Transmission type volume holographic grating design method

Abstract

The invention relates to the technical field of grating design, in particular to a transmission type volume holographic grating design method, which uses two diffraction theories to cooperatively design a short-wave infrared transmission type volume holographic grating within the application range of a Kogelnik coupling wave theory. According to the diffraction efficiency and the wave bandwidth formula of the Kogelnik coupling wave theory and the diffraction characteristic analysis of the strict coupling wave theory, the influence of each parameter of the grating on different diffraction performances is obtained, an optimization iteration thought is established, the initial parameter range is calculated based on the polarization sensitivity, the diffraction efficiency and the Kogelnik coupling wave theory, and the optimal parameter range is calculated based on the polarization sensitivity, the diffraction efficiency and the Kogelnik coupling wave theory. And iteratively searching a grating parameter group meeting requirements based on a strict coupling wave theory and constraint conditions, and finally outputting an optimal transmission type volume holographic grating design result. The volume holographic grating design method is less in iterative data, high in calculation speed and high in calculation precision, and the designed grating is high in diffraction efficiency, low in polarization sensitivity and large in wave bandwidth.

Description

Technical Field

[0001] The present invention relates to the technical field of grating design, and specifically provides a transmission type volume holographic grating design method. Background Art

[0002] In recent years, with the continuous intensification of the greenhouse effect, the relevant detection technology for the concentration of carbon dioxide, an important greenhouse gas in the atmosphere, has been continuously developed. Volume holographic gratings have attracted much attention due to their high diffraction efficiency, uniform dispersion, and high spatial resolution of materials. They are used in detection payload imaging spectrometers to improve the detection accuracy of instruments and achieve miniaturization and lightweight. However, how to design high-performance volume holographic gratings that meet the needs of the field of carbon dioxide detection is an important issue.

[0003] The concept of holography was first proposed by Gabor. Later, Densisyuk invented the "volume holography" by combining Lippmann's "volume grating" and Gabor's holography. The volume holographic grating is the basic form of volume hologram. It is an optical element with periodic modulation of internal refractive index. It has the advantages of high diffraction efficiency, high signal-to-noise ratio, uniform dispersion, and low production cost. It is widely used in optical communication, holographic display, laser, imaging spectrum and other fields. Diffraction theory is the premise of grating design, including scalar diffraction theory, thin grating analysis theory, strict mode theory, Kogelnik coupled wave theory and strict coupled wave theory. At present, the latter two theories are widely used in the design of volume holographic gratings.

[0004] There are currently two main methods for designing volume holographic gratings: 1. Based on the rigorous coupled wave theory, the grating diffraction characteristics are calculated by solving the complex coupled wave equations. The tool software VirtualLab Fusion, Gsolver or self-compiled calculation program design can be used. Although this method is more accurate in theory, it faces many challenges in actual operation: the large amount of iterative data and slow calculation speed make the design process inefficient. At the same time, the constraint setting is complex, and it is difficult to perform quantitative analysis intuitively, which increases the difficulty and uncertainty of the design. 2. Self-compiled program design based on Kogelnik coupled wave theory. Although this method improves the flexibility of the design through self-compiled programs, due to the use of approximate conditions, the design results are often not accurate enough and cannot meet the needs of precise quantitative analysis.

[0005] In the visible light band and under the conditions of a small Bragg angle, both methods can achieve the design goals of high diffraction efficiency, low polarization sensitivity, and a wide spectral range to a certain extent, and maintain a certain linear dispersion capability. However, in the infrared light band, in order to achieve high diffraction efficiency and low polarization sensitivity, it is usually necessary to sacrifice the dispersion capability of the grating, and only consider the single case of TE wave or TM wave incidence. According to the current design results of high-performance volume holographic gratings, when applied to the wavelength range of carbon dioxide detection and requiring high spectral resolution, the above two methods cannot simultaneously meet the balanced requirements of the three diffraction properties of diffraction efficiency, polarization sensitivity and wavelength bandwidth. This means that under the current design framework, it is impossible to directly design the most ideal volume holographic grating to meet the requirements of this specific application scenario, so the above methods are not the most ideal design solutions. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a transmission type volume holographic grating design method, which utilizes Kogelnik coupled wave theory and strict coupled wave theory to collaboratively complete the volume holographic grating design, and fully combines the advantages of Kogelnik coupled wave theory for simple calculation and strict coupled wave theory for high flexibility, so that the designed volume holographic grating has the advantages of high diffraction efficiency, low polarization sensitivity and wide bandwidth.

[0007] The present invention provides a method for designing a transmission type volume holographic grating, comprising: S1: Compare the similarity and coincidence of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory, and obtain the applicable scope of Kogelnik coupled wave theory and strict coupled wave theory; S2: Determine the initial parameter iteration range of the volume holographic grating based on Kogelnik coupled wave theory; S3: Based on the initial parameters of the volume holographic grating, the relationship between the diffraction efficiency of the volume holographic grating and the thickness of the volume holographic grating is calculated when different polarized light is incident; based on the Bragg angle range, multiple sets of volume holographic grating parameters are obtained that satisfy the diffraction efficiency of transverse electric waves and transverse magnetic waves greater than the diffraction efficiency threshold; S4: setting a first constraint condition, and screening volume holographic grating parameters that meet the first constraint condition from multiple sets of volume holographic grating parameters; S5: Taking the maximum value of the refractive index modulation within the applicable range of Kogelnik coupled wave theory and strict coupled wave theory as the second constraint, the volume holographic grating parameters with the largest wave bandwidth among the volume holographic grating parameters in S4 are calculated and obtained as the final volume holographic grating parameters.

[0008] Preferably, the method for obtaining the applicable scope of Kogelnik coupled wave theory and strict coupled wave theory is: under the condition of transverse electric wave incidence, the similarity of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory is compared by Spearman correlation coefficient, and the overlap of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory is compared by Euclidean distance.

[0009] Preferably, the diffraction theory is applicable to the following range: the volume holographic grating spacing is less than 1.7 μm, the volume holographic grating thickness is greater than 12 μm, and the volume holographic refractive index modulation is less than or equal to 0.06.

[0010] Preferably, the initial parameters of the holographic grating include thickness, period, Bragg angle and refractive index modulation.

[0011] Preferably, the initial parameter iteration range is: the Bragg angle is in the range of 33.2° to 37.1°.

[0012] Preferably, the diffraction efficiency threshold is 0.95.

[0013] Preferably, the first constraint condition is that the polarization sensitivity of the volume holographic grating is less than 10% and the wavelength bandwidth is maximum.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: The embodiment of the present invention creatively adopts Kogelnik coupled wave theory and strict coupled wave theory to collaboratively design a transmission type volume holographic grating. According to the diffraction characteristic analysis of Kogelnik coupled wave theory, the influence of various grating parameters on different diffraction performances is obtained, the initial Bragg angle and grating period are obtained, and the strict coupled wave theory and parameter influence iterative optimization are used to output the best grating design parameters. This design method can reduce the amount of data that needs to be iterated in the design process and narrow the parameter range. Based on Kogelnik coupled wave theory, the grating period and Bragg angle that meet the application performance requirements can be quickly determined. The calculation results are close to the results of strict coupled wave theory. The influence of each grating parameter on the diffraction performance is decomposed, and the order of iterative parameters is determined according to the influence. Based on the strict coupled wave theory, a high-performance volume holographic grating is designed, which solves the problem of low polarization sensitivity of volume holographic gratings in the infrared band, making it possible to apply volume holographic gratings in the field of greenhouse gas detection.

[0015] Compared with the traditional design method, the grating design method provided in the embodiment of the present invention has less iterative data, fast calculation speed and high calculation accuracy, and solves the problem of balancing the diffraction performance of volume holographic grating in the infrared band. The designed volume holographic grating has TE wave and TM wave peak diffraction efficiencies of 95.57% and 99.89%, and the diffraction efficiency of non-polarized light in the spectral range is more than 88%, the average diffraction efficiency is 94.49%, the effective wavelength bandwidth is 32nm, and the polarization sensitivity is less than 10%. The diffraction efficiency is high, the polarization sensitivity is low, and the wavelength bandwidth is large, which verifies the feasibility of using volume holographic grating for carbon dioxide detection, and is of great significance for volume holographic grating design and greenhouse gas detection in different fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a calculation principle diagram of the diffraction theory provided according to an embodiment of the present invention; Figure 2 is a flow chart of volume holographic grating design provided according to an embodiment of the present invention; Figure 3 is a schematic diagram of a first case where the intersection point of the polarization state thickness and the diffraction efficiency curve is equal to 0.95 according to an embodiment of the present invention; Figure 4 is a schematic diagram of a second case where the intersection point of the polarization state thickness and the diffraction efficiency curve is equal to 0.95 according to an embodiment of the present invention; Figure 5 is a schematic diagram of a third case where the intersection point of the polarization state thickness and the diffraction efficiency curve is equal to 0.95 according to an embodiment of the present invention; Figure 6 is a schematic diagram of a fourth case where the intersection of the polarization state thickness and the diffraction efficiency curve is equal to 0.95 according to an embodiment of the present invention; Figure 7 is a flow chart of volume holographic grating parameter iteration according to an embodiment of the present invention; Figure 8 is a graph of wavelength selectivity of different polarization states provided by an embodiment of the present invention; Fig. 9 is a graph of angle selectivity of different polarization states provided according to an embodiment of the present invention; Fig.10 is a polarization sensitivity curve diagram provided according to an embodiment of the present invention; Fig.11 is a non-polarized light wavelength selectivity curve provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0017] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0018] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0019] The embodiment of the present invention provides a transmission type volume holographic grating design method, which involves two diffraction theories of volume holographic grating: Kogelnik coupled wave theory and strict coupled wave theory. The calculation principle of the diffraction theory is shown in FIG1. Figure 1 (a) represents the refractive index modulation of the grating, , and are the refractive indices of regions 1, 2, and 3, respectively. represents the grating period, represents the grating incident plane period, represents a raster vector, represents the grating thickness, represents the inclination angle of the interference fringes. Figure 1 (b), represents the refractive index, Represents the average refractive index of the recording material.

[0020] The transmission type volume holographic grating is a dispersion element that is recorded by two beams of recording light waves on the same side, has a thickness much greater than the grating line spacing, and realizes spectral separation through periodic spatial modulation of the refractive index. The design method of the embodiment of the present invention combines the Kogelnik coupled wave theory and the strict coupled wave theory to design the transmission type volume holographic grating. The specific design method is as follows: Figure 2 As shown, including: S1: In grating design, Kogelnik coupled wave theory and strict coupled wave theory have their own applicable scopes, and Kogelnik coupled wave theory has the disadvantage of inaccuracy when designing gratings. Therefore, it is necessary to determine the applicable scope of the combination of Kogelnik coupled wave theory and strict coupled wave theory, and verify the feasibility of collaboratively designing volume holographic gratings with Kogelnik coupled wave theory and strict coupled wave theory.

[0021] The effect of wavelength on grating diffraction efficiency under transverse electric wave (TE wave) incident conditions is an important aspect in grating design. In order to compare the performance of Kogelnik coupled wave theory and rigorous coupled wave theory (RCWA) on this issue, the similarity and overlap of the predicted curves of the two theories can be analyzed from the perspectives of Spearman correlation coefficient and Euclidean distance. As shown in Table 1, the effect of wavelength on grating diffraction efficiency under transverse electric wave (TE wave) incident condition is compared, the Spearman correlation coefficient is used to compare the similarity of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory, and the Euclidean distance is used to compare the coincidence of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory. According to the comparison results, when the grating spacing is less than 1.7μm, the grating thickness is greater than 12μm, and the refractive index modulation is less than or equal to 0.06, the correlation coefficient between Kogelnik coupled wave theory and strict coupled wave theory is greater than 0.9, which is extremely highly correlated. Kogelnik coupled wave theory and strict coupled wave theory are similar, and can be used in collaboration for volume holographic grating design.

[0022] Table 1 Spearman correlation coefficient and Euclidean distance under different grating parameters

[0023] S2: According to Kogelnik coupled wave theory and strict coupled wave theory, the effects of different parameters on the diffraction performance of volume holographic grating (VPHG) are analyzed through simulation as follows: the grating thickness is inversely proportional to the bandwidth. As the grating thickness increases, the bandwidth will decrease accordingly. When it changes, the Bragg wavelength diffraction efficiency will change along the sine law. It has no effect on the relative position of the coincidence point of the diffraction efficiency of the transverse electric wave (TE wave) and the transverse magnetic wave (TM wave), that is, it has no effect on the optimization of polarization sensitivity. The change of refractive index modulation is proportional to the bandwidth. As the refractive index modulation increases, the bandwidth will increase accordingly. The effect on the Bragg wavelength diffraction efficiency and polarization sensitivity is the same as the thickness. The product of thickness and refractive index modulation remains unchanged. Different value combinations only affect the bandwidth. When the grating period and Bragg angle change, the diffraction efficiency of the Bragg wavelength is affected, the effect on the bandwidth is minimal, and the relative position of the coincidence point of the diffraction efficiency of the TE wave and the TM wave is affected. That is, adjusting the grating period and Bragg angle can be used as a condition to constrain polarization sensitivity.

[0024] When the volume holographic grating is incident at the Bragg wavelength and the wavelength bandwidth is not considered, the main factors affecting the diffraction efficiency are the thickness, refractive index modulation, period and Bragg angle of the volume holographic grating, and the main factors affecting the polarization sensitivity are the grating period and Bragg angle.

[0025] In practical applications, these factors are often not isolated, but interrelated. Therefore, when designing and optimizing volume holographic gratings, it is necessary to comprehensively consider the interaction and balance between these factors in order to achieve the best diffraction performance and polarization sensitivity. First, fix the refractive index modulation, and adjust the period and Bragg angle to meet the requirements of diffraction efficiency and polarization sensitivity. Considering the application scenarios and high performance requirements of volume holographic gratings, it is necessary to calculate the Bragg angle range that satisfies the diffraction efficiency greater than 0.95 and the central wavelength polarization sensitivity less than 3%. For example Figures 3 to 6 As shown, based on the Kogelnik coupled wave theory, the thickness and period of the diffraction efficiency curves of TE and TM waves are The peak diffraction efficiency positions are ,in , the size of a single cycle of TE and TM waves and Can be expressed as: ; ; in, represents the Bragg wavelength, represents the Bragg angle, Represents the refractive index modulation degree.

[0026] Therefore, the period size of TE wave and TM wave can be multiple, that is, the peak diffraction efficiency points of different periods coincide, and the requirements of diffraction efficiency and polarization sensitivity are met under this grating parameter. When the second period of the TE wave curve is close to the first period of the TE wave curve, the performance of the grating meets the requirements. Taking the grating diffraction efficiency of 0.95 as the application condition, the equation can be listed as: ; ; in, Represents the volume holographic grating thickness.

[0027] The Bragg angle range in which the diffraction efficiency of the intersection of the TE wave curve and the TM wave curve is greater than or equal to 0.95 can be calculated. The curves of the diffraction efficiency of the intersection equal to 0.95 at different positions and the variation of the grating thickness are as follows: Figures 3 to 6 As shown, when the Bragg angle is in the range of (33.2°, 37.1°), there is a suitable grating thickness and refractive index modulation degree so that the diffraction efficiency and polarization sensitivity meet the requirements.

[0028] S3: The volume holographic grating designed in the embodiment of the present invention is designed for the absorption band spectrum of CO2, with a spectral range of 1.620μm~1.650μm, a central wavelength of 1.635μm, and a spectral resolution of 0.1nm required for the detection payload. When the Bragg angle range is 33.2°~37.1°, the grating period range is 0.8916μm~0.9822μm according to the Bragg condition, the initial refractive index modulation is 0.04, and the initial grating thickness is 50μm, which meets the conditions for the coordinated design of the two diffraction theories.

[0029] like Figure 7 As shown, in the first stage, the initial volume holographic grating parameters are input, and the relationship between the diffraction efficiency and thickness when different polarized light is incident is calculated. The thickness range needs to be greater than twice the TE wave thickness period under the initial conditions. The diffraction efficiency threshold is set, and the grating thickness is iterated according to the Bragg angle range to obtain multiple sets of parameter values ​​that satisfy the TE wave and TM wave diffraction efficiency greater than the diffraction efficiency threshold. The parameter value here refers to the period of the volume holographic grating. ,thickness , Prague Angle and refractive index modulation In the embodiment of the present invention, the diffraction efficiency threshold value is 0.95.

[0030] S4: Set the first constraint condition, and select the volume holographic grating parameters that meet the first constraint condition. In the embodiment of the present invention, the polarization sensitivity of the volume holographic grating is less than 10% and the wavelength bandwidth is the maximum as the first constraint condition, and multiple groups of parameter values ​​in S3 that satisfy the diffraction efficiency of TE waves and TM waves greater than 0.95 are iterated. When iterating multiple groups of grating parameters, the polarization sensitivity of the volume holographic grating is less than 10% and the wavelength bandwidth is the maximum as the first constraint condition, and the volume holographic grating parameters that meet the constraint condition are obtained. At this time, among the volume holographic grating parameters obtained, the Bragg angle and the grating period are already the optimal values, and the product of the grating thickness and the refractive index modulation is also the optimal value, but it is also necessary to expand the width of the wavelength bandwidth by adjusting the values ​​of each parameter.

[0031] S5: Taking the maximum value of the refractive index modulation in the applicable conditions of the collaborative design of Kogelnik coupled wave theory and strict coupled wave theory as the second constraint, iteratively multiply multiple groups of refractive index modulation and grating thickness with the same product but different values ​​to calculate the volume holographic grating parameters with the largest wave bandwidth in the volume holographic grating parameters in S4, as the final volume holographic grating parameters, the volume holographic grating design is completed. The final parameters of the volume holographic grating are shown in Table 2: Table 2 Volume holographic grating design parameters

[0032] In order to ensure that the diffraction performance of the volume holographic grating corresponding to the designed volume holographic grating parameters meets the requirements, the diffraction performance of the designed volume holographic grating is analyzed. Figures 8 to 11 The diffraction performance analysis curve shown is Figure 8 is the wavelength selectivity curve for different polarization states; Fig. 9 is the selectivity curve diagram of different polarization states; Fig.10 is a polarization sensitivity graph; Fig.11 This is a non-polarized light wavelength selectivity curve. The peak diffraction efficiencies of TE and TM waves are 95.57% and 99.89%, respectively. The diffraction efficiency of TE light in the spectral range is over 93%, and the diffraction efficiency of TM light is over 83%. The bandwidth and effective bandwidth of TE wave are 187nm and 86nm, respectively, and the bandwidth and effective bandwidth of TM wave are 116nm and 32nm, respectively. The diffraction efficiency of TE wave within the 1.6° angular bandwidth range is greater than 90%, and the diffraction efficiency of TM wave within the 0.8° angular bandwidth range is greater than 80%, and the diffraction efficiency within the non-polarized light spectral range is above 88%, the average diffraction efficiency is 94.49%, and the polarization sensitivity is less than 10%. All diffraction characteristics of the grating meet the requirements of CO2 detection applications.

[0033] In particular, the grating designed in the embodiment of the present invention is a short-wave infrared high-performance transmission volume holographic grating, which is used in the field of related detection of greenhouse gas carbon dioxide concentration.

[0034] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0035] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A design method for a transmission volume holographic grating. It is characterized in that include: S1: Compare the similarity and coincidence of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory, and obtain the applicable scope of Kogelnik coupled wave theory and strict coupled wave theory; S2: Determine the initial parameter iteration range of the volume holographic grating based on Kogelnik coupled wave theory; S3: Calculating the relationship between the diffraction efficiency of the volume holographic grating and the thickness of the volume holographic grating when different polarized light is incident according to the initial parameters of the volume holographic grating; and obtaining multiple sets of volume holographic grating parameters that satisfy the diffraction efficiency of transverse electric waves and transverse magnetic waves greater than the diffraction efficiency threshold according to the Bragg angle range; S4: setting a first constraint condition, and screening volume holographic grating parameters that meet the first constraint condition from the multiple sets of volume holographic grating parameters; S5: Taking the maximum value of the refractive index modulation degree in the applicable range of the Kogelnik coupled wave theory and the strict coupled wave theory as the second constraint condition, calculate and obtain the volume holographic grating parameters with the largest wave bandwidth among the volume holographic grating parameters described in S4 as the final volume holographic grating parameters.

2. The method for designing a transmission type volume holographic grating according to claim 1, It is characterized in that The method for obtaining the applicable range of Kogelnik coupled wave theory and strict coupled wave theory is: under the condition of transverse electric wave incidence, the similarity of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory is compared by Spearman correlation coefficient, and the coincidence of the wavelength-diffraction efficiency curves of Kogelnik coupled wave theory and strict coupled wave theory is compared by Euclidean distance.

3. The method for designing a transmission type volume holographic grating according to claim 2, It is characterized in that The diffraction theory is applicable to the following ranges: the volume holographic grating spacing is less than 1.7 μm, the volume holographic grating thickness is greater than 12 μm, and the volume holographic refractive index modulation is less than or equal to 0.

06.

4. The method for designing a transmission type volume holographic grating according to claim 1, It is characterized in that The initial parameters of the holographic grating include thickness, period, Bragg angle and refractive index modulation.

5. The method for designing a transmission type volume holographic grating according to claim 4, It is characterized in that The initial parameter iteration range is: the Bragg angle is in the range of 33.2° to 37.1°.

6. The method for designing a transmission type volume holographic grating according to claim 1, It is characterized in that The diffraction efficiency threshold is 0.

95.

7. The method for designing a transmission type volume holographic grating according to claim 1, It is characterized in that The first constraint condition is that the polarization sensitivity of the volume holographic grating is less than 10% and the wavelength bandwidth is the largest.

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