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Abstract
Volume Bragg grating is one-step fabricated with femtosecond laser direct-writing technology inside a high nonlinearity chalcogenide glass of As2S3. As the generated femtosecond laser filamentation effect could combined with the cylindrical lens focusing method, a two-dimensional refractive index change interface could spontaneously grow along the incident direction with either the laser pulse energy or number increasing. A number of two-dimensional refractive index change interfaces are periodically arranged to stack into a volume Bragg grating. Through periodically moving the sample stage, a grating of 2 mm × 2 mm × 1.7 mm can be fabricated in 15 minutes. And the maximum diffraction efficiency of grating reached 95.49% under the optimal parameters. This study provides a new processing strategy for femtosecond laser direct-writing volume Bragg grating with high processing efficiency and excellent structural performance.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Femtosecond (fs) lasers, characterized by extremely short pulse durations and high peak powers, show a series of unique advantages in micromachining in many materials [1,2]. These unique advantages, including rapid energy transfer, three-dimensional (3D) energy deposition, small heat affected area and strong nonlinear effect, enable fs laser to induce many novel microstructures [3,4], such as bionic structure [5], microfluidic channels [6], photonics devices [7] and high-density data storage [8]. Therefore, fs laser processing has become more and more popular in functionalized microstructure manufacturing over the past few decades.
Volume Bragg grating (VBG) is a special type of phase grating in transparent materials. Compared with other diffraction gratings, the VBG has a 3D structure with high thickness, which can increase the diffraction efficiency up to 100% [9]. VBG have been widely used in many fields, such as laser pulse stretching and compression [10], laser wavelength selection [11], and optical modulation/detector [12]. Generally, most of VBG are formed by permanently adjusting the refractive index of the Photo-thermo-refractive glass through the photo-thermo-induced effects [13], but this method is insufficient for the efficiency and convenience of manufacturing. Using fs laser to fabricating VBG can solve these shortcomings well and has become a rapidly maturing manufacturing process [14–16]. When a fs laser propagates inside the material, the laser filamentation caused by the Kerr effect will extend the laser focus. By reasonably optimizing the laser parameters, a VBG with high thickness and high diffraction efficiency can be fabricated, and the processing efficiency can be greatly improved [17].
Some groups tried to develop fs laser filamentation technology to fabricate VBG inside transparent materials. In 2009, Cheng et al. [18] used a cylindrical lens to focus a low-power fs laser to process Foturan glass, and then combined with subsequent heat treatment to fabricate a large volume grating, which owns high diffraction efficiency. This is recognized to be the earliest work to process VBG by using cylindrical lens focusing combined with fs laser filamentation effect. In 2019, Azkona et al. [19] fabricated VBG inside CdSxSe1−x doped borosilicate glass by fs laser, and measured the maximum diffraction efficiency 67%. Next, Zhang et al. [20] fabricated VBG in a highly nonlinear Ge-As-S chalcogenide glass by harnessing the filamentation effect, thus high thickness VBG was rapidly fabricated by one-step fs laser scanning. Recently, Stankevic et al. [21] used the deep focusing fs laser to induce a filamentation effect at a depth of 2-5 mm in fused silica, achieving a one-dimensional phase grating with a diffraction efficiency of up to 96%. However, in the previous reports, most of the methods for preparing thick VBG in transparent materials relied on fs laser multi-layer scanning and stacking, and resultingly the thickness, period consistency and diffraction efficiency of VBG are not good enough. There are still great limitations on the fabricating efficiency of a large VBG.
In this study, VBG was fabricated one-step in As2S3 glass by combining fs laser filamentation technology with cylindrical lens focusing. As2S3 glass is selected due to its large infrared transmission range, high nonlinear refractive index, excellent thermal stability, and band gap adapted to the processing laser wavelength. The morphology of the writing grating was characterized both from the top and side of the sample by an optical microscope. The fabricated VBGs have excellent period consistency, and their periods can be accurately adjusted through control of the stage moving. The prepared gratings show clear diffraction patterns and high diffraction efficiency measured by a He-Ne laser (632.8 nm). The area of refractive index change in the prepared VBG can be delineated by change of either energy or number of laser pulse, and the thickness of VBG can be as high as 1.7 mm. After optimizing the parameters, using only 15 minutes of processing time, the VBG could be well fabricated in a 2 mm × 2 mm × 1.7 mm area of As2S3 glass, and the interface width is 2.5 µm, the aspect ratio is nearly 700, the diffraction efficiency is 95.49%.
2. Experimental
The sample used is a synthetic red transparent ChGs glass with a chemical formula of As2S3. The full size is 8 mm × 8 mm × 1.7 mm. Six sides have been polished to meet the requirements of laser manufacturing and measurement.
Figure 1 shows a schematic diagram of fs laser direct-writing system. A fs laser (FemtoYL-20, YSL Photonics) emits the 1030 nm pulse train with adjustable pulse width (380 fs-3 ps) and repetition frequency (25 kHz-1 MHz). The fs laser with a spot diameter of 3.8 mm is focused on the bottom surface of the sample. Two convex lenses in the optical path are used to reduce the spot diameter to pass a shutter, and further fit the size of a flat convex cylindrical lens with f = 12.7 mm. During laser processing, the glass sample is fixed on a computer controlling 3D motion stage, and its top surface is perpendicular to the laser beam. The blue box shows the intensity of 200 kHz fs laser spot after focusing by cylindrical lens. The energy of irradiated pulse can be modulated continuously from 5 to 30 µJ. The irradiation time varies from 1 to 10 s, which is controlled by the shutter, the irradiation time is controlled to vary the laser pulse number. At the repetition rate of 200 kHz, the laser pulse number corresponds to increase from 2 × 105 to 20 × 105. In our experiment, 200 kHz is the best choice to ensure that the structure will not be destroyed under the premise of high manufacturing efficiency. Further increasing the repetition rate will lead to a significant thermal effect and lead to destruction of the structure.
Optical images of the laser irradiated area were captured via an optical microscope (VHX-5000, Keyence) (transmission mode). The corresponding retardance images were captured using a polarization/birefringence microscopy (Exicor Micro Imager). The surface morphology of the sample was characterized by an atomic force microscopy (AFM) (Nanosurf C3000 Controller). Raman spectra of the As2S3 glass before and after laser irradiation were collected using a laser confocal Raman microscopy spectrometer (Renishaw, inVia) equipped with a 785 nm laser excitation. Diffraction efficiency and patterns were obtained by a He-Ne laser (DH-HN250) with a wavelength of 632.8 nm. The diffraction efficiency of VBG is achieved by measuring the power ratio of 1-order and 0-order diffraction. The transmission spectra of VBG were measured by a microscopic infrared spectrometer (Nicolet i N10). All the experiments were conducted at room temperature.
3. Results and discussion
When a fs laser is focused in a transparent medium, if its power exceeds the self-focusing critical threshold Pcr = 3.72λ2/8πnn2 [22], a slender filamentation will form along the propagation direction. Where n is the refractive index, n2 is the nonlinear refractivity and λ is the laser wavelength. According to the parameters n = 2.52, n2 = 4.5 × 10−14 cm2/W and λ=1030 nm [23], the Pcr is calculated to be about 14 kW, that corresponds to Ecr = 5.32 nJ when converted into pulse energy. Since the pulse energy used in this experiment far exceeds 5.32 nJ, reaching 5 µJ, which is sufficient to cause the self-focusing effect and then leading to formation of a long plasma channel and filamentation, that is beneficial for a high thickness VBG fabrication. Specifically, the fs laser filamentation effect enables the beam to contract to a very small waist width, but its transmission distance is far greater than the Rayleigh length, a high laser intensity inducing plasma channel can be maintained in the filamentation [24]. In terms of the filamentation effect, there are two different phenomena: tightly focused filamentation and weakly focused filamentation. When fs laser pulses are tightly focused in a transparent medium, a balance between self-focusing and self-defocusing contributes to formation of a long plasma channel, in which the local phase explosions take place at intervals in different regions, leading to the formation of a string of voids [25]. On the other side, weak focusing is more conducive to writing uniform refractive index change in a large area. Yamada et al. [26] one-step wrote an optical waveguide structure with the refractive index change of glass induced by the filamentation of a weakly focused fs laser, the length of the structure of permanent refractive index change is nearly as the same as the length of the filamentation. The uniform change in refractive index is possibly the result of both the weak focusing filamentation and the local melting of materials cooling down [27]. Based on the above discussion, the weakly focused fs laser is more suitable for fabrication of the VBG structure in glass. Besides, current fs laser processing mainly depends on the two-photon absorption (TPA) mechanism, that is, the As2S3 glass with a band gap of 2.4 eV is processed by using a 1030 nm fs laser (1.2 eV). Generally, the fs laser filamentation effect based on TPA is more stable compared to that based on multi-photon absorption [28].
Compared to the traditional objective lens processing, we tend to choose the cylindrical lens for processing, which not only greatly reduces the cost, but also reduces the time required for processing. Both in terms of the periodic stability or the diffraction efficiency, our VBG is greatly superior to the one by using the objective lens processing and then 3D stacking by layer by layer. As shown in Fig. 2, firstly fs laser was focused on the bottom of the glass, the depth was at 1700 mm. And the irradiation time was 4 s, that corresponds the laser pulse number of 8 × 105. Deep focusing is beneficial to induce fs laser filamentation, because surface aberration was purposely harnessed to elongate filamentation tracks [29]. Besides, focusing the laser on the bottom can also avoid the expansion deformation of the material caused by the locally high temperature at the laser focus. Figure 2(a) shows that the structure processed through the 5X, NA = 0.15 objective lens results from a filamentation effect. Such a structure with a length of 554 µm has no merit for fabricating a VBG because of its linear shape. If a large area VBG is fabricated in this way, it will not only take a long time, but the VBG period will also show poor stability. In contrast, Fig. 2(b) shows the structure processing using a cylindrical lens with f = 12.7 mm and NA = 0.15. Because the fs laser spot after the cylindrical lens focusing becomes a blade shape, combined with the filamentation effect generated by deep focusing, the induced structure of refractive index change shows a long interface. This method is better than the old-fashioned stack method. Finally, a 2 mm × 1.7 mm refractive index change interface can be written one-step, and the period of the fabricated VBG can be further controlled by the stage movement. From the Fig. 2(b), it is clear that the fabricated VBG has very good periodic consistency. Current method greatly improves the processing efficiency and structural performance of VBG, and further reduces the processing cost because the expensive objective lens is not used in the optical path.
Fig. 2. Structure comparison between objective lens processing (a) and cylindrical lens processing (b). The black box shows the top view, and the blue box shows the side view.
Then, we employ a physical model in combination of the nonlinear effects of fs laser propagation and the interface spherical aberration effect to explain the fs laser filamentation effect in As2S3 glass. Because the nonlinear coefficient in the As2S3 glass is very large, and the refractive index mismatch with the air will lead to serious spherical aberration [30].
The nonlinear Schrödinger equation is generally used to describe the nonlinear propagation of fs pulses [31]. We use the nonparaxial nonlinear Schrödinger equation to accurately simulate the pulse propagation.
Assuming that the laser propagation is along the optical axis z, the electric field of light beam is expressed as E. The formula describes the beam diffraction, group velocity dispersion, plasma absorption of light and the resulting refractive index change, multiphoton absorption and third-order nonlinear effects. The third-order nonlinear effects include the self-focusing (self-action) term and the self-phase modulation term. The local coordinate system is expressed as τ=t-z/vg, vg is the group velocity. ∇⊥ is the Laplace operator which controls the diffraction. The forbidden band width of the As2S3 is Eg = 2.4 eV, while the photon energy of the wavelength 1030 nm laser is about 1.2 eV. Therefore, it is two-photon absorption, K = 2. β(2) is the two-photon absorption coefficient 2.1 × 10−9 cm/W. ρ is the free electron density, c is the speed of light in vacuum, medium linear refractive index of n0 = 2.52, nonlinear coefficient of n2 = 4.5 × 10−14 cm2/W. Group velocity dispersion coefficient k = n0k0 = n0ω/c. σ is the cross section for inverse Bremsstrahlung.
Where the electron density ρ can be obtained from the following evolution equation:
The coupled Eqs. (1) and (2) above just describe the nonlinear propagation of fs pulses in a single homogenous medium and, in order to further incorporate the effect of interface spherical aberration, the analysis of interface spherical aberration by Török et al. in terms of the electromagnetic diffraction theory should be employed [32]. After taking into account both of the Gaussian properties of incident beam and the influence of the interface spherical aberration, the electric field of light beam just passing through the interface can be expressed as:
A0 is the Gaussian-distribution beam in both time and space domain before passing through the interface. η is the normalization factor for single-pulse energy conversation. $\psi ({{\phi_1},{\phi_2}, - d} )={-} d({{n_1}\textrm{cos}{\phi_1} - {n_2}\textrm{cos}{\phi_2}} )$ is spherical difference function, ${\phi _1}$ and ${\phi _2}$ are respectively the incidence angle and the refraction angle on the interface, ${\boldsymbol{J_0}}$ is the Bessel function of the first kind, of zero order. k is the wave number, where subscripts 1 and 2 denote values corresponding to regions with materials 1 and 2. d is the distance from the interface to the geometrical focus of gaussian beam. rp = (x, y, z) is the position vector pointing from geometrical focus to the arbitrary point in the focal region. τp and τs are the Fresnel coefficients, ${\tau _s} = \frac{{2\,\textrm{sin}\,{\phi _2}\,\textrm{cos}\,{\phi _1}}}{{\textrm{sin}({{\phi_1} + {\phi_2}} )}}$, ${\tau _p} = \frac{{2\textrm{sin}{\phi _2}\textrm{cos}{\phi _1}}}{{\textrm{sin}({{\phi_1} + {\phi_2}} )\textrm{cos}({{\phi_1} - {\phi_2}} )}}.$
Electric field E mentioned above was used as the initial condition for fs laser transmission in the second medium. Then the nonparaxial nonlinear Schrödinger equation [Eq. (1)] and the electric density evolution equation [Eq. (2)] are used to solve the energy flux density distribution in the As2S3 glass.
Figure 3 shows the simulated fluence distribution of the light field when the laser beam with a pulse energy of 2 µJ was focused at 1700µm beneath the front surface by the objective lens of NA = 0.15. This simulates the filamentation effect of Gaussian spot focusing in As2S3 glass, which is highly consistent with the filamentation length measured in Fig. 2(a). A uniform laser fluence has an extended length of about 550 µm. At present, there are still some problems in the simulation diagram of cylindrical lens focusing combined with fs laser filamentation effect, but it can be inferred from Fig. 3 that weak focusing fs laser filamentation contributes to the main mechanism because both of the objective lens and cylindrical lens have similar NA values.
Fig. 3. Simulated fluence distribution of the Gaussian beam focused to the 1700 µm depth with 0.15 NA objective.
As an effective technique for characterizing As2S3 glass and the induced structures [33], Raman spectra before and after cylindrical lens focused fs laser irradiation were measured. As shown in Fig. 4(a), there is no new Raman peak after irradiation except the typical peak of inorganic As2S3 glass. In the Raman spectra of inorganic glasses, the broadband, which is usually observed at a relatively low frequency (about 20 to 100 cm−1), called the Bose peak [34]. The other broadband observed at about 300 to 400 cm−1 corresponds to the asymmetric vibration of the AsS3/2 pyramid, which is the main structural unit of the As2S3 glass [35]. Only the intensity changes of the related peaks in the Raman spectra support the conclusion of glass densification proposed in the literature [36]. Figure 4(b-c) show the birefringence retardance changes of the writing structures by the birefringence microscope. As shown in Fig. 4(b), there is an obvious birefringence retardance in the region where the refractive index changes, which further proves the densification of the material inside the glass caused by fs laser filamentation. And Fig. 4(c) shows that the densification also formed when the refractive index change has not observed under optical microscope. We used AFM to measure the surface of the sample, no surface damage was detected in Fig. 4(d), which proved that the processing only changes a little in the refraction index of irradiation area. In previous studies [37], Juodkazis et al. used fs laser to process As2S3, and believed that photon-darkening was the reason of the induced change. Furthermore, they suggested that photon-darkening could create an array of micro-lenses which would modify the distribution of the light preventing formation deeper into the sample. This phenomenon was not found in our experiments. Combined with the results from the used Raman spectroscopy, we believe that glass densification is the reason of the induced change.
Fig. 4. (a) Raman spectra of the As2S3 glass before and after fs laser irradiation. (b) and (c) The top-view of structures measured by optical (up) and birefringent (down). (d) AFM height image of fs laser irradiated area.
During the fs laser processing, the thickness of VBG could be adjusted by controlling the pulse energy and pulse number. Figure 5(a) shows the side-views of the induced interfaces, which were irradiated with 8 × 105, 10 × 105, 12 × 105, 14 × 105 pulses respectively at the pulse energy of 25 µJ, and the period between two interfaces was 10 µm. As the laser pulse number increased, the structure length increased significantly along the z-axis, and finally reached 1700µm, which was the full thickness of the As2S3 glass. Figure 5(b) and (c) show the enlarged images of the writing structure after 10 × 105 pulses irradiation. The uniformity of refractive index changes is surprising, and the grating period has good consistency between the two regions at the near focus and at the far focus, respectively.
Fig. 5. (a) Side-views of the writing structures by different laser pulse number. (b) and (c) show the zoom-in views in (a).
Moreover, as the laser pulse number increasing, not only the filamentation structure can extend, but also the refractive index increases significantly without affecting the consistency of period. According to the simulation of the focusing of the objective lens in Fig. 3, the single-pulse filamentation length was as long as the length of the writing structure, which gradually formed after irradiation with 8 × 105 pulses, as shown in Fig. 2(a). When a fs laser irradiates into the glass, its filamentation length is supposed to be a fixed value, but the length of structure of refractive index change will increase with the increase of laser pulse number, because the multiple pulse irradiation can continuously increase the refractive index in the area far away from the focus, that is, the filamentation structure seems like growing along the propagation direction.
Figure 6 shows the two thickness dependences of VBGs on laser pulse number and pulse energy, respectively. When the laser pulse number increases, the filamentation length correspondingly increases, and the larger the pulse energy is, the longer the length. Meanwhile, it can also be found that the increase of pulse energy is also beneficial for increasing the length of the filamentation structure.
Fig. 6. (a) Thickness dependence of VBGs on the laser pulse number at two pulse energies of 15 and 25 µJ, respectively. (b) Thickness dependence of VBGs on the pulse energies at two laser pulse numbers of 4 × 105 and 8 × 105, respectively.
Figure 7 shows the side view of a writing structure, in which different interface intervals change from 2.0 to 4.5 µm. Under the laser pulse number of 12 × 105 and pulse energy of 25 µJ, the minimum interface interval of 2.0 µm has been achieved by accurately control of the stage moving, and then a VBG structure with good period stability has been fabricated in As2S3 glass. However, manufacturing of the smaller period needs to further optimize the processing parameters, because the width reduction of filamentation structure cannot be achieved by continuously decreasing the pulse energy due to existence of the critical threshold of self-focusing effect. In addition, it is easy to cause the crosstalk between two neighbor interfaces by only decreasing the stage moving interval. Based on the above considerations, the window of the processing parameters is relatively narrower, and further exploration is needed to carry out.
Fig. 7. (a) The side view of the two-dimensional refractive index change interface with different periods (2.0-4.5 µm). (b) shows a zoom-in view in (a).
Diffraction is determined by numerous parameters, such as grating thickness, refractive index modulation, and incident light angle. To simplify the experimental process, we fixed the irradiation laser pulse numbers to 12 × 105 and used different pulse energies to fabricate VBGs with different thicknesses, and then studied their diffraction efficiencies and patterns. Considering the thickness in our fabricated VBGs, we think that the grating diffraction (η) satisfies the Bragg’s law, that can be expressed as follows [9]:
where D represents the thickness; and λ and θ are respectively the wavelength of the incident light and the angle of the diffracted light. Here, the angle θ can be calculated by the formula of dsinθ = mλ, where d is the period of a VBG, and m is the order of diffraction pattern.We used a He-Ne laser of 632.8 nm normal incident onto a fabricated VBG to collect the diffraction efficiency and observe the diffraction patterns, as shown in Fig. 8(a). High optical performance of the VBG has been evidenced by its clear diffraction pattern and more than 90% diffraction efficiency. Their diffraction efficiencies maintain at a high level in the pulse energy range from 20 µJ to 27.5 µJ. In this event the fs laser filamentation length could exceed up to 1400 mm, and the width of inducing structure with refractive index change remained unchanged from its beginning to end. Therefore, the fabricated VBG is deemed to have a very good period consistency. However, the diffraction efficiency decreased significantly when the pulse energy was below 20 µJ or exceeded 28 µJ. Because when the pulse energy was below 20 µJ, the laser fluence of the filamentation structure was too small, resulting in a little change in the refractive index and a filamentation length of less than 700 µm. And when the pulse energy exceeded 28 µJ, plasma expansion and even plasma explosion happened at the focus, which led to instability of the induced plasma channel and filamentation structure. Although it also may maintain a good period consistency, the diffraction efficiency has been reduced. When the pulse energy increased up to 30 µJ, the inducing filamentation structure was severely damaged due to another side effect of heat accumulation, leading to deterioration of uniformity and the diffraction efficiency decreasing significantly to 75%.
Fig. 8. (a) Dependence of grating diffraction efficiency on pulse energy. The insets in different color boxes show the diffraction patterns under four different pulse energies. (b) Spectral sensitivity of the VBGs fabricated by four different pulse energies (different colors correspond to different pulse energies).
In order to test the wavelength selectivity of VBG, we selected the four VBGs used in Fig. 8(a) to test their transmission spectra by a microscopic infrared spectrometer, as shown in Fig. 8(b). Due to the limitations in measurement instrument, we cannot adjust the VBG to the best test angle, but it is obvious that the wavelength selection peak has appeared at the wavelength of 2480 nm, which is marked with Peak A. Another peak position marked with Peak C is speculated to be caused by remelting of the chalcogenide glass near the focus. As the higher processing laser energy may cause structural irregularity of the VBG, the purple plot of 30 µJ has a new peak marked with Peak B. This phenomenon has also been observed by Mikutis et al [14]. But the Peak B is not found in the other three VBGs with the lower processing laser energy. These results indicate that the glass melting caused by light-thermal effect will lead to the emergence of new peaks.
4. Conclusion
High thickness VBG was one-step fabricated inside ChGs by fs laser direct-writing technology. By the cylindrical lens focusing method, a two-dimensional refractive index change interface spontaneously grows along the incident direction because of generation of a planar fs laser filamentation effect. In addition, the thickness and refractive index change of the fabricated VBG can be changed by controlling the laser pulses energy and number, respectively. We have verified by theoretical simulation that this experiment is based on the uniform refractive index change achieved by the weak focusing filamentation effect of fs laser. Under the optimal laser parameters, the maximum diffraction efficiency of the VBG reaches 95.49% under illumination of a laser of 632.8 nm. It greatly makes up for the insufficiency of fs laser processing VBG through an objective lens focusing. In the future, this processing strategy will be promoted to more common materials such as fused silica, which will greatly promote the preparation and integration of fs laser on other photonic devices.
Funding
National Natural Science Foundation of China (12274280, U20A20211, 11974147); National Key Research and Development Program of China (No. 2021YFB2802000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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