CN115657314A - AR diffraction optical waveguide device based on light field wave front phase modulation - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及衍射光学技术领域,特别涉及一种基于光场波前相位调制的AR衍射光波导装置。The invention relates to the technical field of diffractive optics, in particular to an AR diffractive optical waveguide device based on optical field wavefront phase modulation.
背景技术Background technique
增强现实技术即AR技术是在展示真实场景的同时,通过图像、视频、3D模型等技术为用户提供虚拟信息,实现把周围的视觉环境与虚拟的图形信息融合,即把真实的环境和虚拟的物体实时地叠加到了同一个画面或空间,呈现给用户一个感知效果更丰富的新环境。于是增强现实技术凭借其独特的可将投影的图像叠加到用户感知的真实环境的特点,使其在军事、工业设计与制造、医疗、娱乐及教育等领域得到了广泛的应用,影响甚至改变各行各业生产生活中的某些信息交互方式,有着巨大的潜在应用价值。目前比较成熟的增强现实技术中的光学显示方案主要分为棱镜方案、birdbath方案、自由曲面方案、离轴全息透镜方案和波导(Lightguide)方案。Augmented reality technology or AR technology is to provide users with virtual information through images, videos, 3D models and other technologies while displaying real scenes, so as to realize the integration of the surrounding visual environment and virtual graphic information, that is, to integrate the real environment and virtual Objects are superimposed on the same screen or space in real time, presenting users with a new environment with richer perceptual effects. Therefore, augmented reality technology has been widely used in the fields of military, industrial design and manufacturing, medical treatment, entertainment and education by virtue of its unique feature of superimposing the projected image on the real environment perceived by the user, affecting and even changing all walks of life. Some information interaction methods in the production and life of various industries have huge potential application value. At present, the relatively mature optical display schemes in augmented reality technology are mainly divided into prism schemes, birdbath schemes, free-form surface schemes, off-axis holographic lens schemes and waveguide (Lightguide) schemes.
目前除波导外的方案均有系统尺寸大,装备质量重等问题。波导方案可以在保证成像质量的同时,极大的减小装备的尺寸和重量。利用衍射光学的波导作为目前市场上主流的发展与研究方向,尽管微软(Microsoft)与Magic Leap等公司均有产品输出,但市场上的产品均使用两片式光波导结构,将不同波长的光(红+绿&绿+蓝)输入进入不同的波导片中进行图像或光学信息的传播。在光波导中,利用蓝光和部分绿光的在耦合入射光栅(衍射光学元件1)的衍射效果,将这部分光的传播方向偏转特定的角度,并使其可以在光波导介质中,利用全反射的特性进行传播。同理,利用剩余的绿光和红光在第二片光波导上的耦合入射光栅(衍射光学元件2)的衍射效果,将这部分光的传播方向偏转特定的角度,并使其可以在光波导介质中,利用全反射的特性进行传播。传播到特定的位置后,在每一片的波导中,利用光波导中传播的光在耦合出射光栅(衍射光学元件3)的衍射效果,将传播的光偏转一定的角度,脱离光波导的全反射限制后,光进入人眼最终成像在视网膜上。At present, solutions other than waveguides have problems such as large system size and heavy equipment quality. The waveguide solution can greatly reduce the size and weight of the equipment while ensuring the imaging quality. The waveguide using diffractive optics is currently the mainstream development and research direction in the market. Although companies such as Microsoft (Microsoft) and Magic Leap have product output, the products on the market all use a two-piece optical waveguide structure to integrate light of different wavelengths. (Red+Green&Green+Blue) input into different waveguides for image or optical information transmission. In the optical waveguide, using the diffraction effect of the blue light and part of the green light on the coupling incident grating (diffractive optical element 1), the propagation direction of this part of light is deflected by a specific angle, and it can be used in the optical waveguide medium. The properties of reflection are propagated. Similarly, using the diffraction effect of the remaining green light and red light coupled to the incident grating (diffractive optical element 2) on the second optical waveguide, the propagation direction of this part of light is deflected by a specific angle, and it can be transmitted in the light In the waveguide medium, the characteristics of total reflection are used for propagation. After propagating to a specific position, in each waveguide, the light propagating in the waveguide is used to couple the diffraction effect of the outgoing grating (diffractive optical element 3) to deflect the propagating light by a certain angle, away from the total reflection of the waveguide After confinement, the light entering the human eye is finally imaged on the retina.
如图1所示,光源发出的光经过耦合入射光栅后以不同的角度进入光波导中,并利用光在波导材料与外界(空气)的交界面出的全反射效应,使光在光波导的界面出全反射并且向右传播。在传播到一定距离后,光入射到表面的耦合出射光栅,其中一部分光被耦合出射光栅作用而离开光波导,另一部分被反射并且在下一次入射耦合出射光栅时分光使一部分离开光波导,另一部分反射继续在光波导中传播。在不同位置耦合出射的光被视作不同级次的出射光。As shown in Figure 1, the light emitted by the light source enters the optical waveguide at different angles after being coupled to the incident grating, and the total reflection effect of the light at the interface between the waveguide material and the outside world (air) is used to make the light in the optical waveguide The interface is totally reflected and propagated to the right. After propagating to a certain distance, the light is incident on the coupling-out grating on the surface, a part of the light is acted on by the coupling-out grating and leaves the optical waveguide, and the other part is reflected and split to make part of the light leave the optical waveguide during the next incident coupling-out grating, and the other part The reflection continues to propagate in the optical waveguide. Light coupled out at different positions is regarded as outgoing light of different orders.
现有AR衍射光波导光学系统中存在由于介质材料色散特性导致的不同颜色的光分离的问题、由于不同视场角对应的不同衍射角的情况导致的光束尺寸逐渐增大所带来的不同反射级次之间相互串扰的问题、以及存在大视场角下,原有入射耦合光栅结构所导致的边缘视场角光位置耦合效率下降明显的问题。In the existing AR diffractive optical waveguide optical system, there are problems of separation of different colors of light due to the dispersion characteristics of the medium material, and different reflections caused by the gradual increase of the beam size due to the different diffraction angles corresponding to different viewing angles. The problem of mutual crosstalk between stages, and the problem that the coupling efficiency of the light position at the edge of the field of view caused by the original in-coupling grating structure decreases significantly at large field of view.
发明内容Contents of the invention
鉴于上述问题,本发明的目的是提出一种基于光场波前相位调制的AR衍射光波导装置,基于物理光学波前分析与光学元件对波前调制的特性,设计在片状光波导的几个位置上的衍射光学元件的微结构,来实现各个衍射光学元件对不同位置光场的调制需求(波前调制/整形、与方向偏转)进而实现大视场角下光信息的传播。In view of the above problems, the object of the present invention is to propose an AR diffractive optical waveguide device based on optical field wavefront phase modulation. The microstructure of the diffractive optical element at each position is used to realize the modulation requirements of each diffractive optical element on the light field at different positions (wavefront modulation/shaping, and direction deflection), and then realize the transmission of optical information under a large field of view.
为实现上述目的,本发明采用以下具体技术方案:To achieve the above object, the present invention adopts the following specific technical solutions:
本发明提供一种基于光场波前相位调制的AR衍射光波导装置,包括:光源、耦合出射光栅、第一衍射光学元件、第二衍射光学元件和波导;The present invention provides an AR diffractive optical waveguide device based on optical field wavefront phase modulation, including: a light source, a coupling output grating, a first diffractive optical element, a second diffractive optical element, and a waveguide;
光源发出具有初始波前的入射光束对位于波导上表面的第一衍射光学元件进行照射,入射光束经过第一衍射光学元件进行调制后形成平面波前,并垂直入射至位于波导下表面的第二衍射光学元件,具有平面波前入射光束经过第二衍射光学元件进行波前相位调制后以高衍射效率沿衍射角度θ进行反射进入波导的内部,并继续保持平面波前相位继续在波导中利用全反射进行传播;在波导下表面的不同位置分别设置有耦合出射光栅,入射光束经过不同位置处的耦合出射光栅进行耦合形成不同级次的出射光束进行出射进入人眼,完成成像过程。The light source emits an incident light beam with an initial wavefront to irradiate the first diffractive optical element located on the upper surface of the waveguide. The incident beam is modulated by the first diffractive optical element to form a plane wavefront, and is perpendicularly incident on the second diffractive optical element located on the lower surface of the waveguide. The optical element has a plane wavefront incident light beam that is modulated by the second diffractive optical element and then reflected along the diffraction angle θ into the interior of the waveguide with high diffraction efficiency, and continues to maintain the plane wavefront phase and continues to propagate in the waveguide by total reflection ; Different positions on the lower surface of the waveguide are respectively provided with coupling output gratings, and the incident light beams are coupled through the coupling output gratings at different positions to form different levels of output light beams to enter the human eye to complete the imaging process.
优选地,波导的上下表面互相平行。Preferably, the upper and lower surfaces of the waveguide are parallel to each other.
优选地,入射光束其中一部分光束经耦合出射光栅进行耦合形成第一级次出射光束进行出射;Preferably, a part of the incident beam is coupled through a coupling output grating to form a first-order output beam for output;
另一部分光束被耦合出射光栅反射并且在下一次传播中入射至下一位位置处的耦合出射光栅进行耦合形成第二级次出射光束进行出射,另一部分光束被耦合出射光栅反射继续在波导中利用全反射进行传播。The other part of the beam is reflected by the coupling output grating and is incident on the coupling output grating at the next position in the next propagation to be coupled to form the second secondary output beam for output, and the other part of the beam is reflected by the coupling output grating and continues to be used in the waveguide using the full Reflection propagates.
优选地,第一衍射光学元件4的设计过程为:Preferably, the design process of the first diffractive optical element 4 is:
通过局部线性光栅近似方法建立在某一位置(x,y)处,入射波前局部线性近似光栅周期与出射波前之间的关系;Established at a certain position (x,y) by a local linear grating approximation method, the incident wavefront locally linear approximate grating period and outgoing wavefront The relationship between;
根据出射光束波前方向可以确定: According to the wavefront direction of the outgoing beam, it can be determined:
则可以建立各个位置上,局部线性近似光栅周期与对应位置的入射波前之间的关系式为:Then the local linear approximate grating period can be established at each position The incident wavefront corresponding to the position The relationship between is:
其中,θ为入射波前与光栅法线夹角;Among them, θ is the angle between the incident wavefront and the grating normal;
求解出局部线性近似光栅周期之后,进而的带刻线密度函数N(x,y)=1/d(x,y);Solve the local linear approximation grating period Then, the further band density function N(x, y)=1/d(x, y);
进而求解出初第一衍射光学元件的初步结构;Then solve the preliminary structure of the first diffractive optical element;
再对第一衍射光学元件的初步结构槽型进行优化设计,提升各个位置的衍射效率结果,最终得到优化后的第一衍射光学元件的结构参数。Then optimize the design of the preliminary structural groove shape of the first diffractive optical element, improve the diffraction efficiency results at each position, and finally obtain the optimized structural parameters of the first diffractive optical element.
优选地,第二衍射光学元件的设计过程为:Preferably, the design process of the second diffractive optical element is:
通过严格耦合波分析方法对第二衍射光学元件的光栅周期d内的槽型分布建立电介质常数与空间位置之间的关系ε(x,y,z);Establishing the relationship ε(x, y, z) between the dielectric constant and the spatial position for the groove distribution in the grating period d of the second diffractive optical element by a rigorous coupled wave analysis method;
并且利用第二衍射光学元件的槽型在附近空间内的周期性分布,求解第二衍射光学元件附近空间内的麦克斯韦方程组;and using the periodic distribution of the groove shape of the second diffractive optical element in the nearby space to solve Maxwell's equations in the nearby space of the second diffractive optical element;
根据严格耦合波分析方法,当电解质常数呈现周期性分布时,光场在空间频域中满足以下特征方程:According to the rigorous coupled wave analysis method, when the electrolyte constant presents a periodic distribution, the light field satisfies the following characteristic equation in the spatial frequency domain:
其中,in,
κ=(kx,ky)为在空间频域空间内的坐标;κ=(k x , k y ) is the coordinate in the space frequency domain space;
Ei(κ)(i=x,y)为光场垂直传播方向的X分量和Y分量;E i (κ) (i=x, y) is the X component and Y component of the vertical propagation direction of the light field;
则光场在附近空间内的分布为:Then the distribution of the light field in the nearby space is:
其中,in,
为特征向量对应的不全为零的比例系数; is the proportional coefficient corresponding to the feature vector that is not all zero;
为特征方程的特征向量; is the eigenvector of the characteristic equation;
得到光场在光栅结构中的光场传输矩阵M为:The light field transmission matrix M of the light field in the grating structure is obtained as:
M(x,y)=M[d,z(x,y),ε(x,y,z)]M(x,y)=M[d,z(x,y),ε(x,y,z)]
其中,in,
d为光栅周期;d is the grating period;
z(x,y)为单周期内的高度分布函数;z(x,y) is the height distribution function within a single period;
ε(x,y,z)为电解质常数分布函数;ε(x,y,z) is the electrolyte constant distribution function;
当光场通过多层膜结构时,通过第i层膜的光场为:When the light field passes through the multilayer film structure, the light field passing through the i-th film is:
其中,in,
Ei为第i层膜后的光场;E i is the light field behind the i-th film;
Ei-1为第i-1层膜后的光场;E i-1 is the light field behind the i-1th film;
Ai,Bi,Ci,Di分别为由第i层膜的多维结构参数(介质折射率、膜层厚度)决定的4个系数。A i , B i , C i , D i are four coefficients determined by the multi-dimensional structure parameters (refractive index of the medium, film thickness) of the i-th film, respectively.
则通过多层介质膜的出射光场函数Eoutput为:Then the outgoing light field function E output through the multilayer dielectric film is:
其中,in,
Mi为第i层膜对光场的调制矩阵;M i is the modulation matrix of the i-th film to the light field;
进而得到出射光场函数Eoutput与第二衍射光学元件的入射光场函数Einput之间的关系为:Then the relationship between the outgoing light field function E output and the incident light field function E input of the second diffractive optical element is obtained as:
Eoutput=M2·M1·Einput E output = M2 M1 E input
其中,M1为第一光场传输矩阵;M2为第二光场传输矩阵。Wherein, M 1 is the first light field transmission matrix; M 2 is the second light field transmission matrix.
与现有的技术相比,本发明通过对新型的衍射光学元件1进行设计,将要耦合进入光波导的光场的波前相位,调制成为一个平面波前相位。相位调制成平面波前相位后,利用衍射光学元件2的衍射特性(特定级次的高衍射效率),使平面波前的光束沿特定级次的方向发生反射衍射后,仍旧满足平面波前相位,并且衍射角满足在边界处发生全反射的限制条件,能够保证光在光波导中利用在上下表面处的全反射向后传播。Compared with the existing technology, the present invention modulates the wavefront phase of the light field to be coupled into the optical waveguide into a plane wavefront phase by designing the novel diffractive
在调制成平面波前相位后,光束的尺寸能够得到充分的限制,在后续的传播过程中,仍旧可以保持平面波前相位,保持原有的光束尺寸进行传播。在这种光束尺寸固定的条件下,解决了原有的不同级次的光由于光斑尺寸的增大导致的经历了不同级次出射光之间的串扰问题。After being modulated into the phase of the plane wave front, the size of the beam can be sufficiently limited, and in the subsequent propagation process, the phase of the plane wave front can still be maintained, and the original beam size can be maintained for propagation. Under the condition that the beam size is fixed, the original problem of crosstalk between different orders of light due to the increase of the spot size is solved.
附图说明Description of drawings
图1是现有AR衍射光波导技术的一维光路结构示意图。FIG. 1 is a schematic diagram of a one-dimensional optical path structure of the existing AR diffractive optical waveguide technology.
图2是根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的三维光路结构示意图。Fig. 2 is a schematic diagram of a three-dimensional optical path structure of an AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
图3是根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的二维光路结构示意图。3 is a schematic diagram of a two-dimensional optical path structure of an AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
图4是根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的耦合出射光路结构示意图。Fig. 4 is a schematic diagram of the structure of the coupled outgoing optical path of the AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
其中的附图标记包括:照明区域1、光源11、耦合入射光栅2、耦合出射光栅3、第一衍射光学元件4、第二衍射光学元件5和波导6。Reference numerals therein include:
具体实施方式Detailed ways
在下文中,将参考附图描述本发明的实施例。在下面的描述中,相同的模块使用相同的附图标记表示。在相同的附图标记的情况下,它们的名称和功能也相同。因此,将不重复其详细描述。Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same blocks are denoted by the same reference numerals. With the same reference numerals, their names and functions are also the same. Therefore, its detailed description will not be repeated.
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及具体实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅用以解释本发明,而不构成对本发明的限制。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, but not to limit the present invention.
图2示出了根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的三维光路结构示意图。FIG. 2 shows a schematic diagram of a three-dimensional optical path structure of an AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
图3示出了根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的二维光路结构示意图。FIG. 3 shows a schematic diagram of a two-dimensional optical path structure of an AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
如图2-3所示,本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置包括:照明区域1、光源11、耦合入射光栅2、耦合出射光栅3、第一衍射光学元件4、第二衍射光学元件5和波导6。As shown in Figures 2-3, the AR diffractive optical waveguide device based on light field wavefront phase modulation provided by the embodiment of the present invention includes: an
光源11发出带有初始波前的入射光束对波导6的上表面进行照射,经过位于波导6的上表面的耦合入射光栅2进行调制后垂直入射至波导6的下表面。波导6的上下表面互相平行。The
在本发明的一个实施例中提供的耦合入射光栅2为第一衍射光学元件4。The coupling-
入射光束的初始波前相位被第一衍射光学元件4调制为平面波前相位,即入射光束各个位置上的入射光波矢方向相互平行并且垂直于波导6,经过第一衍射光学元件4的调制后的平面波前并垂直入射至波导6的下表面。带有平面波前相位的光照射到光波导6的下表面后,再次经过第二衍射光学元件5的波前相位调制后沿特定衍射角度θ以高衍射效率进行反射进入波导6的内部,并继续保持平面波前相位继续在光波导中利用全反射进行传播。The initial wavefront phase of the incident light beam is modulated by the first diffractive optical element 4 into a plane wavefront phase, that is, the wave vector directions of the incident light at each position of the incident light beam are parallel to each other and perpendicular to the
由于波导6的上下表面为平行状态,所有在传播过程中光束在波导6的上下表面的入射角等于在第二衍射光学元件5的衍射角度θ(此角度需满足光在光波导材料与空气表面的全反射条件:Because the upper and lower surfaces of the
nwaveguide(λ)*sinθ>nair(λ)/kwaveguide(λ)*sinθ>kair(λ)n waveguide (λ)*sinθ>n air (λ)/k waveguide (λ)*sinθ>k air (λ)
入射光束沿波导6内部进行传播过程中以平面波前相位的形式,传播到人眼附近位置后,经由耦合出射光栅3的波前相位调制,将入射光束耦合后进行出射,并进入人眼成像。When the incident beam propagates along the interior of the
图4示出了根据本发明实施例提供的基于光场波前相位调制的AR衍射光波导装置的耦合出射光路结构示意图。FIG. 4 shows a schematic structural diagram of a coupled outgoing optical path of an AR diffractive optical waveguide device based on optical field wavefront phase modulation provided according to an embodiment of the present invention.
入射光束在光波导6中利用全反射进行传播,在传播过程中经过多个照明区域1,在经过多次的全反射的传播后,入射光束入射至位于波导6下表面的耦合出射光栅3。在波导6下表面的不同位置分别设置有耦合出射光栅3,经过耦合出射光栅3进行耦合出射的光被视作不同级次的出射光。The incident light beam propagates in the
入射光束其中一部分光经耦合出射光栅3进行耦合形成第一级次出射光进行出射,另一部分被反射并且在下一次入射至耦合出射光栅3时进行耦合形成第二级次出射光进行出射,另一部分被反射继续在光波导中传播。A part of the incident beam is coupled through the coupling-out
第一衍射光学元件4的设计过程为:The design process of the first diffractive optical element 4 is:
第一衍射光学元件4用于将各个位置上具有不同方向的波矢的入射光束的光场调制为具有相同方向波矢的波前的光场,并尽可能大的提高各个位置上的衍射效率。The first diffractive optical element 4 is used to modulate the light field of the incident light beam with wave vectors in different directions at each position to the light field of the wave front with the wave vector in the same direction, and improve the diffraction efficiency at each position as much as possible .
根据以上需求,采用局部线性光栅近似方法(Local Linear GratingApproximation),建立某一位置(x,y)处,入射波前局部线性近似光栅以及出射波前的关系。According to the above requirements, the local linear grating approximation method (Local Linear GratingApproximation) is used to establish the incident wavefront at a certain position (x, y). locally linear approximation grating and the outgoing wavefront Relationship.
根据需求的出射波前方向可以确定:则可以建立各个位置上,局部线性近似光栅周期与对应位置波矢之间的方程式为:According to the required outgoing wavefront direction can be determined: Then the equation between the local linear approximate grating period and the wave vector at the corresponding position can be established at each position as:
其中,θ为波矢与光栅法线夹角。Among them, θ is the angle between the wave vector and the grating normal.
求解出局部周期之后,进而求解出刻线密度函数M(x,y)=1/d(x,y),进而求解出初步第一衍射光学元件4的初步结构(刻线分布与局部的槽型宽度),再对槽型进行优化设计,提升各个位置的衍射效率结果。最后得到优化后的第一衍射光学元件4的结构参数。After solving the local period, then solve the reticle density function M(x, y)=1/d(x, y), and then solve the preliminary structure of the preliminary first diffractive optical element 4 (reticle distribution and local groove type width), and then optimize the groove type design to improve the diffraction efficiency results at each position. Finally, the optimized structural parameters of the first diffractive optical element 4 are obtained.
第二衍射光学元件5的设计过程为:The design process of the second diffractive
通过严格耦合波分析方法对第二衍射光学元件单周期d内的槽型分布(高度函数z(x,y))建立电介质常数与空间位置之间的关系ε(x,y,z);Establishing the relationship ε(x, y, z) between the dielectric constant and the spatial position for the groove distribution (height function z(x, y)) within the single period d of the second diffractive optical element by a rigorous coupled wave analysis method;
并且利用第二衍射光学元件的槽型在空间内的周期性分布,求解第二衍射光学元件附近空间内的麦克斯韦方程组;and using the periodic distribution of the groove shape of the second diffractive optical element in space to solve Maxwell's equations in the space near the second diffractive optical element;
根据严格耦合波分析方法,电解质常数呈现周期性分布时,光场在空间频域的空间(k-domain)中满足以下特征方程:According to the rigorous coupled wave analysis method, when the electrolyte constant presents a periodic distribution, the light field satisfies the following characteristic equation in the space (k-domain) of the spatial frequency domain:
式中κ=(kx,ky)代表在空间频域空间内的坐标,Ei(κ)(i=x,y)表示光场垂直传播方向的两个分量,由于其余4个光场分量Ez,Hx,Hy,Hz均可由麦克斯韦方程组结合Ex&Ey计算出来,故不在公式中体现。In the formula, κ=(k x , ky ) represents the coordinates in the spatial frequency domain space, and E i (κ)(i=x, y) represents the two components of the light field perpendicular to the direction of propagation. Since the remaining four light fields The components E z , H x , H y , and H z can all be calculated by Maxwell's equations combined with E x & E y , so they are not reflected in the formula.
则光场在该空间内的分布可以表示为:Then the distribution of the light field in this space can be expressed as:
式中代表各特征向量对应的不全为零的比例系数,为整数数集;代表特征方程的特征向量,根据光的传输需求,消去κ≥2π/λ所代表的消逝波的部分,实际代表计算时仅包含κ<2π/λ的特征向量。其中,特征向量由入射光场及电介质常数分布函数ε(x,y,z)决定,比例系数由入射光场决定的边界条件确定。各个特征向量实际代表了在光传输过程中发生衍射效应对应的不同衍射级次。In the formula Represents the proportional coefficients corresponding to each eigenvector that are not all zero, is an integer number set; The eigenvector representing the characteristic equation, according to the transmission requirements of light, eliminates the part of the evanescent wave represented by κ≥2π/λ, and actually represents only the eigenvector of κ<2π/λ in the calculation. Among them, the eigenvector is determined by the incident light field and the dielectric constant distribution function ε(x, y, z), and the proportional coefficient is determined by the boundary conditions determined by the incident light field. Each eigenvector actually represents the different diffraction orders corresponding to the diffraction effect in the light transmission process.
同时根据光栅周期d,单周期内的高度分布函数z(x,y)以及电解质常数分布函数ε(x,y,z)确定光场在光栅结构中的光场传输矩阵M(x,y)=M[d,z(x,y),ε(x,y,z)]。At the same time, according to the grating period d, the height distribution function z(x,y) in a single period and the electrolyte constant distribution function ε(x,y,z), determine the light field transmission matrix M(x,y) of the light field in the grating structure =M[d,z(x,y),ε(x,y,z)].
将需求级次的衍射光看作方向信息由包含光栅结构信息的光场传递矩阵M作用在对应特征向量决定以及能量信息由入射光决定的衍射级次能量分配比例(与σi有关)上的结果。其整体作用效果可用一个光场调制矩阵M1表示。The diffracted light of the required order is regarded as the direction information is determined by the light field transfer matrix M containing the grating structure information on the energy distribution ratio of the diffraction order determined by the corresponding eigenvector and the energy information is determined by the incident light (related to σ i ) result. Its overall effect can be represented by a light field modulation matrix M1.
光场通过单层介质膜结构的过程可以用矩阵形式表达:The process of the light field passing through the single-layer dielectric film structure can be expressed in matrix form:
则通过多层膜结构下,通过第i层膜的过程可表达为:Then, under the multi-layer film structure, the process of passing through the i-th film can be expressed as:
其中Ei表示第i层膜后的光场,既i+1层膜前的光场,同理,Ei-1表示第i-1层膜后的光场,既i层膜前的光场;Ai,Bi,Ci,Di是由第i层膜的多维结构参数(介质折射率、膜层厚度)决定的4个系数。Where E i represents the light field behind the i-th film, which is the light field in front of the i+1 film. Similarly, E i-1 represents the light field behind the i-1 film, which is the light field in front of the i-th film. field; A i , B i , C i , D i are four coefficients determined by the multi-dimensional structure parameters (refractive index of the medium, film thickness) of the i-th film.
则光场通过整个多层介质膜前后的光场可以用多个矩阵相联系:Then the light field before and after the light field passes through the entire multilayer dielectric film can be connected by multiple matrices:
式中Mi表示第i层膜对光场的调制矩阵,该结果说明多层介质膜结构下对应的光场调制效果可用一个矩阵M2表示。In the formula, M i represents the modulation matrix of the i-th film to the light field. This result shows that the corresponding light field modulation effect under the multilayer dielectric film structure can be expressed by a matrix M2.
进而得到需求衍射级次的光场函数Eoutput与第二衍射光学元件的入射光场函数Einput的关系为:Furthermore, the relationship between the light field function E output of the required diffraction order and the incident light field function E input of the second diffractive optical element is obtained as follows:
Eoutput=M2·M1·Einput E output = M2 M1 E input
通过优化光栅的槽型结构,以及优化介质膜结构的参数使需求级次的光场的能量达到最大。By optimizing the groove structure of the grating and optimizing the parameters of the dielectric film structure, the energy of the light field of the required order can be maximized.
尽管上面已经示出和描述了本发明的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本发明的限制,本领域的普通技术人员在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention, those skilled in the art can make the above-mentioned The embodiments are subject to changes, modifications, substitutions and variations.
以上本发明的具体实施方式,并不构成对本发明保护范围的限定。任何根据本发明的技术构思所作出的各种其他相应的改变与变形,均应包含在本发明权利要求的保护范围内。The above specific implementation manners of the present invention do not constitute a limitation to the protection scope of the present invention. Any other corresponding changes and modifications made according to the technical concept of the present invention shall be included in the protection scope of the claims of the present invention.
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