1.Introduction

Laser-induced periodic surface structures (LIPSSs), also called as ripples, have been intensively studied over nearly 40 years ever since the first discovery by Birnbaum on semiconductor surfaces [1]. A large number of previous reports have confirmed that this could be recognized as a general phenomenon of laser-matter interaction occurring at the low fluence around the ablation threshold, which has been already evidenced on very diverse materials: metals, semiconductors and dielectrics [2–10]. Generally, the obtained spatial period of the ripples closely depends on the material properties as well as the irradiation conditions such as the laser wavelength, the laser energy, the pulse duration, the pulse number, and the incident angle [2, 3, 11–14]. In particular, the ripple period induced by femtosecond lasers can be reduced much less than the laser wavelength [3, 7, 15–17]. On the other hand, for the linearly polarized laser incidence, the available ripple orientation can appear either perpendicular or parallel to the laser polarization depending on the incident energy [18–21].

Recently, many researchers have attempted to investigate the formation of surface structures with different polarization of femtosecond lasers. For example, Varlamova et al. studied the influence of variable laser polarizations of incidence on ceramics like CaF₂ and MgF₂through multi-shot irradiation method [22, 23], and found that different ripple orientations could be created with elliptically polarized femtosecond lasers, but for circular polarization, arrays of spherical nanoparticles began to appear on the material surfaces. They argued that in the latter case no distinguished field direction could be imposed. Furthermore, such a phenomenon of nano-dots formation by the circularly polarized lasers was also reported on other ceramic materials (such as SiC, ZnSe and ZnO) owing to Coulomb explosion process [24–26]. However, in contrast to the aforementioned observations, Zhao et al. recently pointed out that the regular ripple structures could still be produced on the metal surface even under the irradiation of circularly polarized femtosecond lasers, but the ripple orientation seemed to slant by 45° with respect to the linear polarization case [27]. In addition, the slantwise oriented ripple formation by circularly polarized femtosecond lasers has been also evidenced on other metals and semiconductors [28, 29]. In spite of these observations, until present no convincing relevant explanations have been achieved, but which it is very important and interesting to understand the ripple formation physics.

In this paper we present new insights into the ripple formation on metallic materials such as W and Cu by irradiating variable elliptical polarization of 800 nm femtosecond lasers. Firstly we demonstrate evolvement properties of the ripple orientation with varying laser ellipticities in experiment, and the regular rippling structures are shown to grow on the metal surfaces irrespective to the rotation of quarter waveplate (QWP). Theoretical analyses reveal that circular polarization state cannot be obtained through QWP for the incident broad bandwidth of femtosecond lasers, and the ripple orientation is eventually defined by the interference between the major axis of polarization ellipse and excited surface plasmon polaritons.

2. Experimental descriptions

A Ti: sapphire femtosecond laser amplifier system (Spectra Physics HP-Spitfire 50) based on the chirped-pulse-amplification technique was employed as a light source in our experiments, which delivers the linearly polarized pulse trains at the repetition rate of 1 kHz, centered at the wavelength of 800 nm with the pulse time duration of 50 fs. The linear polarization direction of the lasers was checked using a Glan prism. A quartz material based zero-order QWP was inserted into the beam path to transfer the laser polarization into variable elliptical states. Upon rotation of QWP, its azimuth angle θ between the optical axis and the original laser polarization was varied, resulting in different laser polarization ellipticities. The samples were two different metallic plates (Cu, W) with optical polished surfaces, which were mounted on a motorized x-y-z translation stage (New Port UTM100 PPE1) with a resolution of 1 μm. The laser beam was normally focused through a microscopic objective (4 × , N.A = 0.1), and the estimated laser spot size on the sample surfaces was about 60 μm (Gaussian beam diameter at 1/e²). Under the fixed irradiation of femtosecond lasers, the line scribing method was performed at a sample moving speed of 0.2 mm/s parallel to the original laser polarization direction. A schematic diagram of our experimental setup is shown in Fig. 1 . Laser energy was adjusted by a neutral-density filter and measured before the objective. All experiments were carried out in ambient air in a Class 1000 clean room. After irradiation, the samples were cleaned ultrasonically with acetone. The morphological evolvement of the laser-exposed surfaces was examined by means of scanning electronic microscope (SEM, Hitachi S-4800).

 

Fig. 1 A schematic diagram of the experimental setup.

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3. Results and discussion

First, at the azimuth angle of θ = 0°, i.e., the slow axis of QWP is aligned with the original linear polarization of femtosecond lasers, experiments revealed that the periodic ripples were formed on the sample surfaces, accompanying the structure orientation perpendicular to the laser polarization direction. In this case, a typical result obtained on copper surface at the laser fluence of about F = 1.4 J/cm² is shown in Fig. 2 , where the zoom picture indicates that the induced ripple structures consist of an array of groove patterns with the period of Λ≈600 nm. As can be seen, such subwavelength ripples are spatially arranged perpendicular to the direction of an incidence electric field. Moreover, a mass of nanoparticles at hundred-nanometer scale were also produced to cover up the groove ridges. For the sake of convenient study, this kind of ripple alignment direction can be marked as a reference, which is applied throughout the paper.

 

Fig. 2 SEM image of the periodic ripples formed on Cu surface with linearly polarized femtosecond lasers. The bi-directional arrows represent both the sample translation and the laser polarization directions.

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When QWP is gradually rotated in a clockwise direction, femtosecond lasers were ready to change into the elliptical polarization states. Then a series of experiments were performed to investigate their influences on the ripple formation processes, and the corresponding results are summarized in Fig. 3 (a) . As shown clearly, when the azimuth angle of QWP is increased monotonously from θ = 0° to 90°, the laser-induced ripples always appear the grating-like distributions but with the orientation slantwise in a clockwise direction. Moreover, during the variation of laser polarization, the obtained ripple period can remain almost unchanged. For instance, at the azimuth angle of θ = 30°, the slantwise angle of ripples orientation is about γ = 34°. In the case of θ = 45°, at which the so-called circular polarization is referred to obtain in many previous reports [23, 26–28], the laser-induced surface structures cannot only maintain the period grating-like patterns but also posses a large slantwise orientation angle of about γ = 45°, which is much different from the pervious observations on ceramics [22–26]. More interestingly, when the azimuth angle of QWP increased to θ = 60°, the slantwise orientation angle of the ripples surprisingly decreased down to about γ = 34° rather than keeping up to become large. In other words, although the laser-induced ripples were still obliquely oriented clockwise, the slantwise degree of ripples is reduced at this moment. This phenomenon suggests that a maximum angle in the ripple orientation slant should exist for the incidence of elliptically polarized femtosecond lasers. As a matter of fact, at the increased azimuth angle of θ = 90°, the ripple orientation began to turn almost parallel to the reference direction, or the slantwise orientation angle of ripples became zero, γ = 0°.

 

Fig. 3 (a) Evolvement of femtosecond laser-induced ripples on Cu with rotating QWP. At the upper left and right corners of each image the rotation angle of QWP and the obtained laser polarization are indicated, respectively. (b)-(c) Dependences of the slanting ripple orientation on the rotation angle of QWP for two different materials, where the measured data are represented by solid squares and the simulation results are indicated by the red curves.

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On the other hand, as the azimuth angle of QWP continued to increase larger than 90°, the ripple orientation induced by femtosecond lasers was observed to slant again; however, at this time the slantwise orientation became evidently in the counterclockwise direction. Very similar to the above situations, the azimuth angle dependence of the ripple orientation also shows periodic variations. For example, at θ = 120°, 135°, 150° and 180°, the measured slantwise orientation angle of the ripples was approximately γ = −32°, −45°, −30° and 0°, respectively. The maximum slantwise degree appeared at the azimuth angle of θ = 135°. Naturally, if the azimuth angle was further rotated beyond θ = 180°, the above mentioned phenomena would recur, namely, the laser-induced ripple orientation will first periodically slant in a clockwise direction and then in a counterclockwise direction. Anyway, no matter how QWP rotates, the slantwise angle of the ripple orientation was always confined into a range of ± 45°. The measured variation of the ripple orientation vs the QWP azimuth angle for Cu material is shown in Fig. 3(b). Actually, our experiment revealed that this phenomenon can also take place on other metallic materials like W, as shown in Fig. 3 (c). From the obtained results, we can realize some interesting things when comparing the structure formation behaviors on metal surfaces with those on dielectrics especially at the relatively low laser energy incidence: in the former case the material removal is related to the photomechanical effect [30], so that it mainly depends on the major field component of laser ellipse, while in the latter case Coulomb explosion becomes predominant and the material removal in two crossed directions could take place for the elliptical polarization [23]. On the other hand, our observations suggests that ripple formation on metals cannot be simply attributed to the self-organization theory. Moreover, as mentioned by Guo et al [27], the slanting ripple orientation behaviors on metal surfaces can also be used to record both polarization and helicity of the incident lasers.

4. Theoretical analyses

In the following, theoretical analyses are conducted on how the ripple orientation is slanted by the elliptically polarized femtosecond lasers. When the linear polarization of femtosecond lasers pass through QWP, polarization ellipse can be achieved through coupling of the two components due to the birefringence effect, which is described as [31]

In our experiment, the quartz material based QWP has a thickness of d = 28 μm, and its wavelength dependent phase retardation can be calculated by $\phi (\lambda )=\frac{2\pi d}{\lambda }({\Delta }_0+{\Delta }_1\ast \lambda +{\Delta }_2\ast {\lambda }^2)$ (with Δ₀ = 0.011945, Δ₁ = −0.008214 and Δ₂ = 0.005714) [32]. If g(λ) represents the spectral distribution function of the incident femtosecond lasers, the following equation can be obtained:

 

Fig. 4 Calculated polarization ellipticity as a function of the rotation angle of QWP for the incident femtosecond laser with different spectrum widths.

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Figure 5 sketches evolvement of available polarization for femtosecond lasers when the optic axis of QWP is gradually rotated. If the field amplitude of incident linearly polarized lasers is denoted by A, the two field components in QWP will have amplitudes of$A_x=A\cos \theta$ and$A_x=A\sin \theta$, respectively, Within a range $\theta \in (0^o,{45}^o)$, $A_x>A_y$is fulfilled. According to Eq. (2), the major axis of the polarization ellipse (determined by both θ and φ) will move clockwise away from the original linear polarization direction. When the two amplitudes become equal$A_x=A_y$ at$\theta ={45}^o$, the angular position of the major axis becomes$\alpha ={45}^o$. In the case of $\theta \in ({45}^o,{90}^o)$, since$A_x<A_y$is obtained, the angular value of $\alpha$will be reduced, which implies that the major axis of the polarization ellipse moves back towards the original linear polarization. At$\theta ={90}^o$, the linear polarization of femtosecond lasers can be generated owing to no birefringence. On the other hand, when QWP rotation goes into a new range of $\theta \in ({90}^o,{180}^o)$, the major axis of the polarization ellipse can also display the waggling movement behaviors, but at this time their angular positions appear to be mirror symmetric to the above phenomena, which is due to the larger azimuth angle θ and the reverse-ordered alternative increment of two field amplitudes. This result physically indicates that the elliptical laser polarization undergoes transitions between the left and the right helicities, so that the observed slantwise orientation of ripples turns from the clockwise to the counterclockwise directions.

 

Fig. 5 Sketched evolution of the polarization state for the femtosecond lasers passing through QWP with variable rotation angles.

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According to the physical model of ripple formation [6, 7, 18, 31], the ripple orientation results from the optical interference between the incident light and surface plasmon excitation. For the elliptically polarized femtosecond laser irradiation, the effective wave vector of the incident laser is determined by the major axis of the polarization ellipse; thus, the direction of ripple arrangement will be perpendicular to the major axis of the laser ellipse, and of course the ripple orientation is deemed to change in phase. Based on the above discussion, we can simulate variations of the ripple orientation as a function of the rotation angle of QWP, as shown by the solid curves in Figs. 3(b)-(c). Undoubtedly, our simulation results are in consistent with the experimental data, which can confirm the validity of our theory.

5. Conclusions

We have performed a detailed study of how femtosecond lasers passing through QWP affect the ripple formation especially on metal surfaces. Experimental results have revealed that the grating-like ripple structures can always appear on metals no matter whatever rotation angle of QWP. Slantwise orientation of the ripples associated with the maximum angle of ± 45° has been evidenced to oscillate in either clockwise or anticlockwise direction depending on the laser helicity property. Theoretical analyses suggested that dispersion properties of QWP substantially lead to no generation of circular polarization for femtosecond laser incidence. The obtained polarization ellipticity is reduced with increasing femtosecond laser bandwidth. The major axis of the polarization ellipse, being as an effective wave vector of the laser, has been confirmed to be responsible for the ripple alignment. This investigation will be helpful to control the nanostructures formation on metals.