1. Introduction

Femtosecond (fs) lasers enable various kinds of micro/nano processing. An interesting phenomenon of fs laser processing is the spontaneous formation of sub-wavelength periodic structures, which are called ripples, on the surface of solid substrates. Spontaneous formation of ripples has been widely observed during irradiation with linearly-polarized fs laser pulses [1–3]. Ripples could be useful for modifying surface properties such as friction coefficient [4], consequently, the mechanism of ripple formation is still actively investigated [5–8]. The fs laser is also useful for modifying the inside of transparent solid materials without damaging its surface. For example, three-dimensional (3D) optical waveguides have been fabricated inside glasses by scanning the focus position along a line [9]. Sub-wavelength periodic structures can also be fabricated inside transparent solid materials when linearly-polarized fs laser pulses are focused on the inside [10–12]. Periodic structures have also been observed parallel to the optical axis inside transparent solids [13, 14].

Here, we report another kind of periodic structure that spontaneously forms in fs laser processing, but the period is much longer than the wavelength. The periodic structures are formed when fs laser pulses are focused slightly inside the back surface of solid substrate, and the focus is scanned perpendicular to the optical axis (transverse-scanning processing). In transverse-scanning processing, the pitch (distance between neighboring irradiation spots) is usually set to a value smaller than the diameter of individual modified spots. Correspondingly, a line-shaped processed region is expected to be homogeneous along the line. Few articles, however, have described spontaneous formation of inhomogeneous, periodically modulated patterns. For example, Graf et al. reported formation of a pearl-chain structure (a microstructure that looks like pearls periodically aligned along a line) inside of glass [15]. The period of the pearl-like structure (about 7 μm, measured by the present author) was much longer than the pitch. Spontaneous formation of these types of “long” periodic structures with a period much longer than the pitch have also been reported [16–19]. Hereafter, the term “long-periodic” indicates that the pattern is repeatedly changing at the 10 μm scale, whether or not the pattern is completely periodic.

We present a systematic study on the formation of long-periodic patterns that occurred only when fs laser pulses were focused close to the back surface. The formation of the periodic patterns was critically dependent on the distance of the focus from the back surface. We examined the dependence on the focus position along the laser beam axis, the scanning speed, and the repetition rate. We present a new hypothesis based on successive increases in local density. This is distinct from the previous interpretation based on heat accumulation.

2. Experimental

A Ti:Sapphire chirped-pulse amplifier (Spitfire, Spectraphysics) was used as a light source. Its operating wavelength, pulse duration, and maximum repetition rate were 800 nm, 130 fs, and 1 kHz, respectively. The laser beam was introduced into an inverted optical microscope (IX-70, Olympus), and focused by an objective lens that has a correction collar (40×, NA=0.60, LUCPlanFLN, Olympus). Polarization was adjusted before the microscope using a polarizer and waveplates so that the polarization at focus was circular. The pulse energy was fixed at 0.75 μJ (measured before the microscope).

The sample used was a commercial coverslip (C024321, Matsunami) whose nominal thickness is 0.12–0.17 mm. Another coverslip of the same type but a different nominal thickness of 0.45–0.60 mm was also used for comparison, and similar results were obtained. The sample was set on a 3D stage composed of three motorized linear stages (PG615-L05AG-E, Suruga Seiki) with a three-axis micro-stepping controller (MSC-10, Suruga Seiki); the overall resolution was 0.1 μm. During the irradiation of fs laser pulses, the sample was translated perpendicular to the laser beam axis at a constant speed v. The sample was scanned in two counter-propagating directions to check for the presence of the dependence on scanning direction (Quill effect [20]). The arrows in the figures indicate the directions to which the irradiation points were moved.

The focus of the laser pulse was set close to the back surface. The focus position was adjusted by moving the sample up or down. Hereafter, the sample position is denoted by z. An increase in z indicates an increase in the distance between the sample and focusing objective lens; that is, the focus moves to the inside of the sample substrate (Fig. 1(a)). The repetition rate of the laser pulse, F, was also subject to change. The pitch p was adjusted by changing v and F (p = v/F).

 

Fig. 1 a) Explanation of the meaning of the z value. b) Optical micrographs of fs laser modified patterns at different focus position. The values in the left indicate the relative position (in μm) of the sample with respect to the focusing objective lens. c) Scanning electron micrograph of the back surface irradiated at z=4 μm.

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The patterns produced were examined by optical transmission microscopy and scanning electron microscopy (SEM). SEM images were taken on a JSM-6510 (JEOL) instrument. Before taking the SEM images, a thin layer of platinum was deposited on the surface of glass sample.

3. Results and discussion

3.1. Depth-dependence

We observed spontaneous formation of long-periodic patterns by setting the focus slightly inside the back surface of the glass. This is similar to the result of Vitek et al. [16], while they did not study z dependence. We found that the patterns were sensitive to z; that is, they critically depended on the depth to which laser beam was focused. Figure 1(b) shows the depth-dependent patterns (v=100 μm/s, F=1 kHz, p=0.1 μm) for both scanning directions. The numbers on the left indicate the value of z in μm. As seen in the figure, at z=0 μm, homogeneous lines were drawn on the back surface by laser ablation (z=0 μm was defined phenomenologically as the highest position of the sample where homogeneous lines were drawn). Increases in the z value changed the lines from homogeneous to periodic. In the range z=2–5 μm, the patterns were long-periodic in both writing directions. At z=6 μm, the lines written in the opposite directions differed; the line written in the L direction was long-periodic but that in the R direction was chaotic. For z=8 μm, the lines were again homogeneous but thinner than for z=0 μm. Overall, the difference between L and R directions was not very significant, except for z=6 μm. Similar sensitive dependence of Quill effect on the focus position has been reported in bulk by Yang et al. [21].

SEM observation revealed that holes were periodically formed on the back surface. Figure 1(c) shows a close-up image of the surface irradiated at z=4 μm, where long-periodic patterns were formed. As shown, the holes were formed periodically. Formation of holes was observed for other depths. This indicates that ejection of materials occurred periodically during transverse-scanning processing.

The long-periodic range of z had periods of approximately 7–16 μm (in our experience, the periods can be more scattered for other irradiation parameters and other materials). A weak dependency was observed with z: the larger the z value, the smaller the period. The observed period was much longer than the pitch of p=0.1 μm, wavelength (0.8 μm), and the diameter of individual modified spots (≈ 2 μm). Thus, the formation of long-periodic patterns cannot be explained by these parameters.

The following experiments were carried out at around z=5 μm. Even though precise determination of absolute z value was difficult, in a set of experiments (that is, the patterns shown in the same figure), the sample position along optical axis was not changed in order to maintain a constant value for z.

3.2. Scanning speed- and repetition rate-dependence

Figure 2 shows the dependence of the fs laser modified patterns on scanning speed v, where the repetition rate F was fixed to 1 kHz; thus, the pitch p was proportional to v. At v=50 and 100 μm/s, the patterns were long-periodic. The period was roughly 7 μm for v=50 μm/s and 10 μm for v=100 μm/s. This dependence on scanning speed is consistent with previous reports [15, 16, 19]. For larger v (200–500 μm/s), the lines were chaotic, and for v=1000 μm/s, the lines were thinner and did not have clear inhomogeneity.

 

Fig. 2 Scanning speed v dependence of fs laser modified patterns with fixed pulse repetition rate of F=1 kHz.

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In Fig. 3, both v and F were changed. For the same pitch of p=0.1 μm (Fig. 3(a) and 3(b)), fabricated patterns were similar although v and F was differed ten-fold. The lines in Fig. 3(c) were fabricated with the same scanning speed used in Fig. 3(a) and the same repetition rate as in Fig. 3(b) (p=1 μm, accordingly), and the patterns clearly differed from those in Fig. 3(a) and 3(b).

 

Fig. 3 Scanning speed v and repetition rate F dependence of fs laser modified lines.

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3.3. Plausible formation mechanism

The formation of long-periodic patterns has to be correlated to the increase/decrease cycle of a localized material parameter. The parameter must have a specific property; the change in the parameter can be accumulated by successive irradiation of fs laser pulses during transverse-scanning, and the change can be reversed by a spontaneous mechanism. One possibility for this type of parameter is temperature. Some previous articles have interpreted the formation of long-periodic pattern as a phenomenon induced by heat accumulation [15, 17, 19]. In the field of fs laser processing, heat accumulation is generally accepted as nonnegligible only when the repetition rate of the laser is a few hundred kHz or higher [22–24]. The three previously mentioned articles used high repetition rate (≈ 10 MHz) lasers. However, a 1-kHz repetition rate or less was adopted in the present research. Two articles have reported the formation of long-periodic pattern with fs lasers of low (1 kHz) repetition rate [16, 18]. The main interest of both articles was the Quill effect; accordingly, no discussion was given to the formation mechanism of the long-periodic pattern.

Our interpretation is that the parameter is the density of material. Irradiation of a single fs laser pulse can modify density distribution around its focus [25]. When the center of the spot was rarefied and the surrounding region was densified, the density in the densified front is further increased by successive pulses. Increases in density cause an increase in compressive stress. When the stress reached a critical point, the surface of the substrate was disrupted, leaving a hole, and the stress was released. On the other hand, if the stress saturated before reaching the critical point for surface disruption, no long-periodic pattern would be formed, and a continuous line would be drawn.

This scenario is schematically illustrated in Fig. 4 and is consistent with the experimental results summarized as follows: i) long-periodic patterns were formed only when the fs pulses are focused close to the back surface (Fig. 1(b)), ii) holes were generated on the surface (Fig. 1(c)), iii) the formation of a long-periodic pattern mainly depended on the pitch p, while no obvious dependence was observed on the repetition rate F (Figs. 2 and 3). In addition, disappearance of long-periodic pattern for larger p (Fig. 2 (≥500 μm/s) and Fig. 3(c)) would be attributed to smaller saturation value of stress.

 

Fig. 4 Proposed scheme of formation of long-periodic pattern. The gray region corresponds to the modified region (brighter region observed in the experiments), and the thickness of the region corresponds to the degree of increase in density.

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At present, however, no direct evidence is available for the accumulative increase in density. Further experimental and theoretical study is required to fully understand this phenomenon.

4. Conclusion

Transverse-scanning femtosecond laser processing of a glass substrate results in the spontaneous formation of long-periodic patterns. Holes were periodically formed on the surface in these long-periodic patterns with a period of about 7–16 μm. The long-periodic patterns formed only when the focus of the fs pulses was slightly beneath the back surface. A scenario for the formation of long-periodic pattern was proposed: The accumulative increase in density induced by fs laser pulses causes periodic disruption of the surface.