A method for calculating diffraction efficiency of liquid crystal polarization grating

Abstract

The present application relates to a kind of liquid crystal polarization grating diffraction efficiency calculation method, belong to non-mechanical type optical beam deflection field, solve the problem that traditional method cannot accurately calculate the diffraction efficiency of liquid crystal polarization grating under the influence of Fresnel effect.The present application first constructs the corresponding relationship between the spatial spectrum of the mth diffraction order electric field component in the observation medium layer and the total transmission electric field;The expression of the mth diffraction order electric field component is obtained by using spatial fourier inverse transform;The quantitative relationship between the mth diffraction order electric field component in the observation medium layer and the total transmission electric field is deduced;The mth diffraction order electric field component is extracted by combining grating equation and quantitative relationship;The proportion of the light intensity of the mth diffraction order in the total transmission light intensity is calculated as the diffraction efficiency.The present application not only has more accurate calculation result, but also can be well applied to the diffraction efficiency calculation of multilayer liquid crystal polarization grating cascade structure, meet the current calculation demand of liquid crystal polarization grating system diffraction efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of non-mechanical beam deflection, and particularly relates to a diffraction efficiency calculation method of a liquid crystal polarization grating. BACKGROUND

[0002] The beam deflection module is one of core components in many military and civilian fields such as laser radar, deep space exploration, space communication, laser active imaging, etc. The liquid crystal polarization grating is a new type of geometric phase element, which has excellent properties such as large aperture, high efficiency and wide angle. The new non-mechanical beam deflection technology based on the liquid crystal polarization grating can simultaneously meet the two core requirements of large aperture and wide angle, and thus can greatly improve the performance of the beam deflection system, which makes it have good application prospects in many national defense and military fields such as satellite communication, airborne radar, mid-wave infrared staring imaging, laser countermeasure, laser guidance, etc.

[0003] At present, most of the beam deflection technologies based on the liquid crystal polarization grating adopt a cascade structure, and the core is to accurately calculate the diffraction efficiency corresponding to each diffraction order. The traditional diffraction efficiency calculation method of the liquid crystal polarization grating needs to add a corresponding refractive index matching medium to the liquid crystal polarization grating, or the diffraction efficiency calculation can be carried out only on the premise that the medium at the output end of the liquid crystal polarization grating is transparent. However, these measures cannot avoid the Fresnel effect generated by the polarization grating system, and therefore, the traditional diffraction efficiency calculation method can only estimate the diffraction efficiency by calculating the light intensity of some low orders such as 0 order, ±1 order, etc. in the liquid crystal polarization grating, and cannot accurately calculate the diffraction efficiency of any order. The drawbacks of this traditional diffraction efficiency calculation method mainly manifest as that the calculated result of the diffraction efficiency is too large and it is difficult to verify in experiments for a single liquid crystal polarization grating. However, for the cascade structure of N pieces of liquid crystal polarization gratings, the traditional diffraction efficiency calculation method is not applicable, because it is not clear in which diffraction orders the energy of the diffracted beam is mainly distributed from the 2 N orders of the Nth liquid crystal polarization grating. Ultimately, the traditional diffraction efficiency calculation method has many limitations because it cannot avoid the Fresnel effect generated by the liquid crystal polarization grating system. SUMMARY

[0004] The purpose of the present application is to provide a diffraction efficiency calculation method of a liquid crystal polarization grating, which solves the problem that the traditional diffraction efficiency calculation method cannot accurately calculate the diffraction efficiency of the liquid crystal polarization grating under the influence of the Fresnel effect.

[0005] A method for calculating the diffraction efficiency of a liquid crystal polarization grating, wherein the liquid crystal polarization grating comprises a liquid crystal polarization grating film (2), an observation medium layer (3) respectively plated on both sides of the liquid crystal polarization grating film (2), a transition medium layer (4), and an incident front medium layer (1) plated on the transition medium layer (4), wherein both the incident front medium layer (1) and the observation medium layer (3) are composed of isotropic media. The method comprises the following steps:

[0006] Step 1: Construct the mth diffraction order electric field component in the observation medium layer (3) based on Fraunhofer diffraction theory and spatial Fourier transform Spatial spectrum Total transmitted electric field Spatial spectrum The corresponding relationship between them;

[0007] Step 2: Spatial spectrum constructed based on step 1 and spatial spectrum The corresponding relationship between them is used to obtain the m-th diffraction order electric field component using spatial inverse Fourier transform. Expressions of

[0008] Step 3: According to the Floquet-Bloch theorem, the total transmitted electric field After the vector is decomposed, it is expanded into its corresponding Fourier series and the total transmitted electric field is calculated. The Fourier transform is performed and the Fourier transform result is substituted into the electric field component of the mth diffraction order obtained in step 2. From the expression of , the electric field component of the mth diffraction order in the observation medium layer (3) is derived Total transmitted electric field The quantitative relationship between

[0009] Step 4: Combine the grating equation of the liquid crystal polarization grating and the quantitative relationship derived in step 3 to extract the mth diffraction order electric field component under any incident direction

[0010] Step 5: Using the optical power density in the observation medium layer (3) as the light intensity for calculating the diffraction efficiency, according to the extracted m-th diffraction order electric field component Calculate the light intensity I of the mth diffraction order in the observation medium layer (3) m And according to the total transmitted electric field Calculate the total transmitted light intensity I in the observation medium layer (3) total ;

[0011] Step 6: Calculate the light intensity I of the mth diffraction order m In the total transmitted light intensity I total The proportion of The diffraction efficiency of the mth diffraction order of the liquid crystal polarization grating film (2) that is emitted.

[0012] Beneficial effects: the present application provides a liquid crystal polarization grating diffraction efficiency calculation method, which can accurately calculate the diffraction efficiency of any diffraction order of the liquid crystal polarization grating considering the interference of the Fresnel effect generated by the whole liquid crystal polarization grating system. Compared with the shortcomings of the traditional diffraction efficiency calculation method, the diffraction efficiency calculation method proposed in the present application not only has more accurate calculation results, but also improves the calculation accuracy of the liquid crystal polarization grating diffraction efficiency, and can be well applied to the diffraction efficiency calculation of the multi-layer liquid crystal polarization grating cascade structure, meets the current calculation demand of the liquid crystal polarization grating system diffraction efficiency, and further optimizes the performance of the beam deflection module. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The flow chart of the liquid crystal polarization grating diffraction efficiency calculation method described in the embodiments of the present application;

[0014] Figure 2 The structure diagram of one of the liquid crystal polarization gratings that can use the method provided by the present application to calculate the diffraction efficiency;

[0015] Figure 3 The result comparison diagram of the diffraction efficiency of the same liquid crystal polarization grating calculated by the method proposed in the present application and the traditional method respectively.

[0016] Explanation of reference signs: 1, incident front end dielectric layer; 2, liquid crystal polarization grating film; 3, observation dielectric layer; 4, transition dielectric layer. DETAILED DESCRIPTION

[0017] In order to make those skilled in the art better understand the technical solutions of the present application, the present application will be further described in detail below with reference to the drawings and preferred embodiments.

[0018] Embodiment 1

[0019] The present embodiment provides a liquid crystal polarization grating diffraction efficiency calculation method, wherein the structure of the liquid crystal polarization grating is as follows Figure 2As shown, the system primarily comprises an incident front dielectric layer 1, a liquid crystal polarization grating film 2, an observation medium 3, and a transition dielectric layer 4. The observation dielectric layer 3 and the transition dielectric layer 4 are respectively deposited on either side of the liquid crystal polarization grating film 2, with the incident front dielectric layer 1 deposited on the transition dielectric layer 4. Both the incident front dielectric layer 1 and the observation dielectric layer 3 are composed of isotropic media, such as air. The composition of the transition dielectric layer 4 includes, but is not limited to, a single layer of isotropic media, a single layer of anisotropic media, multiple layers of isotropic media, multiple layers of anisotropic media, or a multi-layer cascade of isotropic and anisotropic media, making it well suited for use in various complex liquid crystal polarization grating cascade systems.

[0020] In this embodiment Figure 2 The rectangular coordinate system xyz in the figure is established by setting the thickness direction of the liquid crystal polarization grating film 2 and the grating period direction as the x-axis and the y-axis respectively, and setting the normal direction of the xy plane as the z-axis.

[0021] In this embodiment, the liquid crystal polarization grating film 2 is a polarization element that changes the wavefront by generating a geometric phase. It is also a one-dimensional grating with periodicity in the y direction only. The optical axis of the liquid crystal molecules is in Figure 2 The yz plane in the yz plane changes periodically and continuously, and satisfies the following relationship:

[0022]

[0023] Where, Represents the unit vector of the direction of the optical axis of the liquid crystal molecule, y is the coordinate variable representing the spatial position information in the period direction of the liquid crystal polarization grating film 2, and Λ is the period size of the liquid crystal polarization grating film 2. At the same time, Figure 2 The thickness d of the liquid crystal polarization grating film 2 along the x direction satisfies the half-wave condition:

[0024] d=λ0 / (2Δn) (2)

[0025] Where λ0 is the wavelength in vacuum, Δn = n e -n o , n e and n o The principal axis refractive indices of the liquid crystal molecules are parallel and perpendicular to the optical axis of the liquid crystal molecules, respectively.

[0026] The method for calculating the diffraction efficiency of the liquid crystal polarization grating of this embodiment specifically includes the following steps:

[0027] Step 1: First, construct the mth diffraction order electric field component in the observation medium layer 3 based on Fraunhofer diffraction theory and spatial Fourier transform Spatial spectrum Total transmitted electric field Spatial spectrum correspondence between the spatial spectrum

[0028] Step 1.1: According to the Fraunhofer diffraction theory, for a one-dimensional grating with periodicity in the y direction, the spatial spectrum of the total transmitted electric field exists only in the grating period direction, therefore, the spatial spectrum of the total transmitted electric field The spatial spectrum of the total transmitted electric field

[0029]

[0030] where f y represents the spatial frequency corresponding to the total transmitted electric field , and j represents the imaginary unit;

[0031] Step 1.2: According to the Fraunhofer diffraction theory, the spatial angular frequency of the mth diffraction order electric field component in the y direction is where f ym represents the spatial frequency corresponding to the mth diffraction order electric field component , k0represents the wave number in vacuum, λ0represents the wavelength in vacuum, n3represents the refractive index of the observation medium layer 3, θ m and φ m respectively represent the diffraction polar angle and the diffraction azimuth angle of the mth diffraction order, then the spatial spectrum of the mth diffraction order electric field component

[0032]

[0033] where δ(·) represents the unit impulse function.

[0034] Step 2: Based on the correspondence between the spatial spectrum constructed in step 1 and the spatial spectrum , the inverse spatial Fourier transform can be used to obtain the relationship between the Fourier transform of the mth diffraction order electric field component and the total transmitted electric field , that is, the expression of the mth diffraction order electric field component is obtained as:

[0035]

[0036] where F(·) represents the spatial Fourier transform operator.

[0037] Step 3: According to the Floquet-Bloch theorem, the total transmitted electric field ​​​After the vector is decomposed, it is expanded into its corresponding Fourier series, so that the total transmitted electric field can be calculated The Fourier transform is performed and the Fourier transform result is substituted into the electric field component of the mth diffraction order obtained in step 2. The electric field component of the mth diffraction order in the observation medium layer 3 is derived from the expression of Total transmitted electric field The quantitative relationship between them is:

[0038]

[0039] Where, Indicates along Figure 2 The unit vector in the positive direction of the a-axis, where a = x, y, z; represents the total transmitted electric field exist The complex amplitude of the component in the direction.

[0040] Step 4: Combine the grating equation of the liquid crystal polarization grating and the quantitative relationship derived in step 3 to extract the mth diffraction order electric field component under any incident direction

[0041] According to Huygens-Fresnel diffraction theory and Fraunhofer diffraction theory, we can get Figure 2 The grating equation of the liquid crystal polarization grating shown is:

[0042]

[0043] Where n1 represents the refractive index of the incident front dielectric layer 1, θ0 represents the incident light wave vector and Figure 2 The angle along the positive x direction is usually called the polar angle, φ0 represents the incident light wave vector in Figure 2 The angle between the projection in the yz plane and the positive direction of the y-axis is usually called the azimuth.

[0044] Substituting the grating equation into formula (6), the electric field component of the mth diffraction order under any incident direction can be extracted:

[0045] Step 5: Considering the ease and feasibility of experimental measurement in practice, this embodiment chooses to observe the optical power density in the dielectric layer 3 as the light intensity for calculating the diffraction efficiency. The relationship between them is:

[0046]

[0047] Where n3 is the refractive index of the observation medium layer 3, ε0 is the dielectric constant in a vacuum, and μ0 is the magnetic permeability in a vacuum.

[0048] Based on formula (8), according to the extracted m-th diffraction order electric field component Calculate the light intensity I of the mth diffraction order in the observation medium layer 3 m , the calculation formula is as follows:

[0049]

[0050] According to the total transmitted electric field Calculate the total transmitted light intensity I in the observation medium layer 3 total , the calculation formula is as follows:

[0051]

[0052] Step 6: Finally, calculate the light intensity I of the mth diffraction order of the observation medium layer 3 m In the total transmitted light intensity I total The proportion of As the diffraction efficiency of the mth diffraction order emitted from the liquid crystal polarization grating film 2.

[0053] Specifically, substitute formula (9) and formula (10) into The diffraction efficiency η of the mth diffraction order emitted from the liquid crystal polarization grating can be accurately calculated. m for:

[0054]

[0055] The method for calculating the diffraction efficiency of a liquid crystal polarization grating proposed in this embodiment differs from traditional diffraction efficiency calculation methods in that it does not require the addition of a corresponding refractive index matching medium to the liquid crystal polarization grating film. Instead, it directly extracts the electric field components corresponding to each diffraction order in the observation medium layer to calculate the light intensity value, thereby calculating the diffraction efficiency. Compared to traditional diffraction efficiency calculation methods, this diffraction efficiency calculation method can accurately calculate the diffraction efficiency of any diffraction order of the liquid crystal polarization grating while taking into account the interference of the Fresnel effect generated by the entire liquid crystal polarization grating system, thereby improving the accuracy of the calculation of the diffraction efficiency of the liquid crystal polarization grating. Furthermore, compared to traditional diffraction efficiency calculation methods, the light intensity used in this diffraction efficiency calculation method directly corresponds to the light power density in the observation medium layer, making the calculation results easier to verify through experiments. This diffraction efficiency calculation method can accurately calculate the diffraction efficiency of complex diffraction structures such as multi-layer dielectrics and multi-layer liquid crystal polarization grating cascades at the incident front of the liquid crystal polarization grating. This greatly helps to meet the current demand for the accuracy of diffraction efficiency calculation of liquid crystal polarization grating systems, thereby further optimizing the performance of the beam deflection module.

[0056] Example 2

[0057] The parameters of the liquid crystal polarization grating in this embodiment are set as follows:

[0058] The grating period Λ of the liquid crystal polarization grating film 2 is 15 μm;

[0059] Principal axis refractive index n e is 1.65, n o is 1.55, the vacuum wavelength λ0 is 1064nm, and the thickness d is 5.32μm;

[0060] The composition of the observation medium layer 3 is air;

[0061] The transition medium layer 4 is composed of air;

[0062] The azimuth angle φ0 of the incident light emitted by the observation medium layer 1 is 0°, and the polar angle θ0 is -45° to 45°.

[0063] Based on all the parameters in this embodiment, taking the +1 diffraction order as an example, the diffraction efficiency calculation method proposed by the present invention and the traditional method are used to calculate the diffraction efficiency of the liquid crystal polarization grating, and the results are as follows: Figure 3 As shown. Figure 3 As can be seen from the figure, when the light wave is near vertical incidence, the difference between the diffraction efficiency calculation method of the liquid crystal polarization grating proposed in the present invention and the traditional method is small. This is because the energy of the incident light wave at these incident directions is mainly concentrated in the low diffraction orders, so the traditional method still has a high accuracy at this time. However, the proportion of light wave energy in higher diffraction orders increases with the increase of the incident polar angle. At this time, the accuracy of the traditional diffraction efficiency calculation method will drop significantly, and the diffraction efficiency calculation error near the incident polar angle of ±45° is as high as 7%. Furthermore, if a multi-stage liquid crystal polarization grating cascade is used, this diffraction efficiency calculation error will be geometrically amplified. Therefore, compared with the obvious defects of the traditional diffraction efficiency calculation method, the diffraction efficiency calculation method of the liquid crystal polarization grating proposed in the present invention can well meet the current demand for the accuracy of the diffraction efficiency calculation of the liquid crystal polarization grating system.

[0064] It can be seen from this embodiment that the method for calculating the diffraction efficiency of a liquid crystal polarization grating proposed in the present invention can fundamentally overcome the defects of traditional calculation methods and accurately calculate the diffraction efficiency of a liquid crystal polarization grating system, which will play an important role especially when used in a cascade structure.

[0065] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0066] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for calculating the diffraction efficiency of a liquid crystal polarization grating, characterized in that: The liquid crystal polarization grating is provided with an incident front dielectric layer (1), a transition dielectric layer (4), a liquid crystal polarization grating film (2), and an observation dielectric layer (3) in sequence, and the components of the incident front dielectric layer (1) and the observation dielectric layer (3) are both isotropic media. The method comprises the following steps: Step 1: Construct the mth diffraction order electric field component in the observation medium layer (3) based on Fraunhofer diffraction theory and spatial Fourier transform Spatial spectrum Total transmitted electric field Spatial spectrum The corresponding relationship between them; Step 2: Spatial spectrum constructed based on step 1 and spatial spectrum The corresponding relationship between them is used to obtain the m-th diffraction order electric field component using spatial inverse Fourier transform. Expressions of Step 3: According to the Floquet-Bloch theorem, the total transmitted electric field After the vector is decomposed, it is expanded into its corresponding Fourier series and the total transmitted electric field is calculated. The Fourier transform is performed and the Fourier transform result is substituted into the electric field component of the mth diffraction order obtained in step 2. From the expression of , the electric field component of the mth diffraction order in the observation medium layer (3) is derived Total transmitted electric field The quantitative relationship between Step 4: Combine the grating equation of the liquid crystal polarization grating and the quantitative relationship derived in step 3 to extract the mth diffraction order electric field component under any incident direction ; Step 5: Take the optical power density in the observation medium layer (3) as the light intensity for calculating the diffraction efficiency, and extract the electric field component of the mth diffraction order. Calculate the light intensity of the mth diffraction order in the observation medium layer (3) And according to the total transmitted electric field Calculate the total transmitted light intensity in the observation medium layer (3) ; Step 6: Calculate the light intensity of the mth diffraction order In total transmitted light intensity The proportion of As the diffraction efficiency of the mth diffraction order emitted from the liquid crystal polarization grating film (2).

2. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 1, wherein: Step 1 includes the following steps: Step 1.1: Observe the total transmitted electric field in the dielectric layer (3) according to Fraunhofer diffraction theory Spatial spectrum Using spatial Fourier transform, it can be expressed as: （3） Where, represents the total transmitted electric field The corresponding spatial frequency, represents an imaginary unit; Step 1.2: According to Fraunhofer diffraction theory, the electric field component of the mth diffraction order is obtained Spatial spectrum Expressed as: （4） Where, represents the unit impulse function; represents the electric field component of the mth diffraction order The corresponding spatial frequency satisfies: ,in, is the electric field component of the mth diffraction order The spatial angular frequency of the direction, is the coordinate variable representing the spatial position information in the periodic direction of the liquid crystal polarization grating film (2), represents the wave number in vacuum, represents the wavelength in vacuum, represents the refractive index of the observation medium layer (3), 、 They represent the diffraction polar angle and diffraction azimuth angle of the mth diffraction order respectively.

3. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 2, wherein: The electric field component of the mth diffraction order in step 2 The expression is: （5） Where, represents the spatial Fourier transform operator.

4. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 3, wherein: The quantitative relationship derived in step 3 is: （6） Where, Indicates along The unit vector in the positive direction of the axis, where ; represents the total transmitted electric field exist The complex amplitude of the component in the direction, is the period size of the liquid crystal polarization grating film (2).

5. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 4, wherein: The grating equation of the liquid crystal polarization grating is: （7） Where, represents the refractive index of the incident front medium layer (1), represents the polar angle, Indicates the azimuth.

6. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 5, wherein: Observe the light intensity of the mth diffraction order in the medium layer (3) for: （9） Observe the total transmitted light intensity in the dielectric layer (3) for: （10） Where, is the dielectric constant in vacuum, is the magnetic permeability in vacuum.

7. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to claim 6, wherein: Diffraction efficiency of the mth diffraction order The calculation formula is: （11）。 8. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to any one of claims 1 to 7, wherein: The optical axis of the liquid crystal molecules of the liquid crystal polarization grating film (2) is The continuous change of periodicity in the plane satisfies the following relationship: （1） Where, The unit vector representing the direction of the optical axis of the liquid crystal molecule, is the coordinate variable representing the spatial position information in the periodic direction of the liquid crystal polarization grating film (2), is the period size of the liquid crystal polarization grating film (2); At the same time, the liquid crystal polarization grating film (2) is Thickness in the direction Satisfy the half-wave condition: （2） Where, is the wavelength in vacuum, , and The principal axis refractive indices of the liquid crystal molecules are parallel and perpendicular to the optical axis of the liquid crystal molecules, respectively.

9. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to any one of claims 1 to 7, wherein: The transition medium layer (4) is composed of any one of a single-layer isotropic medium, a single-layer anisotropic medium, a multi-layer isotropic medium, and a multi-layer anisotropic medium, or a multi-layer cascade of an isotropic medium and an anisotropic medium.

10. The method for calculating the diffraction efficiency of a liquid crystal polarization grating according to any one of claims 1 to 7, wherein: The incident front medium layer (1) and the observation medium layer (3) are both composed of air.

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