Nonlinear photonic crystals (NPCs), which feature an artificially modulated second-order nonlinear optical coefficient χ(2)^[1–4], facilitate the renowned quasi-phase-matching (QPM) technique introduced by Bloembergen in 1962 for efficient emissions of optical waves at new frequencies via three-wave-mixing processes^[5]. This concept can be traced back to Berger’s groundbreaking work in 1998 that was inspired by the concept of photonic crystals^[6] and then evolved from periodical χ(2) distribution to non-periodical, enabling the simultaneous engineering of frequencies and wavefronts of optical fields, which are crucial for generating nonlinear structured beams, encoding information via nonlinear holography, and producing multiple types of quantum entanglement^[7–15].

Traditionally, the fabrication of NPCs has relied on electric-field poling, where a high-voltage electric field is applied to create periodic or patterned ferroelectric domains in one or two dimensions^[16–19]. While this method has been widely successful, it could not engineer the χ(2) distribution along the z-axis, making it challenging to achieve 3D NPCs. To overcome these limitations, femtosecond laser writing (FLW) has emerged as a promising alternative, offering two key mechanisms for domain engineering, i.e., domain erasure via localized decrystallization and domain inversion through thermal–electric effects^[20–33]. Domain erasure is usually achieved by inducing amorphization or structural damage with tightly focused femtosecond laser pulses at ∼1kHz, while domain inversion is realized by employing localized heating with focused femtosecond laser pulses at ∼100 MHz. These mechanisms enable unprecedented control over 3D χ(2) distribution, providing a route to not only periodic poling but also the creation of intricate, three-dimensional nonlinear optical structures^{[22,25,26,31]}. However, domain erasure processes inevitably induce unwanted crystal damage, as strong femtosecond pulses damage the crystal lattice, leading to strong linear diffraction of the interacting fields^[34].

Recently, a hybrid fabrication approach was developed that combines femtosecond laser decrystallization with cooling-induced domain inversion via the pyroelectric effect. In this method, FLW locally modifies the material to lower the coercive electric field, followed by cooling to provide a pyroelectric field along the z-axis for large-scale domain inversion^[35–41]. Although it still lacks the capability to engineer χ(2) distribution along the z-axis, it eliminates the need for pre-patterned electrodes and the associated photolithography steps, simplifying the fabrication process. Compared to direct laser poling, it could improve time efficiency. However, the weak pyroelectric fields generated during cooling in an air environment limit the application in ferroelectric materials with large coercive electric fields, such as lithium niobate (LN). This limitation restricts the design periodicity for LN NPC, particularly for high-performance devices operating at shorter wavelengths.

In this work, we address the challenge of enhancing the pyroelectric-based fabrication process by performing the cooling step in a vacuum container, effectively suppressing environmental thermal fluctuations and maximizing the transient pyroelectric field during cooling. To facilitate our investigations, we combine the cooling device with a polarized microscopy system to monitor the inversion of domain structures in real time. Our experiments demonstrate that vacuum cooling significantly improves both the probability and uniformity of domain inversion compared to cooling performed in air. Analysis of the output diffraction spots confirms that this method induces little change in the refractive index. Additionally, we successfully fabricated an inverted domain array with a periodicity of 4 µm, achieving QPM at near-infrared wavelengths. This technique provides a promising approach for creating nonlinear photonic structures in large volumes without the need for a patterned electrode and a high voltage.

The samples in our experiment were fabricated in an LN crystal doped with 5% magnesium oxide, with dimensions of approximately 2mm(x)×10mm(y)×1mm(z). Initially, permanent defects were induced through a homemade FLW system, as shown in Fig. 1(a). The LN crystal was mounted on a triaxial piezoelectric nanometer platform (E727, Physik Instrumente) to enable precise movement for the fabrication of periodic arrays. A laser source (Astrella-Tunable-V-USP-1k, Coherent) with a wavelength of 800 nm, a pulse duration of 35 fs, and a repetition frequency of 1 kHz was used. The output beam was focused by an objective lens (OPLNFL40×, NA = 0.75, Olympus) into the LN crystal, achieving a spot diameter of 1.4 µm. To manage the power inside the LN crystal, a combination of a half-wave plate and a polarization beam splitter was utilized. The energy was further fine-tuned using an electronically controlled half-wave plate (DDR25/M, Thorlabs) in conjunction with a polarization beam splitter, allowing for dynamic control of energy during the fabrication process. Two distinct writing schemes were employed to fabricate the samples. In the first scheme, the focused laser beam was directed along the x-axis while writing along the z-axis to create a single grating structure. To optimize the fabrication quality and minimize birefringence within the lithium niobate (LN) crystal, the laser polarization direction in front of the objective lens was aligned with the y-axis of the crystal. In the second scheme, the z-axis of the crystal was aligned along the focused laser beam, and FLW was also performed along the z-axis to fabricate grating arrays with a smaller period, keeping enough separation for adjacent structural units.

Subsequently, the crystal was placed in the setup shown in Fig. 1(b) to perform vacuum pyroelectric poling. The temperature control stage with a vacuum chamber (THMS350V, Linkam Inc.) serves as the cooling setup, which can be flexibly integrated with a polarized microscope. It offers an extended temperature ranging from −195°C to 350°C under vacuum conditions down to 10−3mbar. There is a transmission hole beneath the sample stage and transparent windows above it. This configuration enables us to carry out transmitted polarization imaging during the cooling process. The crystal was heated above 200°C and then cooled down to a low temperature of 20°C. During the global thermal treatment, the growth of the domains was monitored in real time using a polarized light imaging system, as shown in Fig. 1(b). This polarized imaging system comprises an illumination light source, two polarization filters, an objective lens (NA=0.25), and a CCD camera. It is essential that the polarization directions of the two filters remain orthogonal in order to observe domain inversion via local change of birefringence. The heating and cooling rates were maintained at approximately 30°C/min. The net pyroelectric field Epyr inside the crystal is the difference of Edep and Escr, which can be mathematically expressed as Epyr=Escr−Edep.(1)Here, the direction of Escr is the same as the direction of Ps and is opposite to that of Edep^[35]. At room temperature, the pyroelectric field Epyr is zero because the depolarizing field is completely screened by bulk and surface charges, as illustrated in Stage 1 of Fig. 1(c). As the crystal is heated [Stage 2 of Fig. 1(c)], Ps decreases rapidly, leading to a slower reduction in Edep as well. The faster change of Edep than Escr results in Epyr aligning in the direction of spontaneous polarization (Epyr>0). Under the high-temperature stable condition, charges become thermally activated, resulting in a reduced intensity of Ps compared to the low-temperature state. Consequently, both the Edep and Escr are diminished and equal, as depicted in Stage 3 of Fig. 1(c). During the cooling process in air, spontaneous polarization increases, and Edep rapidly increases in accordance with the cooling rate, as shown in Stage 4 of Fig. 1(c). When the temperature span ΔT is large enough, the direction of the net electric field will be opposite to the direction of spontaneous polarization (Epyr<0).

Domain inversion occurs when |Epyr| exceeds the threshold field for domain nucleation, denoted as Eth. The coercive field will greatly reduce inside the FLW-induced region, and the threshold field Eth for domain nucleation in this area will decrease with it. Concurrently, we assume a higher concentration and more rapid movement for charges inside the FLW-induced region compared to the unmodified crystal volume^[35]. Therefore, the pyroelectric field near the laser processing area is larger, making it easier to achieve domain inversion. If we cool the crystals in a vacuum, the screening charge accumulation on the surface can be suppressed, leading to a smaller Escr. Ultimately, the net pyroelectric field Epyr can be significantly enhanced, as shown in Stage 4 (vacuum) of Fig. 1(c).

Single gratings with different periods were fabricated by the first FWL scheme. The grating structure is located about 25 µm below the surface of the LN crystal normal to the x-axis. The writing energy was 100 nJ, and the speed of writing was 100 µm/s along the z-axis. Figure 2(a) illustrates the domain inversion of a grating fabricated by in-plane writing at 60 s intervals during the cooling process in a vacuum condition. The left image of Fig. 2(a) shows the FLW-induced single-layer grating with a period of 8 µm along the y-axis. In the polarized imaging system, the FLW lithography filaments appear brighter than the surrounding areas. This brightness is due to the amorphization of the LN crystal caused by the femtosecond laser, resulting in enhanced light scattering. Under the influence of the pyroelectric field, inverted domains uniformly grow from the FLW-induced area to the crystal surface along the z-axis. Figure 2(b) presents a comparison of the domain inversion under the same cooling rate of 30°C/min but varying initial high temperatures, while Fig. 2(c) shows a comparison with a consistent high temperature of 200°C but different cooling rates. These results demonstrate that a higher initial temperature combined with a rapid cooling rate can yield a more distinct inverted domain structure. However, it also gives rise to more pronounced domain merging. Figure 2(d) shows the inverted domain structures after cooling, with the same high temperature of 200°C and varying periods along the y-axis. The enlarged images (capturing one period) reveal that the inverted domains are more clearly visible under vacuum conditions than in air, allowing the domain walls to be observed in vacuum. Although the polarized imaging system enables wide-field, real-time monitoring of domain inversion, it cannot resolve the three-dimensional domain structure, limiting the analysis of domain wall sharpness and nucleation density. This limitation could be overcome using Cherenkov second-harmonic (SH) microscopy^[42,43]. The images on the top row and the bottom row show the domain inversion after cooling in vacuum and air, respectively. As the period decreases, the probability of domain inversion decreases. The top of Fig. 2(d) exhibits a higher probability of domain inversion, with the inverted domains appearing more uniform compared to the bottom of Fig. 2(d), indicating that vacuum cooling has significant advantages in improving domain structure precision and quality compared to traditional air cooling. In addition, domain inversion in air is rarely observed in gratings with periods of 4 and 6 µm. As a comparison, the minimum periodicity of the inversion domain has reached 4 µm in vacuum, which is close to the state-of-the-art using electrical poling^[19]. To conduct a comprehensive analysis of the polarized images depicting the domain inversion in Fig. 2(d), we initially implemented advanced low contrast image recognition techniques. Subsequently, these images underwent a binarization process, which was then followed by the meticulous application of an edge detection algorithm. A domain inversion is considered successful when the boundary length of the reversed domain encompasses the entirety of the region within the laser writing area. We calculated and utilized the ratio of the number of successfully reversed periods to the total number of periods to quantitatively assess the domain inversion performance. The inverted ratios for grating periods of 10, 8, 6, and 4 µm are 100%, 95%, 88%, and 75% in vacuum and 50%, 60%, 44%, and 30% in air, respectively.

To further validate the reliability of the vacuum pyroelectric poling, we conduct the experimental characterization of output diffraction from the grating in Fig. 2(b). The experiment employed a tunable femtosecond laser (Chameleon Ultra II, COHERENT) as the fundamental input source, characterized by the following parameters: a tunable wavelength from 690 to 1050 nm, a pulse duration of 140 fs, and a repetition frequency of 80 MHz. To manage the input power, a combination of a half-wave plate and a polarization beam splitter was used, followed by another half-wave plate to adjust the incident linear polarization states. The incident power was set at 300 mW, with the polarization aligned along the z-axis. The power density was further increased by focusing the fundamental beam into the sample with a lens having a focal length of f=75mm, resulting in a beam diameter of approximately 60 µm within the sample. The output far-field diffraction patterns were then projected onto a white screen for analysis.

Figure 3(a) shows the nonlinear Raman-Nath diffraction (RND) process of the inverse domain region. Here, the grating with a periodical change of χ(2) was used so that the periodicity along the y-axis is Λ, i.e., G=2π/Λ. In this diffraction process, the wave vectors of the input fundamental beam and SH beams satisfy |k→2ω|sinθm=mG,(2)|k→2ω|cosθm≠2|k→ω|,(3)where k→ω and k→2ω represent the wave vectors of the fundamental and SH waves, respectively, m is an integer determined by the order of the reciprocal vectors, and θm is the corresponding diffraction angle involved in the nonlinear RND process^[44]. As shown in Fig. 3(b), the emitted SH spots are distributed along the y-axis. Moreover, as the value of Λ decreases, the spacing between the spots increases, in accordance with Eq. (2). For comparison, we also characterized the diffraction of the laser processing area, as displayed in Fig. 3(c). Due to the fact that FLW simultaneously causes the refractive index and the second-order nonlinear coefficient changes, there exists linear diffraction in addition to nonlinear diffraction. The wave vectors of the input and diffracted fundamental beams satisfy |k→ω|sinθn=nG,(4)where n is an integer that determines the order of the reciprocal vectors and θn is the corresponding diffraction angle involved in the linear RND process^[45]. In Fig. 3(d), strong diffraction of the fundamental beam is observed, with the period being double the diffracted SH spots. This observation further confirms that the pyroelectric field can only induce domain inversion without change of the refractive index.

The second FLW scheme is used to fabricate the grating arrays. The processing direction was from the depth to the surface along the z-axis, while writing at a speed of 100 µm/s with an energy that was adjusted to vary linearly with depth. The deepest position was approximately 130 µm below the LN surface with a writing energy of 240 nJ before the objective, and the shallowest position was 60 µm with a writing energy of 150 nJ. After pyroelectric poling, the grating array structure was imaged under a dark-field microscope with the reflected imaging mode, which can get a better display of the grating array structure. Figure 4(a) shows the patterns of the grating array structure fabricated by FLW in the x–y plane and y–z plane with the period Λx=Λy=Λ=4μm, i.e., Gx=Gy=G=2π/Λ, which makes it possible to realize the QPM process in the near-infrared range. The pyroelectric-poling area is located within the white dashed line rectangle in Fig. 4(a), which is difficult to identify using reflected dark-field imaging.

In the QPM process, the wave vectors of the input fundamental beam and SH beams satisfy |k→2ω|sinθl=lGy,(5)|k→2ω|cosθl=2|k→ω|+Gx,(6)where l is an integer referring to the order of the reciprocal vectors along the y-axis involved in the QPM processes. As the femtosecond laser with a wavelength of 902 nm was focused on the domain-inversed area along the x-axis, the resulting diffracted intensity pattern was recorded as depicted in Fig. 4(b). The orange and blue curves in Fig. 4(c) present the dependence of the first-order and second-order SH powers on the input fundamental wavelength. The fundamental beam power is kept at 0.4 W. The output first-order (and second-order) SH power reaches the peak at the fundamental wavelength of 910 nm (and 894 nm), which indicates that the QPM condition is satisfied, assisted by the reciprocal vectors given by Eqs. (5) and (6) with l=1 (and l=2). Figure 4(d), respectively, depicts the power dependence of the first-order second-harmonic generation (SHG) on the input power at the fundamental wavelength of 910 nm and the second-order SHG on the input power at the fundamental wavelength of 894 nm. When the fundamental input power is 0.4 W, the directly measured conversion efficiency for the first-order and second-order SHG reaches approximately 1.63×10−5 and 0.66×10−5W−1. This efficiency is close to the previously reported results^[25], partially owing to the smaller duty cycle, lower pump power density, and shorter interaction length. In addition, the domain uniformity and domain merging within the grating arrays also lower the nonlinear conversion efficiency.

In this work, we use the pyroelectric-based fabrication process by performing the cooling step in a vacuum, suppressing thermal fluctuations and maximizing the pyroelectric field, in which the combination of the cooling device and the polarized microscopy is used to monitor the growth of domain structures in real time. Our experiments demonstrated that the use of vacuum cooling significantly improves domain inversion probability and uniformity compared to air cooling, which is verified by the SH diffraction processes from single gratings with periods from 10 to 4 µm. Further, we successfully fabricated an inverted domain array with a periodicity of 4 µm, achieving QPM at the near-infrared wavelength. When the fundamental input power is 0.4 W, the directly measured conversion efficiency for the first-order and second-order QPM SHG are approximately 10−5W−1. To improve nonlinear efficiency, we can further optimize the cooling temperature range to enhance inversion uniformity and increase the interaction length of grating arrays. This technique provides a promising approach for creating nonlinear photonic structures in large volumes without the need for patterned electrodes and high voltages.