Femtosecond laser inscription of polarized-sensitive volume phase grating in nanoporous glass

With the growth of laser technologies in photonics, the application of ultrashort laser becomes promising and prospective for volume phase elements fabrication in transparent materials. Femtosecond laser writing (FLW) was applied for polarized-sensitive volume phase gratings (VPGs) inscription in a nanoporous silicate matrix (NPSM). The VPGs formed had the thickness L = 54 ± 0.5 μm and 77 ± 0.5 μm, and showed diffraction efficiency of 8% and 14% respectively. VPGs in an NPSM demonstrated polarization sensitivity resulting in different diffraction efficiencies from 2 to 14%. Moreover, the impregnation of the NPSM plate with distilled water, 50% acetone and 10% acetone was investigated. The achieved results provide evidence for a possibility of a VPG in NPSM to be applied as a sensor.


Introduction
The fundamental principles underlying the interaction of ultrashort laser pulses with optical materials resulting in density change or nanogratings self-organization have been an object of ample research over the past few decades (Wang et al. 2021b;Fedotov et al. 2021). The findings are essential for the optical engineering community since the femtosecond laser writing (FLW) method, among other things, is able to change refractive index (Toma et al. 2000), birefringence (Wang et al. 2021a, b) and spectral properties (Jia et al. 2005) locally within optical materials. Studies have shown successful inscription gratings (Beresna and Kazansky 2010), integral optical waveguides (Wang et al. 2022), optical converters (Beresna et al. 2011) and other phase elements for generating structured laser beams.
A typical optical material is fused silica, soda-lime glass or other commercial solid optical silicate glasses having various compositions (Fernandez et al. 2021).
Special attention is now focused on FLW inside nanoporous optical materials -porous glass, sol-gel or aerogel (Cerkauskaite et al. 2017). In 2022, Zheng Xiong et al. (Xiong et al. 2022) mentioned that internal laser-induced structuring of hydrogels converts the latter into "smart" optical devices. Thus, volume phase grating (VPG) was fabricated, and tracking the changes in the diffraction pattern helped to demonstrate the concept of a pHsensor. The single-layer VPG in fused silica shows the diffraction efficiency (η) of 7.9% at 532 nm (Liu et al. 2007). Besides, VPG in gallium lanthanum sulphide chalcogenide glass substrates presented η of 61% at 1300 nm and 24% at 2640 nm (MacLachlan et al. 2013). Previously, our group demonstrated the inscription of the densification tracks inside the plates of nanoporous silicate matrix (NPSM), where we showed the refractive index contrast up to Δn = 1.2·10 − 2 (Lijing et al. 2021), and provided nanogratings with subwave periods Λ ~ 100 nm (Danilov et al. 2021). The results obtained suggest that a single-layer VPG in NPSM will have the following features: (i) tunable phase shift depending on laser processing parameters; (ii) sensitivity to molecules that are captured by the nanoporous framework (Kudryashov et al. 2022) and (iii) the grating sensitivity to the polarization of the transmitted light due to birefringence nature of every track.
In this study, we applied FLW method to fabricate VPG inside a NPSM plate. Despite the increased porosity (~ 50%), we determined the optimal parameters for laser processing and measured the diffraction efficiency. A change in the diffraction efficiency due to the rotation of the polarization vector of incident laser radiation -was an interesting phenomenon discovered. The effect of molecules deposited in VPG was also investigated. The results show the prospective use of VPG in NPSM for sensing applications.

Materials
The composition of a NPSM (15 × 5 × 1 mm) plate is 91.4% SiO 2 , 7.4% B 2 O 3 , 1.2% Na 2 O. An NPSM has 50-54% pores with an average diameter of 17 nm (Bykov et al. 2022). The components for NPSM impregnation step are distilled water, 50% acetone and 10% acetone water solutions. Figure 1(a) presents a schematic image of a FLW setup that includes a fiber laser source (Avesta Ltd. ANTAUS-20 W-20u/1 M), several dielectric mirrors, an objective (20X, NA = 0.4, LOMO ltd.), and an electronically controlled coordinate stage (Thorlabs, DDSM50/M). The setup also includes an observation system consisting of a light source, an optical system and a CMOS camera. The laser source has the maximum output power of 20 W and the initial wavelength of 1030 nm. A second harmonic generator (Avesta, ATsG-O-800) was used to double the optical frequency of the input wavelength to obtain the 515 nm wavelength. Linear polarization is perpendicular to the writing direction. In our experiment, the pulse duration and the frequency were set as τ = 220 fs and ν = 200 kHz respectively, the power was set in the range from 50 to 320 mW.

VPG fabrication and investigation
In the writing part, the objective focuses the laser beam to achieve a beam waist with the diameter of 2 μm and Rayleigh length of 7 μm (Saleh and Teich 2019). The CMOS camera was used to investigate the processing region. The coordinate stage was adjusted in the Z direction to correct the coordinate deviation of the real focus caused by the objective, then to carry the NPSM move linearly with a speed of 25 mm/s in the Y direction. As a result, VPGs with linear arrays were fabricated inside the NPSM with a period of Λ ~ 10 μm.

Setup for evaluating the diffraction efficiency
Diffraction efficiency (η) was measured by the setup in Fig. 1 (b), which includes (i) a 650 nm or a 532 nm laser, (ii) a Glan Prism, (iii) a half-wave plate, (iv) a fixed VPG sample, (v) a laser power meter (Genetec-EO, PH100-SI-HA-D0). Glan Prism was applied to obtain a linearly polarized beam from the incident laser. A half-wave plate was used to rotate the angle of the linear polarization with a 4° precision. The laser transmitted through the VPG produced a diffraction pattern. The registered power of every order was normalized relative to the input power at position A, while the transmission coefficient made 0.8 for NPSM plate (Fig. 1, b). The power meter (v) provided the result of diffraction efficiency with ± 1.5% calibration uncertainty.  Figure 2 shows the volume tracks in NPSM, which were fabricated by FLW with constant τ = 220 fs, ν = 200 kHz, different power (P). It is shown that the tracks referred to as cracks become rough and are accompanied by black areas when P = 139-316 mW. The cracks are formed by plasma explosion under high laser fluence (> 44.2 J/cm 2 ), and they will reduce the transmittance resulting in a decrease in the diffraction efficiency of VPG. With P = 55-124 mW, crack-free tracks were formed. There are no regions of obvious refractive index modification with powers below 55 mW.

VPG investigation
Photo of VPGs is shown in Fig. 3 (a) where light passing through VPG demonstrates the diffraction phenomenon, 0th order and ± 1st orders can be observed. The geometry and homogeneity of VPG 1 and VPG 2 were investigated (Fig. 3, c-h). They were fabricated 0.2 mm under the surface with τ = 220 fs, ν = 200 kHz, Λ = 10 μm, and powers P = 83 mW (VPG 1, Fig. 3, c,d,e) and 107 mW (VPG 2, Fig. 3, f,g,h), respectively. Figure 3(b) shows a schematic image of the VPG in the NPSM and the corresponding cross-section (Fig. 3, c,f) and top view (Fig. 3, d,g). An increase in the laser power from 83 mW to 107 mW resulted in the following differences demonstrated in Fig. 3 (c,d,f,g): (i) Track crosssection length increased from L = 54 ± 0.5 μm to L = 77 ± 0.5 μm. (ii) Track diameter grew from d = 3 ± 0.5 μm up to d = 5 ± 0.5 μm. (iii) Tracks became heterogeneous. It is shown that P = 107 mW has resulted in interruptions along the tracks (Fig. 3, g). Moreover, this laser fluence were enough to form a void-like structure or decompaction of the material. The decompaction of glass material happens then the temperature in the beam waist exceeding the glass softening temperature (Ma et al. 2017). Besides, these two VPGs presented birefringence characteristics shown in their cross-polarization images (Fig. 3, e,h). This can be explained by the type II modification of the refractive index meaning that laser-induced subwavelength gratings can be produced and process optical anisotropy (Lotarev et al. 2019;Drevinskas et al. 2015).
The measured track thickness L (Fig. 3, c,f) refers to the increase of the corresponding Rayleigh length. Initially, it was expected to reach L ~ 14 μm, but it is close to L = 54 ± 0.5 μm and 77 ± 0.5 μm due to the filamentation of the femtosecond laser. This non-linear effect consists in self-focusing and defocusing of high-intensity laser radiation on induced plasma (Couairon and Mysyrowicz 2007). These recurrent processes result in an elongated beam waist and the structure formation. Thus, VPGs obtained bigger thickness that contributed to higher diffraction efficiency η.

VPG diffraction efficiency
The diffraction efficiency (η) was measured by the setup (Fig. 1, b), where every diffraction order intensity was registered by the power meter. As a result of 650 nm laser testing, the η of VPG 1 is about 8%, and of VPG 2 has gone up to about 14% (Fig. 4, a). To explain the mechanism of η increase, the following formula can be used (Yamada et al. 2003): where η is diffraction efficiency, ∆n is refraction index contrast, L is the VPG thickness, λ is incident light wavelength and θ is Bragg's angle.
The constant period Λ = 10 μm brings the same diffraction angle of 3.7° at 650 nm. When P increases, the VPG 2 with a higher thickness L, we also attribute a higher η to a local modification of the refractive index for the NPSM, whereas the higher laser power provides a higher index contrast ∆n (Poumellec et al. 2011). As we mentioned before, some interruptions in the view of microvoids were found along VPG 2. These interruptions may cause optical losses and additional reflection of the transmitted light. We also measured transmission spectra (Fig. 4, b) of the VPGs and NPSM, and it's obvious that VPG 2 possesses higher absorption compared to VPG 1 due to the presence of void-like structures. Moreover, we tested the VPG 2 under 532 nm laser. Bragg's angle changes to 3.0°, the η reaches 13%. Nevertheless, compared to other VPG with similar profile in fused silica (Liu et al. 2007), the NPSM is shown to be able to achieve higher diffraction efficiency.

VPG polarization sensitivity
The experiment has revealed VPGs polarization sensitivity. For this test we used VPG 1, which was irradiated with femtosecond laser pulses with a wavelength of 515 nm and the linear polarization, which was perpendicular to the grating's lines (green arrow in Fig. 5,  a). As a result a typical diffraction pattern was detected in the far field, which includes 3 diffraction orders. The intensity in the orders was significantly reduced when we rotated the VPG to make it parallel to the polarization direction. Therefore, we studied the effect of laser radiation polarization on the VPG efficiency.
The setup used as shown in Fig. 1, b (650 nm) made it possible to rotate the polarization of the laser beam with a precision of 4°. The initial NPSM features some birefringence due to its numerous nanopores across the entire plate thickness. To exclude the initial birefringence of the NPSM, we measured the transmitted laser beam intensity (black curve in Fig. 6). Then, the VPG was set to test the diffraction intensity. The polarization of the laser  radiation was rotated by 180° in several steps, and each time the intensity of the 0th (red curve) and 1st (blue curve) orders was recorded. It is shown that the 0th order intensity gradually decreases from 85 to 65%, on the other hand, the 1st order rises from 0.02 to 11%. Then, the half-wave plate angle was rotated from 45° to 90°, and the intensity was gradually restored to the initial values. This phenomenon can be explained by the birefringence of the VPG, which can be attributed to polarization diffractive gratings (Beresna and Kazansky 2010).

VPG as a sensor
Abundant internal nanopores are the most important feature of NPSM, which allow impregnation by liquids. Because of the polarization sensitivity of VPG as shown in Sect. 3.3, we propose applying VPG in NPSM as a sensor for liquids. In our experiments, distilled water, 50% and 10% acetone were completely impregnated in VPG, respectively. Figure 7 shows the output intensity of VPG 1 by a 532 nm laser. In Fig. 7 (a), the dry VPG curve always lies below the impregnated VPG curves. With the air in the nanopores showing a different refractive index from glass, countless reflections happened in NPSM when the laser beam passed through losing intensity. After the liquids impregnation, the contrast was compensated. It is worth noting that the intensity of VPG 0th shows different values for distilled water and 50% and 10% acetone solutions. The distilled water impregnated VPG shows the highest intensity among them, which can be explained by the refractive index of water being close to that of glass. When water fully fills the nanopores, the refractive loss of VPG decreases. There are different refractive indexes for the 50% and 10% acetone solutions causing different intensity losses.
Despite the fact that the refractive index of the liquid is close to that of the NPSM, the VPG under liquid impregnation still works. By using VPG in NPSM, we transform the change in the refractive index of liquids into visualization of the intensity change. All the impregnation curves are polarization sensitive, they present a gradually decreasing trend from 0° to 90°, and then they gradually grow from 90° to 180°. Fig. 6 Normalized intensity transmitted through NPSM and the VPG's 0th and 1st diffraction orders intensity relative to position A described in Fig. 1 (b) However, the relative VPG refractive index contrast decreased after impregnation, resulting in the 1st intensity not varying with polarization angle (Fig. 7, b). The above discrepancies can be an evidence of VPG acting as a sensor for liquids with different refractive indices.

Conclusion
To summarize, we used the FLW method to fabricate VPGs in the NPSM, and obtained the diffraction efficiency of 13% for 532 nm and of 14% for 650 nm. The efficiency increased from 8 to 14% due to a higher refractive index contrast and a higher VPG thickness provided by the laser self-focusing. Besides, we found VPG to be polarized-sensitive in the NPSM, it has an efficiency from 2 to 14% when the polarized light angles rotate from 0° to 180°. Moreover, separate impregnation experiments of a VPG in distilled water, 10% and 50% acetone solutions show the results different from those for a dry VPG. It has to be mentioned that not all the typical wavelengths were used to test VPGs, and there was a limited range of fluid types used in impregnation experiments. Despite the above limitations, our experiments show VPGs to be sensitive to polarization angle and to liquids with different refractive indices. Fig. 7 (a) 0th intensity and (b) 1st intensity comparison of a dry VPG and a VPG impregnated with distilled water, 50% acetone and 10% acetone