阅读说明：本技术 基于法布里珀罗共振的光学介质金属超构光栅 (Optical medium metal super-structure grating based on Fabry-Perot resonance ) 是由 徐亚东 孙宝印 曹燕燕 高雷 孟庆权 于 2019-11-05 设计创作，主要内容包括：本发明公开了一种基于法布里珀罗共振的光学介质金属超构光栅,其特征在于,所述超构光栅包括若干周期性分布的超晶胞,每个超晶胞包括金属基体,金属基体上设有若干周期性重复分布的凹槽,凹槽内填充有厚度不同的介质材料,且满足：<Image he="84" wi="700" file="DDA0002260288320000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>其中,k<Sub>0</Sub>＝2π/λ为平面波真空的波矢,N为正整数,ε为介质材料的介电常数,介质材料的磁导率为1,m为超晶胞内介质材料的单元数,即一个超晶胞内的凹槽数量,d<Sub>i</Sub>和d<Sub>i+1</Sub>为第i和i+1个单元内介质材料的高度。本发明中基于法布里珀罗共振的光学介质金属超构光栅结构简单、易于实现,只需在单元内填充厚度渐变的同一种介质材料(阻抗不匹配),即可实现近乎完美效率的异常衍射现象。(The invention discloses an optical medium metal super-structure grating based on Fabry-Perot resonance, which is characterized by comprising a plurality of periodically distributed super-cells, wherein each super-cell comprises a metal base body, a plurality of periodically and repeatedly distributed grooves are arranged on the metal base body, and medium materials with different thicknesses are filled in the grooves and meet the following requirements: wherein k is 0 2 pi/lambda is the wave vector of plane wave vacuum, N is a positive integer, epsilon is the dielectric constant of the dielectric material, the magnetic permeability of the dielectric material is 1, m is the number of units of the dielectric material in the supercell, namely the number of grooves in one supercell, and d is the number of the grooves in one supercell i And d i+1 The height of the dielectric material in the i-th and i + 1-th units. The Fabry-Perot resonance-based optical dielectric metal super-structure grating has a simple structure, is easy to realize, and can realize approximate thickness change only by filling the same dielectric material with gradually changed thickness (impedance mismatching) in the unitAnomalous diffraction phenomena of perfect efficiency.)

1. The utility model provides an optical medium metal super structure grating based on fabry-perot resonance which characterized in that, super structure grating includes a plurality of periodically distributed's super cell, and every super cell includes the metallic matrix, is equipped with the recess of a plurality of periodic repetitive distributions on the metallic matrix, and the recess intussuseption is filled with the dielectric material of different thickness, and satisfies:

wherein k is₀2 pi/lambda is the wave vector of plane wave vacuum, N is a positive integer, epsilon is the dielectric constant of the dielectric material, the magnetic permeability of the dielectric material is 1, m is the number of units of the dielectric material in the supercell, namely the number of grooves in one supercell, and d is the number of the grooves in one supercell_iAnd d_i+1The height of the dielectric material in the i-th and i + 1-th units.

2. The fabry-perot resonance based optical dielectric metal super-structure grating as claimed in claim 1, wherein the phase of the plane wave passing through the dielectric material in the ith groove in the super cell and reaching the transmission interface is:

when the plane wave passes through the dielectric material in the (i + 1) th groove in the super cell and reaches the transmission interface, the phase is as follows:

wherein the content of the first and second substances,

3. The fabry-perot resonance based optical dielectric metal super-structure grating as claimed in claim 2, wherein the transmission phase difference of adjacent units in the super-cell on the transmission interface is

4. The Fabry-Perot resonance-based optical dielectric metal super-structure grating as claimed in claim 1, wherein the number m of dielectric material units in the super-cell in the super-structure grating is greater than or equal to 2.

5. The fabry-perot resonance based optical dielectric metal super-structured grating of claim 1, wherein N-1, 2 or 3 in the super-structured grating.

6. The Fabry-Perot resonance-based optical dielectric metal metamaterial grating of claim 3, wherein the transmission phase difference of adjacent units in the superlattice on the transmission interface is

7. The fabry-perot resonance-based optical dielectric metal super-structure grating as claimed in claim 1, wherein the super-structure grating has a unit number m of dielectric materials in super-cell of 3, a dielectric constant e of dielectric materials of 9, N of 1, and thicknesses of dielectric materials in 3 units of d₁＝0.48μm，d₂＝0.97μm，d₃＝1.46μm。

8. The fabry-perot resonance based optical dielectric metal super-structure grating as claimed in claim 7, wherein the transmission phase difference of adjacent units in the super-cell on the transmission interface is

9. The fabry-perot resonance-based optical dielectric metal super-structure grating as claimed in claim 1, wherein the super-structure grating has a unit number m-4 of dielectric materials in a super-cell, a dielectric constant e-4 of the dielectric materials, N-1, and thicknesses d of the dielectric materials in 4 units₁＝0.73μm，d₂＝1.45μm，d₃＝2.18μm，d₄＝2.9μm。

10. The fabry-perot resonance based optical dielectric metal super-structure grating as claimed in claim 9, wherein the transmission phase difference of adjacent units in the super-cell on the transmission interface is

Technical Field

The invention relates to the technical field of optics, in particular to an optical medium metal super-structure grating based on Fabry-Perot resonance.

Background

In recent years, the super-structured grating has attracted great attention in the field of electromagnetic wave regulation and control, and various abnormal optical phenomena and devices are realized. Recently, research has revealed that the new diffraction law of the super-structured grating, namely the abnormal transmission/reflection conversion related to the parity of the number m of grating units, has the principle that the phase gradient causes extra multiple total reflection in the high-order diffraction of the grating, and the total reflection number is related to m. Therefore, the angular asymmetric absorption of the metal grating can be realized by utilizing the principle, and the degree of the asymmetric absorption is also related to m.

Therefore, the number m of units of the super-structured grating is an important degree of freedom, and it is an important aspect to study the influence of different numbers m on the super-structured grating. Wherein, the abnormal transmission/reflection conversion research related to m parity is designed based on the acoustic super-structure grating, and each unit of the super-structure grating satisfies the gradient phase required on the transmission interface through the designed microstructure. However, for optical super-structured gratings, artificially designed microstructures may increase the complexity of the super-structured grating system. The simplest way to satisfy the phase gradient of the transmission interface is to fill the cell with a dielectric material, such as a dielectric material of the same thickness but with a gradient refractive index. Furthermore, in order to ensure a high transmittance of the optical super-structured grating, the material filled in the cell is generally required to be impedance matched.

The above design method is difficult to implement in experiments because it is almost impossible to find several materials whose refractive indices are just graded and impedance matched. How to use only one dielectric material and impedance mismatch to realize the requirement of interface phase gradual change and ensure high transmissivity of the super-structure grating is an urgent problem to be solved.

Much research has also been done before on how to improve the transmission of the grating. Wherein FP resonance is an important means, such as normal incidence of wave to a one-dimensional acoustic grating, and using resonance of FP excited in the grating slit results in high transmission of the grating; and the transmission efficiency of the single slit is improved by using FP resonance by combining the single slit and the metal grating.

Therefore, in view of the above technical problems, there is a need to provide a fabry-perot resonance-based optical dielectric metal super-structured grating.

Disclosure of Invention

In view of the above, the present invention provides a fabry-perot resonance-based optical dielectric metal super-structured grating to achieve a nearly perfect abnormal diffraction phenomenon.

In order to achieve the above object, an embodiment of the present invention provides the following technical solutions:

the utility model provides an optical medium metal super structure grating based on fabry-perot resonance, super structure grating includes a plurality of periodically distributed super cell, and every super cell includes the metal base member, is equipped with the recess of a plurality of periodic repetitive distributions on the metal base member, and the recess intussuseption is filled with the dielectric material that the thickness is different, and satisfies:

wherein k is₀2 pi/lambda is the wave vector of plane wave vacuum, N is a positive integer, epsilon is the dielectric constant of the dielectric material, the magnetic permeability of the dielectric material is 1, m is the number of units of the dielectric material in the supercell, namely the number of grooves in one supercell, and d is the number of the grooves in one supercell_iAnd d_i+1The height of the dielectric material in the i-th and i + 1-th units.

As a further improvement of the invention, the phase of the plane wave passing through the dielectric material in the ith groove in the super cell and reaching the transmission interface is as follows:

when the plane wave passes through the dielectric material in the (i + 1) th groove in the super cell and reaches the transmission interface, the phase is as follows:

wherein the content of the first and second substances,

the initial phase of the plane wave incident to the super-structure grating is shown, and h is the total thickness of the super-structure grating.

As a further improvement of the invention, the transmission phase difference of adjacent units in the super cell on the transmission interface is

As a further improvement of the invention, the unit number m of the dielectric material in the super cell in the super-structure grating is more than or equal to 2.

As a further improvement of the present invention, in the super-structured grating, N ═ 1, 2, or 3.

As a further improvement of the invention, the transmission phase difference of adjacent units in the super cell on the transmission interface is

In a further improvement of the present invention, in the above-mentioned super-structured grating, the number m of units of the dielectric material in the super-cell is 3, the dielectric constant ∈ of the dielectric material is 9, N is 1, and the thicknesses of the dielectric materials in 3 units are d₁＝0.48μm，d₂＝0.97μm，d₃＝1.46μm。

As a further improvement of the invention, the transmission phase difference of adjacent units in the super cell on the transmission interface is

In a further improvement of the present invention, the number m of units of the dielectric material in the superlattice is 4, the dielectric constant e of the dielectric material is 4, N is 1, and 4 units are intercalated in the superlattice gratingThe thickness of the material is d₁＝0.73μm，d₂＝1.45μm，d₃＝2.18μm，d₄＝2.9μm。

As a further improvement of the invention, the transmission phase difference of adjacent units in the super cell on the transmission interface is

The invention has the beneficial effects that:

the Fabry-Perot resonance-based optical dielectric metal super-structure grating has a simple structure and is easy to realize, and the abnormal diffraction phenomenon with nearly perfect efficiency can be realized only by filling the same dielectric material with gradually changed thickness (impedance mismatching) in the unit.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic cross-sectional structural diagram of an optical dielectric metal super-structured grating based on Fabry-Perot resonance according to the present invention;

FIG. 2 is a phase difference of the transmission interface of the metal super-structured grating of the optical medium of the present invention

A graph of theoretical dependence on dielectric constant epsilon;

FIG. 3 is a graph showing the transmittance and the transmission phase of a super-structured grating as a function of the thickness of the dielectric material when the dielectric constant ε is 9 according to an embodiment of the present invention;

FIG. 4 shows an embodiment of the present invention, in which the dielectric material has a dielectric constant ε 9 and a thickness d₁＝0.48μm，d₂＝0.97μm，d₃1.46 μm, total magnetic field of the super-structured gratingA map and corresponding magnetic field strength and phase map;

fig. 5 is a graph showing the variation of the transmission/reflection rate of different orders of the super-structured grating with the incident angle when the number of units m is 3 and the dielectric constant e of the dielectric material is 9 according to an embodiment of the present invention;

FIG. 6 shows an embodiment of the present invention, in which the number of units m is 3, the dielectric constant ε is 9, and the incident angle θ is_iWhen the angle is minus 30 degrees, a total magnetic field graph of the super-structure grating is obtained;

FIG. 7 shows an embodiment of the present invention, in which the number of units m is 3, the dielectric constant ε is 9, and the incident angle θ is_iWhen the angle is 30 degrees, a total magnetic field graph of the super-structure grating is obtained;

FIG. 8 is a graph of the transmittance and the transmission phase of a super-structured grating as a function of the thickness of the dielectric material when the dielectric constant ε is 4 in another embodiment of the present invention;

fig. 9 is a graph showing the variation of transmission/reflection rate with incident angle of different orders of the super-structured grating when the number of units m is 4 and the dielectric constant e of the dielectric material is 4 in another embodiment of the present invention;

FIG. 10 shows an embodiment of the present invention, in which the number of units m is 4, the dielectric constant ε is 4, and the incident angle θ is_iWhen the angle is minus 30 degrees, a total magnetic field graph of the super-structure grating is obtained;

FIG. 11 shows an embodiment of the present invention, in which the number of units m is 4, the dielectric constant ε is 4, and the incident angle θ is_iTotal magnetic field map of the super-structured grating at 30 °.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The invention discloses a simple Fabry-Perot resonance-based optical dielectric metal super-structure grating, namely, a dielectric material (magnetic permeability is 1) with the same dielectric constant and unmatched impedance is filled in units of the super-structure grating, and the dielectric thickness d in different units is gradually changed. When FP resonance (Fabry-Perot resonance) occurs in the medium, the phase distribution requirement on the transmission interface of the super-structured grating can be met, and meanwhile, the super-high diffraction efficiency is achieved. In addition, in the designed dielectric metal super-structure grating, not only the abnormal transmission/reflection of the super-structure grating is related to the parity of the number m of the units, but also the dielectric constant of the filling material in the units and the material thickness d are completely determined by the value of m, the dielectric constant and the thickness d of the material are respectively related to the internal relation of m, and the invention provides a clear expression of the dielectric constant related to m.

Referring to fig. 1, an optical dielectric metal super-structure grating 100 based on fabry-perot resonance in the present invention includes a plurality of periodically distributed super-cells 10, each super-cell 10 includes a metal substrate 11, a plurality of periodically and repeatedly distributed grooves 12 are formed on the metal substrate, the grooves are filled with dielectric materials 13 with different thicknesses, and the requirements are as follows:

wherein k is₀2 pi/lambda is the wave vector of plane wave vacuum, N is a positive integer, epsilon is the dielectric constant of the dielectric material, the magnetic permeability of the dielectric material is 1, m is the number of units of the dielectric material in the supercell, namely the number of grooves in one supercell, and d is the number of the grooves in one supercell_iAnd d_i+1The height of the dielectric material in the i-th and i + 1-th units.

Specifically, the optical dielectric metal super-structured grating in the invention is a dielectric metal super-structured grating with one-dimensional periodic phase gradual change. Referring to FIG. 1, assuming that a plane wave with TM polarization (the incident wave vector is in the xy plane, and the magnetic field is along the z direction) enters the super-structured grating, the super-structured grating in the figure will be described by taking two periods as an exampleThe total thickness of the super-structure grating is h, the super-structure grating has periodicity in the y direction, and the period length is p. Each super cell contains m units with a unit length of a. The metal substrate 11 is made of metal material, such as silver, the upper part of the groove 12 is air, and the lower part of the groove is made of the same dielectric material. The width of the medium is w, the dielectric constant is epsilon, the magnetic conductivity is 1, and the thickness of the medium material filled in different units is d₁，...，d_i，...，d_m。

The phase distribution requirement in one period on the transmission interface of the super-structure grating is gradual change and the change range is covered by 2 pi, so in order to meet the requirement of phase change of the super-structure grating, the dielectric constant and the thickness of the medium also meet certain conditions. Through research, the dielectric constant and the thickness of the needed medium are determined by the value of m, namely for different unit numbers m, the corresponding dielectric constant and the corresponding thickness can be found to meet the requirement of phase gradual change of the super-structured grating.

First, the relationship between the number m of cells and the dielectric constant ε is theoretically analyzed. If a TM polarized plane wave is normally incident to the super-structured grating, the wave passes through the ith groove (the thickness of the filled medium is d)_i) The phase at the transmission interface is:

similarly, the wave passes through the adjacent (i + 1) th groove (the thickness of the filled medium is d)_i+1) The phase at the transmission interface is:

wherein the content of the first and second substances,

is the initial phase of the plane wave incident on the super-structured grating. Between two adjacent grooves on the transmission interfaceThe transmission phase difference is:

meanwhile, in order to ensure that the super-structured grating has high transmittance, it is assumed that the wave undergoes FP resonance (in the x direction) inside the medium, i.e., the medium thickness d_iAnd d_i+1The condition for generating the FP resonance is satisfied. Thus, the waves respectively pass through a thickness d_iAnd d_i+1The difference between the phases of the two materials is also an integral multiple of pi:

by substituting formula (2) for formula (1), it is possible to obtain:

the phase gradient super-structure grating requires the phase difference of adjacent units on a transmission interface to be

Therefore, for different m, the corresponding epsilon meets the requirement of phase gradual change on the transmission interface of the super-structured grating.

Shown in FIG. 2 as formula 3And epsilon, which respectively represent the wave passing thickness d_iAnd d_i+1The difference between the phases added by the two is pi, 2 pi and 3 pi, namely N is 1, 2 and 3. In theory N may be other larger integers and is not drawn too much here. In addition, when designing a phase-gradient super-structured grating, the number of cells is required to be 2 of m, and the value range of the transmission phase difference of adjacent cells is generally within

Therefore, only this need be consideredWithin the range of

And epsilon, the regions of light red and light blue in the figure respectively representing a transmission phase difference of

And

the case (1).

The values of m and epsilon will be described below with N being 1. At this time, when the transmission phase difference range is

The value of the dielectric constant is in the range of epsilon > 1. For example, when m is 3 and epsilon is 9, that is, when the thickness of the dielectric material with the dielectric constant of 9 satisfies the condition of generating FP resonance, the transmission phase difference of the adjacent cells on the transmission interface is

Similarly, when m is 4, epsilon is 4, the corresponding transmission phase difference becomes 4

As shown, the required dielectric constant gradually decreases as m increases ( m 3, 4, 5, 6.). In particular, in the limiting case, when

(m tends to infinity), ε is 1, as shown by the intersection of the curves in the figure. At this time, the phase-gradient super-structured grating is degenerated into a uniform air metal grating, and the characteristic of abnormal diffraction does not exist. But as long as m is 2 and a finite number, there is always a corresponding epsilon that satisfies the phase-grading requirements of the metamaterial grating. The proposed theoretical formula 3 is therefore generic to optical super-structured gratings.

When the transmission phase difference is within the range of

For the condition that m takes different values, unique epsilon can be found on the curve, and the condition of phase gradual change on the transmission interface of the super-structured grating is met. Although the transmission phase difference at this timeBecomes negative, but and

the positive numbers are similar, and the same abnormal diffraction phenomenon exists in the super-structured grating. Therefore, only in the following

The case of positive numbers is discussed further.

In one embodiment of the present invention

The thickness d when FP resonance occurs inside the medium is discussed as an example of ε 9_iAnd m.

Assuming that the plane wave is normally incident on the ith cell (thickness d of the medium in the groove)_i) The grating is a periodic uniform grating, and the specific parameters of the grating are as follows: wavelength 3 μm, grating thickness h 2 μm, period length a 1 μm, groove width w 0.8 μm, and dielectric thickness d_iVarying from 0 μm to 2 μm. Obtaining the thickness d of the medium filled in the groove by adopting comsol software simulation_iVariation, transmissivity T and transmission phase of the grating

The variation of (2).

Referring to fig. 3, curves 1 and 2 represent the transmittance and transmission phase, respectively, of a uniform grating. On the transmittance curve, it can be seen that the transmittance T ═ 1 at several peaks (indicated by broken lines). These full transmission points are caused by FP resonance occurring inside the medium of the grating, not by the entire grating thickness h (the entire grating thickness h is fixed to 2 μm). Transmission phases corresponding to three adjacent FP resonance points on fig. 3Shown by solid points 1, 2, and 3, and the transmission phase difference therebetween is

To prove this, the thickness d of the medium in the groove of the uniform grating is set_iThe thickness values at three points 1, 2 and 3 in the figure are respectively: d₁＝0.48μm，d₂＝0.97μm，d₃The total magnetic field of the uniform grating is plotted at 1.46 μm for further illustration.

Referring to fig. 4, the right side of the diagram is a total magnetic field diagram of one unit of the uniform grating, the plane wave is normally incident from the left side, and the arrows represent the incident direction and the transmission direction. When the thickness of the grating medium is d₁＝0.48μm，d₂＝0.97μm，d₃At 1.46 μm, it can be seen from the overall magnetic field diagram that the magnetic field strength inside the medium is significantly increased compared to air. Also, as the thickness of the medium increases, the magnitude of the magnetic field strength inside the medium also increases, i.e., the strength of the FP resonance also increases.

In order to see the magnetic field variation more clearly, the magnetic field strength and phase are plotted at the black dashed line in the figure, as shown on the left side of fig. 4. The curve without solid points in the figure represents the magnetic field strength and the curve with solid points represents the phase of the magnetic field, wherein the grey areas represent the interior of the medium. It can be seen that as the thickness of the medium increases, the magnitude of the magnetic field inside the medium also increases. In addition, two solid points on the curve represent the phases of the magnetic fields at the upper and lower surfaces of the medium, from which it can be seen that the plane wave has a thickness d₁、d₂And d₃The phases added in the medium are pi, 2 pi and 3 pi respectively, and the characteristic of FP resonance is met.

The above analysis proves that the dielectric constant epsilon required by the medium can be determined according to the formula (3) for different unit numbers m of the optical medium metal super-structure grating in the invention, and the thickness d required by the medium can be known by utilizing the condition that FP resonance occurs in the medium_iThe phase difference on the transmission interface obtained by the method can exactly meet the phase gradual change requirement of the super-structured grating

And then, constructing the super-structure grating by using the dielectric constant and the dielectric thickness which are found by the analysis, obtaining a transmission/reflection curve chart and a field chart of the super-structure grating through numerical simulation, and verifying the effect of realizing high-efficiency abnormal diffraction by the dielectric metal super-structure grating. Let h be 2 μm in thickness of the super-structured grating, p be 3 μm in period length, 3 grooves in one period, 0.8 μm in groove width, 9 in dielectric constant of the medium in the groove, and d in thickness of the medium₁＝0.48μm，d₂＝0.97μm，d₃＝1.46μm。

The curves of the transmission/reflection rate of different orders of the super-structured grating along with the incident angle are shown in FIG. 5. As can be seen from FIG. 5, the incident angle θ of the plane wave_iAt < 0 °, it manifests itself primarily as low order (n ═ 1) transmission (solid blue line), where θ is_iWhen the temperature is minus 30 degrees, the efficiency of abnormal transmission reaches 99.7 percent; when the incident angle theta of plane wave_iAt > 0 °, since m ═ 3 is an odd number, it appears mainly as a high-order (n ═ 1) reflection (red dotted line) where θ is_iAt 30 °, the efficiency of anomalous reflection reached 99.3%.

FIGS. 6 and 7 show the respective angles of incidence θ_i-30 ° and θ_iThe black arrows on the graph indicate the incident direction and the abnormal transmission/reflection direction of the plane wave, namely the total magnetic field map corresponding to 30 °. The field diagram is well reflected, and when m is 3, the medium metal super-structure grating can almost perfectly convert incident waves into abnormal transmission/reflection waves.

In another embodiment of the present invention

And e, taking 4 as an example, finding out the thickness required by the medium, constructing a medium metal super-structure grating, and verifying the abnormal diffraction characteristic of the medium metal super-structure grating.

As shown in fig. 8, similar to the case of study m being 3, assuming that the plane wave is normally incident on the uniform grating, the specific parameters of the grating are set as: wavelength 3 μm, grating thickness h 3.5 μm, period length a 0.75 μm, groove width w 0.6 μm, and dielectric thickness d_iAt 0 mum to 3.5 μm. The numerical simulation results in the transmittance T (curve without solid points) and the transmission phase of the grating as the thickness di of the medium changes

(curve with solid dots) variation. There are 4 transmission peaks due to FP resonance in the medium, their corresponding transmission phases are indicated by solid dots, and the corresponding medium thicknesses are indicated by gray dashed lines, d₁＝0.73μm，d₂＝1.45μm，d₃＝2.18μm，d₄2.9 μm. It can be seen that when the medium thickness satisfies the FP resonance condition, the corresponding transmission phase difference between the neighbors is also satisfied

And constructing the super-structure grating by using the dielectric constant and the dielectric thickness which are found at the moment, wherein the thickness h of the super-structure grating is 3.5 mu m, the period length p is 3 mu m, one period comprises 4 grooves, the groove width w is 0.6 mu m, the dielectric constant of the medium in the grooves is epsilon 4, and the dielectric thickness d is₁＝0.73μm，d₂＝1.45μm，d₃＝2.18μm，d₄＝2.9μm。

A graph of the transmission/reflection of the super-structured grating is obtained by numerical simulation, as shown in fig. 9. When the incident angle theta of plane wave_iTransmission (T) of low order (n ═ 1) is mainly expressed at < 0 DEG_-1) Wherein at θ_iWhen the temperature is minus 30 degrees, the efficiency of abnormal transmission reaches 98.5 percent; when the incident angle theta of plane wave_iWhen the angle is larger than 0 deg., m is 4 and is even number, so that it is mainly expressed as high-order (n is 1) transmission (T)₁) Wherein at θ_iAt 30 °, the efficiency of anomalous transmission reached 98.5%.

FIGS. 10 and 11 show the respective angles of incidence θ_i-30 ° and θ_iThe black arrows on the graph indicate the incident direction and the abnormal transmission direction of the plane wave, namely the total magnetic field map corresponding to 30 °. The field pattern is well reflected, and when m is 4, the dielectric metal super-structure grating can also realize high-efficiency wavefront control.

Therefore, combining the examples of m-3 and m-4, it is proved that in the dielectric metal super-structured grating of the present invention, the dielectric constant of the filling material in the unit and the thickness of the material have a definite relationship with the number m of the unit and conform to the theoretical formula (3) given by us.

The optical medium metal super-structure grating has a simple structure, is easy to realize, and can realize the abnormal diffraction phenomenon with nearly perfect efficiency only by filling the same medium material with gradually changed thickness (impedance mismatching) in the unit.

The optical super-structure grating in the invention not only has the abnormal diffraction characteristic related to the parity of the number m of the units, but also more importantly, the dielectric constant epsilon and the material thickness of the material filled in the units are determined by the value of m. The principle is that for different unit numbers m, a determined dielectric constant exists, so that when FP resonance occurs in the medium, phase accumulation provided by the air part and the medium part in the groove together just meets phase distribution required by a transmission interface of the super-structure grating. And the invention provides a definite relation between the dielectric constant epsilon and m.

Therefore, the super-structured grating model and the theoretical formula in the invention have certain guiding significance for realizing the optical super-structured grating with simple structure and high efficiency.

According to the technical scheme, the invention has the following beneficial effects:

the Fabry-Perot resonance-based optical dielectric metal super-structure grating has a simple structure and is easy to realize, and the abnormal diffraction phenomenon with nearly perfect efficiency can be realized only by filling the same dielectric material with gradually changed thickness (impedance mismatching) in the unit.

It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.