CN110794662B - Design method of amplitude type super surface computer hologram for eliminating zero-order light - Google Patents
Design method of amplitude type super surface computer hologram for eliminating zero-order light Download PDFInfo
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- 239000011449 brick Substances 0.000 claims abstract description 92
- 238000004364 calculation method Methods 0.000 claims abstract description 19
- 238000005315 distribution function Methods 0.000 claims abstract 2
- 238000009826 distribution Methods 0.000 claims description 25
- 230000010287 polarization Effects 0.000 claims description 20
- 238000005457 optimization Methods 0.000 claims description 16
- 239000000463 material Substances 0.000 claims description 11
- 239000000758 substrate Substances 0.000 claims description 11
- 230000008030 elimination Effects 0.000 claims description 9
- 238000003379 elimination reaction Methods 0.000 claims description 9
- 238000004422 calculation algorithm Methods 0.000 claims description 6
- 238000001093 holography Methods 0.000 claims description 6
- 238000004088 simulation Methods 0.000 claims description 5
- 238000005388 cross polarization Methods 0.000 claims description 3
- 230000033228 biological regulation Effects 0.000 abstract description 2
- 230000005540 biological transmission Effects 0.000 description 11
- 238000006243 chemical reaction Methods 0.000 description 4
- 238000002834 transmittance Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 3
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- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 1
- BQCADISMDOOEFD-UHFFFAOYSA-N Silver Chemical compound [Ag] BQCADISMDOOEFD-UHFFFAOYSA-N 0.000 description 1
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- 239000002127 nanobelt Substances 0.000 description 1
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- G—PHYSICS
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/0005—Adaptation of holography to specific applications
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- G—PHYSICS
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/0443—Digital holography, i.e. recording holograms with digital recording means
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- G—PHYSICS
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
- G03H1/0808—Methods of numerical synthesis, e.g. coherent ray tracing [CRT], diffraction specific
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- G—PHYSICS
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
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Abstract
The invention discloses a design method of an amplitude type super-surface computer hologram for eliminating zero-order light. By constructing a new amplitude distribution function, the amplitude type calculation holographic zero-order image is eliminated by virtue of the amplitude regulation and control characteristic of the super-surface nano brick, so that a clear, zero-order-free and high-imaging-quality reproduced image is obtained. The invention can be applied to the fields of high-end anti-counterfeiting, image display and the like.
Description
Technical Field
The invention relates to the technical field of micro-nano optics and image display, in particular to a design method of an amplitude type super-surface computer-generated hologram for eliminating zero-order light.
Background
The common photography is based on the principle of geometric optical imaging, the intensity of light wave is recorded, the space object is imaged on a plane, and the three-dimensional information of the object is lost due to the loss of the phase of the light wave. The optical holography records the light wave emitted by an object in the form of interference fringes by utilizing the interference principle, and because the amplitude and phase information of the object light wave are stored in the recording medium, a three-dimensional image which is lifelike to the original object can be formed. However, the conventional hologram has strong zero-order light, which greatly affects the imaging quality of the reproduced image and interferes with the observation of the reproduced image.
Disclosure of Invention
The invention aims to provide a design method of an amplitude type super-surface computer generated hologram for eliminating zero-order light.
In order to achieve the above object, a first aspect of the present invention provides a method for designing an amplitude-type super-surface hologram for eliminating zero-order light, comprising: the method comprises the following steps:
(1) principle for eliminating amplitude type calculation holographic zero-order image
First, the original amplitude distribution f (x, y) on the computed hologram is obtained from the far-field target image and an optimization algorithm, such as the GS algorithm. The amplitude distribution of the far-field holographic image is then:
as can be seen from the above formula (1), the zero-order image of the far-field hologram is:
combine (1) to (2) if
The far field holographic image distribution of f' is then:
when u-v-0, F1(0, 0) -F (0, 0) -a00; therefore, the far-field hologram of f' is the zero-order-eliminated far-field hologram of f (x, y); according to the above principle, according to the formula
A new amplitude distribution f' (x, y) on the hologram can be recalculated; since the range of f' (x, y) is (-1, 1). Therefore, to eliminate the zero order also requires finding a medium that can record negative amplitudes.
(2) Super-surface amplitude regulation principle
Assuming a nano brick Jones matrix of
The rotation angle is theta, the incident light is linearly polarized light, and the Jones matrix is
The emergent light Jones vector after passing through the nano brick is as follows:
simplifying to obtain:
for equation (5), when the polarization analysis direction is α2When the analyzer analyzes the deviation, the Jones matrix of the emergent light is as follows:
the transmitted light intensity at this time is:
when the polarization direction of the polarizer is vertical to that of the analyzer, the transmitted light intensity is:
the amplitude of the emergent light is:
if the nano brick is a polarizer, then a is 0, B is 1 or a is 1, B is 0, then the rotation angle range of the nano brick polarizer is [0 °,180 ° ]]In that [ -1/2,1/2 ] can be realized]Continuous amplitude modulation of the range. If the nano-brick is a half-wave plate, A is 1, B is-1, and the rotation angle range of the nano-brick polarizer is [0 DEG, 180 DEG ]]In, can realize [ -1,1 [ ]]Continuous amplitude control of the range when the nanobelt is a polarizer, the emergent intensity of the transmitted light is 1/4sin (2 theta-2 α)1) When the nano-brick is a half-wave plate,the emergent light intensity of the transmitted light is sin (2 theta-2 α)1) Therefore, compared with the zero-eliminating level calculation holographic plate designed based on the nano-brick polarizer, the zero-eliminating level calculation holographic plate designed based on the nano-brick half-wave plate has higher diffraction efficiency.
(3) Nano brick structure parameter optimization
The nano brick unit structure comprises a substrate and a nano brick arranged on the substrate, wherein the interface of the substrate and the nano brick is a working surface. The nano-brick and the substrate form a nano-brick structural unit. Setting the directions of two edges parallel to the working surface as an x axis and a y axis respectively to establish an xoy coordinate system, wherein the surface of the nano brick parallel to the working surface is provided with a long axis L and a short axis W, and the steering angle theta of the nano brick is the included angle between the long axis L of the nano brick and the x axis direction;
the nano brick unit structure can be any anisotropic structure. If the nano brick is a polarizer, the method for optimizing the unit structure parameters of the nano brick polarizer comprises the following steps: the method comprises the steps of scanning a nano brick polarizer unit structure under a working wavelength by taking the linear polarized light with the polarization direction along the long axis of a nano brick as a reflection target and the linear polarized light with the polarization direction along the short axis of the nano brick as a transmission target or the linear polarized light with the polarization direction along the long axis of the nano brick as a transmission target and the linear polarized light with the polarization direction along the short axis of the nano brick as a reflection target, and obtaining the structural parameters of the nano brick unit structure required by the target through electromagnetic simulation optimization.
If the nano brick is used as a half-wave plate, the method for optimizing the unit structure parameters of the half-wave plate of the nano brick comprises the following steps: the method comprises the steps of scanning a nano brick structure unit under a working wavelength by taking the optimization target of vertically incidence of circularly polarized light with the working wavelength to the nano brick structure unit, wherein the cross polarization efficiency of emergent light is not lower than 80% and the same-direction polarization efficiency of the emergent light is not higher than 5%, and obtaining the structural parameters of the nano brick structure unit required by the target through electromagnetic simulation optimization;
based on the principle, the amplitude type calculation holographic zero-order image elimination design based on the super surface material can be realized according to the following steps:
(1) firstly, according to a far-field target image and an optimization algorithm, obtaining an original amplitude distribution f (x, y) on a computed hologram.
(2) According to the principle of eliminating amplitude type calculation holographic zero-order image, a new amplitude distribution f' (x, y) on the holographic plate is designed.
(3) And finally, distributing the steering angle theta values of the nano bricks corresponding to the positions obtained by calculation on each structural unit in the super-surface structure array, so as to obtain the super-surface material capable of eliminating zero-order far-field amplitude type holography.
(4) The polarizer and the analyzer are arranged in the light path, the polarizer is arranged in front of the super-surface structure and used for generating linear polarization light, and the analyzer is arranged behind the super-surface structure and used for unifying the polarization direction of emergent light. When the polarizer is perpendicular to the direction of the analyzer, an amplitude calculation holographic image of zeroth elimination order can be formed in a far field.
The invention also provides an application of the amplitude type calculation holographic zero-order image elimination method based on the metamaterial in designing the metamaterial.
Compared with the prior art, the invention at least has the following advantages and beneficial effects:
1) the amplitude calculation holographic zero-order image elimination method based on the super surface material can effectively eliminate the zero order of the reproduced holographic image, improve the diffraction efficiency and improve the image quality of the holographic image. Therefore, the method has very wide application prospect;
2) the sizes of the nano brick structure units are all sub-wavelength levels, so the super surface designed by the invention has small volume, light weight and high integration, and is suitable for the development of miniaturization in the future.
3) The amplitude calculation holographic zero-order image elimination method based on the super surface material not only can be suitable for Fresnel holographic design but also is suitable for Fourier holographic design.
4) The method for eliminating the amplitude calculation holographic zero-order image based on the super surface material can be used for eliminating any anisotropic structure of a super surface unit structure. And is therefore insensitive to manufacturing errors.
5) The zero order can be well eliminated by utilizing the super-surface half-wave plate structure to design amplitude type calculation hologram. The zero order can be eliminated and the diffraction efficiency can be improved by designing the amplitude type computer generated hologram by utilizing the super-surface half-wave plate structure. Compared with the holographic plate designed based on the super-surface polarizer structure, the diffraction efficiency of the holographic plate can be 4 times higher.
6) The amplitude type calculation hologram designed by the method can realize zero-order image elimination in a broadband wavelength range, and the image contrast is unchanged.
Drawings
FIG. 1 is a schematic diagram illustrating the effect of the super-surface structure array according to the present invention;
FIG. 2 is a schematic structural view of a super-surface structure unit according to the present invention;
FIG. 3 is a scanning result graph of the transmittance and reflectance of the nano-brick polarizer according to the wavelength variation in the present invention;
FIG. 4 is a far field target holographic image 1 of the present invention;
FIG. 5 is a holographic image based on a nano polarizer design without eliminating the zero order image;
FIG. 6 is a holographic image based on the design of nano-brick polarizer to eliminate the zero-order image.
FIG. 7 is a graph of the scanning results of the transmittance of the half-wave plate of the nano-brick according to the wavelength variation;
FIG. 8 is a far field target holographic image 2 of the present invention;
FIG. 9 is a holographic image without zero order image elimination based on nanometer half-wave plate design in the present invention;
FIG. 10 is a holographic image based on a nanometer half-wave plate design to eliminate a zero-order image in the present invention.
Detailed Description
The invention is described in further detail below with reference to specific figures and specific embodiments.
Example 1: [ NANO BRICK POLARIZER ]
In view of the defects of the conventional holography in application, the invention provides a super-surface-based amplitude type calculation holographic zero-order image elimination method, and the invention is described in more detail with reference to the embodiment below:
the super-surface array comprises a plurality of super-surface unit structures, wherein the structural schematic diagram of the super-surface array is shown in FIG. 1. All the nano-brick units have the same geometric dimension and only different rotation angles; the center intervals of the adjacent nano brick unit structures are the same. A schematic of the super-surface unit structure is shown in fig. 2. As can be seen from fig. 2, the super-surface unit structure comprises a substrate 2 and a nano-brick 1 deposited on the substrate. The nano brick 1 and the substrate 2 form a nano brick unit structure. Wherein, the substrate is made of fused quartz glass material, and the nano brick is made of silver material.
In order to enable the super-surface to be equivalent to a polarizer, the reflection can be realized when linearly polarized light with the polarization direction along the long axis of the nano-brick is incident, and the transmission can be realized when the linearly polarized light with the polarization direction along the short axis of the nano-brick is incident by optimizing the structural parameters of the unit structure of the nano-brick.
Specifically, taking the working wavelength λ as 633nm as an example, electromagnetic simulation software is adopted to model and simulate, and with the linear polarization light along the long axis and the short axis of the nano brick as the perpendicular incidence nano brick unit structure at the same time, and with the light reflection efficiency along the long axis of the nano brick being the highest and the light transmission efficiency along the short axis of the nano brick being the highest as the optimization target, the parameters of the second nano brick unit are preferably obtained as follows: the major axis L is 125nm, the minor axis W is 60nm, H is 70nm, and the working face side length C is 400 nm. Under the structural parameters, the results of reflection and transmission efficiency of the nanoblock structural unit to the linearly polarized light with two orthogonal polarization states vibrating along the major axis and minor axis directions thereof are shown in fig. 3, wherein Rx and Ty represent the reflectivity of the linearly polarized light vibrating along the major axis direction and the transmittance of the linearly polarized light vibrating along the minor axis direction of the nanoblock structural unit, respectively, and Ry and Tx represent the reflectivity of the linearly polarized light vibrating along the minor axis direction and the transmittance of the linearly polarized light vibrating along the major axis direction of the nanoblock, respectively. As can be seen from FIG. 3, at incident light wavelengths between 600nm and 650nm, the values of Rx and Ty are relatively high and the values of Ry and Tx are relatively low. Especially at an operating wavelength of 633nm, Rx is about 80%. Ty is close to 100%, Ry and Tx are less than 3%. Therefore, the optimized nano brick structure unit can be equivalent to the function of a polarizer.
Firstly, according to a far-field target image (fig. 4) and an optimization algorithm, obtaining an amplitude distribution f (x, y) on a computed hologram, and then the far-field holographic image amplitude distribution designed based on the hologram is as follows:
fig. 5 is a theoretical far-field holographic image thereof. As can be seen, the zero level occupies a large amount of energy (within the red circle), and the target image is too weak to be observed because only one bright spot is visible in the center of the image.
Constructing a new amplitude distribution f' (x, y) ═ f (x, y) -A0/MN, wherein
The far field holographic image amplitude distribution due to f' is
When u-v-0, F1(0, 0) -F (0, 0) -a00; therefore, the far-field hologram of f' is the zero-order-eliminated far-field hologram of f (x, y); according to the above principle, according to the formula
A new amplitude distribution f' (x, y) on the hologram can be recalculated;
and calculating to obtain a turning angle theta value of the nano bricks in each structural unit in the super-surface structure array based on the newly constructed amplitude distribution f' (x, y), and finally arranging the turning angle theta values of the nano bricks corresponding to the positions obtained by calculation on each structural unit in the super-surface structure array, so as to obtain the super-surface material capable of eliminating zero-order far-field amplitude type holography. Fig. 6 is a far-field hologram image calculated according to the newly constructed amplitude distribution f' (x, y theory).
Example 2: [ NANO BRICK HALF-WALL SHEET ]
The schematic diagram of the unit structure of the nano-brick half-wave plate is also shown in fig. 2. Taking the working wavelength lambda as 633nm as an example, electromagnetic simulation software is adopted for modeling and simulation, the nano brick is vertically incident by circularly polarized light, and structural parameters of a nano unit, including L, W, H, C, are scanned under the working wavelength, so that the optimization goals of high transmission cross polarization efficiency and low transmission homodromous polarization efficiency are achieved. The parameters of the first nanobrick building block obtained are preferably: 150nm, 60nm, 385nm, 300 nm. Under the structural parameters, the transmission co-polarization conversion efficiency and the transmission counter-polarization conversion efficiency of the nano-brick are shown in fig. 7. Where T _ Cross is the transmission reverse polarization conversion efficiency and T _ Co is the transmission Co-polarization conversion efficiency. As can be seen from FIG. 7, at 633nm of the operating wavelength, T _ Cross is higher than 87%, and T _ Co is less than 1%, indicating that the optimized nano-brick unit structure can be equivalent to the function of a half-wave plate.
Firstly, according to a far-field target image (fig. 8) and an optimization algorithm, obtaining an amplitude distribution f (x, y) on a computed hologram, and then the far-field holographic image amplitude distribution designed based on the hologram is as follows:
fig. 9 is a theoretical far-field holographic image thereof. As can be seen, the zero level occupies a large amount of energy (within the red circle), and the target image is too weak to be observed because only one bright spot is visible in the center of the image.
Constructing a new amplitude distribution f' (x, y) ═ f (x, y) -A0/MN, wherein
The far field holographic image amplitude distribution due to f' is
When u-v-0, F1(0, 0) -F (0, 0) -a00; therefore, the far-field hologram of f' is the zero-order-eliminated far-field hologram of f (x, y); according to the above principle, according to the formula
A new amplitude distribution f' (x, y) on the hologram can be recalculated;
and calculating to obtain a turning angle theta value of the nano bricks in each structural unit in the super-surface structure array based on the newly constructed amplitude distribution f' (x, y), and finally arranging the turning angle theta values of the nano bricks corresponding to the positions obtained by calculation on each structural unit in the super-surface structure array, so as to obtain the super-surface material capable of eliminating zero-order far-field amplitude type holography. Fig. 10 is a far-field hologram image calculated in accordance with the newly constructed amplitude distribution f' (x, y) theory.
Claims (3)
1. A design method of amplitude type super surface computer hologram for eliminating zero-order light is characterized in that: the method comprises the following steps:
1) obtaining original amplitude distribution f (x, y) on the computed hologram according to a target image of a far field and an optimization algorithm; the far field holographic image amplitude distribution is:
2) constructing a new amplitude distribution function
Wherein A is0F (0, 0), the far-field hologram distribution due to F' is:
when u is equal toWhen v is 0, F1(0, 0) is F (0, 0) -a00; therefore, the far-field hologram of f' is the zero-order-eliminated far-field hologram of f (x, y); according to the above formula
A new amplitude distribution f' (x, y) on the hologram can be recalculated;
3) constructing a nano brick unit structure, and optimizing to obtain the structural parameters of the nano brick unit structure; the nano brick unit structure comprises a substrate and a nano brick arranged on the working surface of the substrate, wherein the nano brick and the working surface form a nano brick structure unit; setting the directions of two edges parallel to the working surface of the substrate as an x axis and a y axis respectively to establish an xoy coordinate system, wherein the surface of the nano brick parallel to the working surface is provided with a long axis L and a short axis W, and the steering angle theta of the nano brick is the included angle between the long axis L of the nano brick and the x axis direction; the structural parameters of the nano brick structural unit comprise a long axis L, a short axis W and a height H of the nano brick and the size of the side length C of the working face; the nano brick unit structure is any anisotropic structure, namely a long axis L is not equal to a short axis W;
4) calculating to obtain a turning angle theta value of the nano bricks in each unit structure in the super-surface structure array according to the new amplitude distribution f' (x, y) based on the unit structure parameters of the nano bricks, and finally arranging the turning angle theta values of the nano bricks corresponding to each position obtained by calculation on each unit structure in the super-surface structure array, so as to obtain the super surface material capable of eliminating zero-order far-field amplitude type holography;
5) a polarizer and an analyzer are arranged in a light path, the polarizer is arranged in front of the super-surface structure and used for generating linear polarized light, and the analyzer is arranged behind the super-surface structure and used for unifying the polarization direction of emergent light; when the polarizer is perpendicular to the direction of the analyzer, the amplitude calculation holographic pattern of the zeroth elimination order can be formed in the far field.
2. The design method of amplitude type super surface computer hologram for eliminating zero order light according to claim 1, wherein:
if the nano brick unit structure is a nano brick half-wave plate, the structural parameters of the nano brick half-wave plate can be optimized according to the following method: the method comprises the steps of scanning a nano brick structure unit under a working wavelength by taking the optimization target of vertically incidence of circularly polarized light with the working wavelength to the nano brick structure unit, wherein the cross polarization efficiency of emergent light is not lower than 80% and the same-direction polarization efficiency of the emergent light is not higher than 5%, and obtaining the structural parameters of the nano brick structure unit required by the target through electromagnetic simulation optimization;
if the nano-brick unit structure is a nano-brick polarizer, the structural parameters of the nano-brick polarizer can be optimized according to the following method: the method comprises the steps of scanning a nano brick unit structure under a working wavelength by taking the linear polarized light with the polarization direction along the long axis of the nano brick as an optimization target, reflecting the linear polarized light with the polarization direction along the short axis of the nano brick, and transmitting the linear polarized light with the polarization direction along the short axis of the nano brick as an optimization target, and obtaining the structural parameters of the nano brick unit structure required by the target through electromagnetic simulation optimization.
3. Use of a method of designing a zero order light-annihilating amplitude-type super-surface computer hologram according to claim 1 or 2 for designing a super-surface material.
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