CN112666641B - Design method of broadband low-dispersion chirped mirror - Google Patents

Abstract

A design method of a broadband low-dispersion chirped mirror structure, the initial film structure is:

where S represents the substrate, H and L represent high and low refractive index materials with an optical thickness of λ/4, respectively,

is the bottom high-reflection film layer, m ₁ is the period number of the high-reflection film layer,

is the symmetrical periodic chirp layer, an _n is the chirp layer coefficient, m ₂ is the period number of the periodic chirp layer, and A is air. In the present invention, a periodic chirped layer is added to the low-dispersion mirror of the high-reflection film layer structure, so that different wavelengths are reflected at the same time after passing through the same optical thickness in the film layer, that is, by giving all wavelengths the same group delay time (group delay time) , GD), and make the group delay dispersion (group delay dispersion, GDD) zero, and also achieve the effect of low dispersion. By adjusting the parameters m ₁ , an and _{m 2} , the group delay time and reflectivity in different bandwidths can be regulated. The broadband low-dispersion chirped mirror effectively improves the low-dispersion bandwidth of the dielectric film, which is of the most important significance for the development of ultrafast laser technology.

Description

Design Method of Broadband Low Dispersion Chirped Mirror

technical field

The invention belongs to an ultrafast laser thin film, in particular to a design method of a broadband low dispersion chirped mirror.

Background technique

With the development of ultra-intense and ultra-short laser technology, laser pulses have been compressed to several femtoseconds, and the peak power can reach the petawatt level. Low-dispersion mirrors are one of the most commonly used optical components in ultra-short pulse laser systems. Short laser technology places new demands on optical thin films: wider operating bandwidth and effective dispersion control. By providing zero group delay dispersion (Group delay dispersion) within the reflection bandwidth, the low-dispersion mirror ensures that after the ultra-short pulse is reflected by the low-dispersion mirror, only the transmission direction changes without additional dispersion. However, because the reflection bandwidth, dispersion and damage threshold of low-dispersion mirrors influence and restrict each other, designing and fabricating low-dispersion mirrors with wider reflection bandwidth and higher damage threshold is a research focus of high-power ultrashort pulse lasers. Conventional high-reflection mirrors are made of stacks of high- and low-refractive-index materials with an optical thickness of a quarter wavelength, and their high-reflection and low-dispersion bandwidths are positively correlated with the ratio of high and low refractive indices. For example, the reflection bandwidth of the structured dielectric film composed of HfO ₂ /SiO ₂ is about 90 nm, while the reflection bandwidth of the structured dielectric film composed of TiO ₂ /SiO ₂ is about 150 nm.

With the development of ultra-intense and ultra-short lasers to higher energy and pulse width pulses, the spectrum of laser pulses exceeds 200 nm, and traditional low-dispersion mirrors with regular film systems can no longer meet the needs. Therefore, increasing the high-reflection and low-dispersion bandwidth of low-dispersion mirrors is crucial for the development of ultra-intense ultrashort lasers. The traditional quarter-wavelength thickness regular low-dispersion mirror reflects all wavelengths at the surface simultaneously to achieve low dispersion, and the low dispersion bandwidth is limited by the ratio of the refractive indices of high and low refractive index materials.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is to propose a low-dispersion mirror initial structure and design method based on a periodic chirped structure. A periodic chirped layer is added to a film with a thickness of one wavelength. By giving all wavelengths the same group delay time, the effect of low dispersion can also be achieved. Using the initial structure of the low-dispersion mirror with a high-reflection layer at the bottom and a periodically chirped layer at the top, and selecting appropriate parameters, the desired low-dispersion mirror can be obtained after optimization by the film system design software.

The technical scheme solved by the present invention is as follows:

其中，S表示基底，H和L分别代表光学厚度为λ/4的高折射率材料、低折射率材料，

为底部高反射膜层，m₁为底部高反射膜层的周期数，

为对称的周期啁啾层，a_n为单调递增或递减的数组的系数，m₂为周期啁啾层周期数，A代表空气；A method for designing a broadband low-dispersion chirped mirror, which is characterized by an initial structure of a low-dispersion mirror based on a periodic chirped layer, and the initial film structure is:

Among them, S represents the substrate, H and L represent the high-refractive index material and the low-refractive index material with an optical thickness of λ/4, respectively,

is the bottom high-reflection film layer, m ₁ is the period number of the bottom high-reflection film layer,

is a symmetrical periodic chirp layer, an is the coefficient of the monotonically increasing or decreasing array, _{m 2} is the period number of the periodic chirp layer, and A represents air;

By giving all wavelengths the same group delay time, the structure enables each wavelength to propagate through the same optical path in the film and then reflect at the same time, thereby achieving a wider bandwidth and low dispersion effect. After selecting appropriate parameters and optimizing, the final structure of the desired low dispersion mirror can be obtained.

The above-mentioned initial structure and design method of the low dispersion mirror are characterized in that the method comprises the following steps:

1) According to the group delay time, reflectivity, polarization, incident angle and bandwidth of the dispersive mirror to be prepared, select appropriate high-refractive index materials and low-refractive index materials. Commonly used high-refractive index materials include Nb ₂ O ₅ , Ta ₂ O ₅ , HfO ₂ , etc., the low refractive index material is SiO ₂ , the refractive index n _H of the high refractive index material and the refractive index n _L of the low refractive index material are obtained by inversion in the actual coating experiment;

2) The initial structure of the low dispersion mirror based on the periodic chirp layer:

为底部高反射膜层，m₁为高反射膜层的周期数，

为对称的周期啁啾层，a_n为单调递增或递减的数组，m₂为周期啁啾层周期数，A代表空气。选择合适的参数：高反射膜层的周期数m₁一般选择在10-30，周期啁啾层啁啾系数a_n的选择范围为0.5-1.5，周期数m₂的选择范围为1-20，m₁和m₂均为正整数；where S represents the substrate, H and L represent high and low refractive index materials with an optical thickness of λ/4, respectively,

is the bottom high-reflection film layer, m ₁ is the period number of the high-reflection film layer,

is a symmetrical periodic chirp layer, an _is an array of monotonically increasing or decreasing values, m ₂ is the period number of the periodic chirp layer, and A represents air. Select appropriate parameters: the period number m ₁ of the high-reflection film layer is generally selected in the range of 10-30, the selection range of the chirp coefficient an of the period chirped layer is 0.5-1.5, the selection range of the period number _{m 2} is 1-20, m ₁ and m ₂ are both positive integers;

3) Determine the basic parameters of the low dispersion mirror, including reflectivity, polarization state, incident angle, working bandwidth, target group delay time, and high and low refractive index materials used, and determine the parameters of the initial structure of the low dispersion mirror, including _{m 1} , an and The value of m ₂ , after that, use the film system design software (TFCalc, Essential Macleod and Optilayer, etc.) and the corresponding algorithm (variablemetric, gradientevolution, needleoptimization, etc.) and the corresponding algorithm to optimize the film system to obtain the final required results;

4) Observe whether the final result meets the index requirements of the low dispersion mirror. If the group delay time requirement of the required low dispersion mirror cannot be met, the initial structural parameters of the low dispersion mirror are modified by adjusting the period number m ₂ of the periodic chirped layer cavity, and steps 2 and 3 are repeated for multiple optimizations until the final low dispersion mirror is satisfied. Dispersive mirror requirements; if the reflectivity requirements of the required low-dispersion mirrors cannot be met, by increasing the period m ₁ of the high-reflection coating layer, repeat steps 2 and 3 for multiple optimizations until the requirements of the low-dispersion mirrors are finally met; To meet the bandwidth requirement of the low dispersion mirror, by adjusting the coefficient an of the periodic _chirped layer cavity, repeat steps 2 and 3 until the requirements of the low dispersion mirror are finally met.

Compared with the prior art, the technical effect of the present invention

1. An initial design of a low dispersion mirror is proposed. The periodic chirped layer is added to the regular quarter-wavelength film thickness, and the effect of low dispersion is achieved by giving all wavelengths the same group delay time. The design utilizes the characteristics of the wide reflection bandwidth of the chirped layer to realize an ultra-wide bandwidth low dispersion mirror.

2. Based on this initial design, the dispersion curve can be further optimized under the premise of ensuring broadband low dispersion, so that dispersion compensation is better.

Description of drawings

FIG. 1 is a structural diagram of the initial film system of the first embodiment of the broadband low dispersion chirped mirror of the present invention.

FIG. 2 is the final film structure of the first embodiment of the broadband low dispersion chirped mirror of the present invention.

FIG. 3 is a graph showing the group delay time and reflectivity of the first embodiment of the broadband low dispersion chirped mirror of the present invention.

FIG. 4 is a group delay dispersion curve diagram of the first embodiment of the broadband low dispersion chirped mirror of the present invention.

FIG. 5 is a structural diagram of the initial film system of the second embodiment of the broadband low-dispersion chirped mirror of the present invention.

FIG. 6 is the final film structure of the second embodiment of the broadband low-dispersion chirped mirror of the present invention.

FIG. 7 is a graph showing the group delay time and reflectivity of the second embodiment of the broadband low-dispersion chirped mirror of the present invention.

FIG. 8 is a group delay dispersion curve diagram of the second embodiment of the broadband low dispersion chirped mirror of the present invention.

Detailed ways

The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the protection scope of the present invention should not be limited by this.

Please refer to FIG. 1. FIG. 1 is a schematic diagram of the structure of the low dispersion mirror based on the periodic chirped structure of the present invention. As shown in the figure, it is composed of a periodic chirped layer and a high reflection film layer, and the periodic chirped layer is regular at a quarter wavelength. The top of the high-reflection layer of the film system. The high-reflection film layer and the periodic chirped layer are alternately composed of high and low refractive index materials.

Example 1

The indicators of the low dispersion mirror in this embodiment are: group delay time 120fs, group delay dispersion 0fs ² , reflectivity>98.5%, P-polarized light, incident angle of 45 degrees, corresponding bandwidth of 200nm, and center wavelength of 800nm.

The design steps are as follows:

确定，如表1所示。1. According to the group delay time, group delay dispersion and bandwidth requirements, the group delay time is longer and the bandwidth is wider, so the high refractive index material Ta ₂ O ₅ with higher refractive index is selected, and the low refractive index material is SiO ₂ , with high and low refractive index. The refractive index parameter of the rate material is given by the Cauchy formula

OK, as shown in Table 1.

A₀ A₁ A₂ SiO₂ 1.44293 1.1622618e-2 -3.705533e-4 Ta₂O₅ 2.01486 3.01116301e-2 -7.635062e-4

Table 1

2. According to the target group delay time of the low dispersion mirror, the group delay dispersion value and the reflectivity requirements, select the appropriate parameters: m ₁ =20, m ₂ =11, a _{n is} the first item a is 0.75, the tolerance is 0.05, the number of items is n is an arithmetic sequence of 4, and the expression of the low-dispersion mirror based on the periodic chirped structure is: S/(HL) ²⁰ [(0.75H0.80L0.85H0.9L)(0.9H0.85L0.8H0.75L)] ¹¹ /A, where S is a fused silica substrate, H and L represent Ta ₂ O ₅ and SiO ₂ materials with an optical thickness of λ/4, respectively, and A represents air. The membrane structure is shown in Figure 1.

3. Based on the initial design of S/(HL) ²⁰ [(0.75H0.80L0.85H0.9L)(0.9H0.85L0.8H0.75L)] ¹¹ /A, the reference wavelength is 865nm, and the incident angle is selected at 45 degrees For the P-polarized light, set the optimal target value: the group delay time is 120fs, and the target group delay dispersion is 0fs ² . The film system design software TFCalc is used to optimize, and the final film system structure is shown in Figure 2.

4. Figure 3 shows the reflectivity and group delay time curve of the low dispersion mirror that meets the requirements, and Figure 4 is the group delay dispersion curve of the low dispersion mirror that meets the requirements. 925nm is 120fs, and the group retardation dispersion is 0±25fs ² at 725-925nm, and the film structure that finally meets the requirements of low-dispersion mirrors is obtained.

Embodiment 2

The indicators of the low dispersion mirror in this embodiment are: group delay time 140fs, group delay dispersion 0fs ² , reflectivity>99.5%, P-polarized light, incident angle of 45 degrees, corresponding bandwidth of 240nm, and center wavelength of 850nm.

The design steps are as follows:

确定，如表2所示。1. According to the group delay time, group delay dispersion and bandwidth requirements, the group delay time is longer and the bandwidth is wider, so the high refractive index material Nb ₂ O ₅ with higher refractive index is selected, and the low refractive index material is SiO ₂ , with high and low refractive index. The refractive index parameter of the rate material is given by the Cauchy formula

OK, as shown in Table 2.

A₀ A₁ A₂ SiO₂ 1.44293 1.1622618e-2 -3.705533e-4 Nb₂O₅ 2.15786 3.61226445e-2 2.024012e-3

Table 2

2. According to the target group delay time of the low dispersion mirror, the group delay dispersion value and the reflectivity requirements, select the appropriate parameters: m ₁ =15, m ₂ =16, a _{n is} the first item a is 0.8, the tolerance is 0.05, the number of items is n is an arithmetic sequence of 3, and the expression of the low-dispersion mirror based on the periodic chirped structure is: S/(HL) ¹⁵ [(0.80H0.85L0.9H)(0.9L0.85H0.8L)] ¹⁶ /A, Among them, S is a fused silica substrate, H and L represent _Nb2O5 and _SiO2 materials with an optical thickness of λ/ ₄ , respectively, and A represents air. The membrane structure is shown in Figure 1.

3. Based on the initial design of S/(HL) ¹⁵ [(0.80H0.85L0.9H)(0.9L0.85H0.8L)] ¹⁶ /A, the reference wavelength is 900nm, and the P-polarized light at an incident angle of 45 degrees is selected , set the optimization target value: the group delay time is 140fs, and the target group delay dispersion is 0fs ² . The film system design software TFCalc is used to optimize, and the final film system structure is shown in Figure 2.

4. Figure 3 is the reflectivity and group delay time curve of the low dispersion mirror that meets the requirements, and Figure 4 is the group delay dispersion curve of the low dispersion mirror that meets the requirements. 970nm is 140fs, and the group retardation dispersion is 0fs ² at 730-970nm, and a film structure that finally meets the requirements of low dispersion mirrors is obtained.

The invention has important significance for the design of the low dispersion mirror, and helps to promote the application of the low dispersion mirror in the ultrafast laser system.

Claims (3)

1. A method of designing a broadband low dispersion chirped mirror, the method comprising the steps of:

1) the method is characterized in that a periodic chirp layer is added on a high-reflection layer, and an initial film system structure is designed as follows:

wherein S represents a substrate, H and L represent high and low refractive index materials having an optical thickness of lambda/4, respectively,

is a bottom highly reflective film layer, m₁Is the number of cycles of the high reflection film layer,

is a symmetrical periodically chirped layer, a_nFor monotonically increasing or decreasing arrays, m₂Selecting proper number m of periods of high reflection film layer for different designed bandwidth, dispersion amount and reflectivity₁Chirp coefficient of periodic chirp layer a_nAnd the number m of repetition periods₂；

2) Selecting a substrate layer material, a high refractive index material, a low refractive index material and the number m of cycles of a reflectivity film layer according to the requirements of group delay time, reflectivity, polarization, incidence angle and bandwidth of the designed broadband low-dispersion mirror₁Periodic chirp layer chirp coefficient a_nAnd the number m of cycles₂；

3) Optimizing the film system by using film system design software on the basis of the initial structure, and observing whether the result meets the indexes required by the low-dispersion mirror:

if the group delay time of the needed low dispersion mirror can not be reached, the period number m of the period chirp layer is adjusted₂Then, returning to the step 2) for further optimization, and entering the step 4) if the index requirement required by the low-dispersion mirror is met;

if the bandwidth of the low dispersion mirror can not be achieved, the chirp coefficient a of the period chirp layer is adjusted_nThen, returning to the step 2) for further optimization, and entering the step 4) if the index requirement required by the low-dispersion mirror is met;

thirdly, if the reflectivity requirement of the low dispersion mirror can not be met, the number m of cycles of the high-reflectivity film layer is increased₁Returning to the step 2) for further optimization, and entering the step 4) if the index requirement required by the low-dispersion mirror is met;

4) and finishing the design of the broadband low-dispersion mirror meeting the required indexes.

2. The method of designing a broadband low-dispersion chirped mirror according to claim 1, characterized in that: the material of the substrate layer is quartz glass or CaF₂(ii) a The high refractive index material comprises TiO₂、Nb₂O₅、Ta₂O₅、HfO₂、ZrO₂Fluoride, sulfide or Si; the low refractive index material is SiO₂、Al₂O₃Or MgF₂。

3. The method of designing a broadband low-dispersion chirped mirror according to any one of claims 1 to 2, wherein the number m of periods of the high reflectivity film layer is₁Is selected from the range of 10-30, and the chirp coefficient a of the periodic chirp layer_nIs selected in the range of 0.5-1.5, number of cycles m₂Is selected in the range of 1-20.

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