A third-order dispersion compensating mirror and its design method

Abstract

A high-dispersion-capacity third-order dispersion-compensating mirror comprises, from bottom to top, a substrate, a high-reflectivity film layer, a third-order dispersion resonant layer, and a thickness modulation unit. The initial film system structure is: S / (HL)^n(Hx1L)^m1[(Hx2L)^a(HL)^b]^m2 / A. This invention provides high reflectivity through the high-reflectivity film layer, which, combined with the third-order dispersion resonant layer, achieves intracavity reflection and resonance, providing uniform dispersion compensation over a wide bandwidth. Furthermore, the design of the thickness modulation unit, while ensuring a uniform film thickness structure, introduces an embedding effect that significantly enhances the dispersion control capability and third-order dispersion compensation of the entire film system, meeting the requirements for dynamic changes and precise dispersion control during chirped pulse amplification.

Description

Technical Field

[0001] This invention pertains to ultrafast laser thin films, specifically a high-dispersion third-order dispersion compensation mirror and its design method used in pulse compression optical elements of ultrashort pulse lasers. Background Technology

[0002] In 1994, scientists Szipocs and Ferencz et al. from the Institute of Solid State Physics in Hungary first proposed using chirped mirrors for dispersion compensation in ultrafast lasers. By modulating the periodic structure of the films in a multilayer mirror, they controlled the intracavity dispersion of a solid-state femtosecond laser. In the development of ultra-intense and ultrashort laser technology, the quality of dispersion compensation directly affects the generation and stable operation of ultrafast laser pulses. Currently, for ultrafast laser systems, especially those below 10 femtoseconds, dispersive mirrors ensure the output quality of laser pulses and have become an indispensable dispersion compensation element. In 2009, Luo Zhenyue et al. proposed an initial film system design based on a hybrid structure of conjugate and GT cavities. The design was applied to CPO systems and femtosecond laser microscopy systems to provide negative group delay dispersion compensation, specifically illustrating the practicality of this initial structure with multiple conjugate cavities connected in series with GT cavities. In 2015, Chen Yu et al. proposed an initial design for a high-dispersion mirror based on a series connection of a conjugate cavity and a GT cavity. The resulting high-dispersion mirror was used in Ti:sapphire lasers and Ti:sapphire chirped amplifiers for pulse compression and broadening, and could provide the required greater dispersion compensation by utilizing multiple reflections. In 2019, Zhang Yuhui et al. proposed a broadband high-threshold combined dielectric low-dispersion mirror structure and its design method. By adjusting the film thickness, the electric field distribution within the film was controlled, thereby designing a broadband high-threshold low-dispersion mirror that meets the requirements for pulse transmission in ultrafast laser systems. In 2020, Zhang Yuhui et al. proposed a composite functional dispersion mirror structure and its design method. By replacing the high-reflectivity film layer of the standard Gires-Tournois interferometer (GTI) mirror with an antireflection structural unit, it can achieve high transmission at the pump wavelength while maintaining a certain reflectivity in the laser response band and possessing group delay dispersion compensation functionality. In 2021, Chen Ruiyi et al. proposed a design method for a broadband low-dispersion chirped mirror structure. By adding a periodic chirped layer to the low-dispersion mirror of the high-reflection film structure, the same group delay time is given to all wavelengths, achieving low dispersion effect while improving the bandwidth of the dielectric film. This is of great significance to the development of ultrafast laser technology.

[0003] Current research and applications of dispersive mirrors primarily focus on group delay dispersion (GDD) compensation, with less discussion on third-order dispersion (TOD), especially compensation for high-dispersion third-order dispersion. However, when the pulse width of an ultrashort pulse is sufficiently narrow, residual TOD can cause distortion in the pulse after broadening and recompression. The pulse is broadened and its lobes become larger, leading to a decrease in the main pulse energy.

[0004] Current traditional third-order dispersion compensation methods are primarily based on grating pairs and prism pairs. However, adjusting the spacing and angle of prism and grating pairs presents challenges in optical path adjustment and the inability to independently adjust second- and third-order dispersion, failing to meet the dynamic and nonlinear dispersion control requirements of chirped pulse amplification. While low-third-order dispersion compensation mirror pairs are currently available for commercial use, they are unsuitable for specific applications requiring substantial third-order dispersion compensation. Therefore, to address the needs of ultrafast and ultrashort laser systems, it is necessary to investigate how to balance bandwidth, dispersion, and damage threshold while providing a significant amount of negative third-order dispersion to output higher-quality ultrashort pulses.

[0005] In 2012, Niu Hailiang et al. from Zhejiang University designed and fabricated a third-order dispersion compensation device with a value of -10000 fs based on the Gires-Tournois (GT) cavity. 3 A third-order dispersion compensation mirror with a compensation bandwidth of 1030nm~1050nm, applied to a Yb-doped photonic crystal fiber femtosecond nonlinear laser amplification system, significantly reduced pulse pedestal degradation in practical systems. In 2013, Liao Chunyan, Qin Junjun, and others used thin-film optics theory to calculate the dispersion of various orders introduced by Gires-Tournois (GT) mirrors and systematically analyzed the influence of each component on the performance of Gires-Tournois (GT) mirrors. Third-order dispersion compensation mirrors based on thin-film design have shown valuable practical significance and application prospects. However, in recent years, research on the film structure of third-order dispersion compensation mirrors has been relatively limited, and research on how to obtain thin films with precise control of third-order high dispersion within the bandwidth is still insufficient. Therefore, carrying out related work is of great importance and significance. Summary of the Invention

[0006] This invention proposes a design method for a third-order dispersion compensation mirror based on the need for high dispersion compensation. The initial film system of this dispersion mirror achieves intracavity reflection and resonance through a combination of a high-reflectivity film layer and a third-order dispersion resonant layer, providing uniform dispersion compensation over a wide bandwidth. Simultaneously, combined with a thickness modulation unit design, the uniform film thickness structure and the introduced embedding effect significantly improve the dispersion control capability and third-order dispersion compensation of the entire film system. Based on the initial film system structure and optimization target values ​​of the third-order dispersion compensation mirror, a combination of local and global optimization methods is used to balance the bandwidth, reflectivity, and third-order dispersion in the initial design.

[0007] The technical solution provided by this invention is as follows:

[0008] A third-order dispersion compensation mirror based on high dispersion is characterized in that the initial film structure, from bottom to top, includes a substrate, a high-reflectivity film layer, a third-order dispersion resonant layer, and a thickness modulation unit. The thickness modulation unit includes a multi-period bandwidth modulation unit and a high-reflectivity layer. Optimization targets are designed based on the required bandwidth, reflectivity, and third-order dispersion, and the initial film structure is optimized by combining local and global optimization methods to balance the bandwidth, reflectivity, and third-order dispersion required by the initial design.

[0009] The initial film structure of the third-order dispersive mirror is: S / (HL)^n(Hx1L)^m1[(Hx2L)^a(HL)^b]^m2 / A, where S represents the substrate, H and L represent high- and low-refractive-index materials with optical thicknesses of λ / 4, respectively, and the high-reflectivity film (HL) is the high-reflectivity film layer. n A is a regular film system consisting of a quarter-wavelength film thickness, where n is the number of periods of the high-reflectivity film layer, m1 and m2 are the number of periods of the third-order dispersive resonator layer and the thickness modulation unit, respectively, x1 and x2 are the thicknesses of the resonator layer and the bandwidth modulation unit, respectively, a and b are the number of periods of the bandwidth modulation unit and the high-reflectivity layer, respectively, and A is the incident medium air.

[0010] A design method for a third-order dispersion compensating mirror, characterized by the following steps:

[0011] Step 1: Select Nb2O5, Ta2O5 or HfO2 as the high refractive index material H, and select SiO2 as the low refractive index material L;

[0012] Step 2: The high-reflectivity film layer is composed of alternating high and low refractive index materials with an optical thickness of λ / 4, and the number of periods n ranges from 8 to 14.

[0013] Step 3: Third-order dispersive resonator layer (Hx1L)^m1, the thickness of the resonator layer x1 is between 1.25 and 4, and the number of resonator layer periods m1 is between 8 and 15;

[0014] Step 4: In the thickness modulation unit [(Hx2L)^a(HL)^b]^m2, the thickness x2 of the bandwidth modulation unit is between 1.25 and 4, the number of cycles a is between 1 and 8, the number of cycles b of the high inflection layer is between 1 and 8, and the number of cycles m2 of the thickness modulation unit is between 1 and 6.

[0015] Step 5, the third-order dispersive mirror optimization method specifically includes the following steps:

[0016] Step 5.1: After initially selecting the parameters of the initial structure of the dispersive mirror, set the optimization target value according to the technical specifications. First, achieve the required third-order dispersion within the bandwidth of -5000 fs. 3 Generate a linear target value for group delay dispersion, ensuring that the group delay dispersion is close to 0 fs at the center wavelength of 920 nm. 2 At the same time, the target reflectivity and the wavelength range covered are set.

[0017] Step 5.2: Based on the optimization target value set in Step 5.1, local optimization is first performed using algorithms such as progressive optimization and pin optimization in the optical thin film design software OptiLayer. This ensures high reflectivity within the required bandwidth while achieving the required group delay dispersion in the initial design and ensuring uniform actual physical thickness of the film layer.

[0018] Step 5.3: Based on the preliminary optimization results in Step 5.2, observe the effect of the third-order dispersion curve after preliminary optimization using optical thin film design software EssentialMacleod or TFCalc. Further reduce the third-order dispersion oscillation through global optimization and balance the bandwidth, reflectivity and third-order dispersion in the initial design.

[0019] Step 6: Observe whether the results meet the required indicators. If the bandwidth or reflectivity requirements of the required low dispersion film are not met, you can select a material with a higher high-low refractive index ratio or increase the number of periods n of the high-reflection layer or the number of periods m1 of the resonant layer. Repeat step 5 for multiple optimizations until the requirements of the third-order dispersion compensation mirror are finally met, and the final third-order dispersion mirror film structure is obtained.

[0020] Compared with the prior art, the technical effects of the present invention

[0021] 1. A third-order dispersion mirror based on thin film design is used to compensate for the third-order dispersion in the system, replacing traditional methods such as adjusting the spacing and angle of prism pairs or grating pairs. This avoids the drawbacks of traditional methods, such as complex optical paths, difficult adjustment, and inability to independently adjust the second and third-order dispersion. It has the advantages of compact structure, simple operation, and higher damage threshold, and can meet the control requirements of dynamic changes and precise dispersion compensation during chirped pulse amplification.

[0022] 2. A design method for a third-order dispersion compensation mirror based on high dispersion is proposed, which improves the dispersion control capability and third-order dispersion compensation within a wide bandwidth. By combining local optimization and global optimization, the bandwidth, reflectivity and third-order dispersion in the initial design are balanced. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the structure of the third-order dispersion compensation mirror of the present invention.

[0024] Figure 2 This is a diagram of the initial film structure of the third-order dispersion compensation mirror of the present invention.

[0025] Figure 3 This is the final membrane structure of the present invention after optimization of the target value.

[0026] Figure 4 This is a graph showing the third-order dispersion and reflectance of the final film structure of this invention.

[0027] Figure 5 This is a group delay dispersion curve of the final film structure of the present invention. Detailed Implementation

[0028] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0029] Please see Figure 1 , Figure 1 The figure shows the initial structural schematic diagram of the present invention. From bottom to top, it includes a substrate 1, a high-reflectivity film layer 2, a third-order dispersive resonant layer 3, and a thickness modulation unit. The thickness modulation unit includes a bandwidth modulation unit 4 and a high-reflectivity layer 5. The high-reflectivity film layer, the third-order dispersive resonant layer, and the thickness modulation unit of the film system are composed of alternating high and low refractive index materials.

[0030] The initial structure of the third-order dispersion compensation mirror is S / (HL)^n(Hx1L)^m1[(Hx2L)^a(HL)^b]^m2 / A, where S represents the substrate, H and L represent high and low refractive index materials with an optical thickness of λ / 4, respectively, the high-reflectivity film (HL)n is a regular film system composed of a quarter-wavelength film thickness, n is the number of periods of the high-reflectivity film, m1 and m2 are the number of periods of the third-order dispersion resonant layer and the thickness modulation unit, x1 and x2 are the thicknesses of the resonant layer and the bandwidth modulation unit, a and b are the number of periods of the bandwidth modulation unit and the high-reflectivity layer, and A is the incident medium air.

[0031] The required low-dispersion film specifications are: third-order dispersion -5000 fs 3 The reflectivity is greater than 99.9% in the 895~945nm range, and the group delay dispersion is close to 0 fs at the center wavelength of 920nm. 2 .

[0032] The design steps are as follows:

[0033] 1. Based on the requirements of third-order dispersion and bandwidth, a relatively large dispersion and wide bandwidth are desired. Therefore, high-refractive-index materials such as Ta₂O₅ or Nb₂O₅ are selected, while SiO₂ is chosen as the low-refractive-index material. The refractive index parameters of the high- and low-refractive-index materials are determined by the Cauchy formula. Sure.

[0034] 2. Based on the requirements of the third-order dispersive mirror, select appropriate parameters and substitute them into the film structure expression S / (HL)^n(Hx1L)^m1[(Hx2L)^a(HL)^b]^m2 / A to obtain the film structure as follows: Figure 2 As stated above.

[0035] 3. Based on the initial design in section 2, with a reference wavelength of 920 nm, p-polarized light at an incident angle of 6 degrees is selected, and the target value for optimization, third-order dispersion (TOD), is set to -5000 fs. 3 First, local optimization is used to improve reflectivity within the required bandwidth and reduce oscillations in the second-order dispersion curve. Then, pin-based optimization further refines the film structure to ensure uniform actual physical thickness. Finally, global optimization is used to perfect the design, balancing bandwidth, reflectivity, and third-order dispersion. The optimized film structure is shown below. Figure 3 .

[0036] 4. For example Figure 4 The reflectance and third-order dispersion curves of the optimized third-order dispersive mirror film structure are shown. Figure 5 The corresponding group delay dispersion curves are shown, where the reflectivity is greater than 99.9% in the 895-945 nm range, and the third-order dispersion reaches -5000 fs in the 895-945 nm range. 3 The group delay dispersion (GDD) approaches 0 fs at the center wavelength of 920 nm. 2 ,

[0037] This invention is of great significance for the design of third-order dispersion compensation mirror pairs and will help promote the application of dispersion mirrors in ultrafast laser systems.

Claims

1. A design method for a third-order dispersion compensating mirror, characterized in that, Based on a third-order dispersion compensation mirror, the initial film structure of the third-order dispersion compensation mirror, from bottom to top, includes a substrate (1), a high-reflection film layer (2), a third-order dispersion resonator layer (3), and a thickness modulation unit. The thickness modulation unit includes a bandwidth modulation unit (4) and a high-reflection layer (5). The initial film structure is: S / (HL)^n(Hx1L)^m1[(Hx2L)^a(HL)^b]^m2 / A, where S represents the substrate (1), (HL)^n represents the high-reflection film layer (2), and Hx1L represents the third-order dispersion resonator layer (3). The resonant layer (3), (Hx2L)^a(HL)^b represents the thickness modulation unit, the high reflectivity film layer (HL)^n is a regular film system composed of a quarter wavelength film thickness, and n is the number of periods of the high reflectivity film layer; where H and L represent high and low refractive index materials with an optical thickness of λ / 4, respectively, m1 and m2 are the number of periods of the third-order dispersive resonant layer and the thickness modulation unit, respectively, x1 and x2 are the thicknesses of the third-order dispersive resonant layer and the bandwidth modulation unit, respectively, a and b are the number of periods of the bandwidth modulation unit and the high reflectivity layer, respectively, and A is the incident medium air; The design methodology includes the following steps: Step 1: Select Nb2O5, Ta2O5 or HfO2 as the high refractive index material H, and select SiO2 as the low refractive index material L; Step 2, the high reflectivity film (2) is composed of alternating high and low refractive index materials with an optical thickness of λ / 4, and the number of periods n is in the range of 8 to 14; Step 3: Third-order dispersive resonator layer (Hx1L)^m1, the thickness of the resonator layer x1 is between 1.25 and 4, and the number of resonator layer periods m1 is between 8 and 15; Step 4: In the thickness modulation unit [(Hx2L)^a(HL)^b]^m2, the thickness x2 of the bandwidth modulation unit is between 1.25 and 4, the number of cycles a is between 1 and 8, the number of cycles b of the high inflection layer is between 1 and 8, and the number of cycles m2 of the thickness modulation unit is between 1 and 6. Step 5, optimization of the third-order dispersive filter, includes the following steps: Step 5.1: After initially selecting the parameters of the initial structure of the dispersive mirror, set the optimization target value according to the technical specifications. First, achieve the required third-order dispersion within the bandwidth of -5000 fs. 3 Generate a linear target value for group delay dispersion, ensuring that the group delay dispersion is close to 0 fs at the center wavelength of 920 nm. 2 At the same time, the target reflectivity and the wavelength range it covers are set; Step 5.2: Based on the optimization target value set in Step 5.1, local optimization is first performed using the progressive optimization and needle optimization algorithms in the optical thin film design software OptiLayer. This ensures high reflectivity within the required bandwidth while achieving the required group delay dispersion in the initial design and ensuring uniform actual physical thickness of the film layer. Step 5.3: Based on the preliminary optimization results in Step 5.2, observe the effect of the third-order dispersion curve after preliminary optimization using optical thin film design software Essential Macleod or TFCalc. Further reduce the third-order dispersion oscillation through global optimization and balance the bandwidth, reflectivity and third-order dispersion in the initial design. Step 6: Observe whether the results meet the required indicators. If the bandwidth or reflectivity requirements of the required low dispersion film are not met, repeat step 5 multiple times to optimize by selecting a material with a higher high-low refractive index ratio or by increasing the number of periods n of the high-reflection layer or increasing the number of periods m1 of the resonant layer, until the requirements of the third-order dispersion compensation mirror are finally met, and the final third-order dispersion mirror film structure is obtained.

2. The design method of the third-order dispersion compensation mirror as described in claim 1, characterized in that, The target value for third-order dispersion is -5000 fs. 3 The reflectivity is greater than 99.9% within the bandwidth of 895~945nm, and the group delay dispersion is close to 0 fs at the center wavelength of 920nm. 2 .

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