CN114217370A - Microstructure wave zone plate for broadband achromatic focusing and polarization regulation and design method - Google Patents
Microstructure wave zone plate for broadband achromatic focusing and polarization regulation and design method Download PDFInfo
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- 229910001218 Gallium arsenide Inorganic materials 0.000 claims description 2
- 229910052581 Si3N4 Inorganic materials 0.000 claims description 2
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 claims description 2
- GWEVSGVZZGPLCZ-UHFFFAOYSA-N Titan oxide Chemical compound O=[Ti]=O GWEVSGVZZGPLCZ-UHFFFAOYSA-N 0.000 claims description 2
- 229910052732 germanium Inorganic materials 0.000 claims description 2
- GNPVGFCGXDBREM-UHFFFAOYSA-N germanium atom Chemical compound [Ge] GNPVGFCGXDBREM-UHFFFAOYSA-N 0.000 claims description 2
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- G02B5/00—Optical elements other than lenses
- G02B5/18—Diffraction gratings
- G02B5/1876—Diffractive Fresnel lenses; Zone plates; Kinoforms
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
Abstract
The invention discloses a broadband achromatic focusing and polarization regulation micro-structure zone plate and a design method thereof. The invention can realize achromatic focusing of ultra-wide wave band from visible light to long wave infrared wave band; the polarization state of any wavelength can be regulated and controlled; the invention has the functions of broadband achromatic focusing and polarization regulation and control, and has important practical value for the fields of ultra-wide spectrum imaging detection, target identification and polarization imaging.
Description
Technical Field
The invention relates to the technical field of electromagnetic wave regulation, in particular to a microstructure wave zone plate for broadband achromatic focusing and polarization regulation and a design method.
Background
With the development of modern manufacturing technology, various micro-optical elements represented by binary optical elements are produced, and the application field of the optical elements is greatly expanded. Fresnel zone plates have attracted continuous attention since their introduction by Lord Rayleigh in 1871 as the most widely used micro-optical element. The zone plate consists of a substrate and a plurality of concentric zone plate structures arranged on the substrate, and the optical path difference from each two adjacent zone plate structures to a focal point is half of the wavelength, so that the diffracted optical fields formed by all the zone plate structures can be superposed and enhanced on the focal plane to focus the light beam.
The Fresnel zone plate is designed to realize the modulation of optical path difference by adjusting the width of each zone plate structure, thereby realizing focusing. Because the width of the zone plate structure is fixed, the optical path difference of the light waves with different wavelengths passing through the Fresnel zone plate is different, and the light waves are focused at different positions, chromatic aberration is generated, and the imaging quality is not high. In addition, the shorter the wavelength, the narrower the width of the corresponding zone plate structure, and in order to realize the focusing of the short wavelength, the width of the narrowest zone plate structure of the fresnel zone plate needs to be set to be several tens of nanometers, which brings great difficulty to the manufacturing. Moreover, the fresnel zone plate is difficult to regulate and control the polarization state of the light wave by the modulation principle of the optical path difference.
Disclosure of Invention
The invention provides a microstructure wave zone plate for broadband achromatic focusing and polarization regulation and a design method thereof, and aims to solve the problem that the prior art cannot realize broadband spectral achromatic focusing and regulate and control the polarization state of light waves at the same time.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a broadband achromatic focusing and polarization-regulating micro-structure zone plate comprises a substrate and a plurality of zone plate structures which are concentrically arranged above the substrate, wherein the heights of the zone plate structures are different, micro-structure arrays are arranged on the upper surface of the zone plate structures in a single row along the circumference of the zone plate, the heights of the micro-structure arrays on the same zone plate structure are the same, the heights of the micro-structure arrays on different zone plate structures are different, and the transverse size of each component in the micro-structure arrays is smaller than that of the zone plate structures.
Further, the substrate, the zone plate structure and the microstructure array are made of silicon oxide, silicon nitride, titanium oxide, silicon, germanium or gallium arsenide.
Further, each of the constituent parts of the above-described microstructure array is of a cylindrical type or a rectangular block type.
The design method of the microstructure zone plate for broadband achromatic focusing and polarization regulation comprises the following steps:
the first step is as follows: based on the diffraction theory and combined with a numerical iterative calculation method, the required focal length, the size of a light spot, the caliber of an element and the width of each zone plate structure are given, and the total height of the composite structure of the zone plate structure and the micro-structure array as an integral unit is reversely solved.
And secondly, solving the size parameters of the composite structure of an integral unit: setting the heights of the zone plate structure and the micro-structure array respectively by taking the total height of the composite structure obtained in the first step as a limiting condition, wherein the total heights of the zone plate structure and the micro-structure array are consistent with the total height of the composite structure obtained in the first step; after the height is determined, the length and the width of the microstructure array are adjusted, phase difference values of outgoing light waves of composite structures with different sizes in the y direction and the x direction are obtained through a parameter scanning method, and parameters meeting the regulation and control of the polarization state of the light waves are selected;
the third step: and repeating the second step, solving the size parameter of each composite structure, and constructing the microstructure wave zone plate for broadband achromatic focusing and polarization regulation.
Compared with the prior art, the invention has the beneficial effects that:
1. the working mode that the Fresnel zone plate adjusts the zone width to change the optical path difference is changed into the adjustment of the structural height of the zone plate, the adjustment and control of the optical wave phase are realized through the height change, and the achromatic focusing of the ultra-wide wave band from visible light to long-wave infrared wave band (0.4-11 mu m) can be realized by combining a numerical value iterative calculation method.
2. The invention takes the wave zone plate structure and the micro-structure array as a whole, and can realize the regulation and control of any light wave polarization state by regulating the height of the structure and the length and width of the micro-structure array.
3. The design freedom degree of the provided design method is remarkably improved, and the sizes of the zone plate structure and the micro-structure array can be flexibly adjusted according to the corresponding wavelength. The Fresnel zone plate has the width gradually narrowed from the inside to the outside, and the width of the bottom zone plate structure of the method is consistent, so that the manufacturing is facilitated. The height, the length and the width of the microstructure array at the top can be adjusted, the precise regulation and control of the phase can be realized aiming at any wavelength, and the degree of freedom of design is large.
Description of the drawings:
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a partial schematic view of FIG. 1;
FIG. 3 is a coordinate axis mapping of the focal plane and the element plane;
FIG. 4 is a diagram of the overall height-limiting distribution of a near-infrared band broadband achromatic focusing and polarization-modulated microstructure zone plate;
FIG. 5 is a diagram showing a phase difference distribution between outgoing light waves y and x directions of a composite structure unit of a micro-structured zone plate of a near-infrared band;
FIG. 6 is a graph of transmittance distribution of a composite structural unit of a near infrared band microstructured zone plate;
FIG. 7 is a diagram of the height distribution of a near-infrared band broadband achromatic focusing and polarization-modulated microstructure zone plate;
FIG. 8 is a diagram of broadband achromatic focusing effect of a microstructure zone plate for near-infrared band broadband achromatic focusing and polarization modulation;
FIG. 9 is a distribution diagram of electric field intensity of a near-infrared band broadband achromatic focusing and polarization-controlled microstructure zone plate along the element section direction;
FIG. 10 is a distribution diagram of the size of the focal spot of a near-infrared band broadband achromatic focusing and polarization-modulated microstructure zone plate as a function of wavelength;
FIG. 11 is a distribution diagram of the focusing efficiency of a near-infrared band broadband achromatic focusing and polarization-controlled microstructure zone plate as a function of wavelength;
FIG. 12 is a diagram showing a phase difference distribution of outgoing light waves in y and x directions of a microstructure zone plate for complex broadband achromatic focusing and polarization modulation of a near-infrared band;
FIG. 13 is a schematic structural diagram of a microstructure zone plate for broadband achromatic focusing and polarization modulation of a medium-wave infrared band;
FIG. 14 is a diagram of the focusing effect of a microstructure zone plate for broadband achromatic focusing and polarization modulation of a medium-wave infrared band;
FIG. 15 is a distribution diagram of the size of the focal spot of a microstructure zone plate with wavelength variation for broadband achromatic focusing and polarization modulation of a medium-wave infrared band;
FIG. 16 is a distribution diagram of the focusing efficiency of a micro-structured zone plate with wavelength variation for broadband achromatic focusing and polarization modulation of a medium-wave infrared band;
fig. 17 is a phase difference distribution diagram of outgoing light waves in y and x directions of a microstructure zone plate for broadband achromatic focusing and polarization control of a medium-wave infrared band.
Detailed Description
The invention will be further described with reference to specific examples, but the scope of the invention is not limited thereto.
The invention provides a microstructure zone plate for broadband achromatic focusing and polarization regulation, which is shown in figure 1 and comprises silicon oxide (SiO)2) A substrate, 16 zone plate structures above the substrate (bottom structure) and an array of microstructures disposed above the zone plate structures (top structure). The same zone plate has the same structure height, and different zone plate structures have different heights. The zone plate is structurallyThe micro-structure arrays are arranged on the surface in a single row along the circumference of the zone plate, the micro-structure arrays on the same zone plate structure have the same height, and the micro-structure arrays on different zone plate structures have different heights. Each component of the microstructure array has a lateral dimension that is less than a lateral dimension of the zone plate structure.
Example 1, for a wavelength band of 0.7 to 0.8 μm, each constituent part in the microstructure array is a rectangular block type having a square cross section, see fig. 2.
The design method of the embodiment comprises the following steps:
the method comprises the following steps of firstly, based on diffraction theory, giving a required focal length, a required light spot size, an element caliber and a width of each zone plate structure of a zone plate, and reversely solving the total height of a composite structure of the zone plate structure and a microstructure array as an integral unit.
And secondly, solving the size parameters of the composite structure of an integral unit: setting the heights of the zone plate structure and the micro-structure array by taking the total height of the composite structure obtained in the first step as a limiting condition, wherein the total heights of the zone plate structure and the micro-structure array are consistent with the total height of the composite structure obtained in the first step; after the height is determined, the length and the width of the microstructure array are adjusted, phase difference values of the outgoing light waves of different composite structures in the y direction and the x direction are obtained through a parameter scanning method, and parameters meeting the regulation and control of the polarization state of the light waves are selected;
the third step: repeating the second step to solve the size parameter of each composite structure, in this embodiment, the size parameter of each composite structure can be obtained by calculating the 16 zone plate structures for 15 times, and the three-dimensional structure of the microstructure zone plate is established. So far, the design of the microstructure zone plate for broadband achromatic focusing and polarization regulation is completed.
The specific description is as follows:
(1) determining the total height of the zone plate structure and the microstructure array as an integral unit
First, a coordinate axis corresponding relationship between the focal plane and the component plane is established, as shown in FIG. 3, x and y are coordinates of any point of the component plane, and x 'and y' are focal planesCoordinates of any point of the surface, x'min,x′maxAnd y'min,y′maxThe aperture of the element is determined, and the radius of the element satisfies the following formula
The complex amplitude of the focal plane is determined by
Where, λ is the incident wavelength,
is the wavenumber, d is the propagation distance, g (x, y; λ) ═ 1 in this embodiment the plane wave incidence is set to unity amplitude, and i represents the i-th incident wavelength. T (x, y; lambda) is the transmission coefficient of the corresponding element plane, and is determined by the following equation
T(x,y；λ)＝eiφ(x,y；λ)＝eikΔh(n-1) (3)
Wherein the content of the first and second substances,
is the smallest unit of the structural height of the zone plate, hmaxIs the maximum height of the zone plate structure (determined by the manufacturing capability), NlevelsIs the order of the maximum height division. At this time, the width of the zone plate structure
When in design, the number of the zone plate structures, the caliber of elements, the focal length, the wavelength and the refractive index are given, and the expected focusing performance can be obtained only by increasing or decreasing the height of each zone plate structure (the minimum unit of each increase or decrease is delta h).
Therefore, the design problem of the zone plate structure height of the microstructure zone plate is converted into a mathematical optimization problem, and the problem is generally solved by adopting an iterative algorithm. And setting an iteration stop condition, and stopping iteration when the result meets the condition to obtain the structural height of the zone plate. We link the focusing performance (numerical aperture (NA), focal spot size, focal length and focusing efficiency) as a constraint with the iteration stop condition. Here, the iteration stop condition is defined as an evaluation coefficient FOM, which is proportional to the focusing efficiency.
Where ω is due to broadband incidenceiIs set as a weighting factor for different incident wavelengths, N is the number of wavelengths contained in the broadband, and is usually
μiIs defined as the efficiency factor, εiDefined as normalized absolute difference, determined by the following two equations:
here, Ii(x′,y′)＝|U(x′,y′；)|2Is the intensity corresponding to the ith wavelength in the focal plane. Will the objective function Fi(x ', y') is defined as coordinates
A central Gaussian function with a full width at half maximum (FWHM, corresponding to the focal spot size) WiDetermined by the far field diffraction limit. Objective function Fi(x ', y') focal spot size WiAnd the numerical aperture NA is determined by the following three formulas:
wherein λ isiIs the ith incident wavelength, D is the aperture of the microstructured zone plate, and f is the designed focal length.
Equations (5) to (9) are associated with equation (4), and the greater the value of the iteration stop condition FOM, the higher the focusing efficiency. Therefore, the caliber D of the microstructure zone plate is given, the ring width is 0.3 μm, the focal length f, the numerical aperture NA and the size of a focal spot are given; setting initial height distribution of the microstructure zone plate, starting iteration from the height of a first zone plate structure, and sequentially increasing or decreasing delta h (in the embodiment, the height of the zone plate structure is between 0 and 3.6 mu m) to judge the numerical value of FOM; the same calculation (increase or decrease Δ h) is performed for each zone plate structure height until the FOM value reaches the set size, and the iteration terminates, outputting an optimized height distribution of 16 zone plate structures, as shown in fig. 4.
(2) Determining dimensional parameters of zone plate structures and microstructure arrays
After the height distribution of 16 zone plate structures is obtained, the height distribution is used as a limiting condition to design the size parameters of the microstructure zone plate. Taking the first zone plate structure (outermost ring) as an example, the height limit obtained by numerical iteration is 1.58 μm, and the zone plate structure is divided into an upper part and a lower part, wherein the bottom part is SiO2A zone plate structure with SiN on topxThe microstructure array has an aspect ratio dependent on the refractive index of the material. When a beam of left-handed circularly polarized light enters, the beam of left-handed circularly polarized light can be regarded as superposition of a beam of y-directional linearly polarized light and a beam of x-directional linearly polarized light, and in order to realize conversion of the polarization state of the beam of left-handed circularly polarized light (emergent light is right-handed circularly polarized light), the phase difference between the y direction and the x direction of the emergent light wave is close to 180 degrees, the phase difference is taken as a design target, and a time domain finite difference method is adoptedSetting the incident light wave to be 0.7 μm and the light wave to be normal incidence, and adjusting the SiO at the bottom2Height, top SiN for zone plate structurexThe height, length and width (0.05-0.3 μm) of the microstructure array are calculated by parameter scanning to obtain the phase difference distribution of the emergent light wave in the y and x directions (as shown in FIG. 5) and the transmittance distribution under the corresponding structural parameters (as shown in FIG. 6). The phase difference between the y direction and the x direction of the emergent light wave is close to 180 degrees while the transmittance higher than 90 percent is ensured. The dimensional parameters of the zone plate structure and the microstructure array satisfying the conditions can be obtained, in this embodiment, the SiO at the bottom of the first zone plate structure2The height of the wave zone plate structure is 0.48 mu m, and the length and width are consistent with the ring width and are 0.3 mu m; the height of the top microstructure array was 1.1 μm, the length of the microstructure array was 0.29 μm and the width was 0.11 μm.
(3) The remaining 15 microstructured zone plates were structurally designed using the same calculation method. The height of the bottom zone plate structure, the height, the length and the width of the top microstructure array are adjusted, size parameters are optimized until the phase difference between the y direction and the x direction of the emergent light wave meets the requirement value of polarization state conversion, (in the embodiment, the phase difference between the y direction and the x direction of the emergent light wave needs to be close to 180 °), and finally, the structure parameters of 16 composite structures are respectively selected. The final calculated dimensions of the silica zone plate structure at the bottom of this example are 0.3 μm x 0.3 μm in length and width (consistent with the ring width of the zone plate), and the heights of the bottom structures of the 16 zone plate structures are 0.48 μm, 0.62 μm, 0.17 μm, 1.36 μm, 0.02 μm, 0.12 μm, 1.38 μm, 1.64 μm, 0.13 μm, 1.22 μm, 1.50 μm, 0.68 μm, 0.87 μm, 0.04 μm, 0.13 μm, 1.32 μm, in order from the outside to the inside. The dimensions of the top microstructure array of the 16 zone plate structures are shown in table 1 (row 17 is the center circular hole parameter, no microstructure).
TABLE 1 dimensional parameters of top microstructure arrays
| Height (mum) | Length (mum) | Width (mum) | |
| 1 | 1.1 | 0.29 | 0.11 |
| 2 | 1.3 | 0.28 | 0.155 |
| 3 | 0.8 | 0.29 | 0.09 |
| 4 | 1.6 | 0.28 | 0.18 |
| 5 | 0.5 | 0.29 | 0.08 |
| 6 | 0.9 | 0.29 | 0.085 |
| 7 | 1.6 | 0.28 | 0.18 |
| 8 | 1.8 | 0.28 | 0.2 |
| 9 | 0.8 | 0.29 | 0.09 |
| 10 | 1.6 | 0.29 | 0.115 |
| 11 | 1.7 | 0.28 | 0.19 |
| 12 | 1.4 | 0.28 | 0.13 |
| 13 | 1.5 | 0.28 | 0.14 |
| 14 | 1.1 | 0.29 | 0.1 |
| 15 | 1.2 | 0.28 | 0.16 |
| 16 | 1.6 | 0.29 | 0.115 |
| 17 | 0 | 0 | 0 |
According to the above parameters, the height distribution of the present embodiment is as shown in fig. 7, and after left-handed circularly polarized light with a bandwidth of 0.7 to 0.8 μm is incident on the micro-structured zone plate, the broadband achromatic focusing effect is as shown in fig. 8, and has the same focal length at 0.7 to 0.8 μm. The electric field intensity distribution of the microstructure zone plate along the element section direction is shown in fig. 9, the focal spot sizes of different wavelengths are shown in fig. 10, the focusing efficiencies of different wavelengths are shown in fig. 11, and the focusing efficiencies are all more than 33%. For 0.7 μm incident left-handed circularly polarized light, the phase difference between the initial y and x directions is-90 °, the light wave passes through the microstructure zone plate, the phase difference of the outgoing light wave with the wavelength of 0.7 μm becomes +85 °, as shown in fig. 12, it is seen that the polarization state of the outgoing light becomes right-handed circularly polarized light. The phase difference between the y direction and the x direction of the incident light is close to 180 degrees with the phase difference of the emergent light, which proves that the three-dimensional structure of the microstructure zone plate realizes the conversion from left-handed circularly polarized light to right-handed circularly polarized light.
Example two:
in the embodiment, for a medium wave infrared band of 3-5 μm, the substrate, the zone plate structure and the microstructure array are all made of silicon materials, the caliber of each element is 99 μm, 16 zone plate structures are provided, and the ring width of each zone plate structure is 3 μm. The design method is the same as that of example 1, and the overall limiting height of each zone plate structure from outside to inside is calculated to be 1.51 μm, 3.27 μm, 3.55 μm, 3.55 μm, 4 μm, 7.76 μm, 9.88 μm, 4.42 μm, 2.96 μm, 4.84 μm, 4.8 μm, 5.32 μm, 4.87 μm, 1.57 μm, 5.08 μm and 5.1 μm in sequence by using a numerical iteration algorithm; the center is a cylindrical structure and the height is 3.29 mu m. The design of the dimensional parameters of the bottom zone plate structure and the top microstructure array is performed with the overall height of each zone plate structure as a constraint. The length and width of the bottom zone plate structure calculated in this example is 3 μm × 3 μm by using the same parameter scanning method as in example 1, and the dimensional parameters of the 16 bottom zone plate structures and the top microstructure array are shown in table 2
TABLE 2 dimensional parameters for bottom zone plate structures and top microstructure arrays (microstructures for short)
According to the parameters in table 2, the three-dimensional structure of the microstructure zone plate for establishing broadband achromatic focusing and polarization modulation is shown in fig. 13.
When left-handed circularly polarized light with the bandwidth of 3-5 mu m enters the micro-structure zone plate, the left-handed circularly polarized light and the micro-structure zone plate are focused in an emergent field and have the same focal length, and the broadband achromatic focusing effect of the invention is shown in FIG. 14. The focal spot sizes of different wavelengths are shown in fig. 15, the focusing efficiencies of different wavelengths are shown in fig. 16, and the focusing efficiencies are all above 32%. For 3 μm incident left-handed circularly polarized light, the phase difference between the initial y and x directions is-90 °, the light wave passes through the micro-structured zone plate, and the phase difference of the outgoing light wave with a wavelength of 3 μm becomes +87 °, as shown in fig. 17, it is seen. The polarization state of the emergent light is changed into right-handed circularly polarized light. The phase difference between the y direction and the x direction of the incident light is close to 180 degrees with the phase difference of the emergent light, which proves that the microstructure zone plate realizes the conversion from left-handed circularly polarized light to right-handed circularly polarized light. Therefore, the microstructure wave zone plate provided by the invention realizes the control of the polarization state of the light wave while realizing the broadband achromatic focusing, and can popularize the broadband achromatic focusing and polarization control characteristics to the medium-wave infrared wave zone.
Claims (4)
1. The utility model provides a broadband achromatic focus and micro-structure zone plate of polarization regulation and control, includes the zone plate structure of a plurality of concentric settings above base and the base, its characterized in that: the zone plate structure has different heights, the micro-structure arrays are arranged on the upper surface of the zone plate structure in a single row along the circumference of the zone plate, the micro-structure arrays on the same zone plate structure have the same height, the micro-structure arrays on different zone plate structures have different heights, and the transverse size of each component in the micro-structure arrays is smaller than that of the zone plate structure.
2. The broadband achromatic focusing and polarization modulation microstructured zone plate of claim 1, wherein: the substrate, the zone plate structure and the microstructure array are made of silicon oxide, silicon nitride, titanium oxide, silicon, germanium or gallium arsenide.
3. The broadband achromatic focusing and polarization modulation microstructured zone plate of claim 1 or 2, wherein: each component of the microstructure array is cylindrical or rectangular block-shaped.
4. A design method of a broadband achromatic focusing and polarization-controlled microstructure zone plate comprises the following steps:
the first step is as follows: based on a diffraction theory and combined with a numerical iterative calculation method, giving a required focal length, a light spot size, an element caliber and the width of each zone plate structure, and reversely solving the total height of a composite structure of the zone plate structure and the micro-structure array as an integral unit;
and secondly, solving the size parameters of the composite structure of an integral unit: setting the heights of the zone plate structure and the micro-structure array respectively by taking the total height of the composite structure obtained in the first step as a limiting condition, wherein the total heights of the zone plate structure and the micro-structure array are consistent with the total height of the composite structure obtained in the first step; after the height is determined, the length and the width of the microstructure array are adjusted, phase difference values of outgoing light waves of composite structures with different sizes in the y direction and the x direction are obtained through a parameter scanning method, and parameters meeting the regulation and control of the polarization state of the light waves are selected;
the third step: and repeating the second step, solving the size parameter of each composite structure, and constructing the microstructure wave zone plate for broadband achromatic focusing and polarization regulation and a design method.
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