1. Introduction

Recently, birefringence modification caused by the formation of embedded nanogratings (NG) in the femtosecond (fs) laser direct writing track has attracted attention because the orientation of the slow axis and retardance of the NG can be independently controlled by the light polarization and the laser fluence respectively [1, 2]. Additionally, the materials to form NG have been expanded to germanium-doped fused silica [3], multi-component silicate glass [4], and several crystalline materials (e.g. TeO₂ [5] and Al₂O₃ [6]). A few polarization optical elements have been developed by taking advantages of its high stability and anisotropic reflection [7–9].

At the same time, another intriguing phenomenon about fs laser direct writing in glass is the directional dependence of the writing structure (often called quill writing), which is regarded as a consequence of asymmetry of the laser beam [10–14]. In the past ten years, a lot of research has been focused in this area. Kazansky et. al. proposed that the pulse front tilt (PFT), which usually originates from distortion of temporal and spatial chirp in fs pulse, is the main factor to cause material modification changing from NG to bubbles formation when a reversed scan direction is applied [10]. Also, Vitek et al. utilized the simultaneous spatial and temporal focusing (SSTF) system to tune the PFT value at focus up to 16,000 fs/mm, resulting in relaxed depth-dependence nonreciprocal structures for either dots or Chevron shapes [11]. Salter et al. used a spatial liquid modulator (SLM) to adjust the PFT or the asymmetry intensity distribution at the focus to achieve the control of directional dependent writing [12]. Lately, Poumellec’s group suggested that a space-charge built from pondermotive force ($\overrightarrow{\nabla }{\overrightarrow{E}}^2$) is associated with the PFT [13], which might be interpreted as the formation of an asymmetric stress field [14]. Our group also observed the orientation of the writing NG in glass depends on the correlation between the polarization plane azimuth and the PFT [15].

In the following sections of this paper, we provide further evidences to prove that PFT has the capability of forcing NG rotation in glass in 3D space through the observation of the transversal cross-section of laser tracks by using a scanning electron microscope (SEM). In addition to varying the light polarization plane with respect to the PFT, we can see that reversing scan direction is another practical method to control the rotation of NGs, which shows obvious directional dependence of writing. Such results indicate that a scan along the tilted intensity plane may produce a positive feedback driven plasma due to the low threshold of self-trapped exciton (STE) which have been existing at the front edge. By decreasing the energy for ionization, more pulse energy will increase the pondermotive force to affect the orientation of NG. This behavior provides a new approach to control the structure transformation of NG across from 2D to 3D space.

2. Experimental

A regeneratively amplified mode-locked Ti: sapphire laser system (Coherent: RegA 9000) was used in our project. The spatial-temporal parameters of the incident pulse were measured with a commercialized ultrafast laser diagnosis device, GRENOUILLE 8-20USB. The PFT value in front of the objective lens was measured to be 88.8 fs/mm.

A set of parallel lines with varying polarization directions were directly written in glass by moving the sample perpendicular to the propagation direction of the laser beam. Each line was only written by one pass. The pulse energy after the microscope objective was fixed at 2.8 µJ and the sample moving speed was set at 50 µm/s. The beam spot size was estimated about 2.5 μm at the focus. Other details of experiment methods can be found in reference 15.

3. Results and discussion

Figure 1 shows SEM images of transversal cross-sections of the written lines with varied polarization plane azimuth. The NG inside the written structures rotates clockwise in the plane of the transversal cross-section when the polarization plane azimuth of the incident pulse increases from 10° to 170°. And it presents a chiral distribution with a center at $\theta \text{=90}°$. Furthermore, we compared the textures between two different azimuths of $\theta \text{=10}°$ and $\theta \text{=190}°$. The NGs are extremely alike for both their orientations and periods, which verifies their rotational symmetry corresponding to the period of 180°.

 

Fig. 1 SEM images of self-organized NGs in transversal cross-section of the written lines with varied polarization plane azimuth. The red curve highlights the varying trend for the longitudinal length of NG.

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Moreover, the longitudinal length of NGs in Fig. 1 gradually decreases from the center (90°) to both sides (10° and 170°), whereas lateral outlines of these tracks are essentially uniform regardless of the polarization plane azimuth applied. From the architectural perspective of NGs, these initially formed, slightly tilted, alternately refractive-index-arranged nanoplanes appearing in the head can serve themselves as a grating to reflect the subsequent pulse energy when the incident light is focused. And their reflectivity depends on the width of the apertures, which is determined by the slope of the nanoplanes. Hence, the larger the inclined angle is, the more the energy loss is. Eventually, the self-organized periodic nanostructures are the power shortage of development and they tend to be disordered, which leads to them finally disappearing. Another possible explanation is that the anisotropic photosensitivity which originates from the mutual orientation of a light polarization plane and the PFT of fs pulse causes the absorbance change of the modified region [16].

Generally, the orientation of the written NG is widely considered to be only dependent on the light polarization [17–19]. Note that the laser beam used here was nearly Gaussian spatial profile and was focused into the glass with the normal direction. Here we define the NG orientation angle $\beta$ as the inferior angle from the wave vector $\overrightarrow{k}$ to the normal of NGs clockwise in the polished cross-section. We will make use of the orientation angle $\beta$ and the gap d (the distance between two adjacent nanocracks) to discuss the orientation of the written NG in 3D space.

The most likely reason causing this phenomenon is the tilted intensity-front of the fs pulse, which shifts the electric field plane from the phase front to the intensity front. The formed NG therefore rotates in the transversal cross-section. Figure 2(a) shows the schematic of 3D rotation of NG in this case. The scan direction is along + y (S direction) or –y (S’ direction), and the blue plane is the tilted intensity plane, which is perpendicular to the Poynting vector $\overrightarrow{P}$. In order to simplify the model, the plane consisting of $\overrightarrow{k}$ and $\overrightarrow{P}$ is set to be parallel to the y-z plane. As for the tilted intensity front, $\phi$ is the angle between the pulse front and the phase front. We polished the transversal cross-section in x-z plane and observe the plane from the -y direction. The pair of black lines represents two adjacent nanocrack planes with the grating period Λ labelled with the red line, which is parallel to the electric field direction. The solid green line represents the projection of the grating period Λ in the x-z plane. By doing so, the gap d between two nanocracks in the polished plane can then be expressed by the entire green line. After a series of geometrical transformation, the gap d can eventually be represented as $d=(\lambda /2n)\times [1/{(1-{\cos }^2\theta {\cos }^2\phi )}^{1/2}]$ and the NG orientation angle $\beta$ can be represented as $\beta =\pi /2+{\tan }^{-1}(-\sin \phi /\tan \theta )$. With both expressions, we can describe and calculate the NG orientation. We plot a 3D structure diagram of NGs in Fig. 2(b) with $\phi$ at 4.9° from Fig. 4(b) and $\theta$ at 10°, 50° and 90° respectively. It turns out that they behave the same way as the actual nanostructures in the corresponding SEM images.

 

Fig. 2 (a) Schematic of 3D rotation of NGs by a PFT fs laser direct writing. (b) The architectural diagram of NGs when $\phi$ = 4.9 ° and $\theta$ = 10°, 50° and 90° respectively.

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Figure 3(a) shows the sketch of fs laser writing NG in fused silica. The white tilted plane in the focused laser beam represents the tilted intensity plane. The PFT value measured by GRENOUILLE is shown in Fig. 3(b). In Fig. 3(c), we picked out three typical cross-section images with different polarization plane azimuth 10°, 90°, and 170° accordingly from Fig. 1. These written lines were along the S direction. We also placed the contrasts with the same laser parameters but the opposite direction S’. Surprisingly, the NGs in the bottom part of Fig. 3(c) were arranged in parallel to the $\overrightarrow{k}$ direction in the x-z plane, and their orientations are obviously different from those in the upper part.

 

Fig. 3 (a) Sketch of a PFT fs laser direct writing NG in glass. (b) The sheet containing the laser parameters measured by GRENOUILLE. (c) SEM images of the written NGs in the transversal cross-section with two opposite scan directions S and S’.

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In order to have a deep study on this matter, we measured and analyzed the space arrangement in both situations. The data of gap d was collected by reading the distance between two neighboring nanocracks and the angle $\beta$ was acquired by comparing the orientation of nanocracks respect to the incidence from the SEM images. Each dot in Fig. 4 represents an average of over 50 points randomly from the center part of the NGs. Figure 4(a) shows the dependence of the gap d on the polarization plane azimuth with two scan directions. The data fit well with the equation $d=(\lambda /2n)\times [1/{(1-{\cos }^2\theta {\cos }^2\phi )}^{1/2}]$. Note that the empirical period $\lambda /2n$ here was replaced by the measured period (about 230 nm) at $\theta =90°$ to match the actual conditions. According to the fitting line, we then deduced the PFT angle $\phi$ to 4.6° in the case that the laser beam moves along S direction. The fact that the writing NGs are parallel to the wavevector $\overrightarrow{k}$ when the scan direction was reversed indicates that this case is not sensitive to the PFT. Besides, we can also draw the similar conclusion from the fitting result of $\beta =\pi /2+{\tan }^{-1}(-\sin \phi /\tan \theta )$ in Fig. 4(b). These two results point out the significance of PFT in quill writing. Note that the value of $\phi$ corresponding to the measured Pulsefront Tilt of 88.8 fs/mm is about 1.5° by the conversion formula $\tan \phi =c\times (\partial t/\partial x)$ [20], which is smaller than the one in both experimental fitting results. This is because we measured the laser parameters in front of the objective lens while the PFT feature is strongly enhanced in the focal regime as the beam diameter shrinks.

 

Fig. 4 Dependence of the gap d (a) and the orientation angle $\beta$ (b) on the polarization plane azimuth of laser pulse. The blue and red dots present the experimental data on S and S’ scan directions respectively. Solid lines correspond to the fitting results of geometrical formulas. The error bars come from a calculation of mean square root (MSR) error.

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In the view of current results, we can get the conclusion that writing NGs depends on the correlation between the sample movement and the PFT, and two scan directions have distinct rotation styles. In our previous experience, the rotation of 3D NGs was once considered to be caused by the slope of the light polarization plane and it can be weighed by the component ${\overrightarrow{E}}_{\perp }$, i.e., the project of the electric field vector $\overrightarrow{E}$ in the $\overrightarrow{k}$ direction [15]. In other words, writing NGs should remain the same even when a reversed direction scan is applied, but this is not the case here. Therefore, there must be another potential factor causing the rotation of NG besides the light polarization.

In recent studies, the ponderomotive force ($\overrightarrow{\nabla }{\overrightarrow{E}}^2$) stemming from PFT was put forward as the major driver of the quill writing effect of ultrafast lasers [13, 16, 21]. In the scheme, a force perpendicular to the tilted intensity plane pushes free electron plasma forward in the front of the pulse (similar to a snow-plough behavior). That process may increase the amount of STE with an asymmetrical confinement. Then these repeated excited plasmons will experience an anisotropic extension in the electric field plane and finally form a self-organized periodic nanostructure in the writing track. Typically, if the Poynting vector has a horizontal component along the scan direction as shown in Fig. 3(a), the pondermotive force will trap and displace the excited electron plasmas along the moving direction, so there is always a quantity of STE existing at the front edge even after the glass cooling [19]. When the next pulses arrive at the front edge, more free electrons will be excited due to the lower threshold of STE in contrast to the original substrate. That process benefits from the pulse-to-pulse memory effect [22] and is a positive feedback on the increase of concentration of plasma. After a certain period of accumulation, the plasma at the focus will reach saturation and even make it easier to modify with a small part of pulse energy. Then most of the energy could convert into the pondermotive force to compress the induced plasma into the shape along the intensity front plane in which the NG is imprinted. Through these means, controlling the laser polarization then affects the 3D orientation of NG. On the opposite scan direction, however, most of the pulse energy is focused to excite the electron plasma due to the lack of the above STE accumulation effect, which forms a sort of relaxation of electron plasma in the focus center. In this situation, the remaining energy is hard to produce the pondermotive force to press the plasma, i.e., the electrical field plane is not sensitive to the PFT and will turn back to the phase front plane. Therefore, the NG keeps the intrinsic orientation. We think that a direction-dependent pondermotive force resulting from the correlation between the PFT and the scan direction plays an important role in the transformation from 2D to 3D rotation of NGs.

4. Conclusion

In summary, our result shows that it is possible to modulate the transversal rotation of self-organized NGs in glass with PFT fs laser quill writing. The whole process can be summarized as follows: (1) A pulse-to-pulse memory effect produces a positive feedback for the excited electron plasma and the related STE at the front edge with the sample moving along S direction; (2) Then most of the pulse energy may convert into the light pressure to squeeze the electron plasmas to shift their electrical field plane; (3) The opposite scan is very hard to create sufficient pondermotive force to tilt the electrical field plane due to an unmatched geometry between PFT and the scan direction.