1. Introduction

Periodically poled ferroelectric crystals, also known as nonlinear photonic crystals (NPCs), are excellent media for studying nonlinear wave dynamics and to construct scientific applications involving the conversion of laser frequencies. The NPCs possess a homogeneous refractive index, but the second-order nonlinear optical coefficient (χ⁽²⁾) spatially varies to ensure efficient energy exchanges among optical waves of different frequencies via the so-called quasi-phase matching [1,2]. Moreover, properly designed χ⁽²⁾ modulations in the transverse direction can be used to engineer the phase of the generated waves to achieve desired beam profiles in near or far field [3–6]. This also offers an efficient way to engineer the properties of entangled light in the process of spontaneous parametric down conversion [7–9].

The nonlinear photonic crystals can be fabricated via the electric field poling of ferroelectric crystals, such as LiNbO₃ and LiTaO₃ crystals with excellent nonlinear optical properties. The term of poling means the alignment of the spontaneous polarization along the external electric-field direction. The sign of the second-order nonlinearity χ⁽²⁾ of the crystal is sensitive to the orientation of spontaneous polarization, which thereby can be reversed by flipping the applied electric-field. This electric-field poling has been extensively used to fabricate high quality and large-scale NPCs of 1D and 2D structures in the last few decades [10–12]. However, it cannot be used in χ⁽²⁾ nonlinearity engineering in three dimensions, due to the lack of practical ways to modulate an poling electric field periodically along the depth of ferroelectric crystals.

As a solution, all optical poling using near infrared femtosecond pulses has been proposed recently [13]. This optical method utilizes nonlinear absorptions of infrared light to produce high temperature gradient. The resulting thermoelectric field locally inverts the sign of χ⁽²⁾ nonlinearity in the focal volume of the beam. Since the near-infrared pulses can be focused deep inside any transparent materials, the femtosecond laser poling offers unique capability for χ⁽²⁾ nonlinearity engineering in three dimensions [14–16]. The optically induced 3D NPCs have been employed for demonstrations of novel effects and applications in laser frequency conversion [14,15,17,18], nonlinear beam shaping [19,20], and nonlinear holography [21–23].

Till now, the infrared femtosecond laser induced ferroelectric domain inversions have been mainly implemented using the Ti:sapphire laser (operating at the wavelength around 800 nm). The tested ferroelectric crystals included strontium barium niobate (SBN) [18], calcium barium niobate (CBN) [24], lithium niobate (LiNbO₃) [25], barium calcium titanate (BCT) [14], and 0.62Pb(Mg_1/3Nb_2/3)O₃-0.38PbTiO₃ (PMN-PT) [26]. Meanwhile, a recent work utilized the Yb:KGd(WO₄)₂ laser operating at the wavelength of 1026 nm to engineer LiNbO₃ crystal [27]. While the infrared femtosecond laser poling has been a powerful technique for fabricating 3D nonlinear photonic crystals, the impacts of the femtosecond laser wavelength and other processing conditions on the light-induced ferroelectric domain inversions are still sketchy. In this work, we explore femtosecond laser poling of a ferroelectric strontium barium niobate (Sr_0.61Ba_0.39NbO₃, SBN) crystal. We compare the optical thresholds for domain inversions at different wavelengths to find out the optimal poling wavelength. The impact of femtosecond laser power, exposure time, processing depth, and the longitudinal movement of laser focus is also experimentally studied. These findings contribute to a deeper understanding of light-induced ferroelectric domain inversions. They are also useful to fabricate high quality 3D nonlinear photonic crystals, which has great potentials in nonlinear photonics and quantum optics.

2. Results and discussion

2.1 Changes induced by broadband femtosecond lasers: domain inversion, permanent χ⁽²⁾ modification and optical damage

The experimental setup of femtosecond laser poling is exhibited by Fig. 1. The experiment was conducted in a z-cut as-grown SBN crystal. The crystal dimensions are 5 × 5 × 1 (x × y × z) mm³, with the z-surfaces being polished for femtosecond laser processing. The SBN crystal was mounted on a translational stage that can be automatically positioned along three orthogonal directions with a resolution of ∼100 nm. A Ti:sapphire laser oscillator (Chameleon Ultra II, Coherent) was used to deliver the femtosecond pulses for laser poling. The pulse duration and repetition rate are 140 fs and 80 MHz, respectively. The linearly polarized femtosecond laser beam (of diameter 1.2 ± 0.2 mm) was tightly focused with a 50×microscope objective (NA = 0.65) to illuminate the SBN crystal along its z-axis. The laser power for optical poling was adjustable by using a half wave plate followed by a polarizer, the operating pulse energy in poling process is about 1.5-4 nJ. The exposure time was controlled by an automatic shutter (SH05, Thorlabs).

 

Fig. 1. Schematic diagram of the experimental setup for femtosecond laser poling.

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The impact of the femtosecond laser wavelength on the light-induced inversion of ferroelectric domains was studied by conducting the laser poling experiment at wavelengths of 700, 750, 800, 850, and 900 nm, respectively. For each wavelength, the laser powers were gradually increased to find out the optical threshold for domain inversions. The laser processed areas of the medium constitute a two-dimensional 5 × 5 square lattice (period =10 µm) at a fixed depth of 20 µm below the surface of the crystal. The shutter was “on” for 0.5 seconds at each lattice point. After the laser processing, the obtained nonlinear optical structures were characterized using the Čerenkov second harmonic microscopy, which works on the principle of stronger noncollinear second harmonic emissions owing to the abrupt variation of χ⁽²⁾ nonlinearity across ferroelectric domain walls [28,29]. The recorded microscopic images are displayed in Fig. 2(a). It can be seen the weak femtosecond laser pulses illuminations, e.g., 130 mW, did not cause any change of χ⁽²⁾ nonlinearity in the SBN crystal (marked by the yellow squares in Fig. 2(a). When the laser power increased to 150 mW, the femtosecond pulses at 750 nm induced obvious changes inside the SBN crystal, but the crystal remained unaffected at other wavelengths. Increasing the laser powers further to 170 mW, the pulses of 700 and 800 nm started producing obvious changes to the crystal. However, no changes were observed for the femtosecond pulses at 850 and 900 nm until the laser powers were increased to 210 and 310 mW, respectively. It is worth noting that the as-grown SBN crystal has naturally random micro-scale ferroelectric domain structures, so the Čerenkov microscopic images did not show a dark background, but a noise-like bright and dark background corresponding to the originally random domains [Figs. 2(a) and (b)].

 

Fig. 2. The structures induced by femtosecond laser pulses at different wavelengths and powers (a) before and (b) after annealing at 300°C for 30 minutes. The yellow squares in (a) indicate the cases in which the femtosecond laser did not cause any changes of χ⁽²⁾ nonlinearity in the SBN crystal. The red squares in (b) show the cases that laser-induced structures disappeared after annealing above the Curie temperature, which is an indication of ferroelectric domain inversion. The blue squares in (b) correspond to the situations where the femtosecond laser writing induced permanent change of χ⁽²⁾ nonlinearity, which cannot be removed by the annealing. The black dots in (b) are optical damages caused by the femtosecond laser pulses. (c) The optical thresholds for ferroelectric domain inversion at different wavelengths. The black dots are experimental results, and the red rhombi are theoretical predictions. (d) The measured nonlinear absorption coefficients of the SBN crystal at the tested wavelengths.

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Considering that the femtosecond pulses illumination may induce complex changes not limited to the ferroelectric domain inversion, e.g., the reduction of χ⁽²⁾ value due to material modifications (partial or complete amorphization) [15], the laser-written SBN crystal was annealed at 300°C for 30 minutes to identify the physical origin of the observed changes. The Curie temperature of the relaxor ferroelectric SBN crystal is about 74°C [30], so annealing at 300°C can cause any laser-induced ferroelectric domain structures to disappear while the crystal returns to the originally random status, during cooling. However, the laser-induced χ⁽²⁾ reduction due to material modification is a permanent effect, which cannot be removed by annealing above the Curie temperature. Figure 2(b) shows the Čerenkov second harmonic microscopic image of the annealed sample. We can see the laser-induced patterns created at modest powers [e.g., 150 to 190 mW for all the wavelengths, refer to the cases marked by the red squares in Fig. 2(b)] disappeared after annealing, proving that they were indeed created by ferroelectric domain inversions. At higher level of laser power, instead of ferroelectric domain inversion, the femtosecond laser pulses illumination led to permanent index (and χ⁽²⁾) changes to the crystal, which could not be removed by the annealing treatment [these structure are marked by the blue squares in Fig. 2(b)]. Increasing the laser power to the even higher levels, e.g., 250 mW at 800 nm, the femtosecond pulses illumination caused optical damages to the crystal, which are shown as the dark spots in the microscopic images [Fig. 2(b)]. It should be mentioned the femtosecond laser induced changes of the linear optical properties of the crystal has been excluded from the Čerenkov microscopic images because the sole change of linear optical parameters, such as the refractive index, does not lead to any intensity fluctuations of the Čerenkov second harmonic wave [28].

2.2 Impact of femtosecond laser wavelength on optical threshold of domain inversion

Figure 2(c) shows the variation of the optical threshold, namely the minimal laser power to invert ferroelectric domains in the SBN crystal, on the femtosecond laser wavelength. The black dots in the graph represent the experimental values and the red rhombi are theoretical predictions. It is seen that they agree well with each other. The threshold attains its minimum around 750 nm, and gradually increases towards shorter or longer wavelengths. For lasers operating at the wavelength longer than 900 nm [31], the domains may also be inverted with high pulse energy as reported by recent work in lithium niobate [27]. To interpret this wavelength-dependent behavior, we need to consider the physical mechanism of light-induced ferroelectric domain inversion. The infrared pulses are absorbed by the SBN crystal via nonlinear absorption, heating locally the crystal such that strong temperature gradient induces thermoelectric field [13] which inverts spontaneous polarization.

It is reasonable to assume the required minimal number of the excited electrons is the same for domain inversion at each wavelength, so, the number of absorbed photons should be the same for all the wavelengths (set as N). To simplify the analysis, we further assume the nonlinear absorption in the tested spectral range is dominated by the band to band two-photon absorption (the band gap of SBN is about 2.6 eV) [32]. The total energy of the absorbed photons I_N can be expressed by:

The absorbed energy via two-photon absorption could be deduced by the nonlinear absorption coefficient β following the function [33]:

The two-photon absorption coefficient of the SBN crystal was measured at the tested wavelengths using the Z-scan technique and the results are shown in Fig. 2(d). Refer to Supplement 1 for more details. It is seen the nonlinear absorption shows a peak value at 750 nm. Using these measured coefficients into Eq. (1), the threshold energy I_inv (normalized) as a function of the laser wavelength can be obtained, which is shown by the red rhombi in Fig. 2(c). The good agreement between the experiment and theory is clear.

2.3 Impact of femtosecond laser wavelength on domain morphology

The laser-induced ferroelectric domain structures were also imaged in three-dimensions using the Čerenkov second harmonic microscopy, to reveal the impacts of the laser power on the morphologies of inverted domains. In Figs. 3(a) and (b), the measured average diameters and lengths of inverted domains are shown as the function of laser power for all the tested wavelengths. The side-view of the inverted domains induced with different laser powers at the same wavelength of 750 nm is displayed in Fig. 3(c) as a representative. It is clearly seen both diameters and lengths of the inverted domains increase with the femtosecond laser power. Depending on the laser power and wavelength, the average diameter of the light-induced inverted domains ranges from 2.7 to 3.5 µm. Considering the moderate amplitude of such fluctuations, the attempt to obtain larger duty cycles of inverted domains by using higher laser power is unlikely to be successful. A more practical way would be writing two inverted domains that are close enough to merge into a larger one. In the used z-cut SBN crystal, the average length of the needle-like inverted domains varies from 32.5 µm (170 mW, 700 nm) to 46.2 µm (250 mW, 850 nm). Such length scales are not favorable for the quasi-phase matching applications, as the latter often require χ⁽²⁾ modulation periods in the range of 2 to 30 µm (depending on the operating wavelength). To reduce the length of inverted domains, instead of writing them dot by dot, the line scanning of the femtosecond laser pulses may be a better option [21].

 

Fig. 3. The variations of (a) diameter and (b) length of light-induced inverted domains on laser powers for all the tested wavelengths. (c) The side view of the domain structures induced with femtosecond laser wavelength of 750 nm, obtained by the Čerenkov second harmonic microscopy.

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2.4 Impact of femtosecond laser exposure time on all-optical poling

It is generally accepted the thermoelectric effect plays a crucial role in ferroelectric domain engineering with femtosecond laser pulses, where the laser-induced high temperature gradients across the focal volume leads to a thermoelectric field for domain inversion. It is thereby essential to investigate the influence of exposure time of femtosecond laser pulses on the light-induced ferroelectric domain inversions. We used a mechanical shutter (SH05, Thorlabs) to control the exposure time, which facilitates the shortest exposure time of 0.06 second. Accordingly, four exposure durations, 0.06, 0.10, 0.30, and 0.50 seconds, were examined in experiment. Figure 4 shows the results, obtained at the laser power of 230 mW and wavelength of 800 nm. It is a good indication that a single domain can be inverted by laser illuminations as short as 0.06 second, which will save the processing time for large-scale domain engineering. The average diameters and lengths of the inverted domains increase gradually at longer exposure durations, as shown in Fig. 4(b). For the shortest exposure time of 0.06 second, the average diameter and length of the inverted domains were 4.5 and 29.4 µm, respectively. They grew to 5.4 and 36.2 µm when the exposure time was increased to 0.5 second. This is to be expected, as the increased exposure time leads to expansion of the heating region in both, transverse and longitudinal directions, giving rise to inverted ferroelectric domains of larger sizes.

 

Fig. 4. The impact of femtosecond laser exposure time on the size of inverted domains. (a) The side view of the light-induced ferroelectric domains obtained with different laser exposure durations, imaged using the Čerenkov second harmonic microscopy. (b) The variations of the measured diameters and lengths of the inverted domain structures on the laser exposure time at 800 nm.

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2.5 Impact of laser processing depth and axial movement on all-optical poling

The capability of three-dimensional ferroelectric domain engineering is one of the unique advantages of femtosecond laser poling. This unavoidably involves creating inverted domains at different depths inside the crystal. Because of the spherical aberration and focus splitting due to the birefringence of crystals, the quality of the tightly focused laser beam gets worse and the light intensity becomes weaker inside the crystal [34]. Therefore, it is important to know how the laser processing depth affects the optical threshold and the morphologies of inverted domains. To this end, the femtosecond laser poling was conducted at depths of 10, 20, 30, 40, and 50 µm below the surface of the SBN crystal. For each depth, laser power was varied to allow us to find the corresponding optical threshold for domain inversion. The laser wavelength and exposure time were selected to be 750 nm and 0.5 second. Figure 5(a) shows the measured threshold power, which increases with writing depth inside the crystal. With the used laser writing system, the deepest position that we can realize domain inversion is about 730 µm in the z-cut SBN crystal. The measured average length of the inverted domains obtained at different processing depths are shown in Fig. 5(b), and the Čerenkov second harmonic microscopic image of the corresponding domain structures is shown in Fig. 5(c). The average length of inverted domains reduced rapidly from 43 to 19 µm when the depth of laser processing increases from 10 to 50 µm below the surface. Such reductions are beneficial to improving the resolution ability of domain engineering along the depth direction of the crystal, which is critical for fabrications of 3D NPCs. As we have mentioned above, the domains in length of tens of micrometers are still too long for the quasi-phase matching applications. The line scanning of the femtosecond laser focus may lead to much better resolution in the z-cut SBN crystal.

 

Fig. 5. (a) The measured optical thresholds for domain inversion at different depths inside the z-cut SBN crystal. (b) The variation of the average lengths of inverted domains on the laser processing depths. (c) The side views of the domain patterns created at different depths inside the crystal, imaged by the Čerenkov second harmonic microscopy.

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In the experiments above, the focus of the femtosecond laser pulses was kept at the same position to accomplish an individual ferroelectric domain inversion. However, in previous works, the laser focus was always translated over a certain distance along the laser beam to assist the domain inversion [19,24]. Based on our experimental results shown above, pushing the laser focus is not an essential condition for domain inversion. To reveal the influence of axial movement of laser focus on domain inversion, we performed optical poling experiment with different pushing distances of laser focus. The results showed translating the laser focus along the beam direction did not help us to reduce the optical threshold for domain inversions, but on the other hand, was indeed beneficial to achieve longer inverted domains. As shown in Fig. 6, the average length of inverted domains increases from 23 to 27, 34, and 68 µm, when the pushing distance increases from 1 to 5, 10, and 370 µm, respectively. In this experiment, the laser focus moves at a speed of 10 µm/s and the acceleration of 500 µm/s². The laser wavelength was selected to be 750 nm and the laser power was 170 mW.

 

Fig. 6. 3D Čerenkov second harmonic microscopic views of the inverted domains obtained by pushing the laser focus into the sample at a distance of (a) 1 µm, (b) 5 µm, (c) 10 µm, and (d) 370 µm, respectively.

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3. Conclusion

In conclusion, the femtosecond laser induced ferroelectric domain inversion has been systematically investigated in the z-cut SBN crystal. The domain inversion was realized with femtosecond pulses in a broad spectral range from 700 to 900 nm, but the optical threshold for domain inversion strongly varied with the wavelength, which was explained by considering the thermoelectric model of femtosecond laser poling and the wavelength-dependent nonlinear absorption coefficients of the crystal. The influence of the laser power, exposure time, processing depth, and the longitudinal movement of the laser focus on the optical threshold and the morphologies of light-induced inverted domains were also experimentally studied. While the results were obtained with the SBN crystal, similar properties may also be found in other ferroelectric materials. This work thereby contributes to a deeper understanding of the infrared femtosecond laser poling. It also paves the way towards fabrications of high-quality 3D nonlinear photonic crystals, which is essential for nonlinear optical and quantum applications that require efficient energy transfer between light of different frequencies.