CN114815229A - Broadband light-splitting micro-nano diffraction grating design method - Google Patents
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Abstract
The invention relates to a design method of a broadband light-splitting micro-nano diffraction grating, which overcomes the defects of large error, large calculated amount and the like of the traditional grating design mode. The method comprises the following steps: designing a theoretical model of the grating by adopting a strict coupled wave method; determining the diffraction intensity distribution and the diffraction order of the grating based on a theoretical model; determining the action waveband of the diffraction grating according to the requirement; determining grating parameters according to the action wave band: material, duty cycle, period, depth, sidewall verticality, grating shape and other parameter ranges; establishing a grating model by using simulation software; and optimizing the grating parameters according to the simulation result to obtain the grating parameters of the required action wave band. The method can be used for designing the light-splitting broadband grating of each waveband as required, the designed diffraction grating is convenient and simple, and can be used in the fields of high-power laser, laser processing, laser medical treatment, micro-imaging, laser radar, structured light illumination and laser display and the like.
Description
Technical Field
The invention relates to the field of micro-nano gratings, in particular to a design method of a broadband light-splitting micro-nano diffraction grating.
Background
The diffraction grating is a micro-nano optical element formed by etching steps or a continuous relief structure on a substrate or the surface of a traditional optical device by using a super-large-scale integrated circuit manufacturing process by using a computer-aided design based on a light wave diffraction theory. The basic principle of the diffraction grating is that steps (gratings) with certain depth are prepared on the surface of an element by utilizing the diffraction theory, and different optical path differences are generated when light beams pass through, so that the Bragg diffraction condition is met. The divergence angle of the light beam and the appearance of the formed light spot are controlled through different designs, and the function of forming a specific pattern by the light beam is realized.
The development of diffractive optical elements has shown great application potential in the fields of high-power laser, laser processing, laser medical treatment, microscopic imaging, laser radar, structured light illumination, laser display and the like. Especially in the field of low-light night vision technology, the micro-nano diffraction grating is introduced into the core device image intensifier, the deflection of light beams can be realized through the beam splitting function of the grating, and the utilization rate of the low-light image intensifier to photons is further enhanced. The action wave band of the low-light level image intensifier is 380nm-960nm, and the central wavelength is 670 nm. To maximize the utilization of photons of the micro-optical image intensifier, it is necessary to expand the bandwidth of the diffraction grating as much as possible, so that the central wavelength of the grating action is about 670nm, and the diffraction energy is concentrated in the first order diffraction as much as possible, and an optical medium is used as the grating material.
The diffraction spectral bandwidth of the all-dielectric grating designed by the traditional grating design method is not very wide and generally does not exceed 40 nm. In order to improve the photon utilization rate of the image intensifier through the grating, a light splitting type micro-nano diffraction grating design method needs to be invented, so that the designed grating has a wider spectral range.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a method for designing a broadband light-splitting micro-nano diffraction grating, wherein the central wavelength range of the grating effect designed by the method comprises 380nm-960 nm. The technical scheme is as follows:
a method for designing a broadband light-splitting micro-nano diffraction grating comprises the following steps:
s1, solving a correlation equation of a strict coupled wave theory through Fourier transform to obtain a transmission equation of the grating;
s2, obtaining a Fraunhofer diffraction intensity distribution expression of the grating by using a transmission equation of the grating;
s3, obtaining diffraction peaks of different diffraction orders by the intensity distribution expression of Fraunhofer diffraction;
s4, determining the target diffraction order and depth of the final grating by the diffraction peaks of different diffraction orders;
s5, determining the period of the grating according to the actual grating action waveband, the processing and manufacturing process and the target diffraction order;
s6, determining the duty ratio of the grating according to the grating material and the coating material;
s7, optimizing the period, duty ratio and depth of the grating through simulation, wherein the optimization criterion is as follows: by continuously adjusting the period, duty ratio and depth of the grating, the acting central wave band of the grating is close to the target central wave band, and meanwhile, the transmissivity is as small as possible.
Further, the grating is composed of two materials of a material A and a material B, and the refractive indexes of the material A and the material B are n respectively 1 And n 2 Each width is d 1 And d 2 I.e. the grating period a ═ d 1 +d 2 H for height and L for total width; the grating transmission equation t from step S1 when the wavelength of the incident light is λ(x) Comprises the following steps:
in the formula: x is the width of the contact with the incident light,
further, the raster fraunhofer diffraction intensity distribution expression of step S2 is:
in the formula: m is the number of diffraction orders, λ is the wavelength of the incident light,
and theta is an incident light diffraction angle.
Further, when m is 0,
when m is equal to 1, the compound is,
further, when m is 0, the zero-order diffraction peak intensity is:
when m is 1, the first order diffraction peak intensity is:
by analogy, diffraction peak values of different levels with m being more than or equal to 2 can be obtained;
in step S4, the zero-order diffraction peak I satisfies the following relationship 0peak 0, the first order diffraction peak is maximum:
wherein h is the grating depth.
Further, in step S5, the diffraction peak intensity distribution is related to the grating period a according to the formula
In order to ensure the maximum intensity of the first-order diffraction peak, the grating period a needs to be close to the wavelength lambda of incident light, namely, a is approximately equal to lambda.
Further, in step S6, the duty ratio of the grating is the ratio of the width of the opaque slit to the period of the grating, the visible light transparent material a is the opaque region, the opaque material B is the transparent region, and the duty ratio is the ratio of the width of the material B to the period of the grating under the condition of the cross section with the maximum width of the material a, that is, the duty ratio
Further, in step S7, the diffraction efficiency and the wavelength band of the grating are related to the period, duty cycle, and depth of the grating, and the calculated period, duty cycle, and depth of the grating are optimized through simulation to obtain the required grating.
The invention discloses a design method of a micro-nano diffraction grating, which relates to multi-parameter optimization design, and comprises the steps of selecting a plurality of grating parameters, setting the range of each parameter, calculating the transmission spectrum of the grating under each group of parameters, evaluating according to the minimum value of the transmissivity and the central wavelength, continuously optimizing the parameters, and obtaining the grating parameters as the required design result when the minimum value of the transmissivity and the central wavelength meet the requirements.
According to the grating structure model, the specific optimized grating parameters and the selection criteria are as follows:
1. in the micro-nano diffraction grating structure, the period, the duty ratio and the depth of the grating have influence on the diffraction efficiency and the bandwidth of the grating. These three variables are included in the optimization.
2. The micro-nano diffraction grating transfers patterns by adopting an etching process, and the verticality of the side wall of a grating hole is one of the difficulties of the etching process needing to be involved, so that the influence degree of the parameter on the performance of the diffraction grating needs to be determined during the optimization design.
3. In the actual etching process, the problem of protrusion of the bottom of a grating hole is caused when the verticality of the side wall of the micro-nano grating is changed, and in order to determine the influence of the protrusion of the bottom on the grating performance, the protrusion degree of the bottom of the hole needs to be brought into simulation calculation.
By combining the analysis, the multi-parameter optimization design method adopted by the invention comprises five variables of the period, the duty ratio, the depth, the side wall verticality and the hole bottom protrusion degree of the grating. The optimization process is to improve the diffraction efficiency of the grating and adjust the diffraction center wavelength to a target waveband by adjusting five variables.
The invention has the beneficial effects that:
based on the diffraction grating design method, the broadband diffraction grating can be designed. Solving a correlation equation of a strict coupled wave theory through Fourier transform, establishing a grating transmission equation, obtaining a Fraunhofer diffraction intensity distribution expression of the grating, obtaining diffraction peak values of different diffraction levels, determining the designed diffraction order of the final grating, determining the period, duty ratio and depth of the grating according to the actual grating action wave band and the diffraction order determined by a processing and manufacturing process, and optimizing the period, duty ratio and depth of the grating through simulation. The grating action center wavelength range designed by the method comprises 380nm-960nm, and the peak wavelength of the grating action center wavelength range can be adjusted and applied to a low-light-level image intensifier, so that the photon utilization rate of the grating action center wavelength range can be obviously improved.
Drawings
Fig. 1 is a flow chart of a design method of a broadband spectroscopic micro-nano diffraction grating of the present invention.
Fig. 2 is a front view of a grating designed by the design method of the present invention.
Fig. 3 is a cross-sectional view of a grating designed by the design method of the present invention.
Fig. 4 is a grating transmission spectrum designed by the design method of the present invention.
Fig. 5 is a diffraction diagram of a grating designed by the design method of the present invention.
FIG. 6 is a comparison of the spectral response spectra of a grating microimage intensifier designed with and without the design method of the present invention.
In the figure: 1-material a, 2-material B.
Detailed Description
As shown in fig. 2, the grating front designed by the design method of the present invention has a circular hole and is distributed in a regular hexagon shape.
As shown in fig. 3, the grating profile is designed using the design method of the present invention. The grating material and the filler material have different refractive indices.
The specific design and optimization process of the invention is described in detail below with reference to the design example of the grating for the low-light image intensifier with the action waveband of 380-960 nm.
Example 1
As shown in fig. 1, according to the grating use condition or the grating preparation process condition, the value ranges of the parameters are as follows:
the substrate for the broadband diffraction grating is SiO 2 The refractive index is 1.47-1.48, the refractive index of the filling material is 2.2-2.3, and the simulated incident light band is 380-960 nm.
The grating period is based on the band of use of the sub-micron structure, i.e. 380nm to 960 nm. For convenience of calculation and subsequent processing, the period takes an integer value, so the period values for simulation are 400nm, 600nm, 800nm and 1000 nm.
The selection of the numerical value of the duty ratio of the diffraction grating needs to comprehensively consider the diffraction efficiency and the processing process conditions, the diffraction efficiency is maximum when the duty ratio is 0.5, and 0.5 can be set as the middle level value of the duty ratio. With the reduction of the duty ratio, when the grating period is increased, the characteristic size of the grating structure is continuously reduced, and 0.4 is set as the lower limit value of the duty ratio in consideration of the difficulty of the preparation process, so that the value range of the duty ratio is 0.4 to 0.7.
The depth of the grating is based on a theoretical calculation value of 410nm, and when the depth value is optimized, the depth value is an integer value, 50nm is an interval, and the final values are respectively set to 300nm, 350nm, 400nm and 450 nm.
The theoretical maximum value of the perpendicularity of the side wall is 90 degrees, and values are taken at intervals of 5 degrees, so that the final value of the perpendicularity is 75 degrees, 80 degrees, 85 degrees and 90 degrees.
The effect is best when the bottom bulge of the grating hole is 0, values are taken at intervals of 25mm, and the final values are respectively 0nm, 25nm, 50nm and 75 nm.
According to actual conditions, five factors are set in the simulation optimization of the grating parameters, and the selected four levels of the five factors are shown in table 1.
The results of the simulation are shown in table 2 according to the parameter combinations of table 1.
TABLE 1
| Duty ratio F/% | Period a/nm | Depth h/nm | Side wall perpendicularity alpha/° | Bottom hole protrusion/nm |
| 0.4 | 400 | 300 | 75 | 0 |
| 0.5 | 600 | 350 | 80 | 25 |
| 0.6 | 800 | 400 | 85 | 50 |
| 0.7 | 1000 | 450 | 90 | 75 |
TABLE 2
As can be seen from the simulation data in table 2:
with increasing duty cycle, T min Gradually increase in T min The corresponding center wavelength gradually decreases;
with increasing period, T min The diffraction efficiency of the grating is slightly influenced by the period, namely the diffraction efficiency of the grating is reduced firstly and then increased, but the range value is 0.04; with increasing period, T min The corresponding center wavelength is gradually increased;
with increasing depth, T min The difference value is 0.03, which shows that the influence of the etching depth on the diffraction efficiency of the grating is small; with increasing depth, T min The corresponding center wavelength is gradually increased;
gradually approaches 90 degrees along with the verticality of the side wall, T min The diffraction efficiency of the grating is less influenced by the period, which is shown by the fact that the difference value is 0.04; gradually approaches 90 degrees along with the verticality of the side wall, T min The corresponding central wavelength fluctuates between 610nm and 650 nm;
t increases with the bottom bulge min Between 0.81 and 0.86 waveAnd the corresponding central wavelength distribution fluctuates between 610nm and 650nm, so that the bottom bulge does not have obvious influence on the optical performance of the grating.
Parameter optimization: minimum value T of diffraction efficiency and transmittance of grating min Correspondingly, the smaller the transmission minimum, the higher the diffraction efficiency, the central wavelength of the image intensifier being 670 nm. Therefore, the parameter optimization process is as follows: adjusting five parameters of the duty ratio, the period, the depth, the side wall verticality and the bottom protrusion of the grating through simulation software, so that the grating enables the T to be close to 670nm wavelength min And minimum. Through simulation design and considering the existing processing precision, the grating parameters finally used for the image intensifier are as follows: period of 600nm, duty ratio of 0.4 and grating depth of 400nm ， . The influence of the verticality of the side wall and the bottom bulge on the diffraction performance of the grating is not large and is not considered temporarily.
FIG. 4 shows the grating transmission spectrum after the parameters are optimized, the wave trough is 560nm-770nm, the working bandwidth is 210nm, and the bandwidth is obviously expanded compared with 40nm of a common grating. Fig. 5 shows a diffraction diagram of a grating designed by the design method of the invention, and the light splitting effect is obvious. Fig. 6 shows the spectral response spectrum of the micro-optical image intensifier using the grating under the parameter, and it can be seen that the photocathode response efficiency of the micro-optical image intensifier is obviously improved after the grating is used.
By combining the detailed analysis and the example demonstration, the design method of the broadband light-splitting micro-nano diffraction grating provided by the invention can be used for rapidly designing grating parameters according to actual requirements, is simple and small in calculated amount, can be used for obtaining the broadband light-splitting diffraction grating through parameter optimization, and can be used for obviously improving the performance of a low-light image intensifier.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A method for designing a broadband light-splitting micro-nano diffraction grating is characterized by comprising the following steps:
s1, solving a correlation equation of a strict coupled wave theory through Fourier transform to obtain a transmission equation of the grating;
s2, obtaining a Fraunhofer diffraction intensity distribution expression of the grating by using a transmission equation of the grating;
s3, obtaining diffraction peaks of different diffraction orders by the intensity distribution expression of Fraunhofer diffraction;
s4, determining the target diffraction order and depth of the final grating by the diffraction peaks of different diffraction orders;
s5, determining the grating period according to the actual grating action waveband, the processing and manufacturing process and the target diffraction order;
s6, determining the duty ratio of the grating according to the grating material and the coating material;
and S7, optimizing the period, duty ratio and depth of the grating through simulation.
2. The design method according to claim 1, wherein:
the grating is composed of a material A and a material B, wherein the refractive indexes of the material A and the material B are n respectively 1 And n 2 Each width is d 1 And d 2 I.e. the grating period a ═ d 1 +d 2 H for height and L for total width; when the wavelength of the incident light is λ, the grating transmission equation t (x) of step S1 is:
in the formula: x is the width of the contact with the incident light,
3. the design method according to claim 1, wherein:
the expression of the diffraction intensity distribution of the grating fraunhofer in step S2 is:
in the formula: m is the number of diffraction orders, λ is the wavelength of the incident light,
and theta is an incident light diffraction angle.
4. The design method according to claim 3, wherein:
when m is equal to 0, the compound is,
when m is equal to 1, the compound is,
5. the design method according to claim 4, wherein:
when m is 0, the zero-order diffraction peak intensity is:
when m is 1, the first order diffraction peak intensity is:
by analogy, diffraction peaks of different levels with m being more than or equal to 2 can be obtained.
6. The design method according to claim 5, wherein:
in step S4, the zero-order diffraction peak I satisfies the following relationship 0peak 0, the first order diffraction peak is maximum:
wherein h is the grating depth.
7. The design method according to claim 4, wherein:
in step S5, the diffraction peak intensity distribution is related to the grating period a according to the formula
In order to ensure that the intensity of the first-order diffraction peak is maximum, the grating period a is close to the wavelength lambda of incident light, namely a is approximately equal to lambda.
8. The design method according to claim 2, wherein:
in step S6, the duty ratio of the grating is the ratio of the opaque slit width to the grating period, the visible light transparent material a is an opaque region, the opaque material B is a transparent region, and the duty ratio is the ratio of the material B width to the grating period under the cross-sectional condition of the maximum width of the material a, i.e., the duty ratio
9. The design method according to any one of claims 1 to 8, wherein: in step S7, the optimization criteria are: by continuously adjusting the period, duty ratio and depth of the grating, the acting central wave band of the grating is close to the target central wave band, and meanwhile, the transmissivity is as small as possible, so that the diffraction efficiency of the grating is improved.
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