A method for preparing a phase mask plate for inhibiting a fabry-perot effect
By optimizing the groove depth distribution and refractive index modulation of the phase mask, the Fabry-Perot effect is suppressed, solving the problem of difficult-to-control the flatness of the reflection spectrum of the dispersive fiber grating, and improving the output performance and stability of the femtosecond laser system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGSU AOYI TECHNOLOGY CO LTD
- Filing Date
- 2026-04-03
- Publication Date
- 2026-06-05
Smart Images
Figure CN122151346A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of ultrafast lasers, specifically relating to a method for preparing a phase mask to suppress the Fabry-Perot effect. Background Technology
[0002] High-peak-power femtosecond lasers have demonstrated irreplaceable value in fields such as ultra-precision machining, life sciences, and medicine. To obtain stable and high-quality femtosecond pulses, systems commonly employ chirped pulse amplification schemes. By broadening the pulse before amplification, nonlinear effects are significantly reduced, thereby ensuring the controllability of high-energy output. As application scenarios continue to demand higher pulse quality, the reflectance spectrum flatness of dispersive fiber gratings has gradually become one of the key factors affecting system performance, as it directly determines the broadening uniformity of different frequency components of the seed laser. However, the grating fabrication process based on improved laser writing is highly sensitive to scanning path, velocity modulation, and energy stability, making the final processing results significantly affected by process fluctuations, and making it difficult to obtain highly flat, stable, and repeatable grating quality. Summary of the Invention
[0003] Purpose of the invention: The purpose of this invention is to provide a method for preparing a phase mask to suppress the Fabry-Perot effect. By simply adjusting the groove depth distribution of the phase mask used for writing, the Fabry-Perot effect can be effectively suppressed, thereby improving the reflectance spectrum flatness of the dispersive fiber grating.
[0004] Technical solution: The present invention provides a method for preparing a phase mask template to suppress the Fabry-Perot effect, comprising:
[0005] A dispersive fiber grating model is established, and the coupled-mode equation of the dispersive fiber grating is solved using the design parameters of the dispersive fiber grating model. The solution results are simulated to obtain the reflection spectrum, transmission spectrum and group delay curve of the dispersive fiber grating.
[0006] A model of the super Gaussian apodization function was established, and the super Gaussian apodization functions of different orders were obtained.
[0007] The reflection and transmission spectra of the dispersive fiber grating are optimized based on the super-Gaussian apodization function, and the optimized reflection spectrum, transmission spectrum, and group delay curve of the dispersive fiber grating are obtained. Then, the refractive index modulation depth distribution curve of the phase mask grating region is obtained.
[0008] The refractive index modulation depth distribution curve of the phase mask grating region is optimized to improve the flatness of the reflection spectrum, resulting in an optimized refractive index modulation depth distribution curve. Based on the optimized refractive index modulation depth distribution curve, the diffraction efficiency distribution curve is calculated, and the phase mask groove depth is calculated based on the diffraction efficiency distribution curve.
[0009] Optimize the phase mask based on the slot depth of the phase mask.
[0010] Furthermore, the expression for the superGaussian apodization function model is as follows:
[0011] ;
[0012] in, Let be the full width at half maximum (FWHM) of the superGaussian apodization function; Let be the order of the superGaussian apodization function.
[0013] Furthermore, the order of the superGaussian apodization function The value of is in the range of 1 to 4, and it is used to represent the super Gaussian apodization function of different orders.
[0014] Furthermore, the expression for the refractive index modulation depth distribution curve of the phase mask grating region is as follows:
[0015] ;
[0016] in, This is the proportionality coefficient; The intensity of the incident laser beam; The diffraction efficiency is ±1 order for the phase mask template.
[0017] Furthermore, the optimization of the refractive index modulation depth distribution curve of the phase mask grating region to improve the flatness of the reflection spectrum, resulting in an optimized refractive index modulation depth distribution curve, includes:
[0018] Introducing the decapitation ratio parameter Used to characterize the actual apod length of the grating With the total length of the grating The ratio; setting the apodization distance between the left and right ends of the CFBG grating region, the CFBG reflection spectrum, transmission spectrum, and group delay curve are obtained. Based on the spectral flatness, the optimal curve for the refractive index modulation depth distribution under the optimal condition is calculated. The refractive index modulation depth function in the middle of the CFBG gate region is: Optimized curve of refractive index modulation depth distribution The expression is as follows:
[0019] .
[0020] in, This is the length of the gate area; The slope is denoted as .
[0021] Furthermore, the step of calculating the diffraction efficiency distribution curve based on the refractive index modulation depth distribution optimization curve, and calculating the phase mask slot depth based on the diffraction efficiency distribution curve, includes:
[0022] Based on the optimized refractive index modulation depth distribution curve, the diffraction efficiency distribution curve is calculated, and the expression is as follows:
[0023] ;
[0024] The depth of the phase mask slot is calculated based on the diffraction efficiency distribution curve, as follows:
[0025] The ±1st order diffraction efficiency of the phase mask template was calculated. and groove depth The ±1 order diffraction efficiency of the phase mask is controlled by designing the groove depth distribution of the phase mask, and the spectral flatness is calculated using the spectral flatness evaluation function SFM.
[0026] Furthermore, the ±1st order diffraction efficiency of the phase mask template The expression is as follows:
[0027] ;
[0028] in, The zero-order diffraction efficiency of the phase mask template; Aspect Ratio; The phase difference is caused by the depth of the slot in the phase mask.
[0029] Furthermore, the phase difference caused by the depth of the phase mask slot The expression is as follows:
[0030] ;
[0031] in, The depth of the groove; To inscribe the laser wavelength; The refractive index of the quartz substrate used as the phase mask material. The refractive index of air, The aspect ratio.
[0032] Furthermore, the spectral flatness evaluation function The calculation method is as follows:
[0033] ;
[0034] in, This represents the number of sampling points; This represents the power value of the reflected spectrum. This indicates the total number of sampling points.
[0035] Furthermore, the dispersive fiber grating model uses PM980-XP fiber as the carrier fiber.
[0036] Beneficial Effects: Compared with existing technologies, the significant technical effects of this invention are as follows: By optimizing the design of the groove depth of the phase mask used for writing, this invention overcomes the bottleneck of controlling the flatness of the reflection spectrum in traditional grating fabrication; the scheme has a simple structure and high degree of controllability, providing a new technical path for the fabrication of high-performance dispersive fiber gratings and laying the foundation for improving the output pulse quality of femtosecond laser systems. Achieving a highly flat reflection spectrum is a key objective in the design of dispersive fiber gratings. Attached Figure Description
[0037] Figure 1 This is a schematic diagram of the process of the present invention;
[0038] Figure 2 Simulation diagrams of the reflection spectrum and group delay curve of the dispersive fiber grating at a refractive index modulation depth of 0.0005 in this invention, as well as simulation diagrams of the transmission spectrum.
[0039] Figure 3 This is a schematic diagram of the superGaussian apodization function of different orders in this invention;
[0040] Figure 4 This is a schematic diagram illustrating the principle and template groove type of fiber optic grating fabrication using ultraviolet laser lithography based on a phase mask in this invention.
[0041] Figure 5 The diagram shows the distribution of CFBG reflection spectrum, transmission spectrum, group delay curve, and refractive index modulation function under different apodization distances at the left and right ends of the CFBG gate region in this invention.
[0042] Figure 6 This is a schematic diagram of the nonlinear diffraction efficiency and the phase mask groove depth distribution in this invention;
[0043] Figure 7 The transmission and reflection spectra of a dispersive fiber grating fabricated using a designed phase mask are shown. Detailed Implementation
[0044] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.
[0045] like Figure 1 As shown, a method for preparing a phase mask template to suppress the Fabry-Pérot effect according to the present invention includes the following steps:
[0046] S1. Establish a dispersive fiber grating model, solve the dispersive fiber grating coupled mode equation using the design parameters of the dispersive fiber grating model, and simulate the solution results to obtain the reflection spectrum, transmission spectrum and group delay curve of the dispersive fiber grating.
[0047] like Figure 2 As shown, Figure 2(a) Figure 2 The image shows a simulation of the reflection spectrum and group delay curve. Figure 2 Figure (b) shows the simulated transmission spectrum. The grating length of the dispersive fiber grating model is 10 cm, and the chirp rate is... The refractive index modulation depth is 0.0005. The dispersive fiber grating model uses PM980-XP fiber as the carrier fiber. The parameters of PM980-XP fiber are: core diameter 6 μm, cladding diameter 125 μm, and core NA 0.12. Based on the above design parameters, the coupled-mode equations of the dispersive fiber grating are numerically solved, and the CFBG reflection spectrum, transmission spectrum, and group delay curve are obtained through simulation. The effect of the abrupt change in refractive index at both ends of the grating can be observed. The effect causes jitter in the reflection spectrum over the bandwidth, with an oscillation amplitude of approximately 0.5 dB and a side-mode suppression ratio of less than 20 dB. This leads to increased oscillation in the group delay curve, system dispersion mismatch, and ultimately degrades the output pulse quality, severely impacting its practical application in femtosecond lasers.
[0048] It should be noted that the reflection spectrum reflects the effect caused by the abrupt change in refractive index at both ends of the grating. The effect causes fluctuations in the reflection spectrum over the bandwidth. The transmission spectrum is used to represent reflectivity, while the group delay curve is used to supplement this representation. It has an inhibitory effect.
[0049] S2. Establish the super Gaussian apodization function model and obtain the super Gaussian apodization function at different orders.
[0050] like Figure 3 As shown, the expression for the superGaussian apodization function model is as follows:
[0051] ;
[0052] in, It is a superGaussian apodization function; The full width at half maximum (FWHM) of the super-Gaussian apodization function, i.e., the refractive index modulation amplitude exceeding... Partial gate length; Let be the order of the superGaussian apodization function; This represents the gate length.
[0053] The order of the superGaussian apodization function The value of is in the range of 1 to 4, used to represent the superGaussian apodization function at different orders. In this embodiment, when Initially a typical Gaussian function, the function gradually becomes more "square" beyond 1, with full width at half maximum (FWHM) and full height at half maximum (FWHM). Taking 3 / 5 of the grating length, i.e., the full width at half maximum (FWHM) of the super-Gaussian apodization function is 6 cm, the order is... By taking values from 1 to 4, we obtain superGaussian apodization functions of different orders. Using the apodization function reduces the usable bandwidth. Designed to be 8cm, number of steps To ensure that spectral flatness is improved.
[0054] S3. Based on the super-Gaussian apodization function obtained in step S2, the reflection and transmission spectra of the dispersive fiber grating obtained in step S1 are optimized to obtain the optimized reflection spectrum, transmission spectrum, and group delay curve of the dispersive fiber grating, and then the refractive index modulation depth distribution curve of the phase mask grating region is obtained. Specifically, as follows:
[0055] like Figure 4 As shown, the expression for the refractive index modulation depth distribution curve of the phase mask grating region is as follows:
[0056] ;
[0057] in, This is the proportionality coefficient; The intensity of the incident laser beam; Let be the ±1st order diffraction efficiency of the phase mask. The ±1st order and zeroth order diffraction efficiencies of the phase mask can be expressed as:
[0058] ;
[0059] During CFBG writing, when the ultraviolet laser emitted by the ultraviolet laser is incident directly on the surface of the phase mask, the phase difference caused by the depth of the phase mask groove... Defined as:
[0060] ;
[0061] in, The depth of the groove; To inscribe the laser wavelength; The refractive index of the quartz substrate used as a phase mask material; The refractive index of air; For aspect ratio, , The width of the slotted boss in the phase mask template. The period of the phase mask.
[0062] In practical applications, it is typically required that the energy of the zero-order diffracted beam be suppressed to less than 5% of the incident beam energy, and the energies of the ±1st order diffracted beams be adjusted to 40% of the incident light energy, respectively. To improve the flatness of the CFBG reflection spectrum, the diffraction efficiency of the phase mask grating region, the groove depth, and the CFBG refractive index modulation depth need to be redesigned.
[0063] S4. Optimize the refractive index modulation depth distribution curve of the phase mask grating region to improve the flatness of the reflection spectrum and obtain the optimized refractive index modulation depth distribution curve; calculate the diffraction efficiency distribution curve based on the optimized refractive index modulation depth distribution curve, and calculate the phase mask groove depth based on the diffraction efficiency distribution curve.
[0064] The specific implementation process of step S4 is as follows:
[0065] S4.1 Optimize the refractive index modulation depth distribution curve of the phase mask grating region to improve the flatness of the reflection spectrum, resulting in an optimized refractive index modulation depth distribution curve, including:
[0066] like Figure 5 As shown, Figure 5 Figure (a) shows the CFBG reflection spectrum, transmission spectrum, group time delay curve, and refractive index modulation function distribution when the apodization distance between the left and right ends of the CFBG gate region is 1 cm. Figure 5 Figure (b) shows the CFBG reflection spectrum, transmission spectrum, group delay curve, and refractive index modulation function distribution when the apodization distance between the left and right ends of the CFBG grating is 1.5 cm. Figure 5 Figure (c) shows the distribution of CFBG reflection spectrum, transmission spectrum, group time delay curve, and refractive index modulation function when the apodization distance between the left and right ends of the CFBG grating is 2 cm.
[0067] Introduce the decapitation ratio parameter, i.e. Used to characterize the actual apod length of the grating With the total length of the grating The ratio; with the apodization distances at the left and right ends of the CFBG grating region being 1cm, 1.5cm, and 2cm respectively, the CFBG reflection spectrum, transmission spectrum, and group delay curve were obtained. Based on the spectral flatness, the optimal curve for the refractive index modulation depth distribution under the optimal condition was calculated. The refractive index modulation depth function in the middle of the CFBG gate region is: Optimized curve of refractive index modulation depth distribution The expression is as follows:
[0068] .
[0069] in, This is the length of the gate area; The slope;
[0070] It can be seen that the actual apod length of the grating It is 4cm, that is At a ratio of 2 / 5, the CFBG side-mode suppression ratio is optimal, exceeding 45 dB, and the spectral flatness and group delay curve are most significantly improved over the bandwidth: [Compared to...] Figure 1Compared to CFBG, the oscillations in the reflection spectrum are eliminated and the oscillation amplitude of the group delay curve is significantly reduced.
[0071] S4.2, such as Figure 6 As shown, the optimized curve based on the refractive index modulation depth distribution is... The diffraction efficiency distribution curve is calculated, and the phase mask slot depth is calculated based on the diffraction efficiency distribution curve, including:
[0072] Based on the optimized refractive index modulation depth distribution curve, the diffraction efficiency distribution curve is calculated, and the expression is as follows: ;
[0073] The depth of the phase mask slot is calculated based on the diffraction efficiency distribution curve, as follows:
[0074] The ±1st order diffraction efficiency of the phase mask template was calculated. and groove depth The details are as follows:
[0075] In this embodiment, the ±1st order diffraction efficiency of the phase mask is... The expression is as follows:
[0076] ;
[0077] in, The zero-order diffraction efficiency of the phase mask template; Aspect Ratio; The phase difference is caused by the depth of the slot in the phase mask.
[0078] Phase difference caused by the depth of the phase mask slot The expression is as follows:
[0079] ;
[0080] in, The depth of the groove; To inscribe the laser wavelength; The refractive index of the quartz substrate used as the phase mask material. The refractive index of air, For aspect ratio, .
[0081] By designing the groove depth distribution of the phase mask and thus controlling the ±1st order diffraction efficiency, an effective means is provided for fabricating fiber gratings with highly flat reflection spectra. A spectral flatness evaluation function is then used. The spectral flatness is calculated as follows:
[0082] The spectral flatness of the evaluation function is calculated as follows:
[0083] ;
[0084] in, This represents the number of sampling points; This represents the power value of the reflected spectrum. This represents the total number of sampling points. Based on the formula, the spectral flatness (SFM) of the optimized dispersive fiber grating's reflection spectrum within a 3dB bandwidth is calculated. In this embodiment, the spectral flatness (SFM) of the dispersive fiber grating's reflection spectrum within a 3dB bandwidth is calculated. Figure 3 The CFBG reflectance spectrum flatness (SFM) was as low as 0.843. By applying this method to improve the reflectance spectrum flatness, the final reflectance spectrum flatness reached 0.991, achieving the ideal flat-top spectrum level.
[0085] S5. Obtain the phase mask template based on the slot depth of the phase mask template.
[0086] Based on the obtained phase mask slot depth d, a nonlinear diffraction efficiency phase mask is designed and prepared. The prepared novel phase mask is used to prepare a dispersive fiber grating to ensure a highly flat reflection spectrum and good compatibility with femtosecond laser systems.
[0087] like Figure 7 As shown, a dispersive fiber grating (FWHM) was etched onto PM980-XP fiber using a phase mask based on super-Gaussian apodization and suppression of the Fabry-Perot effect via ultraviolet laser lithography. It can be concluded that the transmission spectrum of the grating is tilted upwards from short wavelengths to long wavelengths, improving the flatness of the reflection spectrum; the calculated reflection spectrum flatness (SFM) is 0.972. The center wavelength is 1030.28 nm, FWHM = 24.67 nm, the long wavelength portion of the transmission spectrum is greater than 6 dB, the grating reflectivity is ≥75%, and the side-mode suppression ratio is greater than 30 dB. The etched effect is basically consistent with the design simulation.
[0088] The present invention proposes a symmetric super-Gaussian apodization method to address the degradation of reflection spectrum flatness caused by the Fabry-Pérot effect resulting from abrupt changes in refractive index at both ends of a dispersive fiber grating (CFBG). This symmetric super-Gaussian apodization method employs a partial apodization scheme, using a super-Gaussian apodization function to modulate the left and right ends of the grating region to improve spectral oscillations, enhance spectral flatness, and increase the side-mode suppression ratio. This yields an optimized grating region refractive index modulation depth distribution curve, which guides the design parameters of the phase mask's nonlinear diffraction efficiency and groove depth distribution. Ultimately, this results in a symmetric super-Gaussian apodization method for preparing a phase mask that suppresses the Fabry-Pérot effect.
[0089] This invention improves spectral oscillations by designing the nonlinear diffraction efficiency and groove depth distribution of the phase mask to achieve super-Gaussian apodization function modulation in the grating region. This method requires no changes to the fiber grating writing apparatus or fabrication process, resulting in a simple process, and the fabricated grating exhibits good stability, consistency, and reusability. It provides an effective means for fabricating dispersive fiber gratings with highly flat reflection spectra. Compared with existing technologies, the method proposed in this invention has advantages such as low cost, high flexibility, and high stability.
[0090] In summary, this invention can provide new solutions and references for the design and fabrication of hyperspectral flat high-performance dispersive fiber gratings, ultimately contributing to the overall performance improvement of femtosecond lasers.
Claims
1. A method for preparing a phase mask to suppress the Fabry-Perot effect, characterized in that, include: A dispersive fiber grating model is established, and the coupled-mode equation of the dispersive fiber grating is solved using the design parameters of the dispersive fiber grating model. The solution results are simulated to obtain the reflection spectrum, transmission spectrum and group delay curve of the dispersive fiber grating. A super-Gaussian apodization function model was established to obtain super-Gaussian apodization functions of different orders; the super-Gaussian apodization function model was used to suppress the Brie-Perot effect. The reflection and transmission spectra of the dispersive fiber grating are optimized based on the super-Gaussian apodization function, and the optimized reflection spectrum, transmission spectrum, and group delay curve of the dispersive fiber grating are obtained. Then, the refractive index modulation depth distribution curve of the phase mask grating region is obtained. The refractive index modulation depth distribution curve of the phase mask grating region is optimized to improve the flatness of the reflection spectrum, resulting in an optimized refractive index modulation depth distribution curve. Based on the optimized refractive index modulation depth distribution curve, the diffraction efficiency distribution curve is calculated, and the phase mask groove depth is calculated based on the diffraction efficiency distribution curve. Optimize the phase mask based on the slot depth of the phase mask.
2. The method for preparing a phase mask to suppress the Fabry-Perot effect according to claim 1, characterized in that, The expression for the super-Gaussian apodization function model is as follows: ； in, Let be the full width at half maximum (FWHM) of the superGaussian apodization function; Let be the order of the superGaussian apodization function.
3. The method for preparing a phase mask template to suppress the Fabry-Perot effect according to claim 2, characterized in that, The order of the superGaussian apodization function The value of is in the range of 1 to 4, and it is used to represent the super Gaussian apodization function of different orders.
4. The method for preparing a phase mask to suppress the Fabry-Perot effect according to claim 1, characterized in that, The expression for the refractive index modulation depth distribution curve of the phase mask grating region is as follows: ； in, This is the proportionality coefficient; The intensity of the incident laser beam; The diffraction efficiency is ±1 order for the phase mask template.
5. The method for preparing a phase mask for suppressing the Fabry-Perot effect according to claim 1, characterized in that, The optimization of the refractive index modulation depth distribution curve of the phase mask grating region to improve the flatness of the reflection spectrum, resulting in an optimized refractive index modulation depth distribution curve, includes: Introducing the decapitation ratio parameter Used to characterize the actual apod length of the grating With the total length of the grating The ratio; setting the apodization distance between the left and right ends of the CFBG grating region, the CFBG reflection spectrum, transmission spectrum, and group delay curve are obtained. Based on the spectral flatness, the optimal curve for the refractive index modulation depth distribution under optimal conditions is calculated. The refractive index modulation depth function in the middle of the CFBG gate region is: Optimized curve of refractive index modulation depth distribution The expression is as follows: ； in, This represents the gate length; The slope is denoted as .
6. The method for preparing a phase mask template to suppress the Fabry-Perot effect according to claim 1, characterized in that, The process of calculating the diffraction efficiency distribution curve based on the refractive index modulation depth distribution optimization curve, and then calculating the phase mask slot depth based on the diffraction efficiency distribution curve, includes: Based on the optimized refractive index modulation depth distribution curve, the diffraction efficiency distribution curve is calculated, and the expression is as follows: ； The depth of the phase mask slot is calculated based on the diffraction efficiency distribution curve, as follows: The ±1st order diffraction efficiency of the phase mask template was calculated. and groove depth The ±1 order diffraction efficiency of the phase mask is controlled by designing the groove depth distribution of the phase mask, and the spectral flatness is calculated using the spectral flatness evaluation function SFM.
7. The method for preparing a phase mask template to suppress the Fabry-Perot effect according to claim 6, characterized in that, The phase mask has ±1st order diffraction efficiency The expression is as follows: ； in, The zero-order diffraction efficiency of the phase mask template; Aspect Ratio; The phase difference is caused by the depth of the slot in the phase mask.
8. The method for preparing a phase mask template to suppress the Fabry-Perot effect according to claim 7, characterized in that, The phase difference caused by the groove depth of the phase mask The expression is as follows: ； in, The depth of the groove; To inscribe the laser wavelength; The refractive index of the quartz substrate used as the phase mask material. The refractive index of air, The aspect ratio.
9. The method for preparing a phase mask template to suppress the Fabry-Perot effect according to claim 6, characterized in that, The spectral flatness evaluation function The calculation method is as follows: ； in, This represents the number of sampling points; This represents the power value of the reflected spectrum. This indicates the total number of sampling points.
10. The method for preparing a phase mask for suppressing the Fabry-Perot effect according to claim 1, characterized in that, The dispersive fiber grating model uses PM980-XP fiber as the carrier fiber.