CN106681026A - Arbitrary polarization dynamic control device and method based on metamaterial-surface-phase-change-material - Google Patents

Abstract

The invention relates to a device and method for arbitrary polarization dynamic regulation based on metasurface-phase change materials, and belongs to the technical field of micro-nano optics applications. Using a metasurface based on a V-shaped nanoantenna array, the interaction with the light field can generate a surface phase gradient, causing the abnormally transmitted polarized light generated under the normal incidence of linearly polarized light to deviate from the normal direction of the surface; at the same time, the introduction of a periodic The interval modulation layer composed of germanium antimony tellurium tellurium (GST) is arranged to modulate the phase difference of the orthogonal polarization states emitted by different subunits under external excitation, and coherently superimpose in space, thereby realizing arbitrary polarization state synthesis of the outgoing light field. This method is an all-solid-state modulation method that does not require any mechanical modulation means such as stretching or rotation, and can realize the separation of the obtained arbitrary polarized light from the background beam to avoid crosstalk. This approach provides a flexible means for on-chip polarization applications in integrated optics.

Description

Device and method for arbitrary polarization dynamic regulation based on metasurface-phase change materials

technical field

The invention relates to a device and method for arbitrary polarization dynamic regulation based on a metasurface-phase change material, and belongs to the technical field of micro-nano optics applications.

Background technique

The state of polarization is a fundamental property of electromagnetic waves. Controlling the polarization state of electromagnetic waves and realizing arbitrary conversion of different polarization states has a wide range of applications in optoelectronic communication, biosensing, precision measurement, remote sensing and other fields. Traditional polarization modulation methods mainly rely on anisotropic materials, such as birefringent natural crystals such as quartz and calcite, by rotating the angle between the optical axis of the crystal and the incident polarization state to control the phase difference between ordinary light and extraordinary light to achieve polarization state regulation. The traditional geometric optics method is no longer applicable to the fields of integrated optics and planar optics that have emerged in recent years, and has encountered difficulties in the miniaturization, miniaturization, and integration of equipment.

A feasible way to solve the miniaturization and integration difficulties of traditional optical components is to use metasurfaces. Metasurfaces consist of two-dimensional arrays of precision-designed subwavelength-sized metallic or dielectric elements whose thickness is much smaller than the wavelength. Through structural design, the metasurface can change the scattering field of a single pixel point by point in the plane, control the corresponding scattering amplitude, phase or polarization state, and finally realize the arbitrary regulation of the entire transmission field. The use of metasurfaces to control the polarization state has attracted extensive research interest. By precisely designing the structure of single-layer or multi-layer anisotropic metamaterial units, a variety of polarization-state control schemes can be obtained. For example, using complementary small Pore structure can manufacture ultra-thin quarter-wave plate in terahertz band Opt.Express.23, 11114 (2015); double-layer metasurface structure can realize broadband polarization conversion in microwave band J.Appl.Phys.117 , 44501(2015); Precisely designing the parameters of the three-layer anisotropic structure can achieve the specified polarization conversion Phys.Rev.Applied.2, 044011(2014). However, the optical properties of the reported metasurface polarization conversion devices are difficult to achieve dynamic control, that is, the optical properties are completely fixed after the device is fabricated, and can only perform a specified polarization control function, which limits its application.

Combining phase change materials and using appropriate thermal, optical, electrical and other modulation methods can realize dynamically tunable metasurfaces. As a class of phase change materials, germanium antimony tellurium (GeSbTe, GST) has received extensive attention in recent research. Among them, Ge ₃ Sb ₂ Te ₆ (GST-326, GST) is widely used in the mid-infrared band, such as using GST to realize tunable nano-antenna resonance Nano Lett.13, 3470 (2013); Sexual Materials Nano Lett.15, 4255 (2015). A stable and repeatable dynamically adjustable device can be realized by using the phase change material GST. However, in the current literature, uniform GST thin layers are mainly used for adjustment, and the use of GST to realize dynamic tunable polarization conversion devices has not been paid attention to.

Contents of the invention

The purpose of the present invention is to solve the problem that current metasurface polarization devices are difficult to realize dynamic polarization regulation, and provide a device and method for arbitrary polarization dynamic regulation based on metasurface-phase change materials.

The present invention is achieved through the following technical solutions.

An arbitrary polarization dynamic control device based on a metasurface-phase change material, the composite structure of the device is composed of a V-shaped nano-antenna layer, a spacing modulation layer and a base layer. Each periodic unit of the V-shaped nano-antenna layer includes two sub-units. The sub-units are composed of V-shaped nano-antenna arrays with different arrangements. The two sub-units respectively generate linearly polarized scattered light with mutually orthogonal polarization directions. The V-shaped nano-antenna array has a certain surface phase gradient, so that the propagation direction of the target linearly polarized scattered light deviates from the incident direction, that is, it is no longer perpendicular to the surface normal direction, so as to reduce the crosstalk of background light. The spacing modulation layer is composed of periodically arranged silicon and GST to form a one-dimensional grating, which are respectively placed between the two subunits and the substrate to adjust the scattering phase difference between the two subunits. The distance between the two subunits is much smaller than the wavelength, and the scattered light can be considered to be spatially coherent, and the output of any adjustable polarization state can be obtained by overlapping each other in space.

Based on the metasurface-phase change material arbitrary polarization dynamic control method, the light beam incident on the device surface includes the laser to be regulated and the femtosecond laser, and the femtosecond laser is used to realize the dynamic control of the metasurface device. The modulated laser beam and the femtosecond laser beam are combined and irradiated onto the surface of the device. The outgoing light consists of two parts: one part propagates along the device surface normal, which is the background light; the other part propagates away from the device surface normal, including the obtained ellipsometric light with arbitrary polarization, and the target transmits light. The energy of the femtosecond laser is adjusted by the pulse picker to realize the regulation of the refractive index of the GST material in the device, and then realize the regulation of the polarization state of the outgoing target transmitted light.

A device for realizing any polarization dynamic control method based on metasurface-phase change materials, including: laser, polarizer, first mirror, femtosecond laser, attenuator, pulse picker, first 4f telescopic system lens, Second 4f telescopic system lens, beam combining prism, device surface, background light, second mirror, analyzer and power meter.

Connection relationship: The laser emits the modulated laser light and passes through the polarizer to obtain linearly polarized light, which is reflected by the first mirror to the beam combining prism; the femtosecond pulse laser emits the femtosecond pulse laser through the attenuator and pulse selector and the first 4f telescopic system The lens and the second 4f telescopic system lens are then incident on the beam combining prism; the modulated laser and the femtosecond pulsed laser are combined and then incident on the surface of the device to obtain two beams of outgoing light. The background light propagates along the normal line of the sample surface, carrying all The propagation direction of the target transmitted light to be polarized deviates from the normal line of the device surface, passes through the second reflector and the analyzer, and then reaches the power meter.

To complete the design of the above-mentioned arbitrary polarization dynamic control device based on metasurface-phase change materials, V-shaped nano-antenna arrays and spaced modulation layers need to be designed separately. The design methods of each part are as follows:

(1) V-shaped nano-antenna array

The resonance between the V-shaped nanoantenna and the light field can form two eigenmodes: symmetric mode and antisymmetric mode. If the polarization direction of the incident light is parallel to its symmetry axis, only the symmetric mode will be excited; if the polarization direction of the incident light is perpendicular to its symmetry axis, then only the antisymmetric mode will be excited. In general, if linearly polarized light in any direction is perpendicular to the sample surface, then:

Where α and β are the polarization direction of the incident ray polarization, the angle between the antenna symmetry axis and the y-axis, respectively, with Represent the unit vectors parallel to and perpendicular to the symmetry axis of the antenna, respectively, S _i and A _i represent the scattering complex amplitudes of the i-th antenna symmetric mode and anti-symmetric mode in the subunit, respectively. The scattered field of this antenna can be further written as:

where x and y are unit vectors along the x-axis and y-axis, respectively.

It can be seen from formula (2) that the scattered wave can be decomposed into the complex amplitude superposition of symmetric mode and antisymmetric mode, namely (S _i +A _i ) and (S _i -A _i ) components. The angles between their polarization directions and the y-axis are α and 2β-α, respectively. By accurately selecting the antenna structure parameters, |S _i -A _i | can be roughly constant, and the phase difference between (S _i+1 -A _i+1 ) and (S _i -A _i ) is 2π/N, N is The number of antennas in a subunit; while |S _i +A _i | has different amplitudes, and the phases of (S _i+1 +A _i+1 ) and (S _i +A _i ) are basically constant. In this way, the scattered wave of the 2β-α polarization component can propagate along the abnormal refraction angle θ _t = arcsin(λ/D) in the case of normal incidence, where λ is the incident wavelength, D is the length of the subunit in the x direction; The polarized scattered light propagates perpendicular to the sample surface.

At the same time, the two subunits in each periodic unit have exactly the same structural parameters, but there is an offset d in the x direction, as shown in Fig. 1 . Therefore, both subunits can produce anomalous scattered light propagating in the direction of θ _t =arcsin(λ/D), and since the spacing of the subunits along the y direction is much smaller than the wavelength, the scattered light can be considered to be spatially coherent. In addition, the orientation angles β ₁ and β ₂ of the two sub-unit antennas satisfy β ₂ -β ₁ =45°, that is, (2β ₂ -α)-(2β ₁ -α)=90° so that the polarization directions of the two scattered light are perpendicular to each other . Also, the offset d along the x-direction can control the initial phase difference between the two beams of anomalously scattered light produced by the subunit, which satisfies Although the spatial arrangement of the antenna arrays in the two subunits is different, their structural parameters are exactly the same, so the amplitudes of the scattered light obtained from the two subunits are exactly the same, and the ellipsometric light with a definite polarization state can be obtained after spatial overlapping.

(2) interval modulation layer

In order to realize the dynamic adjustment of the polarization state of the metasurface, it is necessary to introduce an adjustable phase mechanism. Therefore, it is considered to introduce the use of a phase change material as a space modulation layer. The spacing modulation layer includes strips of silicon and strips of GST arranged periodically in one dimension, and are respectively located between the subunit 1, the subunit 2 and the substrate. The thickness of the spacing modulation layer can be selected flexibly, but it needs to be within a certain value range to ensure that the subunits can introduce sufficient phase modulation and ensure the scattering efficiency when the GST refractive index changes.

Beneficial effect

1. The technical solution described in the present invention utilizes a metasurface based on a metal V-shaped nano-antenna array, combined with periodically arranged germanium antimony tellurium GST modulation layers, to provide a high-speed, flexible transmission light working in the mid-infrared band The method of arbitrarily adjusting the polarization state can generate ellipsometric transmitted light of any polarization state under the condition of vertical incidence of linear polarization state in any direction, and the obtained polarization state can be dynamically adjusted, which can solve the problem that current metasurface polarizers are difficult to achieve dynamic polarization Regulatory issues. In particular, the present invention can achieve the separation of the resulting target polarized light from the background beam, avoiding crosstalk.

2. The present invention utilizes the phase control characteristic of the metasurface, combined with the phase change material germanium antimony tellurium GST widely used in commercial rewritable data storage, to perform adjustable polarization conversion. The cost of the phase change material is low, and it can flexibly switch between crystalline and amorphous states under external excitations such as femtosecond laser pumping and thermal baking, and can be reused many times, which can significantly improve device stability and expand its dynamic applications. scope.

3. The present invention is an all-solid, ultra-thin, planar device, which does not require any mechanical stretching, rotation and other operations. The invention can be widely used in miniaturization, miniaturization and integration applications, especially in laser communication systems and polarization detection systems, which significantly reduces system complexity and effectively reduces its volume and weight. And it can provide a flexible control method for the on-chip application of integrated optics.

Description of drawings

Figure 1. Schematic diagram of the device structure based on the metasurface-phase change material composite structure to generate an arbitrary tunable polarization state; where the antenna structure diagram (a) and the metasurface-phase change material composite structure diagram (b).

Figure 2 is a schematic diagram of the optical path for generating and detecting dynamically adjustable ellipsometry;

Fig. 3 Polarization analysis of abnormally transmitted light obtained by taking different refractive indices of GST under external excitation; the relationship between the obtained circular polarization degree and the change of GST refractive index (a), the obtained polarization ellipsoid corresponding to different GST refractive index (b), and the obtained polarization with The relation of GST refractive index change.

Among them, 1-laser; 2-polarizer; 3-first mirror; 4-femtosecond laser; 5-attenuator; 6-pulse selector; 7-first 4f telescopic system lens; 8-second 4f telescopic system lens; 9-beam combining prism; 10-device surface; 11-background light; 12-second reflector; 13-analyzer; 14-power meter.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments. The specific implementations described here are only used to explain the present invention, not to limit the present invention.

Taking a metasurface with a working wavelength of λ=4 μm as an example, a device and method for dynamically adjusting arbitrary polarization based on a metasurface-phase change material are proposed below. Among them, a metasurface-phase change material-based arbitrary polarization dynamic control device is composed of a V-shaped nano-antenna layer, a spacing modulation layer and a substrate, as shown in Figure 1. The design process for this device consists of two main steps:

(1) Metasurface V-shaped nanoantenna array design

A single period of a metasurface based on a V-shaped nanoantenna array contains two differently arranged subunits, which are mainly used to generate a surface phase gradient, thereby generating two orthogonally polarized beams that deviate from the sample normal and propagate along the abnormal refraction direction light with a fixed phase difference. The scattered field of a single antenna can be expressed in the form of Equation (2), as shown in Figure 1(a). Its scattered wave can be decomposed into complex amplitude superposition of symmetric mode and antisymmetric mode, that is, (S _i +A _i ) and (S _i -A _i ) components, and their polarization direction and y-axis angles are α and 2β respectively -alpha. For the selection of V-shaped nano-antenna parameters, the following methods can be adopted: place the V-shaped nano-antenna symmetry axis and the y-axis at an angle of 45°, fix the width and thickness of the V-shaped nano-antenna, and use strict vector simulation software to scan the V-shaped nano-antenna When the light wave polarized along the x direction is incident on the metasurface, its 2β-α direction polarization component is just polarized along the y-axis direction, which can effectively reduce the difficulty of simulation data extraction. According to the relationship between the 2β-α component scattering amplitude and phase of the V-shaped nanoantenna obtained by scanning and the arm length and angle of the V-shaped nanoantenna, the appropriate V-shaped nanoantenna parameters can be carefully selected to ensure that |S _i -A _i | is approximately constant, and the phase difference between (S _i+1 -A _i+1 ) and (S _i -A _i ) is 2π/N, where N is the number of antennas in a subunit; and |S _i +A _i |amplitude are not equal, and the phases of (S _i+1 +A _i+1 ) and (S _i +A _i ) are basically constant. By designing the parameters and arrangement of the V-shaped nano-antenna array, the scattered wave of the 2β-α polarization component can propagate along the abnormal refraction direction θ _t = arcsin(λ/D) under normal incidence, while the scattered light along the α polarization The direction of propagation is perpendicular to the sample surface. In this embodiment, N=8 is selected, the incident light polarization angle α=45°, the length of the subunit in the x direction D=7.5 μm, and the side length of the square lattice where each antenna is located is 937.5 nm. For the V-shaped subunit Select 4 groups of different parameters for the nano-antenna, the arm lengths L of the first four antennas are 457nm, 418nm, 302nm and 244nm respectively, and the antenna opening angle θ is 60°, 90°, 120° and 180° respectively, so that (S _i -A _i ) The phase distribution of the components differs by π/8 in turn, and the other four groups of V-shaped nano-antennas only need to rotate the symmetry axis of the above-mentioned antenna by 90° along the y-axis to reverse the phase, so that the antenna array can produce a constant The surface phase gradient and the amplitude remain unchanged, as shown in Figure 1(b), at this time the anomalous refraction angle θ _t =arcsin(λ/D)≈32°. It is worth noting that the opening angles of antennas 4 and 8 are 180° at this time, and their structures have degenerated into single-arm antennas. Compared with the V-shaped nanoantenna, the scattering amplitude of the single-arm antenna is more sensitive to the surrounding dielectric environment. When the GST refractive index increases, the scattering amplitude will experience larger oscillations, but the amplitude change of this individual antenna will not be significant. Vary the scattering efficiency across the metasurface.

Since the two subunits in a single period have exactly the same structural parameters, both subunits can generate anomalous scattered light propagating in the same direction, but the orientation angles β1 and β2 _of the antennas of the _two subunits need to satisfy β2 _- β ₁ =45°, that is, (2β ₂ -α)-(2β ₁ -α)=90° so that the polarization directions of the two anomalous scattered light are perpendicular to each other. In this embodiment, β ₁ =67.5° and β ₂ = 112.5°. This orthogonality has nothing to do with the incident light polarization direction α, but only depends on the difference between the orientation angles β1 and β2 _of the _two subunit antennas. In addition, the offset d along the x-direction can control the phase difference between the two scattered lights, which satisfies Here d can be selected arbitrarily, which only determines the polarization state output by the entire device when the substrate is uniform, and plays a role in phase zeroing. In this implementation, the offset d is taken as D/4=1.875 μm so that when the refractive index of the GST is the same as that of the Si base, the output is circularly polarized light.

(2) interval modulation layer

The spacing modulation layer is mainly used to dynamically adjust the scattering phase difference between the two subunits. GST has a transmission window between 2.8 μm and 5.5 μm, and the absorption of the material in this wavelength range can be ignored. At this time, when GST changes from an amorphous state to a crystalline state, its refractive index will change greatly. And the process is reversible if suitable optical, electrical or thermal means are used. The change of the refractive index of the GST material will significantly affect the local surface plasmon resonance of the V-antenna of the subunit located above the GST layer, which will cause the resonant peak of the V-antenna to shift, and significantly change the light in this multilayer. The phase accumulation in the film system has almost negligible effect on the V-antenna of the subunit located above the silicon layer. The broadband resonance characteristics of the V-shaped nanoantenna make the scattering amplitude change less and the phase undergo a larger change when the GST refractive index changes. Using strict vector simulation software, the V-shaped nanoantenna-GST layer-substrate multilayer structure can be used to verify the modulation of the scattering properties of the V-shaped nanoantenna when the refractive index of the GST layer changes. In the simulation, the angle between the symmetry axis of the V-shaped nanoantenna and the y-axis is also placed at 45° to facilitate the extraction of simulation data.

The parameter that needs to be controlled in the spacing modulation layer is its thickness. The thickness of the GST will affect the translation distance of the antenna resonant peak under the same refractive index change and the phase accumulation of electromagnetic waves in the multilayer film system. Therefore, the thickness of the GST layer can determine the range of phase adjustment. Too small thickness is not enough to bring enough phase accumulation, resulting in a small range of phase adjustment, and too large thickness will cause the resonance peak to shift too much and affect the scattering efficiency. The choice of GST thickness needs to ensure sufficient phase adjustment range and scattering efficiency, so that the antenna on subunit 2 will experience a small amplitude change and maintain a large phase delay change; at the same time, the antenna on subunit 1 scatter The nature remains basically unchanged. At the same time, the range of GST refractive index change is also limited. If the refractive index changes too much, the resonance peak of the V-shaped nanoantenna will be completely moved out of the working wavelength region, resulting in a large loss of scattering amplitude. At the same time, as a proof of concept, the starting point of the refractive index change can be set to n=3. Using strict vector simulation software to simulate, it can be obtained that the thickness of the GST layer is between 500nm and 800nm, and when the refractive index changes from n=3 to n=4.5, the light field scattered by the V-shaped nano-antenna can achieve a phase modulation of π, and Maintain a consistent scatter amplitude. In this embodiment, the thickness of the GST layer is taken as 500 nm. Therefore, the phase difference between the orthogonal linearly polarized scattered light from the two subunits can be controlled by controlling the refractive index of the GST. After the two beams of linearly polarized light overlap in space, tunable polarization state control can be obtained.

A device for realizing arbitrary polarization dynamic control method, as shown in Figure 2, laser 1 emits modulated laser light and passes through polarizer 2 to obtain linearly polarized light, which is reflected by first reflector 3 to beam combining prism 9; femtosecond laser 4 emits femtosecond laser light The second pulse laser is incident on the beam-combining prism 9 after passing through the attenuator 5, the pulse selector 6 and the 4f telescopic system lenses 7 and 8; the modulated laser and the femtosecond pulse laser are incident on the device surface 10 after beam combining to obtain two beams The outgoing light and the background light 11 propagate along the normal of the sample surface, and the transmission direction of the target transmitted light carrying the required polarization state deviates from the normal of the device surface, and then reaches the power meter 14 after passing through the second reflector 12 and the analyzer 13 . The energy output of the femtosecond laser is adjusted by a pulse modulator to control the variation range of the GST refractive index.

The degree of circular polarization, energy distribution, polarization ellipse, representation of the polarization state on the Poincar sphere and the polarization analysis of the obtained polarization state obtained when the metasurface modulates the GST refractive index from n=3 to n=4.5 They are shown in Fig. 3(ad) respectively. Here the degree of circular polarization is defined as |I _LCP -I _RCP |/|I _LCP +I _RCP |, where I _LCP and I _RCP represent the light intensity of left-handed circularly polarized light and right-handed circularly polarized light, respectively. The polarization analysis can be obtained by measuring the output power of the rotating analyzer 13 and the power meter 14 . When n=3.4 and n=4.2, high-quality circular polarization states and linear polarization states can be obtained respectively, and all polarization states in the middle can be continuously obtained, as shown in Fig. 3(b) and (d).

The invention is based on the V-shaped nano-antenna array metasurface, and by introducing a phase modulation layer composed of periodically arranged GSTs, the phase difference of the outgoing orthogonal polarization states of different sub-units can be modulated under external excitation to realize arbitrary polarization state synthesis. This method is an all-solid-state modulation method that does not require any mechanical modulation means such as stretching or rotation, and due to the introduction of the surface phase gradient, the generated abnormally transmitted polarized light has a certain angle with the direction of the original ordinary transmitted light. to avoid crosstalk. This method provides a flexible control method for the on-chip application of integrated optics, and is expected to be widely applicable to the miniaturization, miniaturization, and integration of optical components.

Claims (4)

1. the random polarization dynamic regulation device of super clever surface-phase-change material is based on, it is characterised in that：By V-type nano-antenna layer, Interval modulation layer and basalis are constituted；V-type nano-antenna each periodic unit of layer includes two parts subelement, and subelement is by having The V-type nanotube antenna array for having different arrangement modes is constituted, and two parts subelement generates the mutually orthogonal line in polarization direction respectively Polarization scattering light；The V-type nanotube antenna array has surface phase gradient so that the direction of propagation of score polarization scattering light is inclined From incident direction, that is, surface normal direction is no longer normal to, to reduce the cross-talk of bias light；Interval modulation layer is arranged by the cycle The silicon and GST of row constitute one-dimensional grating, and they are respectively placed in two between subelement and substrate, are used to adjust two subelements Between scattering phase difference.

2. the random polarization dynamic regulation method of super clever surface-phase-change material is based on, it is characterised in that：By modulation laser and femtosecond Laser is irradiated on device surface after closing beam；The energy of femtosecond laser adjusts to realize in device by pulse selector The regulation and control of GST Refractive Index of Material, and then realize the regulation and control to outgoing object penetrating polarization state.

3. the device of the random polarization dynamic regulation method based on super clever surface-phase-change material as claimed in claim 2 is realized, It is characterized in that：Including laser (1), the polarizer (2), the first speculum (3), femto-second laser (4), attenuator (5), pulse Selector (6), 4f telescopic systems lens (7), the 2nd 4f telescopic systems lens (8) beam cementing prism (9), device surface (10), bias light (11), the second speculum (12), analyzer (13) and power meter (14)；

Annexation：Laser (1) outgoing obtains linearly polarized light by modulation laser by the polarizer (2), through the first speculum (3) Reflex to beam cementing prism (9)；Femto-second laser (4) outgoing femtosecond pulse through attenuator (5) and pulse selector (6) and Beam cementing prism (9) is incident to after first 4f telescopic systems lens (7) and the 2nd 4f telescopic systems lens (8)；By modulation laser with Device surface (10) is incident to after femtosecond pulse ECDC beam can obtain two beam emergent lights, and bias light (11) is along sample surfaces method Line is propagated, and the object penetrating optical propagation direction of polarization state deviates device surface normal needed for carrying, by the second speculum (12) Power meter (14) is reached afterwards with analyzer (13).

4. the random polarization dynamic regulation device of super clever surface-phase-change material is based on as claimed in claim 1, and its feature exists In：The method for designing of the V-type nanotube antenna array is as follows：

V-type nano-antenna can form two kinds of eigen modes with the resonance of light field：Symmetric pattern and antisymmetric mode；If incident ray Polarization light polarization direction now only excites its symmetric pattern parallel to its symmetry axis；If incident light polarization direction is right perpendicular to its Claim axle, now then only have antisymmetric mode and be excited；Generally, if any direction linearly polarized light vertical incidence is to sample table Face, then have：

Wherein α and β are respectively the angles of incident ray polarized light polarization direction, antenna symmetry axle and y-axis,WithRepresent respectively parallel With the unit vector of vertical antenna symmetry axis, S_iAnd A_iI-th antenna symmetry pattern and antisymmetric mode in subelement are represented respectively Scattering complex amplitude；The scattered field of the antenna can further be write as：

$\begin{array}{c}{E}_i=\frac{1}{2}(S_i-A_i)\[\cos (2\mathrm{\β}-\mathrm{\α})y+\sin (2\mathrm{\β}-\mathrm{\α})x\]\\ +\frac{1}{2}(S_i+A_i)(\cos \mathrm{\α}y+\sin \mathrm{\α}x)\end{array}---\left(2\right)$

Wherein x and y are respectively the unit vector along x-axis and y-axis；

As can be seen that scattered wave can be broken down into symmetric pattern and is superimposed with the complex amplitude of antisymmetric mode from formula (2), i.e. (S_i +A_i) and (S_i-A_i) component；Their polarization direction is respectively α and 2 β-α with y-axis angle；Joined by accurate selection antenna structure Number, it is possible to achieve | S_i-A_i| substantially constant, and (S_i+1-A_i+1) and (S_i-A_i) difference of phase is 2 π/N, N is that a son is single The number of antenna in unit；And | S_i+A_i| amplitude, and (S_i+1+A_i+1) and (S_i+A_i) phase is substantially constant；So can be with Allow the scattered wave of 2 β-α polarized components in the case of normal incidence along abnormal refraction angle θ_t=arcsin (λ/D) is propagated, λ in formula It is incident wavelength, D is the length in subelement x directions；And along the scattering optical propagation direction of α polarizations perpendicular to sample surfaces；

Meanwhile, two subelements in each periodic unit possess identical structural parameters, but exist in x directions and offset D, as shown in Figure 1；Therefore, two subelements can be produced along θ_tThe anomalous scattering light that=arcsin (λ/D) direction is propagated, and And due to subelement in the y-direction spaced far much smaller than wavelength, it can thus be assumed that its scattering light spatial coherence；Additionally, two sons are single First antenna towards angle beta₁And β₂Meet β₂-β₁=45 °, i.e. (2 β₂-α)-(2β₁- α)=90 ° with cause two scatter light polarization directions It is mutually perpendicular to；Also, offset d in the x-direction can control the initial phase between the two beam anomalous scattering light produced by subelement Potential difference, the phase difference meetsAlthough aerial array spatial arrangement has area in two subelements Not, but its structural parameters is identical, therefore from two subelements gained scattering light amplitude it is identical, after space overlap The oval thickness for determining polarization state can be obtained.