CN113093440A - Broadband polarization converter based on symmetrical multilayer twisted liquid crystal and optimization method thereof - Google Patents

Broadband polarization converter based on symmetrical multilayer twisted liquid crystal and optimization method thereof Download PDF

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CN113093440A
CN113093440A CN202110417648.9A CN202110417648A CN113093440A CN 113093440 A CN113093440 A CN 113093440A CN 202110417648 A CN202110417648 A CN 202110417648A CN 113093440 A CN113093440 A CN 113093440A
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liquid crystal
crystal layer
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CN113093440B (en
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穆全全
陈万
王启东
彭增辉
刘永刚
鲁兴海
宣丽
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/1337—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/13378—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by treatment of the surface, e.g. embossing, rubbing or light irradiation
    • G02F1/133784—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by treatment of the surface, e.g. embossing, rubbing or light irradiation by rubbing
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/133371—Cells with varying thickness of the liquid crystal layer
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
    • G02F1/1333—Constructional arrangements; Manufacturing methods
    • G02F1/1337—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers
    • G02F1/13378—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by treatment of the surface, e.g. embossing, rubbing or light irradiation
    • G02F1/133788—Surface-induced orientation of the liquid crystal molecules, e.g. by alignment layers by treatment of the surface, e.g. embossing, rubbing or light irradiation by light irradiation, e.g. linearly polarised light photo-polymerisation

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  • Spectroscopy & Molecular Physics (AREA)
  • Polarising Elements (AREA)

Abstract

The invention discloses a broadband polarization converter based on symmetrical multilayer twisted liquid crystal and an optimization method thereof, belonging to the technical field of non-mechanical light beam regulation, wherein the broadband polarization converter comprises: the glass substrate, the orientation film and the symmetrical multilayer twisted liquid crystal layer are sequentially distributed along the incident direction; the symmetric multilayer twisted liquid crystal layer comprises M liquid crystal layers, wherein the twist angles and the thickness characteristics of the M liquid crystal layers are respectively distributed in a mirror symmetry mode relative to a mirror symmetry axis, the twist angles of the two mutually symmetric liquid crystal layers are opposite in direction, when M is an odd number, the twist angle of the liquid crystal layer where the mirror symmetry axis is located is zero, and M is larger than or equal to 2. The broadband polarization converter can be combined with effective patterning control in the fast axis direction to form a broadband geometric phase optical element, and can also be independently used as an achromatic wave plate, so that the broadband geometric phase optical element has a wide application prospect; the optimization method can quickly obtain specific optimization parameters by combining the Poincare ball, and is more intuitive and quicker compared with a numerical optimization method.

Description

Broadband polarization converter based on symmetrical multilayer twisted liquid crystal and optimization method thereof
Technical Field
The invention belongs to the technical field of non-mechanical light beam regulation and control, and particularly relates to a broadband polarization converter based on symmetrical multilayer twisted liquid crystal and an optimization method thereof.
Background
Traditionally, a wave plate is an effective means for realizing polarization conversion, and the retardation is regulated and controlled by controlling the relationship between the wavelength and the thickness, so that the emergent polarization state is changed. A conventional geometric phase element can be regarded as a patterned waveplate combination, and polarization state modulation is realized by geometric phase holography. However, for some optical applications that require polarization state adjustment in a wide wavelength band, such as near-eye display, augmented reality display, etc., the conventional geometric phase element has a problem that the operating wavelength band is narrow, the field angle is small, and the like. The polymer liquid crystal layer based on the multilayer twisted structure is an ideal material for realizing broadband regulation and control of the polarization state. More importantly, a broadband circular polarization converter implemented based on a multilayer twisted liquid crystal layer can be easily converted into an ultra-wide band geometric phase element. The broadband circular polarization converter based on the symmetrical multilayer twisted liquid crystal provides a faster design method and means for realizing an ultra-wideband geometric phase element.
Disclosure of Invention
The invention aims to provide a broadband polarization converter based on symmetrical multilayer twisted liquid crystal and an optimization method thereof aiming at the requirement of realizing symmetrical switching of polarization states of input and output, and solves the problems of narrow working waveband, small field angle and the like of the conventional geometric phase element.
In order to achieve the purpose, the invention adopts the following technical scheme:
a broadband polarization converter based on symmetrical multilayer twisted liquid crystal comprises a glass substrate, an orientation film and a symmetrical multilayer twisted liquid crystal layer which are sequentially distributed along an incident direction;
the symmetrical multilayer twisted liquid crystal layer comprises M liquid crystal layers, the twist angles and the thickness characteristics of the M liquid crystal layers are respectively distributed in a mirror symmetry mode relative to a mirror symmetry axis of the symmetrical multilayer twisted liquid crystal layer, the directions of the twist angles of the two mutually symmetrical liquid crystal layers are opposite, when M is an odd number, the twist angle of the liquid crystal layer where the mirror symmetry axis is located is zero, and M is larger than or equal to 2.
The broadband polarization converter based on the symmetrical multilayer twisted liquid crystal not only can form a broadband geometric phase optical element by combining the effective fast axis patterning control through carrying out mirror symmetry distribution on the twist angle characteristic and the thickness characteristic of each liquid crystal layer, but also can be independently used as an achromatic wave plate, such as a half-wave plate, a quarter-wave plate and the like, so that the broadband geometric phase element and the broadband polarization regulation and control are realized, and the broadband geometric phase optical element and the broadband polarization converter based on the symmetrical multilayer twisted liquid crystal have wide application prospects in the fields of laser communication, laser countermeasure, laser radars, non-mechanical beam deflection, VR/AR display and the like, and have important significance in the aspect of broadband optical polarization regulation and control.
Meanwhile, the invention also provides a visual optimization method for the broadband polarization converter based on the symmetric multilayer twisted liquid crystal, which comprises the following steps:
the method comprises the following steps: determining a liquid crystal layer to be optimized of the broadband polarization converter, wherein the liquid crystal layer to be optimized is a front one of the symmetrical multi-layer twisted liquid crystal layer
Figure BDA0003026552050000021
A liquid crystal layer;
step two: determining a design band [ λ ] of the broadband polarization converter1,λ2]An intermediate wavelength lambda ofmidAnd selecting the intermediate wavelength lambdamidCorresponding birefringence Δ n (λ)mid) Initial birefringence Δ n as liquid crystal molecules0；
Step three: randomly giving the twist angle and the thickness of each liquid crystal layer to be optimized, and demonstrating the polarization state evolution process of an incident polarization state passing through each liquid crystal layer to be optimized on a Poincare sphere;
step four: adjusting the thickness of each liquid crystal layer to be optimized to minimize the curvature of an output polarization state curve on the Poincare sphere;
step five: adjusting the twist angle of each liquid crystal layer to be optimized and continuously fine-adjusting the thickness to ensure that the curvature of the output polarization curve is minimum and the curve falls on the equator of a Poincare sphere, thereby obtaining the initial birefringence (delta n)0The twist angle parameter and the thickness parameter of each liquid crystal layer to be optimized;
step six: if necessary, the design band is changed to [ lambda ]1',λ2']Only the corresponding intermediate wavelength lambda needs to be foundmid', and in proportion t ═ Δ n0/Δn(λmid') scaling the thickness parameters to obtain the final thickness parameters of each liquid crystal layer to be optimized.
The visualization optimization method provided by the invention is equivalent to a method that the incident polarization state rotates on a Poincare sphere twice based on the evolution effect of the incident polarization state through a single-layer liquid crystal layer, and realizes the parameter optimization of the broadband polarization converter based on the symmetrical multilayer twisted liquid crystal.
Drawings
FIG. 1 is a schematic diagram of a broadband polarization converter based on symmetric multilayer twisted liquid crystal according to the present invention;
fig. 2 is an operation diagram of a polarization evolution process visualized on a poincare sphere after passing through a single layer liquid crystal layer to be optimized, in which: 1 is the input polarization state Si(λ), 2 is the output polarization state So(lambda), 3,4 are simplified paths of the visual evolution of the polarization state, 5 is the equator of the poincare sphere, 6 is the eigen-polarization state of the single-layer liquid crystal layer to be optimized, 7 is the center of the poincare sphere, 8, 9, 10 are the S of the poincare sphere, respectively1Shaft, S2Shaft, S3Shaft, 1112, south and north poles of poincare sphere, representing left-hand and right-hand circular polarization, respectively;
FIG. 3 is a schematic diagram of a wide-band polarization converter when the symmetric multi-layer twisted liquid crystal layer includes 2 liquid crystal layers;
FIG. 4 is a schematic diagram of a wide-band polarization converter when the symmetric multi-layer twisted liquid crystal layer includes 3 liquid crystal layers;
FIG. 5 is a schematic diagram of a wide-band polarization converter when the symmetric multi-layer twisted liquid crystal layer includes 4 liquid crystal layers;
in FIGS. 1, 3-5, 1 is the input polarization state Si(λ), 2 is the output polarization state So(λ), 3 is a substrate, 4 is an alignment film, 5 is a liquid crystal molecule, and 6 is a liquid crystal layer; in fig. 1, 7 is a mirror symmetry axis;
FIG. 6(a) is a schematic diagram of the evolution process of the polarization state on the Poincare sphere corresponding to the symmetric two-layer twisted liquid crystal layer shown in FIG. 3, in which: 1 is input polarization state, 2, 4 are evolution paths of polarization state in the first and second layers of liquid crystal layer under a certain wavelength, 3 is arc line composed of output polarization state of each wavelength of the first layer of liquid crystal layer, 5 is final output polarization state arc line, 6 is sphere center of poincare sphere, 7, 8, 9 are poincare sphere S1Shaft, S2Shaft, S3A shaft;
FIG. 6(b) is a drawing of the final output S for a symmetric two-layer twisted liquid crystal layer from incident right-handed circular polarization to exiting left-handed circular polarization3A graph of results of (1);
FIG. 7(a) is a schematic diagram of the polarization state evolution process on a Poincare sphere corresponding to the symmetric three-layer twisted liquid crystal layer shown in FIG. 4, in which: 1 is input polarization state, 2, 4, 6 are evolution paths of polarization state in the first, second, and third liquid crystal layers under a certain wavelength, 3, 5 are arcs formed by output polarization state of each wavelength of the first and second liquid crystal layers, 7 is final output polarization state arc, 8 is sphere center of poincare sphere, 9, 10, 11 are S of poincare sphere1Shaft, S2Shaft, S3A shaft;
FIG. 7(b) is a symmetric three-layer twisted liquid crystal for incident right-handed circular polarization to outgoing left-handed circular polarizationLayer, drawing its final output S3A graph of results of (1);
FIG. 8(a) is a schematic diagram of the polarization state evolution process on a Poincare sphere corresponding to the symmetric four-layer twisted liquid crystal layer shown in FIG. 5, in which: 1 is an input polarization state, 2, 4, 6, 8 are evolution paths of the polarization state in the first, second, third, and fourth layers of liquid crystal layer under a certain wavelength, 3, 5, 7 are arcs formed by the output polarization states of the first, second, and third layers of liquid crystal layer, 9 is a final output polarization state arc, 10 is a sphere center of a poincare sphere, 11, 12, 13 are S of the poincare sphere respectively1Shaft, S2Shaft, S3A shaft;
FIG. 8(b) is a drawing of the final output S for a symmetrical four layer twisted liquid crystal layer from incident right hand circular polarization to exiting left hand circular polarization3A graph of results of (1);
FIG. 9(a) is an ultra-wideband geometric phase element implemented by using the symmetric four-layer twisted liquid crystal layer shown in FIG. 8, and the principle and schematic diagram thereof, here illustrated by taking a liquid crystal polarization grating as an example, in which: 1 is a symmetrical four-layer twisted ultra-wideband circular polarization converter, 2 is an input broadband left-hand circular (or right-hand circular) polarization state, and 3 is an output broadband right-hand circular (or left-hand circular) polarization state;
FIG. 9(b) is a broad band geometric phase optical device implemented by a symmetric four-layer twisted liquid crystal layer, which is illustrated by taking a liquid crystal polarization grating as an example, wherein 4 is a substrate and 5 is a liquid crystal molecule;
FIG. 9(c) is a graph of the diffraction efficiency of a symmetric four-layer twisted broadband liquid crystal polarization grating, in which: RCP represents right-handed circularly polarized light, and LCP represents left-handed circularly polarized light.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the accompanying drawings and preferred embodiments.
In one embodiment, the present invention provides a broadband polarization converter based on symmetric multilayer twisted liquid crystal, which addresses the requirement of implementing symmetric switching of polarization states of input and output, specifically: 1) a right-handed circular polarization state and a left-handed circular polarization state; 2) mutually orthogonal linear polarization states; 3) the ellipticity and the inclination angle of the ellipse are the same, but the rotation directions are opposite to each other. The specific symmetry of the broadband polarization converter of the invention is limited as follows: for the special case where the input and output polarized light satisfies symmetry, the structure of the symmetric multilayer twisted liquid crystal layer is selected to be a symmetric structure accordingly. The broadband polarization converter has unique application in the aspect of functions, for example, the broadband circular polarization converter is combined with effective patterning control in the fast axis direction to realize a broadband geometric phase optical element and even a geometric phase optical element with a large viewing angle characteristic, and the problems of narrow working waveband, small viewing angle and the like of the conventional geometric phase optical element can be solved.
Fig. 1 is a schematic structural diagram of a broadband polarization converter with a symmetric structure according to the present invention, which includes a glass substrate, an alignment film, and a symmetric multi-layer twisted liquid crystal layer sequentially distributed along an incident direction, wherein the symmetric multi-layer twisted liquid crystal layer is a core light modulation and control structure of the broadband polarization converter and is also a basis for forming a device object.
Liquid crystal: refers to polymer liquid crystals.
Orientation film: for inducing liquid crystal molecular alignment; alternatively, the alignment film in the present invention induces alignment of the liquid crystal layer by an alignment method of rubbing or light irradiation.
A chiral agent: used for inducing liquid crystal molecules to twist when added into polymer liquid crystal.
The symmetrical multilayer twisted liquid crystal layer comprises M (M is 2,3,4, …) liquid crystal layers, each of which is a twisted liquid crystal film, and the special case of no twist is also included. Assuming that the alignment film has an initial azimuth angle
Figure BDA0003026552050000051
The thickness of the M (1, 2, …, M) th liquid crystal layer is dmThe twist angle is phimAt an initial azimuth angle of
Figure BDA0003026552050000052
If the azimuth of the back surface of the m-1 th layer is equal to the azimuth of the front surface of the m-th layer
Figure BDA0003026552050000053
If the liquid crystal layer is consistent with the liquid crystal layer, the liquid crystal layer is called a self-alignment mode, and at the moment, the rear surface of the liquid crystal layer of the previous layer is an alignment film layer of the liquid crystal layer of the next layer, so that the automatic alignment of the liquid crystal azimuth angle is realized; if the azimuth of the back surface of the m-1 th layer is equal to the azimuth of the front surface of the m-th layer
Figure BDA0003026552050000054
If the liquid crystal layer is not uniform, the liquid crystal layer is called a non-self-alignment mode, and at this time, an alignment film layer needs to be uniformly coated after each liquid crystal layer, and the initial azimuth direction of the next layer is constructed by rubbing or light control on the alignment film layer. The symmetrical multi-layer twisted liquid crystal layer in the present invention can select a self-aligned mode liquid crystal layer or a non-self-aligned mode liquid crystal layer depending on whether additional degree of freedom is required for design and whether processing difficulty and manufacturing cost are considered. When the symmetrical multilayer twisted liquid crystal layer is in a non-self-alignment mode, an orientation film is arranged between any two adjacent liquid crystal layers and is used for constructing the initial azimuth angle of the later liquid crystal layer in the two adjacent liquid crystal layers.
For the self-aligned mode, as shown in FIG. 1(a), the symmetric multilayer twisted liquid crystal layer requires only one alignment film. The method comprises the steps of uniformly coating an orientation film on a glass substrate, inducing the orientation of a first layer of liquid crystal by orientation methods such as friction or illumination, and the like, wherein each layer of liquid crystal needs to be divided into a plurality of sublayers for multiple spin coating, so that the problem of critical thickness is avoided. The twist angle is obtained by adding a chiral agent into polymer liquid crystal and controlling the concentration of the liquid crystal; the thickness is precisely controlled by multiple spin-coating.
For the non-self-aligned mode, as shown in fig. 1(b), an alignment film needs to be uniformly coated in front of each liquid crystal layer to induce liquid crystal alignment, and the rest is the same as the self-aligned structure. While the non-self-aligned mode is relatively difficult to fabricate, there is more design freedom.
Whether the symmetrical multi-layer twisted liquid crystal layer adopts a self-alignment mode or a non-self-alignment mode, the thickness characteristics of M liquid crystal layers in the symmetrical multi-layer twisted liquid crystal layer are in mirror symmetry distribution relative to the mirror symmetry axis of the symmetrical multi-layer twisted liquid crystal layer, meanwhile, the size of the twist angle of the M liquid crystal layers is also in mirror symmetry distribution relative to the mirror symmetry axis of the symmetrical multi-layer twisted liquid crystal layer, the directions of the twist angles of two mutually symmetrical liquid crystal layers are opposite, and particularly, when M is an odd number, the twist angle of the liquid crystal layer where the mirror symmetry axis is located is zero. The mirror symmetry axis of the symmetrical multi-layer twisted liquid crystal layer in the present invention refers to the central axis of the thickness center of the symmetrical multi-layer twisted liquid crystal layer, as shown in fig. 1.
FIG. 3 is a schematic diagram of a wide band polarization converter with a symmetrical multi-layer twisted liquid crystal layer comprising 2 liquid crystal layers, in which the twist angle is chosen to be "+ - (or- +)", i.e., Φ2＝-Φ1Thickness d1＝d2(ii) a FIG. 4 is a schematic diagram of a structure of a broadband polarization converter when a symmetric multi-layer twisted liquid crystal layer includes 3 liquid crystal layers, in which a twist angle is selected to be "+ 0- (or-0 +)", i.e., Φ3＝-Φ1Thickness d1＝d3Thickness d2Based on the input and output decisions; FIG. 5 is a schematic diagram of a wide-band polarization converter with a symmetrical multi-layer twisted liquid crystal layer including 4 liquid crystal layers, in which the twist angle is selected from "+ - - (or- + - +) or" + - - (or- + +) ", i.e., Φ4＝-Φ1，Φ3＝-Φ2Thickness d1＝d4，d2＝d3FIG. 5(a) corresponds to a twist angle of "+ - + -", and FIG. 5(b) corresponds to a twist angle of "+ + -"; the above "+" represents a left-handed chiral twist, "-" represents a right-handed chiral twist, and "0" represents no twist. For M>Other symmetrical structures above 4, similar to the symmetrical multi-layer twisted liquid crystal layer structure with M being 2,3,4, ensure that the twist angle characteristic and thickness characteristic of each liquid crystal layer are distributed in mirror symmetry with respect to the whole mirror symmetry axis during design, and are not described herein again.
For a symmetrical multilayer twisted liquid crystal layer including 4 liquid crystal layers, the thicknesses of the 4 liquid crystal layers sequentially distributed in the incident direction are respectively denoted as d1～d4The corresponding twist angles are respectively designated as phi1～Φ4Then thickness d1～d4And angle of twist phi1～Φ4Value range ofThe following is enclosed:
Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3171,0.3941]
Φ1＝-Φ4∈[29.6,105.7]
Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1225,0.2057]
Φ2＝-Φ3∈[66.3,86.4]
wherein, Δ n (λ)mid) Design band lambda for wide band polarization converter1,λ2]An intermediate wavelength lambda ofmidThe corresponding birefringence. Intermediate wavelength lambdamidGenerally closer to the short wave, the typical selection method is as follows: 1/lambda1+1/λ2＝2/λmid。
Further, the present embodiment provides an example parameter interval of the symmetric four-layer twisted liquid crystal layer as follows: lambda [ alpha ]1＝0.38um，λ2＝1um，Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3313,0.3941]，Φ1＝-Φ4∈[101.7,105.7]，Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1413,0.2057]，Φ3＝-Φ2∈[66.3,70.3]。
Further, the present embodiment provides another example parameter interval of the symmetric four-layer twisted liquid crystal layer as follows: lambda [ alpha ]1＝0.38um，λ2＝1um，Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3171,0.3799]，Φ1＝-Φ4∈[29.6,33.6]，Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1225,0.1853]，Φ2＝-Φ3∈[82.4,86.4]。
In the two example parameter intervals, Δ n, d, λ have a strict relationship, and the wavelength λ is proportional to Δ n · d. In practical application, the wave band [ lambda ] is designed if necessary1,λ2]Is changed to [ lambda ]1',λ2']At this time, the design band [ lambda ] should be used1'-λ2']Internal intermediate wavelength lambdamid' corresponding birefringence Δ n (λ)mid') as Δ n, in a ratio t ═ Δ n (λ)mid)/Δn(λmid') each thickness d of the above parameters is scaled. In the above parameters, the thickness d is in um, and the twist angle Φ is in degrees (°).
The broadband polarization converter based on the symmetrical multilayer twisted liquid crystal provided by the embodiment can be used for forming a broadband geometric phase optical element by combining the patterning control of the effective fast axis direction through carrying out mirror symmetry distribution on the twist angle characteristic and the thickness characteristic of each liquid crystal layer, and can be independently used as an achromatic wave plate such as a half-wave plate and a quarter-wave plate to realize the regulation and control of the broadband geometric phase element and the broadband polarization, so that the broadband geometric phase optical element has wide application prospects in the fields of laser communication, laser countermeasure, laser radar, non-mechanical beam deflection, VR/AR display and the like, and has important significance in the aspect of regulating and controlling the broadband optical polarization state.
In another embodiment, the present invention provides a visualization optimization method for the broadband polarization converter based on symmetric multilayer twisted liquid crystal described in the foregoing embodiments, specifically including the following steps:
the method comprises the following steps: determining a liquid crystal layer to be optimized for the broadband polarization converter. Because the twist angle characteristics and the thickness characteristics of each liquid crystal layer in the symmetrical multilayer twisted liquid crystal layer are in mirror symmetry distribution relative to the whole mirror symmetry axis, the visual optimization method only needs to optimize the parameters of half of the liquid crystal layers in the symmetrical multilayer twisted liquid crystal layer, and the front part in the symmetrical multilayer twisted liquid crystal layer is used in the embodiment
Figure BDA0003026552050000081
A liquid crystal layer as a liquid crystal layer to be optimized, wherein M is a positive integer greater than or equal to 2,
Figure BDA0003026552050000082
presentation pair
Figure BDA0003026552050000083
And carrying out the rounding-down operation, when M is an even number,
Figure BDA0003026552050000084
has a value of
Figure BDA0003026552050000085
The integer itself; when the number of M is an odd number,
Figure BDA0003026552050000086
is a ratio of
Figure BDA0003026552050000087
The small largest integer.
Step two: determining a design band [ lambda ] of a broadband polarization converter1,λ2]An intermediate wavelength lambda ofmidAnd selecting the intermediate wavelength lambdamidCorresponding birefringence Δ n (λ)mid) Initial birefringence Δ n as liquid crystal molecules0. Intermediate wavelength lambdamidOne of the selection methods is as follows: 1/lambda1+1/λ2＝2/λmid。
Step three: and randomly giving the twist angle and the thickness of each liquid crystal layer to be optimized, and demonstrating the polarization state evolution process of the incident polarization state passing through each liquid crystal layer to be optimized on a Poincare sphere.
Step four: the thickness of each liquid crystal layer to be optimized is adjusted to minimize the curvature of the output polarization state curve on the poincare sphere.
Step five: adjusting the twist angle of each liquid crystal layer to be optimized and continuously fine-adjusting the thickness to ensure that the curvature of the output polarization state curve is minimum and the output polarization state curve falls on the equator of a Poincare sphere so as to obtain the initial birefringence index delta n0The twist angle parameter and the thickness parameter of each liquid crystal layer to be optimized are as follows.
Step six: if necessary, the design band is changed to [ lambda ]1',λ2']Only the corresponding intermediate wavelength lambda needs to be foundmid', and in proportion t ═ Δ n0/Δn(λmid') scaling the thickness parameter to obtain each of the to-be-processed thickness parametersThe final thickness parameters of the liquid crystal layer are optimized.
The visualization optimization method of the above embodiment is illustrated below by taking M ═ 4 as an example:
the method comprises the following steps: determining a liquid crystal layer to be optimized of the broadband polarization converter as a first liquid crystal layer and a second liquid crystal layer which are sequentially distributed along the incident direction;
step two: calculating the design wave band [ lambda ]1,λ2]An intermediate wavelength lambda ofmidCorresponding birefringence Δ n (λ)mid) Obtaining the initial birefringence delta n of the liquid crystal molecules0；
Step three: the initial twist angle and initial thickness of the first and second liquid crystal layers are arbitrarily given, e.g. phi1＝70°，Φ2Demonstrating the polarization state evolution process of the incident polarization state passing through each liquid crystal layer to be optimized on a Poincare sphere;
step four: adjusting the thickness d of the first liquid crystal layer1And thickness d of the second liquid crystal layer2The curvature of the output polarization state curve on the Poincare sphere is made as small as possible;
step five: then, the twist angle phi of the first liquid crystal layer is adjusted1And the twist angle phi of the second liquid crystal layer2D is constantly fine-tuned1And d2The initial birefringence Deltan is obtained by making the output polarization curve fall on the equator of the Poincare sphere while ensuring the minimum curvature of the output polarization curve0Thickness parameter d of the first and second liquid crystal layers10And d20And a twist angle parameter phi10And phi20At a design band [ lambda ]1,λ2]The final thickness parameter is d1＝d10And d2＝d20The final twist angle parameter is phi1＝Φ10And phi2＝Φ20。
Step six: designing the wave band lambda if necessary1,λ2]Change to wavelength band [ lambda ]1',λ2']Only the band [ lambda ] needs to be found1',λ2']Intermediate wavelength λ ofmid' andproportional t ═ Δ n0/Δn(λmid') a scaling thickness parameter d10And d20Then the design wave band [ lambda ] can be obtained1,λ2]The final thickness parameter of each next liquid crystal layer to be optimized, namely the final thickness parameter is d1＝t·d10And d2＝t·d20The final twist angle parameter is phi1＝Φ10And phi2＝Φ20。
The polarization state regulation process of each twisted liquid crystal layer can be expressed by a Mueller matrix, and visual analysis and optimization can be carried out by a Poincare spherical coordinate system. In step three of this embodiment, as shown in fig. 2, the polarization evolution process of the incident polarization state on the poincare sphere through any single layer of the liquid crystal layer to be optimized is determined by the following steps:
selecting the azimuth angle of the liquid crystal molecules on the front surface of the single-layer liquid crystal layer to be optimized to coincide with the x axis of the coordinate system shown in fig. 1, and making the incident polarization state incident along the positive direction of the z axis of the coordinate system shown in fig. 1, wherein the Mueller matrix of the single-layer liquid crystal layer to be optimized is as follows:
Figure BDA0003026552050000091
wherein R (phi) is a Miller rotation matrix for effecting coordinate system rotation,
Figure BDA0003026552050000101
Γ is an optical retardation at a wavelength λ, and Γ is 2 π Δ n · d/λ, Δ n is a birefringence of liquid crystal molecules, d is a thickness of a single layer of a liquid crystal layer to be optimized, X satisfies X ═ sqrt (Φ)2+(Γ/2)2) Phi is the twist angle of the single-layer liquid crystal layer to be optimized, and the twist angle phi continuously changes along with the increase of the thickness;
if the front surface liquid crystal molecule azimuth angle of the single-layer liquid crystal layer to be optimized is
Figure BDA0003026552050000102
The mueller matrix of the liquid crystal layer to be optimized can be expressed as:
Figure BDA0003026552050000103
to pair
Figure BDA0003026552050000104
The matrix is split as follows:
Figure BDA0003026552050000105
wherein the content of the first and second substances,
Figure BDA0003026552050000106
ω satisfies tan ω ═ 2 Φ/Γ;
to pair
Figure BDA0003026552050000107
The matrixes obtained after the matrix splitting are all in the form of coordinate system rotation, and according to the reversibility principle of Poincare sphere coordinate system rotation and polarization state coordinate transformation, when one beam of wavelength is lambda and the polarization state is SiWhen the incident light passes through the single-layer liquid crystal layer to be optimized with the twist angle phi and the thickness d, the evolution process of the polarization state on the poincare sphere is as follows: the incident polarization state is firstly rotated clockwise by 2X degrees around the connecting line of the eigenstate point and the sphere center and then rotated around S3The axis is rotated counterclockwise by an angle of 2 phi, wherein the coordinates of the eigen-state points are
Figure BDA0003026552050000108
Figure BDA0003026552050000109
Knowing the functions realized by each liquid crystal layer, the polarization state regulation result generated by each parameter change can be visually monitored in real time on the poincare sphere. The visualization optimization method provided by the embodiment is suitable for the broadband polarization converter in the self-alignment mode and is also suitable for the broadband polarization converter in the non-self-alignment mode. The visualization optimization method provided by the embodiment is equivalent to a method that the incident polarization state rotates on a poincare sphere twice based on the evolution effect of the incident polarization state through a single-layer liquid crystal layer, so that the parameter optimization of the broadband polarization converter based on the symmetric multilayer twisted liquid crystal is realized.
To further illustrate the visualization optimization method for the broadband polarization converter based on the symmetric multilayer twisted liquid crystal according to the embodiment of the present invention, a schematic diagram of a polarization evolution process on a poincare sphere and a polarization output result diagram are respectively given below for a two-layer symmetric twisted structure with M ═ 2, a three-layer symmetric twisted structure with M ═ 3, and a symmetric four-layer twisted structure with M ═ 4.
(1) Symmetrical two-layer twisted liquid crystal layer
The evolution process of the polarization state on the poincare sphere corresponding to the symmetric two-layer twisted liquid crystal layer shown in fig. 3 is as shown in fig. 6(a) (taking right-handed circular polarization to left-handed circular polarization as an example, other symmetric situations are similar), and it is only necessary to optimize the first layer liquid crystal layer to make the output polarization state arc of the first layer liquid crystal layer fall on the equator of the poincare sphere, so that the output can be rotated to a position symmetric about the equator by the anti-twist symmetric structure. FIG. 6(b) shows the output S under optimized parameters for a two-layer symmetric twisted structure that achieves right-handed circular polarization to left-handed circular polarization3It can be seen that only two wavelengths are perfectly converted, and the middle band has a poor interval, and in order to balance the middle band, the bandwidth of the general symmetric two-layer twisted structure is narrow. Typical bandwidths are 450-650 nm. The wavelength band can be shifted to short wave or long wave by fine adjustment and thickness scaling.
(2) Symmetrical three-layer twisted liquid crystal layer
The evolution process of the polarization state on the poincare sphere corresponding to the symmetric three-layer twisted liquid crystal layer shown in fig. 4 is shown in fig. 7(a) (taking right-handed circular polarization to left-handed circular polarization as an example, other symmetric situations are similar), and only the first layer liquid crystal layer and the second layer liquid crystal layer need to be optimized to let the first layer liquid crystal layer and the second layer liquid crystal layerThe output polarisation state arc of the liquid crystal layer and the output polarisation state arc of the liquid crystal layer of the second layer are symmetrical about the equator of the poincare sphere so that the output can be rotated to a position symmetrical about the equator by the anti-twist symmetry of the liquid crystal layers of the third and first layers. FIG. 7(b) shows the output S under optimized parameters for a three-layer symmetric twisted structure that achieves right-handed circular polarization to left-handed circular polarization3It can be seen that only three wavelengths are perfectly converted and that there are two poor bands in the middle, especially in the case of large chromatic dispersion. In order to balance the two poor bands, the bandwidth can be reduced by a proper amount to obtain better polarization conversion characteristics. Typical bandwidth is 450-750 nm. The wavelength band can be shifted to short wave or long wave by fine adjustment and thickness scaling. The middle two peak bands can be made better or worse by scaling the twist angle by an appropriate amount.
(3) Symmetrical four-layer twisted liquid crystal layer
The evolution process of the polarization state on the poincare sphere corresponding to the symmetric four-layer twisted liquid crystal layer shown in fig. 5 is as shown in fig. 8(a) (taking right-handed circular polarization to left-handed circular polarization as an example, other symmetry conditions are similar), and only the first layer liquid crystal layer and the second layer liquid crystal layer need to be optimized to let the output polarization state of the second layer liquid crystal layer fall on the equator of the poincare sphere, so that the output can be rotated to a position symmetric about the equator through the reverse twist of the third layer liquid crystal layer and the second layer liquid crystal layer, and meanwhile, the reverse twist symmetric structure of the fourth layer liquid crystal layer and the first layer liquid crystal layer. FIG. 8(b) shows the output S under optimized parameters to achieve a symmetric four-layer twisted structure from right-handed circular polarization to left-handed circular polarization3It can be seen that only four wavelengths are perfectly converted, but even in the case of chromatic dispersion, their output S3Always less than-0.997, indicating that a symmetric four-layer twisted structure has enabled very wide broadband polarization conversion. A typical bandwidth is 430 and 865 nm.
Fig. 9(a) is a method for implementing an ultra-wideband geometric phase optical element by using a broadband circular polarization converter based on symmetric multilayer twisted liquid crystal, the broadband circular polarization converter provided by the present invention can be used to generate an ultra-wideband geometric phase optical element 9(b) by using the existing geometric phase holography technology, an ultra-wideband polarization grating is taken as an example here for description, and other types of broadband geometric phase optical elements are not repeated here. The thickness and twist angle of the polarization grating structure shown in fig. 9 are the same as the parameters corresponding to the four symmetric twisted liquid crystal layers shown in fig. 5 and 8, and the initial azimuth angles of the first layer of liquid crystal are distributed as shown in fig. 9(a) due to the geometric phase holography technology, so that the ultra-wideband liquid crystal polarization grating is formed. Fig. 9(c) is a graph of first order diffraction efficiency of the ultra-wideband liquid crystal polarization grating shown in fig. 9(b) when the ultra-wideband liquid crystal polarization grating is normally incident with right-handed circularly polarized light and left-handed circularly polarized light, respectively. It can be seen that the wavelength band of 420-865 nm can provide a diffraction efficiency of > 99%, and the wavelength band of 430-865nm can provide a diffraction efficiency of > 99.7%, which is consistent with the corresponding wavelength band of the broadband circular polarization converter. The outstanding bandwidth characteristic and the simple design optimization process are the significance of the invention.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (9)

1. A broadband polarization converter based on symmetrical multilayer twisted liquid crystal is characterized by comprising a glass substrate, an orientation film and a symmetrical multilayer twisted liquid crystal layer which are sequentially distributed along the incident direction;
the symmetrical multilayer twisted liquid crystal layer comprises M liquid crystal layers, the twist angles and the thickness characteristics of the M liquid crystal layers are respectively distributed in a mirror symmetry mode relative to a mirror symmetry axis of the symmetrical multilayer twisted liquid crystal layer, the directions of the twist angles of the two mutually symmetrical liquid crystal layers are opposite, when M is an odd number, the twist angle of the liquid crystal layer where the mirror symmetry axis is located is zero, and M is larger than or equal to 2.
2. The broadband polarization converter based on symmetric multilayer twisted liquid crystal according to claim 1,
an alignment film for constructing an initial azimuth angle of a succeeding liquid crystal layer of the two adjacent liquid crystal layers is disposed between any two adjacent liquid crystal layers.
3. The broadband polarization converter based on the symmetric multilayer twisted liquid crystal according to claim 1 or 2,
the alignment film induces alignment of the liquid crystal layer by an alignment method of rubbing or light irradiation.
4. The broadband polarization converter based on the symmetric multilayer twisted liquid crystal according to claim 1 or 2,
the symmetrical multilayer twisted liquid crystal layer comprises 4 liquid crystal layers, and the thicknesses of the 4 liquid crystal layers sequentially distributed along the incident direction are respectively denoted as d1～d4The corresponding twist angles are respectively designated as phi1～Φ4Thickness d1～d4And angle of twist phi1～Φ4The value ranges are as follows:
Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3171,0.3941]
Φ1＝-Φ4∈[29.6,105.7]
Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1225,0.2057]
Φ2＝-Φ3∈[66.3,86.4]
wherein, Δ n (λ)mid) Design band [ lambda ] for the broadband polarization converter1,λ2]An intermediate wavelength lambda ofmidThe corresponding birefringence.
5. The broadband polarization converter based on symmetric multilayer twisted liquid crystal according to claim 4,
intermediate wavelength lambdamidThe selection method comprises the following steps: 1/lambda1+1/λ2＝2/λmid。
6. The broadband polarization converter based on symmetric multilayer twisted liquid crystal according to claim 5,
λ1＝0.38um，λ2＝1um；
Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3313,0.3941]，Φ1＝-Φ4∈[101.7,105.7]；
Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1413,0.2057]，Φ2＝-Φ3∈[66.3,70.3]。
7. the broadband polarization converter based on symmetric multilayer twisted liquid crystal according to claim 5,
λ1＝0.38um，λ2＝1um；
Δn(λmid)·d1＝Δn(λmid)·d4∈[0.3171,0.3799]，Φ1＝-Φ4∈[29.6,33.6]；
Δn(λmid)·d2＝Δn(λmid)·d3∈[0.1225,0.1853]，Φ2＝-Φ3∈[82.4,86.4]。
8. a visualization optimization method for the symmetric multilayer twisted liquid crystal based broadband polarization converter according to any one of claims 1 to 7, comprising the steps of:
the method comprises the following steps: determining a liquid crystal layer to be optimized of the broadband polarization converter, wherein the liquid crystal layer to be optimized is a front one of the symmetrical multi-layer twisted liquid crystal layer
Figure FDA0003026552040000021
A liquid crystal layer;
step two: determining a design band [ λ ] of the broadband polarization converter1,λ2]An intermediate wavelength lambda ofmidAnd selecting the intermediate wavelength lambdamidCorresponding birefringence Δ n (λ)mid) Initial birefringence Δ n as liquid crystal molecules0；
Step three: randomly giving the twist angle and the thickness of each liquid crystal layer to be optimized, and demonstrating the polarization state evolution process of an incident polarization state passing through each liquid crystal layer to be optimized on a Poincare sphere;
step four: adjusting the thickness of each liquid crystal layer to be optimized to minimize the curvature of an output polarization state curve on the Poincare sphere;
step five: adjusting the twist angle of each liquid crystal layer to be optimized and continuously fine-adjusting the thickness to ensure that the curvature of the output polarization state curve is minimum and the output polarization state curve falls on the equator of a Poincare sphere so as to obtain the initial birefringence index delta n0The twist angle parameter and the thickness parameter of each liquid crystal layer to be optimized;
step six: if necessary, the design band is changed to [ lambda ]1',λ2']Only the corresponding intermediate wavelength lambda needs to be foundmid', and in proportion t ═ Δ n0/Δn(λmid') scaling the thickness parameters to obtain the final thickness parameters of each liquid crystal layer to be optimized.
9. The visual optimization method for the broadband polarization converter based on the symmetric multilayer twisted liquid crystal according to claim 8, wherein the polarization state evolution process of the incident polarization state on the Poincare sphere through any single layer of the liquid crystal layer to be optimized is determined by the following steps:
selecting a liquid crystal molecule azimuth angle on the front surface of the single-layer liquid crystal layer to be optimized to coincide with an x axis of a coordinate system, and enabling an incident polarization state to be incident along a positive direction of a z axis of the coordinate system, wherein a Miller matrix of the single-layer liquid crystal layer to be optimized is as follows:
Figure FDA0003026552040000031
wherein R (phi) is a Miller rotation matrix,
Figure FDA0003026552040000032
Γ is an optical retardation at a wavelength λ, and Γ is 2 π Δ n · d/λ, Δ n is a birefringence of liquid crystal molecules, d is a thickness of a single layer of a liquid crystal layer to be optimized, X satisfies X ═ sqrt (Φ)2+(Γ/2)2) Phi is the twist angle of the single-layer liquid crystal layer to be optimized;
if the front surface liquid crystal molecule azimuth angle of the single-layer liquid crystal layer to be optimized is
Figure FDA0003026552040000033
The mueller matrix of the liquid crystal layer to be optimized can be expressed as:
Figure FDA0003026552040000034
to pair
Figure FDA0003026552040000035
The matrix is split as follows:
Figure FDA0003026552040000036
wherein the content of the first and second substances,
Figure FDA0003026552040000037
ω satisfies tan ω ═ 2 Φ/Γ;
to pair
Figure FDA0003026552040000038
The matrixes obtained after the matrix splitting are all in the form of coordinate system rotation according to the Poincare sphere coordinate system rotation and the polarization state coordinateThe principle of reversibility of conversion is that when a beam has a wavelength of lambda and a polarization state of SiWhen the incident light passes through the single-layer liquid crystal layer to be optimized with the twist angle phi and the thickness d, the evolution process of the polarization state on the poincare sphere is as follows: the incident polarization state is firstly rotated clockwise by 2X degrees around the connecting line of the eigenstate point and the sphere center and then rotated around S3The axis rotates anticlockwise by 2 phi degrees, wherein the coordinate of the eigen-state point is
Figure FDA0003026552040000041
Figure FDA0003026552040000042
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