further clarifies the invention. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0044] Figures 1A to 1E Antenna structure 10 corresponding to different alternative embodiments of the present invention is shown. Antenna structure 10 includes a reflector 12 having a reflecting surface 12a. Furthermore, antenna structure 10 includes an annular dielectric grating 14 disposed on the reflecting surface 12a, the annular dielectric grating 14 extending concentrically along a central axis 100 and forming an omnidirectional reflector for light in the central region of the annular dielectric grating. The annular dielectric grating 14 includes a plurality of double-layer structures 16, each layer consisting of a first layer 16a and a second layer 16b. Figures 1A to 1E The examples shown each include an annular dielectric grating composed of three double-layer structures 16. It is worth noting that other examples may have fewer or more double-layer structures. The first layer is made of a material with a refractive index n1, the second layer is made of a material with a refractive index n2, and the refractive index n1 is less than n2.

[0045] A low-refractive-index central region 18 is disposed at the center of the annular dielectric grating 14, and its refractive index is lower than that of the first layer 16a and the second layer 16b. The low-refractive-index central region 18 is radially surrounded by the annular dielectric grating 14 around the central axis 100. For light emitted perpendicularly to the central axis 100 from a light source (not shown) placed on the central axis 100 within the low-refractive-index central region 18, the dielectric grating 14 forms an omnidirectional reflector. The second layer 16b has a higher refractive index than the first layer 16a. The innermost second layer 16b represents the boundary between the annular dielectric grating 14 and the low-refractive-index central region 18. An optional value for the refractive index of the first layer 16a is 1.38. An optional value for the refractive index of the second layer 16a is 2.58.

[0046] according to Figure 1A In the example shown, the low-refractive-index central region 18 is empty. Depending on the surrounding environment of the antenna structure 10, the low-refractive-index central region may be evacuated or filled with a fluid, such as air, nitrogen, or / and an inert gas. Therefore, the refractive index of the low-refractive-index central region 18 can essentially correspond to the refractive index of a vacuum, air, or other corresponding gas. Thus, the refractive index of the low-refractive-index central region 18 is much lower than the refractive index of the first layer 16a or the second layer 16b, in the range of 1.0 to 1.1.

[0047] The height of the annular dielectric grating 14 can range from 200 nanometers to 1 micrometer, and other instances can also achieve other heights.

[0048] Figure 1B The examples shown are in most respects similar to Figure 1A Similar to the example, except for some differences in the low-refractive-index central region 18. As shown, the low-refractive-index central region 18 is entirely filled with a low-refractive-index material. The low-refractive-index central region 18 can be filled with fused silica with a refractive index lower than that of the first layer 16a and the second layer 16b. For example, for a specific target wavelength, the refractive index of the low-refractive-index central region 18 may be 1.3. In this example, the height of the low-refractive-index central region 18 is equal to the height of the surrounding annular dielectric grating 14. However, in other examples, the height of the low-refractive-index central region 18 may be higher or lower than the height of the surrounding annular dielectric grating 14. As shown in the figure of this example, the low-refractive-index central region 18 filled with solid material can allow for the placement of one or more light sources, such as quantum light sources, single-photon light sources, nanoparticles and / or fluorescent or phosphorescent molecules. In this case, it is preferable to choose a light source capable of emitting light within the filling material of the low-refractive-index central region 18.

[0049] Figure 1C It showed something like Figure 1B The example differs in that it has a low refractive index central region 18. According to Figure 1CFor example, the low-refractive-index central region 18 comprises a solid material 18a, however, this solid material 18a does not radially fill the entire low-refractive-index central region 18. In other words, according to this example, the low-refractive-index central region 18 comprises a solid material 18a centered along the central axis 100 and a surrounding gap layer, which may be empty, evacuated, or filled with air or surrounding fluid. One or more light sources may be disposed in the solid material 18a and / or in the surrounding gaps. Optionally, both the solid material 18a and the gaps in the low-refractive-index central region 18 have a lower refractive index than the second layer 16b of the annular dielectric grating 14.

[0050] Figure 1D Another example of antenna structure 10 is shown, which first refers to... Figure 1C In this example, a top layer element 20 is added. The top layer element 20 is an optical element disposed on top of the annular dielectric grating 14 and covering the dielectric grating 14 and the low-refractive-index central region 18. According to the described example, the top layer element 20 can directly contact the upper end of the dielectric grating 14 and / or the low-refractive-index central portion 18. However, according to other examples, one or more optical layers can also be disposed between the upper end of the annular dielectric grating 14 and the top layer element 20. Figure 1D In the illustrated example, the top element has the same horizontal length as the annular dielectric grating, i.e., the same extension length perpendicular to the central axis 100. However, according to other embodiments, the horizontal extension length of the top element 20 may be less than that of the annular dielectric grating 14, thus not covering the entire upper portion of the dielectric grating 14. According to other embodiments, the top element 20 may extend horizontally beyond the dielectric grating 14 and may optionally extend downwards to the reflector 12, for example, completely surrounding the dielectric grating 14 and the low-refractive-index central region 18. In this way, the top element can also be used to protect the device from foreign objects and / or fluids entering the antenna structure 10.

[0051] The top-layer element 20 can serve as an optical element to influence the emission efficiency of light emitted from a light source within the low-refractive-index central region 18. For this purpose, the top-layer element 20 can have a refractive index matching that of the dielectric grating and / or the low-refractive-index central region 18 to promote and / or enhance the emission efficiency of light emitted within the low-refractive-index central region 18. Additionally, the top-layer element can exhibit refractive and / or diffraction power to alter the beam shape or optical mode of the emitted light, which is beneficial for further coupling the emitted light into the optical fiber.

[0052] Figure 2 A light-emitting device 22 is described, the device comprising, according to Figure 1BThe antenna structure shown is an example of this. The light-emitting device 22 also includes a light source 24 disposed in the low-refractive-index central region 18. According to this example, the center of the light source 24 is located at the central axis 100. However, according to other embodiments, one or more light sources 24 may also be arranged at other off-center locations within the low-refractive-index central region 18.

[0053] Light source 24 is represented by a circular symbol, and the arrow penetrating the circular symbol indicates the direction of the dipole moment, which is perpendicular to the central axis and parallel to the reflecting surface 12a of the reflector. At least a portion of the light emitted by light source 24 within the low-refractive-index central region 18, perpendicular to the central axis 100, is reflected by the annular dielectric grating 14, which acts as an omnidirectional reflector. Light reflected downwards towards the reflecting surface 12a is reflected upwards by the reflecting surface 12a. Therefore, the light-emitting device 22 is designed such that light emitted within the low-refractive-index central region 18 can only exit through the upper surface of the low-refractive-index central portion 18. The dimensions of the low-refractive-index central region 18, the height of the antenna structure 10 along the central axis 100, and other parameters of the light-emitting device can be optimized as needed, for example, the emitted light may require a Gaussian beam profile projection efficiency η of 65% or higher.

[0054] The following will discuss several typical examples of the invention in further detail with reference to specific illustrations.

[0055] Figure 3A A light-emitting device 22 is shown, comprising an antenna structure 10 and a light source 24 within a low-refractive-index central portion 18 arranged along a central axis 100. The antenna structure 10 includes an annular dielectric grating 14, which extends cylindrically along the central axis 100 as an omnidirectional reflector. In this example, the low-refractive-index central portion 18 is empty (except for the light source 24). The central axis 100 is the axis of symmetry of the annular dielectric grating 14. A quarter of the annular dielectric grating 14 is hollowed out to reveal the internal structure. The bottom of the antenna structure 10 is a reflector 12 made of silver, with a reflecting surface 12a on its upper part, to which the annular dielectric grating 14 is attached. Light emitted from the light source 24 is coupled into a defective waveguide mode. The vector x along the axis of symmetry can be represented as radial coordinate r and angular coordinate r. A linear combination. The cut-open annular dielectric grating 18 shows the layered structure of the dielectric grating, having multiple first layers with refractive indices n1 and multiple second layers with refractive indices n2.

[0056] Figure 3BThis diagram displays the simulation results of the dispersion relation for an infinitely long (along the central axis 100) hollow coaxial waveguide with a radius of R = 3a (a = t1 + t2, t1 = 130 nm, t2 = 55 nm). The refractive index of the first layer 16a is n1 = 1.38, and the refractive index of the second layer 16b is n2 = 2.58. The refractive index of the low-refractive-index central portion 18 is n0 = 1.0. The dark areas in the lower and upper parts of the dispersion relation diagram represent the propagation modes throughout the double-layer structure. The dashed lines (black dashed lines) in the bright areas represent the defective waveguide modes in the first bandgap, and the dashed lines (white dashed lines) in the upper part of the diagram represent the defective waveguide modes in the second bandgap.

[0057] Figure 3C For calculation Figure 3A , 3B The electric field intensity distribution of the device in the xz plane (including the central axis 100) is shown. The electric field intensity distribution was calculated using the finite-difference time-domain (BOR-FDTD) method with an azimuth number m=1. An in-plane electric dipole is placed at a distance of 120 nm from the silver mirror reflector in a semi-infinite coaxial waveguide. The black dashed line represents a possible height where the structure can be truncated to obtain a high Gaussian beam profile projection efficiency, which can reach 65% or much higher.

[0058] In this example, the radius of the low-refractive-index central region is R, and its refractive index is n0 (ideally n0=1). The thickness of the first layer 16a of the dielectric double-layer structure 16 is t1, and the thickness of the second layer 16b is t2, with refractive indices n1 and n2, respectively. The periodic enclosing ring of the annular dielectric grating 14 and the low-refractive-index central region 18 forces the light emitted from the light source into the defect waveguide mode. A circular dielectric double-layer stack with a finite height h is placed on a planar silver mirror as a reflector 12. Therefore, light can only exit from one side of the antenna structure 10, i.e. Figure 3A Above the light-emitting device shown. The truncation of antenna structure 10 at an appropriate height h allows the defect-guided mode to be efficiently converted into a Gaussian mode with a refractive index n3 in the homogeneous medium above. We note that the working principle described above is quite different from that of circular gratings previously used for efficient photon collection, as this device does not rely on the Purcell effect.

[0059] For ease of analysis, assume the height of the annular dielectric grating is infinitely long along the central axis 100. This is analogous to the case of an electric dipole radiating in an all-dielectric coaxial waveguide. If the light from the low-refractive-index central region with refractive index n0 does not exceed the Brewster angle of the double-layer structure 16...

[0060]

[0061] And satisfy If the above conditions are not met, then total internal reflection will occur. If not, at least one p-polarized plane wave will be refracted at the n0 / n2 interface and pass through the entire double-layer structure, thus preventing total internal reflection. If a single light source is embedded in a medium with a high refractive index (such as epitaxially grown quantum dots), the medium around the emitter must be partially removed to effectively create the low refractive index environment required for the low refractive index central region. To suppress light coupling into modes with large in-plane wavenumbers, we designed the parameters of the double-layer structure 16 to make the small longitudinal wave vector k z Modes with high in-plane wavenumbers satisfy the Bragg reflection condition. Therefore, each layer should be a quarter-wave layer. The target center wavelength needs to be within the band gap to satisfy...

[0062]

[0063]

[0064] Where λ0 is the wavelength of the light emitted by the light source in the emitter in a vacuum, and k0 is the wave number in a vacuum. i and n i (i=1,2) represents the thickness and refractive index of the i-th layer in the bilayer structure. For a horizontally placed electric dipole source, we find that k z =0.5k0 is a good choice. The radius R of the central region is an important parameter that determines the defective waveguide modes supported by the structure. If R is very small, a single-mode hollow omnidirectional reflection waveguide may exist. However, if R is too small, it will lead to an excessively strong divergent beam. Therefore, after comprehensive consideration, we chose a size of R ~ 3(t1 + t2). This allows the structure to support two to three defective waveguide modes within the wavelength range of interest. If the grating structure is selected with an appropriate height, these modes will evolve into Gaussian modes with small divergence angles.

[0065] Next, we will study the mode characteristics of a dielectric coaxial waveguide. To this end, we apply the transfer matrix method to solve the dispersion equation. Here, we present an example of a device consisting of a 10-layer double-layer structure with thicknesses t1 = 130 nm and t2 = 55 nm, and a target wavelength of... 0 = 640 nm. The refractive indices are set to n0 = 1.0, n1 = 1.38 (e.g., MgF2) and n2 = 2.58 (e.g., TiO2). The innermost ring must be made of a material with a higher refractive index (n2 in our example). Figure 3BIn the diagram, we present a colorized two-dimensional plot of the determinant. It is derived from the dispersion relation equation, which determines the relationship between the normalized frequency and the propagation constant in the z-direction. The plot uses a logarithmic scale. Notably, smaller values ​​indicate the presence of optical modes within the structure. Here, we only plot the upper left corner of the light-colored (thick black) line. Within this region, modes can propagate without attenuation along the z-direction. On the other hand, there is a continuous dark region where modes can propagate throughout the entire bilayer structure. The black (white) dashed lines within the bright (dark) background region represent the defect waveguide modes in the first (second) photonic bandgap of the bilayer structure. Light emitted from the central region's light source can couple into these defect waveguide modes.

[0066] An infinitely long coaxial waveguide is merely the starting point for designing and optimizing a practical antenna structure, where a dielectric grating has only subwavelength height and forms a reflector with a metal mirror below. Quantitatively simulating dipole radiation in such an antenna requires three-dimensional (3D) electromagnetic numerical calculations, which are computationally intensive. This computational burden increases further when multiple geometric parameters need to be optimized. To illustrate the optimization process, we study a dipole located on the central axis of a rotationally symmetric structure (this restriction will be removed later). A linearly polarized dipole perpendicular to the central axis, which we assume is along the x-direction, can be considered as a unit vector in polar coordinates. and (See Figure 3A ):

[0067]

[0068] Where p0 is the magnitude of the electric dipole moment. Due to our chosen excitation source and the given rotationally symmetric structure, the electromagnetic field ( )right Tangible This allows us to use the BOR-FDTD method with an azimuth number m=1. This effectively reduces the computational requirements of the three-dimensional problem, transforming it without loss of accuracy into the computational requirements of the two-dimensional case, thus enabling us to perform rigorous numerical simulations and allowing us to efficiently optimize the structural parameters. The effectiveness of this method has been benchmarked using commercial 3D FDTD solvers (LUMERICAL FDTDSOLUTIONS). The field generated by transverse dipole radiation inside a semi-infinite all-dielectric coaxial waveguide structure placed on a silver mirror was calculated using the BOR-FDTD method with m=1. The parameters of the all-dielectric waveguide structure were set as follows: Figure 3B As shown. Figure 3CThe absolute values ​​of the total electric field amplitude distribution near the low-refractive-index center of the in-plane dipole source placed 120 nm from the mirror are shown. Clearly, the dipole radiation is well confined to the core region, and the field distribution evolves periodically along the z-direction. The field distribution obtained at the black dashed line (z=h) resembles a Gaussian distribution. Therefore, position z=h is a suitable height for the antenna structure, thus ensuring that the emitted light will have a large Gaussian beam projection efficiency.

[0069] To quantify the efficiency of the antenna structure in guiding the radiation of a single photon, we introduce the collection efficiency γ, defined as the ratio of the optical power radiated to the far field to the optical power radiated from the source, and the Gaussian beam projection efficiency η, which is the projection efficiency of the far field light relative to the Gaussian mode. The overall efficiency from the source to the fundamental Gaussian mode is given by γη. To calculate η, we use the numerically calculated electric field in the topmost medium n3. Expanding into Laguerre-Gaussian modes in a completely orthogonal basis. The normalization coefficients of the Gaussian modes are...

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[0071] in Let Gausky mode be the field distribution function. Using cylindrical coordinates, The waist radius is Let z be the waist position. When calculating the integral over the entire plane with z fixed, we find that the coefficient c1 does not depend on z, but rather on... and We can scan. and Integrate to obtain the maximum value The optimal set corresponding to Laguerre-Gaussian modes. Note that the Gaussian beam projection efficiency η is determined by... Given the given information, using the BOR-FDTD method (m=1) and the above evaluation criteria, we can explore various design schemes and optimize key parameters of the truncated omnidirectional reflector. We will now present several example designs to illustrate the performance and versatility of the device. Our design process can be described in two steps: 1) Determine the thickness of each layer of the double-layer structure by satisfying the quarter-wave condition. This initial double-layer structure thickness is only an initial guess of the parameters, as the metal mirror and the uppermost homogeneous medium will change the dispersion relation. 2) Optimize the thickness of each layer of the double-layer structure, the truncation height h, the dipole position d in the low-refractive-index central region, and the radius R of the low-refractive-index central region using BOR-FDTD calculations. The goal here is to achieve the highest overall efficiency γη.

[0072] Figures 4A to 4D One type of light-emitting device for directing a single photon is shown, along with related simulation results. Figure 4AThis is a sketch of the device. The refractive index of the top element 20 is n3 = 2.15. The optimized device geometry parameters are h = 280 nm, d = 160 nm, and R = 570 nm. Other parameters are... Figure 3B The instances are the same. Figure 4B The logarithmic-scale electric field intensity distribution of the transverse dipole radiating along the symmetry axis of the antenna structure is shown. Figure 4C The linear-scale intensity distributions of the antenna structure at three different heights along the central axis 100 are described. These fields resemble the free propagation of a fundamental Gaussian mode (as shown by the red beam). Figure 4D The intensity distribution of the far field of light source 24 in various directions is shown.

[0073] In this example of the light-emitting device 22, we place a transverse dipole light source within a hollow, low-refractive-index central region 18, without any surrounding medium (see schematic diagram). Figure 4A (As shown). The same all-dielectric coaxial waveguide structure parameters as in Figure 3b are used. This structure is truncated at height h, and the refractive index of the top element is n3 = 2.15 (e.g., ZrO2). The top element can be hemispherical in form, functioning as a so-called solid immersion lens (SIL). Unlike planar interfaces, the SIL structure avoids refraction, thus reducing the divergence angle of light leaving the device. The perpendicular position of the dipole source relative to the SIL plane is denoted as d. The Gaussian beam profile projection efficiency is optimized to h = 280 nm and d = 160 nm. Figure 4B The logarithmic-scale electric field intensity distribution of the dipoles radiating inside the structure is shown. It can be clearly observed that although some light fields penetrate vertically through the metal substrate of the reflective surface 12a and horizontally through the annular dielectric grating 14, the vast majority of the light fields are confined to the core region and propagate upwards for collection. Figure 4C The intensity distribution on three horizontal planes at different heights within medium n3 is shown. This is analogous to the free propagation of a Gaussian beam. Here, we use the Lorentz reciprocity theorem to calculate the far-field emission mode of the emitter in the planar multilayer system from the near-field electric and magnetic fields (calculated via BOR-FDTD). The specific calculation method can be found in Yang et al.'s paper in ACS Photonics 2016, 3, 395-402. Figure 4D As shown, the far-field distribution clearly resembles a Gaussian distribution in wave vector space. The divergence angle θ of the outgoing light is 23.6 degrees. Our calculations show γ = 97.9% and η = 97.3%, indicating an overall efficiency of 95.1% in converting the outgoing light to Gaussian modes.

[0074] Figures 5A to 5D Other examples of the light-emitting device 22 are illustrated. The upper half of each figure is a schematic diagram of the device structure, and the lower half shows the angular light intensity distribution and collection efficiency. For example... Figures 5A to 5D As shown, the second design of the device considers a case, namely... Figure 5A As shown in the upper part, the light source is embedded in a solid medium with a refractive index of 1.5. To meet the conditions... We removed part of the medium surrounding the light source to effectively reduce the refractive index in the central region. As shown in the figure, only a nanodisk with a diameter of 100 nm remains in the center, its height equal to the height of the grating structure. Here, we retained the refractive index n3 = 2.15 and modified the refractive index n1 = 1.5. The material with a refractive index of 1.5 can be selected from polymers including silicon dioxide, polymethyl methacrylate (PMMA), or polyvinyl alcohol (PVA). In several cases shown in the figure, n2 = 2.58 and n1 = n e = 1.5, where n e The refractive index is that of a nanodisk with a central region diameter of 100 nm, which serves as the host material for the embedded light source. This results in variations in the thickness of the bilayer structure (t1 = 110 nm, t2 = 50 nm), which, after optimization, results in h = 280 nm. Figure 5A The top element of the device shown has a refractive index of n3 = 2.15. The optimal structural parameters are d = 145 nm and R = 590 nm. The device exhibits performance of γ = 98.1% and η = 96.9%. The inset shows the angular light field intensity distribution with a divergence angle of 24.5°. The high refractive index SIL maintains a low divergence angle. Considering the difficulty in obtaining high numerical aperture objectives at low temperatures, this structure also offers the advantage of cryogenic compatibility. Figure 5B The refractive index of the top element of the device shown is n3=1.5. The optimal structural parameters are d=180 nm and R=600 nm. Figure 5B The inset and lower half of the diagram show that the emitted light maintains a largely Gaussian distribution. However, the divergence angle is now as high as 37.3°. The device's performance is γ=97.8% and η=90.3%. This antenna structure is designed to be combined with an oil immersion objective. Finally, as... Figure 5C The top element of the device shown has a refractive index of n³ = 1.0. The optimal structural parameters are d = 140 nm and R = 550 nm. The device exhibits performance of γ = 96.2% and η = 90.7%. The morphology of the emitted light is distorted, and the divergence angle is now 50°. However, a microscope objective with a numerical aperture of 0.95 can still capture the emitted photons. The examples discussed so far all rely solely on coupling to defect modes in the first photon bandgap. They offer good performance but require small geometries. Defect modes in a second bandgap (such as...) can also be considered. Figure 3B (As shown by the white dashed line in the upper left corner). Figure 5DThe device utilizes a second photonic bandgap. It has a top-level element with n3=2.15. The optimized structural parameters are t1=200 nm, t2=90 nm, d=265 nm, and R=500 nm. The device exhibits performance of γ=97.9%, η=96.2%, and a minimum divergence angle of 26.4°. Figure 5D The collection efficiency at different angles was demonstrated. In this design, the device geometry is doubled, making actual nanofabrication easier.

[0075] Figures 5A to 5D All four designs shown rely on suppressing transverse light propagation and enhancing light coupling into defect modes. The Purcell effect is not necessary. The Purcell factors of the structures we simulated are all close to 1. Next, we explored the effects of spectral characteristics and light source position on the results. Figure 6A and 6B Showing Figures 5A to 5D The spectral responses of the collection efficiency and projection efficiency of the structures studied are shown. Here, a to d are related to... Figures 5A to 5D The devices shown correspond one-to-one. Except for the case where n3 = 1.0, we achieved collection efficiencies exceeding 97% in every case over a fairly wide spectral range. For both cases with n3 = 2.15, the spectral bandwidth is greater than 200 nm, while for n3 = 1.5, the bandwidth remains approximately 150 nm. Taking n3 = 1.0 as an example, collection efficiencies exceeding 90% are achieved in the 100 nm range. All structures exhibit high projection efficiencies (see...). Figure 6B The higher the refractive index of the top medium, the higher the collection efficiency and projection efficiency. For Figure 5A For the device shown, we also investigated the dependence of emission on the longitudinal position of the light source. Figure 6C The results show γ and η as functions of the light source d. If we move the light source from its optimal position by ±25 nm, we can observe changes in both collection and projection efficiencies of less than 1%. We also simulated a light source with lateral displacement. Again, when the deviation is within 25 nm, the effect on both collection and projection efficiencies is less than 0.5%. In our simulations, we used silver as the material for the metallic mirror. However, calculations show that similar performance can be achieved using gold as the mirror material (with a collection efficiency 1-2% lower compared to silver).

[0076] Figure 7A Figure 7e further illustrates the influence of antenna structure height on Gaussian beam projection efficiency η.

[0077] Figure 7A It is based on Figures 3A to 3CThe electric field distribution within the annular dielectric grating is simulated using the antenna structure shown. The simulation assumes the annular dielectric grating has an infinite height in the z-axis. Figure 7A As can be seen, the electric field intensity distribution within the low-refractive-index central region exhibits an approximate standing wave distribution along the z-axis 100. The first intensity maxima are located near the lower end of the low-refractive-index central region. The distance between the second maxima and the first maxima along the z-direction is approximately 1 μm. Figure 7B Showing with Figure 1A The information is the same, except that one uses a linear scale for intensity and the other a logarithmic scale. The white dashed line indicates the selectable cutoff height. When the antenna structure is cut off at a specified height, the Gaussian beam projection efficiency of the emitted light will be higher.

[0078] Figures 7C to 7E The overall efficiency γη( was shown) Figure 7C ), collection efficiency γ ( Figure 7D ) and Gaussian beam projection efficiency η( Figure 7E The curves are plotted relative to the cutoff height of the antenna structure (ring dielectric grating). The overall efficiency is plotted over a height range of approximately 200 nm to approximately 1300 nm, while the collection efficiency and projection efficiency are plotted over a height range of approximately 200 nm to approximately 3500 nm. The collection efficiency shows a stable value between 0.96 and 0.99 across the entire height range. Therefore, the height of the antenna structure appears to be irrelevant for the collection efficiency of the emitted light. However, the height of the ring dielectric grating has a significant impact on the projection efficiency and the corresponding overall efficiency. The projection efficiency is high at a height of approximately 700 nm, decreasing from a value close to 1 to approximately 0.9. Therefore, within a height not exceeding 700 nm, a cutoff antenna structure can achieve a projection efficiency of over 85%. When the projection height exceeds 700 nm, the projection efficiency exhibits strong fluctuations with multiple maxima and minima. By selecting an appropriate cutoff height, within this range, if the ring antenna structure is cut off at a point where the electric field strength is approximately 0.3 to 0.8 times the respective nearest maximum, high projection efficiencies of over 65% or even over 80% can also be obtained. Therefore, when the cutoff height is greater than 700 nm, the emitted light can still achieve high projection efficiency by taking into account the undulating distribution of the electric field intensity along the central axis.

[0079] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An antenna structure for guiding directional light radiation includes: A reflector with a reflective surface. An omnidirectional reflector arranged on a reflective surface, consisting of an annular dielectric grating extending concentrically along a central axis perpendicular to the reflective surface and a low-refractive-index central region surrounded by the annular dielectric grating. The annular dielectric grating is composed of two alternating layers: a first layer with a refractive index n1 and a second layer with a refractive index n2, wherein the refractive index n2 is greater than the refractive index n1, and the refractive index of the low-refractive-index central region is less than the refractive index n1. At least one light source is placed in the low-refractive-index central region; The antenna structure allows light emitted from the low-refractive-index central region along the central axis onto the dielectric grating to have a projection efficiency η of over 65% relative to a Gaussian beam.

2. The antenna structure according to claim 1, characterized in that, The projection efficiency η of the outgoing light relative to the Gaussian light represents the degree of overlap between the outgoing light field distribution and the Gaussian light field distribution.

3. The antenna structure according to claim 1 or 2, characterized in that, The projection efficiency η of the emitted light relative to Gaussian light is at least 70%.

4. The antenna structure according to any one of claims 1 to 3, characterized in that, The low-refractive-index central region extends in at least one direction perpendicular to the central axis, with an extension length of D.

5. The antenna structure according to claim 4, characterized in that, The low-refractive-index central region has a circular cross-sectional shape in at least one plane perpendicular to the central axis, and the diameter of the circle corresponds to the extension length D.

6. The antenna structure according to claim 4 or 5, characterized in that, The extension length D does not exceed 1 mm.

7. The antenna structure according to any one of claims 4 to 6, characterized in that, The extension length D is at least 100 nanometers.

8. The antenna structure according to any one of claims 4 to 7, characterized in that, The height of the annular dielectric grating along the central axis does not exceed D.

9. The antenna structure according to any one of claims 1 to 8, characterized in that, The height of the annular dielectric grating along the central axis does not exceed 10 mm.

10. The antenna structure according to any one of claims 1 to 9, characterized in that, The height of the annular dielectric grating along the central axis is at least 50 nanometers.

11. The antenna structure according to claim 10, characterized in that, The second layer, having a refractive index n2, forms the innermost layer that restricts the low-refractive-index central region.

12. The antenna structure according to claim 10 or 11, characterized in that, The value of the refractive index n2 is greater than 1.75 and / or the value of the refractive index n1 is between 1.1 and 1.

75.

13. The antenna structure according to any one of claims 10 to 12, characterized in that, The dielectric layer having a refractive index n1 is composed of at least one of the following materials: magnesium difluoride, silicon dioxide, polymethyl methacrylate, diamond, cubic zirconium oxide, gallium arsenide, indium gallium phosphide, indium gallium arsenide, and aluminum gallium arsenide.

14. The antenna structure according to any one of claims 10 to 13, characterized in that, The dielectric layer having a refractive index n2 is composed of at least one of the following materials: titanium dioxide, gallium arsenide, diamond, and indium gallium arsenide.

15. The antenna structure according to any one of claims 1 to 14, characterized in that, The low-refractive-index central region is empty or at least partially filled with a material with a refractive index lower than n1, and the low-refractive-index central region is at least partially filled with air or nitrogen.

16. The antenna structure according to any one of claims 1 to 15, characterized in that, The refractive index range of the low-refractive-index central region is 1 to 1.

1.

17. The antenna structure according to claim 16, characterized in that, The height of the annular dielectric grating needs to be such that the upper end of the dielectric grating is between 0.3 and 0.8 times the maximum value of the electric field strength.

18. The antenna structure according to any one of claims 1 to 17, characterized in that, It also includes the top element above the annular dielectric grating.

19. The antenna structure according to claim 18, characterized in that, The top element has a hemispherical shape and may optionally be a solid immersion lens.

20. A light-emitting device comprises: An antenna structure as described in claim 1; At least one light source is placed in the low-refractive-index central region, wherein the light emitted from the low-refractive-index central region is emitted by this one or more light sources.

21. The light-emitting device according to claim 20, characterized in that, At least one of the one or more light sources is a single-photon source.

22. A method for designing the antenna structure of claim 1 for a light-emitting device having a predetermined emission wavelength, the method comprising the steps of: Step i: Determine the thickness of the first layer and the thickness of the second layer of the annular dielectric grating, and extend it along the direction perpendicular to the central axis of the reflective surface to form an omnidirectional reflector surrounding the low refractive index central region, wherein the thickness of the first layer and the second layer are determined by comparing the optical thickness of each layer with a quarter of the length of the predetermined emission wavelength; Step ii: Optimize the thickness of the first and second layers, the height of the dielectric grating, the position of the light source in the low refractive index central region, and the diameter of the low refractive index central region through numerical simulation, so as to maximize the projection efficiency η of the light emitted from the light source to the outside of the instrument relative to the Gaussian light.

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