Method for designing long-focal-depth microstructure lens based on gradient photonic crystal

Abstract

The invention discloses a design method of a long-focal-depth microstructure lens based on a gradient photonic crystal, a multi-beam common-path double-cone interference model is constructed by using a double-parameter topless hexagonal prism, and a new method for designing the long-focal-depth microstructure lens is realized. Firstly, based on the double-cone interference model, a GPC structure is designed; then, on the basis of the GPC structure, the size of the dielectric cylinder is designed to be gradually changed, then the effective refractive index of the lens is adjusted and controlled through gradual change, the corresponding lens is constructed, the test result shows that the designed GPC micro-structure lens has the characteristic of long focal depth, and the method provides a new way for design of the long-focal-depth micro-structure lens.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-nano structure lens design and light field regulation, and particularly relates to a design method of a long focal depth micro-structure lens based on a gradient photonic crystal. Background Art

[0002] Compared with photonic crystals, GPC has the characteristic of gradually changing structural parameters and can control the light field without adding defects. Therefore, GPC is a new type of photonic crystal structure that can achieve many novel functions, such as beam focusing, super bending, black hole effect, coupler, self-collimation, etc. Due to the compact structure of the GPC lens, it is beneficial to the integration and miniaturization of the optical path system. The micro-structure lens based on GPC can achieve functions that are difficult to achieve by traditional photonic crystals, such as sub-wavelength focusing, ultra-large transmission bandwidth, and extremely small aberration, providing a new alternative method for photonic crystals to regulate electromagnetic waves. The key to designing the GPC structure depends on adjusting the parameters of the micro-nano structure, that is, completing the design of the gradually changing refractive index distribution to effectively regulate the light wavefront. Generally, researchers form an effective refractive index gradient by changing the lattice spacing of GPC, the size of the micro-structure columns / holes, or the refractive index of the filling material to design different types of GPC structures.

[0003] Due to the wide application of GPC, there is an urgent need to develop a new method for preparing GPC structures quickly, over a large area, and at low cost to promote the industrial application of GPC. Researchers can use electron beam lithography or ion beam etching technology to obtain GPC structures with arbitrary patterns. However, the low preparation efficiency and high cost of these two methods seriously affect the industrial application of GPC and are mainly applied under laboratory conditions. Nanoimprint technology also provides a low-cost method for preparing GPC structures. However, due to the need to use mechanical deformation for preparation, incomplete pattern transfer may occur during the nanoimprint process, affecting the quality and yield of the prepared products. Holographic lithography using a programmable spatial light modulator is considered an efficient method for fabricating GPC structures over a large area and quickly. However, compared with the design of GPC structures by multi-beam direct interference method, the use of a spatial light modulator has the defect of increasing the complexity of the lithography system. It is particularly important to obtain smaller-sized GPCs for the rapid, large-area, and low-cost preparation of GPC structure devices. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a design method of a long focal depth micro-structure lens based on a gradient photonic crystal, proposes a new GPC structure design method, and designs a GPC micro-structure lens with long focal depth characteristics based on this structure, providing a new way for the design of long focal depth micro-structure lenses.

[0005] To solve the above technical problems, a technical solution provided by the present invention is: a design method of a long depth-of-field microstructure lens based on a gradient photonic crystal, characterized in that:

[0006] Use a two-parameter roofless hexagonal prism to construct a multi-beam common-path double-cone interference model. By changing the number, amplitude, and main and secondary angles of the beams, the light intensity distribution of the interference structure pattern can be regulated.

[0007] Obtain a double-periodic GPC structure through six-beam interference, extract a single GPC superlattice structure, and determine appropriate interference structure dimensions: lattice period and interference bright spot radius.

[0008] Use the obtained GPC structure to design a gradient of the medium column size of the GPC lens, and then gradually regulate the effective refractive index of the lens to achieve long depth-of-field focusing and complete the construction of a single microstructure lens.

[0009] Further, the construction method of the multi-beam common-path double-cone interference model is: construct a two-parameter roofless hexagonal prism from quartz material, and make six laser beams incident from six side faces of the two-parameter roofless hexagonal prism respectively. According to the structural parameters of the two-parameter roofless hexagonal prism, construct a multi-beam common-path double-cone interference model.

[0010] Further, the construction process of the two-parameter roofless hexagonal prism is: two regular hexagonal bases are arranged parallel to each other up and down, and are connected by six side faces between the upper base and the lower base. The upper base is blocked by opaque material, and the six side faces are evenly divided into two groups. The three side faces in each group are spaced apart from each other, and the angles between the three side faces in the same group and the base are the same.

[0011] Further, the structural parameters of the two-parameter roofless hexagonal prism are the angles between the two groups of side faces and the base and the angles between the laser beams and the axis.

[0012] Further, the method for obtaining the double-periodic GPC structure is: under the condition that the number and amplitude of the laser beams remain unchanged, according to the relationship between the structural parameters of the two-parameter roofless hexagonal prism and the light intensity distribution of the interference structure pattern, adjust the structural parameters of the two-parameter roofless hexagonal prism to obtain a double-periodic GPC structure.

[0013] Further, the construction process of the microstructure lens is: expose a negative photoresist material with ultraviolet light, extract the radius size and coordinate position of the interference bright spots in the GPC structure, and replace the interference bright spots with medium columns of a material with an appropriate refractive index to obtain a planar GPC lens structure and its array with a gradient of the medium column size, and obtain the microstructure lens.

[0014] To solve the above technical problems, another technical solution provided by the present invention is: a long focal depth microstructured lens based on a gradient photonic crystal, comprising a substrate and dielectric columns, characterized in that: the radius size and the coordinate position on the substrate of the dielectric columns match the radius size and the coordinate position of the interference bright spots determined by the above-mentioned design method.

[0015] Further, the dielectric columns are cylindrical and have the same height.

[0016] The beneficial effects of the present invention are:

[0017] This application uses a double-parameter non-topped hexagonal prism to design a GPC structure. Then, based on the GPC structure, the size of the dielectric columns is designed to be gradually changed, and further, the effective refractive index of the lens (phase control) is gradually adjusted to achieve long focal depth focusing, providing new possibilities for the large-area and rapid fabrication of GPC structures, and providing a new method for the design of long focal depth microstructured lenses.

[0018] In order to make the above and other objects, features, and advantages of the present invention more obvious and understandable, the following specific preferred embodiments are given, and detailed descriptions are made in conjunction with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only eight of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0020] Figure 1 It is a flow chart of the design method of this application;

[0021] Figure 2 It is a schematic diagram of the design of a GPC structure based on multi-beam interference of a non-topped hexagonal prism;

[0022] Figure 3 It is a GPC structure diagram generated by interference;

[0023] Figure 4 It is a relationship diagram between the main angle θ1 and the large period and small period of the designed GPC structure;

[0024] Figure 5 It is a GPC superlattice structure diagram.

[0025] Figure 6 It is a schematic diagram of a single GPC microstructured lens and its unit structure;

[0026] Figure 7 It is a focusing and energy intensity distribution diagram of the designed GPC microstructured lens when the light intensity threshold is 17.18;

[0027] Figure 8 Focus size diagrams at different positions. Detailed implementation manners

[0028] Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. On the contrary, these embodiments are provided to more thoroughly and completely understand the present invention. It should be understood that the drawings and embodiments of the present invention are only for exemplary purposes and are not used to limit the protection scope of the present invention.

[0029] Embodiment

[0030] As Figure 1 shown, a design method of a long depth-of-field micro-structured lens based on a gradient photonic crystal is provided, which is characterized in that:

[0031] A multi-beam common-path double-cone interference model is constructed by using a bi-parameter non-apical hexagonal prism. By changing the number, amplitude, and main and secondary angles of the beams, the light intensity distribution of the interference structure pattern can be regulated.

[0032] A double-period GPC structure is obtained through six-beam interference, and a single GPC superlattice structure is extracted to determine appropriate interference structure dimensions: lattice period and interference bright spot radius.

[0033] The size of the GPC lens dielectric column is designed to be gradually changed by using the obtained GPC structure, and then the effective refractive index of the lens is gradually regulated to achieve long depth-of-field focusing and complete the construction of a single micro-structured lens.

[0034] Among them, the construction method of the multi-beam common-path double-cone interference model is as follows: A bi-parameter non-apical hexagonal prism is constructed of quartz material, and six laser beams are respectively incident from six side surfaces of the bi-parameter non-apical hexagonal prism. According to the structural parameters of the bi-parameter non-apical hexagonal prism, a multi-beam common-path double-cone interference model is constructed.

[0035] The construction process of the bi-parameter non-apical hexagonal prism is as follows: Two regular hexagonal bases are arranged parallel to each other up and down, and are connected by six side surfaces between the upper base and the lower base. The upper base is blocked by an opaque material, and the six side surfaces are evenly divided into two groups. The three side surfaces in each group are spaced apart from each other, and the angles between the three side surfaces in the same group and the base are the same.

[0036] The structural parameters of the bi-parameter non-apical hexagonal prism are the angles between the two groups of side surfaces and the base and the angles between the laser beams and the axis.

[0037] The dual-periodic GPC structure is obtained by adjusting the structural parameters of the dual-parameter roofless hexagonal prism according to the relationship between the structural parameters of the dual-parameter roofless hexagonal prism and the light intensity distribution of the interference structure pattern, while keeping the number and amplitude of the laser beams unchanged, so as to obtain the dual-periodic GPC structure.

[0038] As Figure 2 shown, in the dual-parameter roofless hexagonal prism, the angles between the main sides 1, 3, 5 and the bottom surface of the hexagonal prism are all equal, denoted as The angles between the secondary sides 2, 4, 6 and the bottom surface are also all equal, denoted as The upper bottom surface of the hexagonal prism is blocked by an opaque material, so that the laser beam is incident from the six sides. As Figure 2 (a) is a schematic diagram of the structural parameters of the roofless hexagonal prism. As shown by the purple solid and dashed lines with arrows, the incident beam is refracted in six different directions on the side. The refracted beams on the six sides are also divided into two groups: the main beam group: the beams with wave vectors k1, k3, k5 respectively, and the angles with the z-axis are all equal, denoted as θ1, and called the main angle or inner cone angle; the secondary beam group: the beams with wave vectors k2, k4, k6 respectively, and the angles with the z-axis are also equal, denoted as θ2, and called the secondary angle or outer cone angle. As Figure 2 (b) shows a schematic diagram of the double-cone interference theoretical model formed by the beam passing through the dual-parameter roofless hexagonal prism. If the refractive index of the material of the hexagonal prism is set to n, then according to refraction, there are:

[0039]

[0040] These six refracted beams form interference on the lower bottom surface of the hexagonal prism, and the interference light intensity is expressed as follows:

[0041]

[0042] Among them, E p =A p exp(ik p ·r), E m =A m exp(ik m ·r), p = 1, 3, 5, m = 2, 4, 6. The amplitude of the p-th beam is expressed as A p , the amplitude of the m-th beam is expressed as A m , and the position vector is expressed as r. The wave vectors of the main and secondary beam groups can be expressed as:

[0043]

[0044] Among them, k = 2π / λ, where λ is the wavelength of the laser light used for lithography. According to formula (3), by changing the number, amplitude, and main and secondary angle sizes of the beams, the light intensity distribution of the interference structure pattern can be adjusted.

[0045] The above-mentioned theory is verified as follows: According to the double-cone interference theory model, different principal and secondary angles θ1, θ2, and the laser wavelength λ (355 nm) are substituted into formulas (3)-(5), and the light intensity distribution diagram of the six-beam interference is calculated based on programming software. Next, the characteristics of the GPC structure generated by interference are mainly studied when the principal and secondary angles θ1 and θ2 change and the incremental angle θ1 - θ2 is fixed. As Figure 3 shown, the incremental angle of the hexagonal prism is fixed at 2°. (a) and (b) are the two-dimensional structure generated when θ1 = 15° and the light intensity distribution along the one-dimensional direction (x = 0); (c) and (d) are the two-dimensional structure generated when θ1 = 30° and the light intensity distribution along the one-dimensional direction. From Figure 3 (a), it can be seen that the generated interference structure has obvious double-period characteristics, such as the large period L and small period a marked by the red solid line in the figure. The interference bright spots in a single GPC superlattice structure are also periodically distributed, and the light intensity gradually weakens from the center to the edge, and the corresponding radius of the interference bright spots also gradually decreases, as Figure 3 (b) the one-dimensional light intensity distribution curve extracted along x = 0 shows. According to Figure 3 (b) and (d) the one-dimensional light intensity distributions, the large periods L of the two different GPC structures can be calculated to be 8.54 and 9.41 μm respectively, and the small periods a are 1 and 0.54 μm respectively.

[0046] As Figure 4 shown, to obtain more data on the large and small periods by changing θ1, the red dotted solid line and blue dotted solid line therein are the relationship curves of the large and small periods changing with the principal angle respectively. It can be seen that the small period a gradually decreases with the increase of θ1, and the large period L has an increasing trend. Therefore, if the angles between the side surface and the bottom surface of the hexagonal prism are reasonably changed and to control the angles θ1 and θ2 between the incident light and the z-axis, different GPC structures formed by the six-beam interference can be designed.

[0047] The construction process of the microstructured lens is as follows: The negative photoresist material is exposed to ultraviolet light, the radius and coordinate positions of the interference bright spots in the GPC structure are extracted, and the interference bright spots are replaced by dielectric columns of an appropriate refractive index material to obtain a planar GPC lens structure and its array with gradually changing dielectric column sizes, thus obtaining the microstructured lens.

[0048] The main design method is: Based on the two-dimensional GPC structure generated by the six-beam interference (as Figure 3As shown in [figure], the radius and coordinate position of the interference bright spots (corresponding to the dielectric columns) in a single GPC superlattice structure (i.e., the GPC lens) are extracted. If the interference bright spots are replaced by dielectric columns of a material with an appropriate refractive index, a planar GPC microstructure lens can be constructed. In the laboratory, ultraviolet light with a wavelength of 355 nm can be used to expose a negative photoresist material to record the GPC gradually varying light intensity distribution designed above, and a two-dimensional GPC lens structure with gradually varying dielectric column sizes and its array can be obtained.

[0049] Next, as shown in Figure 3 (c), taking the GPC structure generated when the main angle is 30° as an example, a GPC lens with specific parameters is designed. As shown in Figure 5 (a) is the two-dimensional structure light intensity distribution in the central interference region of Figure 3 (c). The region within the red dashed line represents a single GPC superlattice, that is, the single GPC lens to be designed. Figure 5 (b) shows the one-dimensional light intensity distribution along the x = 0 direction in Figure 5 (a). The two red dashed lines are the light intensity threshold intervals to be selected. Figure 5 (c) represents the radius values of the interference bright spots that form a single GPC superlattice structure from the center to the edge at different light intensity thresholds. In Figure 5 (b), the distance between two adjacent light intensity peaks is the interval between two adjacent bright spots in the GPC superlattice structure, which is called the lattice period, that is, the small period a of the double-period GPC structure. From the calculation results in the previous section, it can be known that the lattice period of the GPC superlattice is 0.54 μm. Figure 5 The six light intensity thresholds selected in (c) are between the two red dashed line light intensity thresholds in Figure 5 (b). At the coordinate positions corresponding to the same light intensity peak, if a smaller light intensity threshold is selected, the corresponding interference bright spot radius is larger; if a larger light intensity threshold is selected, the corresponding interference bright spot radius is smaller.

[0050] Since under the TM polarization condition, the GPC lens has a wider transmission bandwidth and better focusing performance. Therefore, the following research work is all based on the TM polarization light mode. When the main angle is set to 30° and the light intensity threshold is 17.18, Figure 6 (a) and (b) are the top view of the constructed GPC lens model and the side view of its unit structure. When the main angle is 30°, the diameter of the lens is 5.94 μm. The refractive index of the dielectric column material in the unit structure is 1.52, the height is 1.5 μm, and the refractive index of the substrate is 1.45.

[0051] Another technical solution disclosed in the present application is thus formed. This technical solution is: a long focal depth microstructure lens based on a gradient photonic crystal, including a substrate and dielectric columns. The radius size and the coordinate position on the substrate of the dielectric columns are arranged according to the radius size and the coordinate position of the interference bright spots determined by the above-mentioned design method; and the dielectric columns are cylindrical and have the same height.

[0052] The characteristics of the long focal depth microstructure lens constructed in the present application are analyzed below.

[0053] Since the designed GPC lens is a planar lens, the height of the dielectric columns is the same, and the realization of focusing stems from the gradual change of the effective refractive index. The finite element method is used to study its focusing characteristics. The working wavelength is selected as 632 nm, and the polarization state is the TM mode. Under different conditions of the light intensity threshold, the corresponding numerical values of the radius of the dielectric columns are different. As Figure 7 shown in (a), the focusing effect of the GPC lens constructed when the light intensity threshold is 17.18. Figure 7 (b) and (c) are the electric field energy intensity distributions along the z-axis and the focal plane respectively. The designed lens has a focal length of about 19.6 μm, a full width at half maximum (FWHM) of 1.49 μm, and a numerical aperture NA of 0.15.

[0054] Regarding the focal depth and the focal spot size of the lens, according to the paraxial approximation and the theory of scalar diffraction: ΔX = k1λ / NA, ΔZ = k2λ / NA 2 , where ΔX is the minimum resolvable feature size in the transverse dimension, ΔZ is the focal depth, λ is the wavelength, NA represents the numerical aperture of the lens, and k1 and k2 are constants related to the criteria adopted.

[0055] Increasing the focal depth ΔZ will increase the minimum resolvable feature size ΔX at the same time. Therefore, the focal depth and the focal spot size of the lens are a pair of mutually restrictive indicators.

[0056] From Figure 7 (a) and (b), it can be seen that the designed GPC lens has obvious long focal depth characteristics. Generally speaking, the theoretical focal depth value of the lens is defined as DOF = λ / (NA) 2 . According to this formula, Figure 7 the focal depth of the GPC lens designed in (a) is 28 μm, which is about 44.3 times the wavelength.

[0057] In addition, the transverse size of the focal spot is also a core index to measure the performance of the long focal depth lens. Researchers always expect that in the range of long focal depth, the transverse size of the focal spot remains basically unchanged. As Figure 8(a) The transverse intensity distribution of the focus near the sidelobe at different z - coordinates. The white dotted lines marked in the inset are multiple z - axis coordinate positions parallel to the front and back of the focal plane. Calculate the focus size at these positions to more clearly analyze the focusing characteristics of the focal depth extension. From Figure 7 the transmission field distribution of (a) and Figure 8 the inset of (a), it can be seen that there are obvious sidelobes beside the focus, and the effective focal depth does not include this part. For further analysis, the transverse intensity distributions of the focus at multiple positions near the sidelobe are extracted. According to Figure 8 the transverse intensity distributions shown when z is 11 and 12 μm in (a), it can be seen that in the range where z is less than 13 μm, there are obvious sidelobes, and the peak value of the sidelobe is very close to the peak value of the focus at that position. And in this range, the focus size exceeds 2.5 μm. As Figure 8 described in (b), the FWHM at different z - coordinate positions. The FWHM values corresponding to the two red dots on the left differ greatly from the central focus size of 1.49 μm (blue dotted line) when z = 19.6 μm. At the same time, the focus size corresponding to z = 24 μm is 2.11 μm, which also differs greatly from the central focus size. The minimum focus size value is 1.33 μm corresponding to z = 15 μm. Therefore, in the focal depth range where z is from 13 to 23 μm, the transverse size range of the focus is from 1.33 to 1.84 μm, and the change range is not large, which can be considered as the effective focal depth range. Figure 8 The numerical values in the black dot area of (b) also show that the focus does not diverge greatly along the propagation direction. Through the above analysis, the effective focal depth of the designed GPC lens is about 10 μm, which is 15.8 times the working wavelength.

[0058] The descriptions of the above embodiments tend to emphasize the differences between the embodiments. Their similarities or similarities can be referred to each other. For the sake of brevity, this application will not elaborate further.

[0059] Note that the above is only the preferred embodiment of the present invention and the technical principles applied. Those skilled in the art will understand that the present invention is not limited to the specific embodiments here. Various obvious changes, re - adjustments and substitutions can be made by those skilled in the art without departing from the protection scope of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments. Without departing from the concept of the present invention, more other equivalent embodiments can be included, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A method for designing a long-focus, deep-microstructure lens based on gradient photonic crystals, characterized in that: A dual-parameter topless hexagonal prism is used to construct a multi-beam common optical path double-cone interference model. By changing the number, amplitude, and main and secondary angles of the beams, the light intensity distribution of the interference structure pattern can be adjusted. The double-periodic GPC structure is obtained by six-beam interference, and a single GPC superlattice structure is extracted to determine the appropriate interference structure size: lattice period, interference bright spot radius; The obtained GPC structure is used to design a gradual change in the size of the GPC lens dielectric column, and then the effective refractive index of the lens is gradually adjusted to achieve long-focus deep focusing and complete the construction of a single microstructure lens.

2. The method for designing a long focal depth microstructure lens based on gradient photonic crystal according to claim 1, characterized in that: The multi-beam common light path double cone interference model is constructed in the following manner: a double-parameter topless hexagonal prism is constructed from quartz material, six laser beams are incident from six sides of the double-parameter topless hexagonal prism respectively, and a multi-beam common light path double cone interference model is constructed according to the structural parameters of the double-parameter topless hexagonal prism.

3. The method for designing a long focal depth microstructure lens based on gradient photonic crystal according to claim 2, characterized in that: The construction process of the dual-parameter topless hexagonal prism is as follows: two regular hexagonal bottom surfaces are arranged in parallel up and down, and the upper bottom surface and the lower bottom surface are connected by six side surfaces, the upper bottom surface is blocked by an opaque material, and the six side surfaces are divided into two groups, the three side surfaces in each group are arranged at intervals from each other, and the three side surfaces in the same group have the same angle with the bottom surface.

4. The method for designing a long focal depth microstructure lens based on gradient photonic crystal according to claim 2, characterized in that: The structural parameters of the dual-parameter topless hexagonal prism are the angles between the two groups of side surfaces and the bottom surface and the angle between the laser beam and the axis.

5. The method for designing a long focal depth microstructure lens based on gradient photonic crystal according to claim 1, characterized in that: The dual-period GPC structure is obtained by adjusting the structural parameters of the dual-parameter topless hexagonal prism according to the relationship between the structural parameters of the dual-parameter topless hexagonal prism and the light intensity distribution of the interference structure pattern while keeping the number and amplitude of the laser beams unchanged.

6. The method for designing a long focal depth microstructure lens based on gradient photonic crystal according to claim 1, characterized in that: The construction process of the microstructure lens is as follows: using ultraviolet light to expose the negative photoresist material, extracting the radius size and coordinate position of the interference bright spot in the GPC structure, replacing the interference bright spot with a dielectric column of a suitable refractive index material, obtaining a planar GPC lens structure with a gradient dielectric column size and its array, and obtaining a microstructure lens.

7. A long-focus, deep-microstructure lens based on gradient photonic crystal, comprising a substrate and a dielectric column, characterized in that: The radius size and coordinate position of the dielectric column on the substrate match the radius size and coordinate position of the interference bright spot determined by the design method described in any one of claims 1-6.

8. The long-focus microstructure lens based on gradient photonic crystal according to claim 7, characterized in that: The medium columns are cylindrical and have the same height.

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