Lithium niobate (${\mathrm{LiNbO}}_3$) is widely recognized for its high electro-optic and nonlinear optical coefficients, making it an exceptional material for optical applications. To maximize the utilization of its nonlinear optical properties, achieving quasi-phase matching throughout its entire transparency range is essential for efficient wavelength conversion. One solution to this challenge is periodically poled lithium niobate (PPLN),1 in which the poled domain periods are meticulously designed to satisfy phase-matching conditions across different wavelengths, compensating for the phase mismatch between the fundamental and converted waves.

PPLN has remarkable optical properties, supporting the creation of various optical devices, including electro-optic modulators, optical deflectors, and nonlinear frequency converters.2^–7 Lithium niobate films can also be wafer-bonded with other semiconductors, enabling integration with on-chip passive photonic devices.8^,9 Widely used in mesoscopic and integrated optics, $z$-cut PPLN is particularly effective in micro-resonators of integrated photonic chips. Compared with $x$-cut PPLN, $z$-cut offers superior wavelength conversion efficiency, as demonstrated by Lu et al.,10 with 15% second-harmonic generation (SHG) efficiency at $115\mu \mathrm{W}$, and by Lu et al., achieving a 1% single-photon nonlinear anharmonicity.11 Ma et al.12 also generated photon pairs at 36.3 MHz with $13.4\mu \mathrm{W}$ in $z$-cut PPLN micro-resonators. Periodically poled structures in integrated ${\mathrm{LiNbO}}_3$ devices are essential for high photon efficiency, using quasi-phase matching and fabrication methods such as electron beam exposure,13 laser writing,14^,15 and electric field poling.16 However, crystal defects and poling field variations challenge precise domain growth. Characterization methods such as hydrofluoric acid etching, PFM, and SHG microscopy are crucial. SHG microscopy, dating to the 1990s,17^,18 offers noncontact, high-resolution detection, distinguishing domain boundaries via phase interference. Reitzig et al.19 applied SHG to $x$-cut photonic polymer thin film ${\mathrm{LiNbO}}_3$ (PP-TFLN), whereas Zhao et al.20 observed sub-200 nm patterns. However, a traditional SHG microscope, with a transverse electric field parallel to the optical axis, suits $x$-cut but limits $z$-cut PPLN imaging.

In this research, we present a microscope system designed to enhance SHG imaging of $z$-cut PPLN by utilizing the longitudinal electric field generated by tightly focused radially polarized light. In the focal region, radially polarized light exhibits a dominant longitudinal electric field component ($E_z$) along the optical axis of the lens, as shown in Fig. 1(b). This $E_z$ component aligns with the optical axis of $z$-cut ${\mathrm{LiNbO}}_3$, allowing for full utilization of the material’s largest nonlinear coefficient (${\mathrm{d}}_{33}$) for SHG, as illustrated in Fig. 1(a). Consequently, $z$-cut ${\mathrm{LiNbO}}_3$ demonstrates increased sensitivity to the longitudinal component of the excitation light, resulting in an enhanced image contrast between domain walls and surrounding poled regions. In addition, radially polarized light produces a smaller focal spot size ($0.16{\lambda }^2$) compared with tightly focused linearly polarized light ($0.26{\lambda }^2$).21 This improved transverse resolution enables precise determination of domain wall positions, thereby improving the accuracy of polarization period and duty cycle measurements.

Radially polarized light can be represented as a superposition of the ${\mathrm{HG}}_{10}$ mode polarized along the $x$-direction and the ${\mathrm{HG}}_{01}$ mode polarized along the $y$-direction.22 According to the work of Richards and Wolf,23 when radially polarized light passes through a spherical aperture with a radius of $f$, the light field distribution near the focus can be determined using Debye integration, $$\overrightarrow{E}=-\frac{ik}{2\pi }{\iint }_{\mathrm{\Omega }}\overrightarrow{A}(\theta ,\varphi )e^{ik(\widehat{s}·\overrightarrow{r})}\mathrm{d}\mathrm{\Omega }.$$(1)

In Eq. (1), the vector amplitude $\overrightarrow{A}(\theta ,\varphi )$ is related to the field distribution and can be represented as $$\overrightarrow{A}(\theta ,\varphi )=f{\cos }^{1/2}\theta E_0(\theta ){{\mathit{e}}_{\mathit{r}}}^{\prime }.$$(2)

The unit vector ${{\mathit{e}}_{\mathit{r}}}^{\prime }$ is perpendicular to the direction of the refracted light ray $\mathit{s}$. Assuming $\theta$ as the polar angle, the expression for the electric field vector near the focus is obtained by the Debye integral $$E(r,\phi ,z)=\left(\begin{array}{l}{E}_x\\ E_y\\ E_z\end{array}\right)=-\frac{ikf}{2\pi }{\int }_0^{\alpha }{\int }_0^{2\pi }\sqrt{\cos \theta }{E}_0(\theta )\left(\begin{array}{l}\cos \theta \cos \phi \\ \cos \theta \sin \phi \\ \sin \theta \end{array}\right)\times e^{ik[z\cos \theta +r\sin \theta \cos (\varphi -{\phi }_s)]}\sin \theta \mathrm{d}\varphi \mathrm{d}\theta .$$(3)

In Eq. (3), $\alpha =\arcsin$ ($\mathrm{NA}/n$) represents the aperture angle of the lens, where NA is the numerical aperture and $n$ is the refractive index. Based on Eq. (3), we simulated the field intensity distribution after tight focusing. Unlike a Gaussian beam, the intensity distribution of radially polarized light before focusing is characterized by zero intensity at the optical axis, with maximum intensity in the annular region surrounding the optical axis, as shown in Fig. 2(a). Figure 2(b) illustrates the longitudinal electric field generated by radially polarized light during tight focusing. We also performed simulations to analyze the intensity distribution curves of various electric field components in the focal plane, specifically examining the longitudinal and transverse electric field components to gain a comprehensive understanding of their respective energy distributions, as shown in Fig. 2(c). Chen et al.24 demonstrated that the larger the numerical aperture (NA) of the objective lens, the stronger $E_z$ component at the tightly focus. Therefore, in the simulation, we used an objective with $\mathrm{NA}=0.95$. Similarly, Wang et al.25 and Meng et al.26 simulated the field distribution in the focal plane after tight focusing of radially polarized light using a high-NA objective, showing that the field at the tightly focused position is dominated by the longitudinal component, which is consistent with Fig. 2.

When excited by radially polarized light, the second-order nonlinear polarization intensity generated in $z$-cut ${\mathrm{LiNbO}}_3$ can be expressed as follows:27$$P_{\mathrm{SH}}=\left(\begin{array}{c}{P}_x\\ P_y\\ P_z\end{array}\right)=2{\epsilon }_0\left(\begin{array}{cccccc}0& 0& 0& 0& d_{31}& -d_{22}\\ -d_{22}& d_{22}& 0& d_{31}& 0& 0\\ d_{31}& d_{31}& d_{33}& 0& 0& 0\end{array}\right)\left(\begin{array}{c}{E}_x^2\\ E_y^2\\ E_z^2\\ 2E_z{E}_y\\ 2E_z{E}_x\\ 2E_x{E}_y\end{array}\right).$$(4)

The typical values of these nonlinear polarization coefficients are ${\mathit{d}}_{33}\approx 36\mathrm{pm}/\mathrm{V}$, ${\mathit{d}}_{31}\approx 6\mathrm{pm}/\mathrm{V}$, and ${\mathit{d}}_{22}\approx 3\mathrm{pm}/\mathrm{V}$.28 According to Fig. 2 and Eq. (4), the maximum polarization intensity of $z$-cut PPLN is achieved when excited by the longitudinal component, $E_z$. Assuming the ratio of the longitudinal to the transverse component near the focus is 9:1, the contribution of the longitudinal component to $P_z$ is $\sim 54$ times that of the transverse component. Furthermore, the $z$-component of the polarization intensity ($P_z$) is roughly an order of magnitude greater than the $y$-component ($P_y$). When the fundamental wave is perpendicular to the surface of $z$-cut ${\mathrm{LiNbO}}_3$, the detector receives second harmonics originating from both forward-scattered and backward-scattered second harmonics. Based on the mechanism of SHG in ${\mathrm{LiNbO}}_3$,29 the intensity of the forward second harmonic surpasses that of the backward second harmonic by 2 to 3 orders of magnitude. As a result, despite the low reflectance of the second harmonic in ${\mathrm{LiNbO}}_3$, the signal detected in the backward direction is still primarily due to the reflection of the forward signal. A typical SHG microscope is used to collect the second-harmonic signal, as shown in Fig. 3. The intensity of the second harmonic received by the detector can be expressed as30$$I^{2\omega }(z)\propto {\left|{\int }_L^z\frac{e^{i\mathrm{\Delta }k{z}^{\prime }}}{(1+2i{z}^{\prime }/b)}\mathrm{d}{z}^{\prime }\right|}^2$$(5)

In Eq. (5), $z$ represents the axial coordinate of the focal depth of radially polarized light, defined as the distance between the focal point and the surface of $z$-cut ${\mathrm{LiNbO}}_3$. $L$ denotes the axial coordinate of the bottom interface of ${\mathrm{LiNbO}}_3$. $\mathrm{\Delta }k$ represents the phase mismatch, and $b=\mathit{k}{\omega }_0^2$, where ${\omega }_0$ is the beam radius. When focused on the $z$-cut ${\mathrm{LiNbO}}_3$, the phase difference between the region with polarization reversal and other regions is $\pi$.

The experimental setup is shown in Fig. 3. The fundamental wave is generated by a femtosecond fiber laser with a central wavelength of 1040 nm, a repetition rate of 80 MHz, and an output power of 100 mW ($\sim 100\mathrm{fs}$), providing the necessary peak intensity for SHG. Even in the presence of some phase mismatch, the signal remains highly sensitive to defects in the lithium niobate structure and changes in symmetry. The polarization modulation system consists of a half-wave plate and a spiral phase plate, which modulate the fundamental wave into radially polarized light. The topological charge of the spiral phase plate is 1. A two-dimensional Galvo mirror (Thorlabs, Newton, New Jersey, United States, GVS112) precisely controls the beam’s deflection angle, enabling accurate scanning imaging. The fundamental wave is directed onto the objective’s entrance pupil through an infinity-corrected $4f$ system, consisting of a scanning lens (Thorlabs, Newton, New Jersey, United States, SL50-CLS2) and an infinity-corrected tube lens (Thorlabs, Newton, New Jersey, United States, TTL200-MP). The scanning lens has an effective focal length of 50 mm and a maximum field of view of 14.1 mm, whereas the tube lens has an effective focal length of 200 mm. This $4f$ system, being telecentric, produces collimated light focused at infinity, with conjugation between the Galvo mirror’s center and the objective’s entrance pupil, eliminating vignetting. The fundamental wave is focused onto $z$-cut ${\mathrm{LiNbO}}_3$ by an objective (Olympus, Shinjuku City, Japan, $\mathrm{NA}=0.95$), generating second-harmonic (SH) light around 520 nm. The back-reflected second harmonic returns along the original path, separates from the fundamental wave at a dichroic mirror (Thorlabs, Newton, New Jersey, United States, DMLP735B), and is collected by a photomultiplier tube (PMT) (Thorlabs, Newton, New Jersey, United States, PMT1001/M).

Due to the high NA, the system achieves a theoretical resolution of 547 nm $[(0.5\mathrm{nm}\times 1040\mathrm{nm})/0.95]$. In the experiment, as the beam does not fully fill the objective’s entrance pupil, the NA may be less than 0.95, causing a slight reduction in resolution. Depth resolution decreases when focusing on a refractive medium, though lateral resolution remains largely unaffected.31 As the fundamental wave is focused on the surface of $z$-cut ${\mathrm{LiNbO}}_3$, the lateral resolution is preserved. During imaging, SHG tomography along the z-axis is performed with a step size of 200 nm, enabling tomographic scanning and optimal imaging results. Figure 4(a) shows the SH intensity as a function of focal depth. The longitudinal size of the fundamental optical focal spot is $\sim 2.3\mu \mathrm{m}$$[(2\mathrm{nm}\times 1040\mathrm{nm})/{0.95}^2]$. The thickness of the ${\mathrm{LiNbO}}_3$ thin film is 600 nm. The $z$-axis position corresponding to the strongest SH signal was selected, and the lateral resolution of the SHG microscope was measured using the domain boundary ($\sim 57\mathrm{nm}$). The measured data were normalized and fitted with a Gaussian function to calculate the point spread function (PSF). At the domain boundary, the SHG intensity is weakened due to phase mismatch. Figure 4(b) presents the PSF of the SHG microscope under radially polarized light, which is 525 nm. Figure 4(c) presents the PSF of the SHG microscope under linearly polarized light, which is 607 nm. The results indicate that the use of radially polarized light provides a higher resolution.

To verify the imaging quality of SHG microscopy, a $z$-cut ${\mathrm{LiNbO}}_3$ sample was fabricated. The structure of the thin-film ${\mathrm{LiNbO}}_3$ wafer, from top to bottom, consists of a $z$-cut ${\mathrm{LiNbO}}_3$ layer, a silicon dioxide (${\mathrm{SiO}}_2$) buffer layer, and a silicon (Si) substrate. The thickness of the $z$-cut ${\mathrm{LiNbO}}_3$ layer is 600 nm, the ${\mathrm{SiO}}_2$ layer is $2\mu \mathrm{m}$ thick, and the silicon substrate serves as the supporting material, as shown in Fig. 5(c). Before polarization reversal, the sample exhibited a single-domain structure with the polarization direction along the z-axis pointing upward. After poling with an external electric field, the polarization direction in the reversed domain region along the z-axis is pointed downward. A region where the electrode had been removed was selected for imaging. In this region, the polarization period was $\sim 20\mu \mathrm{m}$, with a duty cycle of 37.5%. The power of radially polarized light focused on the $z$-cut ${\mathrm{LiNbO}}_3$ was 30 mW. The focus of the fundamental wave was placed within the ${\mathrm{LiNbO}}_3$ thin film layer to ensure efficient SHG, as shown in Fig. 5(c).

As expected, a dark line appeared at the domain wall, leading to the disappearance of the SHG intensity, as shown in Fig. 5. The field of view of the images in Fig. 5 is $78.5\mu \mathrm{m}$. We compared the imaging contrast provided by radially polarized light and linearly polarized light, as shown in Table 1.

The imaging contrast $V$ can be expressed as $$V=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }},$$(6)where $I_{\text{max}}$ and $I_{\text{min}}$ refer to the maximum and minimum second-harmonic intensities, respectively. The data are sourced from Fig. 5(b), where the curve represents the gray values corresponding to the second-harmonic intensity at the same positions in Fig. 5(a). Other results are derived from second-harmonic intensity curves.19^,32 The second-harmonic intensity is represented by the output voltage of the PMT after amplification (unit: V). Imaging with radially polarized light achieves a contrast ratio of 0.39, compared with 0.22 for linearly polarized light. These results demonstrate that imaging with radially polarized light produces higher contrast. Using radially polarized light, the contrast is enhanced, allowing us to reduce the pixel dwell time by $\sim 40\%$ without significantly compromising the signal quality. The use of radially polarized light enables the acquisition of SHG images ($512\text{pixel}\times 512\text{pixel}$) within 2 s.

Previous studies on the visualization of domain structures in ${\mathrm{LiNbO}}_3$33^,34 used Gaussian beams as the fundamental wave, which resulted in limited imaging contrast. In this work, we demonstrated the visualization of domain structures in $z$-cut ${\mathrm{LiNbO}}_3$ using radially polarized light. Our results show a 1.77-fold enhancement in contrast ratio in SHG imaging with radially polarized excitation compared with conventional linearly polarized excitation. This method offers rapid imaging and achieves lateral resolution near the diffraction limit. It represents a significant advancement in traditional optoelectronic detection technology, providing precise data on polarization distribution and serving as a valuable reference for the development of integrated photonic devices. Furthermore, this technique retains the advantages of being noncontact and nondestructive, inherent to SHG imaging technology. We believe the findings of this study will contribute to the enhancement of performance characterization techniques for optoelectronic materials and devices, extending beyond $z$-cut ${\mathrm{LiNbO}}_3$.

Acknowledgment. This work was supported by the National Key Research and Development Program of China (Grant Nos. 2022YFC3401100 and 2022YFF0712500), the Guangdong Major Project of Basic and Applied Basic Research (Grant No. 2020B0301030009), the National Natural Science Foundation of China (Grant Nos. 12204017, 12004012, 12004013, 12041602, 91750203, 91850111, and 92150301), the China Postdoctoral Science Foundation (Grant No. 2020M680220 and 2020M680230), and the Clinical Medicine Plus X—Young Scholars Project, Peking University, Fundamental Research Funds for the Central Universities.

Biographies of the authors are not available.