1. Introduction

It is well known that an inhomogeneous isotropic medium behaves with respect to the average field, such as a homogeneous but anisotropic medium [1–3] with the so-called effective permeabilities $\tilde{\varepsilon },\tilde{\mu }$. The effective medium theory [1] shows that, in a finely stratified medium with two alternating layers, the form birefringence effect occurs when the period d is much shorter than the wavelength λ of the propagating optical field ($d \ll \lambda /\sqrt {\tilde{\varepsilon }\tilde{\mu }}$). Such media can serve as a material platform for various optical metamaterials and metasurfaces, namely, nanocomposites with a regular structure and physical properties that differ significantly from those of traditional materials [4]. Characteristics such as enhanced nonlinear response [5] and optical chirality [6] begin to prevail in the stratified media, as a key-enabling optical platform for the fabrication of polarizing elements [3,7–10], polarization-independent optical elements [11], bio-sensors [12], and sensors of molecular chirality [13].

There are many optical materials with high refractive index in the visible [14] and near-infrared [15] ranges, with Si being the most popular and studied material. It provides the fastest nanostructure integration while keeping the complementary metal-oxide semiconductor (CMOS)-compatible technological advantages. Another promising area of such nanopatterned Si application is the analysis and transformation of the state of polarization of light (SOP). Currently, nanorods [15], wire grids [9,16], conical needles [17], and nanodisks [18] have been proposed for this purpose. However, most of the aforementioned structures either are formed in thin conductor/semiconductor films (e.g., steel, Ge, Si, and Al) deposited on a glass substrate [9,19,20] or require complex technological implementation [17,19]. Meanwhile, the optical activity of achiral anisotropic surfaces was recently observed [21], which holds promise in providing fully ellipsometric measurements.

Usually, SOP measurements imply mechanically rotating parts of the polarizer or a liquid crystal retarder. In recent decades, polarization-sensitive optical radiation detectors have been introduced. They are based on polarizers with four fixed azimuths in the form of nanometer wire gratings integrated directly onto the surface of the CMOS semiconductor structure. Such a system is similar to the scheme with a rotating polarizer and can determine two of the three normalized Stokes parameters, which are sufficient in many cases [22,23]. In addition, such system is characterized by a short measurement time, which is shorter than that of systems based on liquid and electro-optical crystals [24], and relies on rather simple calculations.

This study is focused on the characterization of the polarizing properties of a Si structure fabricated by one-step femtosecond laser nanopatterning of Si wafers. The polarizing properties acquired over the entire visible range of 380–740 nm for unpolarized normally incident light, using both ellipsometric and polarimetric setups, exhibited partial linear polarization with slight chirality.

2. Experimental details

Nanopatterned commercial Si (100) wafer was fabricated via single-pass scanning of a 2×2-cm²-wide and 0.4-mm-thick piece using a laser nano/micromachining workstation [25]. The nanopatterning was performed by 1030-nm, 300-fs linearly polarized pulses of a fiber laser (Satsuma, Amplitude Systemes), delivered at 5 µJ of pulse energies (TEM₀₀ mode) and a repetition rate f of 100 kHz, focused onto the sample surface in a glass beaker into a focal spot with a 1/e radius σ_1/e of ∼15 µm (peak fluence of ∼1 J/cm²) through 5-mm-thick carbon disulfide (CS₂) (Fig. 1), with the intention of fabricating oxygen-free nanopattern. Surface scanning was performed with 100 lines/mm of surface filling and 13 µm of inter-spot distance in the lines at a scan velocity V of 10 mm/s (the corresponding surface exposure N = 300 shots/spot). After the fabrication process the CS₂ layer is removed by rinsing the sample with water. The surface topography and chemical composition of the nanopatterned samples were characterized using a scanning electron microscope (JSM-7001F, JEOL) equipped with an energy-dispersive X-ray spectroscopy module, revealing regular surface nanopatterns in the form of one-dimensional (1D) arrays of vertically aligned, weakly doped amorphous Si nanosheets [25,26].

 

Fig. 1. Optical scheme for wet sub-picosecond-laser filament-mediated nanopatterning in the 5-mm-thick liquid carbon sulfide (CS₂) layer.

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These 1D surface nanopatterns were fabricated in the regime of weak homogeneous ablation (sub-filamentary regime) of the Si wafer across the focused Gaussian beam enhanced by strong nanoscale surface plasmon ablation. The latter ablation mechanism is well known to provide homogeneous regular 1D arrays of Si nanoripples (Fig. 2(a)) with their ridge orientation perpendicular to the laser polarization, similar to that of common surface ripples [6,9,25,26]. The role of surface plasmons in the ablation process of the was previously reported in more detail in [26]. Apart from the role of plasmons, the fabrication process was studied not only in the liquid CS₂, but in other media, such as air and water. The study on the influence of the Si absorption and reflectance in the IR range on the ablation process was previously carried out in [27,28].

 

Fig. 2. (a) Side view (40°) of the scanning electron microscopy images of the 0.3-ps Si surface nanoripples produced at F = 1 J/cm² and N = 300 pulses/spot. (b) FFT spectrum corresponding to image (a). (c) Reconstructed image from the FFT spectrum (b) after applying the filtering mask (d); there is also a 1-by-1 µm enlarged pattern with a small pitch p inserted here. (e) Reconstructed image from the FFT spectrum (b) after applying the filtering mask (f).

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3. Experimental results and discussion

To determine the orientation of the structures induced on the surface of the Si wafer, we calculated a 2D fast Fourier transform (FFT) spectrum (Fig. 2(b)). Two distinct frequency peaks can be identified by determining the orientation of the spectrum and taking the projection of the maxima of the real part on the collinear frequency axis. Based on the obtained distributions, 2D filters were generated. Subsequently, the frequency peaks of the spectrum were identified to analyze the corresponding 1D textures. By multiplying the original spectrum with the 2D filter (Fig. 2(d)) and performing an inverse Fourier transform, we found a subwavelength 1D grating with a period p of ∼0.17 µm (Fig. 2(c)), which appears to be the source of the optical birefringence in the Si wafer. After filtering the FFT spectrum (Fig. 2(b)) with another mask (Fig. 2(f)), we obtained a low-frequency 1D grating with a period P of ∼9.3 µm (Fig. 2(e)). Both masks are shown on the same scale as the spectrum in Fig. 1(b), thus, we magnified a small fragment of the mask (Fig. 1(f)) by х40 times, obtaining optimal resolution. The masks were chosen to demonstrate the non-collinearity between wave vectors of the obtained patterns with the resulting angle between them ∼41° (Fig. 2(e)). In this case, the low-frequency grating (∼105 lines/mm) polarizes the wave reflected from the surface of the Si wafer. Then, the polarized wave obtained as a result of diffraction on a low-frequency grating acquires a phase shift induced by birefringence due to the subwavelength grating (∼5903 lines/mm). Such a combination of gratings can qualitatively explain the phenomenon of partial chirality of the reflected radiation.

To measure the polarizing property, we employed an optical setup, where the white unpolarized light, incident on the nanopatterns almost in a normal direction, specularly reflected and passed the broadband quarter-wave plate and polarizer and, finally, was registered by a multichannel spectrometer. For the degree of polarization (DOP) and SOP measurements, we used the well-known technique described in [29,30]. The experimental setup is shown in Fig. 3, where our primary concern was the prevention of any intrinsic SOP changes during all operations. For this purpose, the illumination and detection were carried out at small angles (β/2 ≤ 0.5°); therefore, despite the significant refraction of the Si (Fig. 4), the effect of the Fresnel reflection coefficients (<10⁻⁴) was below the accuracy of our instruments even for a shorter wavelength of 380 nm.

 

Fig. 3. Experimental setup for measuring the Stokes parameters of the light reflected from the sample: P, – Glan-Thompson polarizing prism; QWP, achromatic quarter-wave plate.

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Fig. 4. Experimental spectrum of the DOP of the light reflected from the sample; reference spectra of the refractive index n and the extinction coefficient k of the silicon (after [31]).

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Unpolarized light from a broadband radiation source, i.e., tungsten halogen bulb LS-1 (OceanOptics), was directed through the 400-µm core fiber, collimated by an achromatic lens (Lens₁) and illuminated a 2-m remoted sample with an aperture of ∼5×5 mm². In the case of our ellipsometric measurements, the reflected light passed through the quarter-wave plate (QWP) with the azimuth Ψ_QWP, then passed through a polarization prism with the azimuth Ψ_P, coupled to an 800-µm core fiber using Lens₂, and, finally, entered the Avaspec-2048-USB2-UA spectrometer (Avantes). In the case of polarimetric measurements, QWP was removed from the scheme.

The magnification of the lenses and the core diameter of the fibers together worked as a spatial Fourier filter parallel to the optical axis beams. In addition, the output face of the 800-µm core fiber was out of the focal plane of Lens₂, so that only the central region of the formed image of the sample entered the fiber. To exclude the effect of scattered light, we attached the backside of the sample to a needle with an anti-glare coating. The results of a series of preliminary measurements carried out with metallic and polished Si mirrors helped convince us that the system is insensitive to the residual polarizing effect, which arises from the use of fibers. Here, the main source of errors was the insufficiently achromatic QWP (10RP54-1, Newport); the error in the retardance reached a value of ∼8% at the end of the range, which was an additional concern during data processing and thus needed corrective calculations.

The results of measuring the Stokes parameters are shown on Fig. 5(a). The parameters Ŝ₁ and Ŝ₂ that were measured using both techniques (ellipsometric and polarimetric) are in good agreement with each other. The parameter Ŝ₃ that was measured only using the ellipsometric setup was nonzero. The obtained Stokes parameters corresponded mainly to linearly polarized light with the azimuth ψ (Fig. 5(b)), almost coinciding with the direction of the wave vector of the self-induced grating during Si nanopatterning. According to the values of the Stokes parameters, there was a small azimuthal rotation at an increasing wavelength (ψ∼0° around 470 nm). The highest degree of polarization (≥15%) was achieved in the long-wavelength region of the spectrum, whereas in the region near 380 nm, less than 5% of the reflected polarized light was observed (Fig. 4).

 

Fig. 5. (a) Experimental spectra of the normalized Stokes parameters and (b) experimentally measured azimuth $2\psi = \arctan ({S_2}/{S_1})$ and ellipticity $2\chi = \arctan ({S_3}/\sqrt {{S_1}^2 + {S_2}^2} )$ of the obtained nanorelief.

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For a possible origin of the obtained birefringent structure, which induces light chirality, one can consider the dynamic polarization rotation of the femtosecond laser pulses in their filaments in the liquid carbon disulfide studied in [26]. As is well known, femtosecond laser filaments generated by ultrashort laser pulses induce a remarkable birefringence over the entire filament length in both atomic and molecular gases [32–34], with potentially even stronger effects in liquids. Any linearly polarized femtosecond laser pulse probing this filament will be decomposed into two orthogonal polarization components propagating at different speeds, resulting in an elliptical polarization, owing to the instantaneous electronic or delayed molecular response, depending on the different types of gases [32–34]. Liquid carbon disulfide supports both electronic and molecular orientational Kerr nonlinearities [35], converting the incident linearly polarized pulses into elliptically polarized ones. In the multi-shot mode of the Si nanopatterning the induced orthogonal polarization could drive the orthogonal surface plasmons on the nanopatterned surface, producing either a 2D square array of Si nanopillars (similar to circularly polarized laser pulses on glass surfaces [36]) or just a damage to the main 1D array of Si nanosheets, if the induced orthogonal polarization component is insufficiently strong to produce its surface nanorelief. Apparently, wet femtosecond laser nanopatterning involves these phenomena, resulting in the remarkable properties of the obtained Si nanopatterns.

We note here that by increasing the contribution of the high-period structure into light scattering, one can increase DOP, but most likely, the broadband character of the spatial spectrum (see Fig. 2(b)) will play an important role and will limit the maximum attainable DOP. Chirality, in turn, depends on the strength of the effective birefringence and the effective depth of the interaction between electromagnetic radiation and the surface. So, according to the [17], the chirality can reach ±1 for the indicated wavelengths (400–700 nm). A decrease in the amplitude of the reflected wave, which is inversely proportional to the degree of polarization can be a downside here.

4. Conclusions

The femtosecond laser nanopatterned Si surface was demonstrated to be capable of polarizing the optical radiation at a normal incidence owing to the material and structural dispersion of the Si nanopatterns. A polarization degree of ≥15% was achieved in the range of 650–740 nm and decreased to ∼5% for the short-wavelength visible range. The polarization type in the entire spectral range was mainly linear, with an azimuth ψ dictated by the processing mode of the femtosecond laser radiation. The nonzero chirality was apparently provided by the birefringent structure, which was obtained after femtosecond laser processing of Si in the presence of liquid carbon disulfide and polarization rotation during laser filamentation in the latter fluid. These polarizing properties allow the polarimetric analysis of light by a simple setup, and a further increase in the chirality of the reflected light would allow ellipsometric measurements. The facile laser-assisted fabrication process is highly CMOS-compatible, paving the way for the design of a new generation of polarization-sensitive integrated sensors and devices.