Second harmonic generation by quasi-phase matching in a lithium niobate thin film

Honghu Zhang; Qingyun Li; Houbin Zhu; Lutong Cai; Lutong Cai; Hui Hu

doi:10.1364/OME.452483

1. Introduction

Single-crystal lithium niobate thin film (lithium niobate on insulator, LNOI) was a very promising material platform for realizing high-density integration and high-performance photonic devices [1–3], owing to its high-refractive-index-contrast and excellent optical properties (such as electro-optic, acousto-optic and nonlinear optical properties [4–8]). For optical frequency conversion such as second harmonic generation (SHG), quasi-phase matching was used, which compensated the phase mismatch caused by refractive index dispersion by periodically reversing the direction of crystal polarization [9]. In addition, quasi-phase matching could utilize the largest nonlinear coefficient (d₃₃), and optical waveguides in LNOI had a larger mode overlap integral due to its high refractive index contrast [10–12]. Therefore, implementing quasi-phase matching in LNOI could achieve high SHG efficiency. In recent years, PPLN waveguides had been reported in x-cut lithium niobate thin film [13,14] with high SH normalized conversion efficiency [15,16]. High-efficiency SH conversion efficiencies were also realized by combining the microring and periodic poling in x-cut or z-cut lithium niobate thin films [17,18]. And, spontaneous parameter down conversion (SPDC) had been reported in quasi-phase-matched device for quantum light sources [19–21]. In addition, excellent works had also been done on the realization of small period poling in LNOI [22–26].

However, there were still needs to make a further study on the poling and nonlinear processes. In this paper, periodic poling with a periodicity of 3.8 µm was realized by poling with external electric field. The reversed domain was characterized by piezoresponse force microscopy (PFM) and the confocal Raman spectroscopy. The SH had been realized in a 2-µm-wide LNOI waveguide. The normalized conversion efficiency was measured to be 684%W⁻¹cm⁻². The contributions of different factors to the second harmonic curve were analyzed. The inhomogeneities effective index along the waveguide was the main course of the broadening of the phase matching peak. The poling periods were simulated for various waveguide geometries. The results showed that the phase matching was very sensitive to the waveguide geometry. For example, the phase matching peak would shift by 10 nm if the LN thin film thickness was changed by 1.2 nm. These results were useful for the study of nonlinear process in LNOI.

2. Experiment and result

The x-cut LNOI (by NANOLN) consisted of a 500-nm thick lithium niobate film, a 2-µm thick silicon dioxide insulating layer and a 500-µm thick silicon substrate. The chip was located about 2.5 cm from the edge of the wafer. In order to achieve periodic poling, the comb-shaped chromium electrodes with a thickness of 60 nm were formed on the LNOI surface by deposition and lift-off process. The distance between the opposite electrodes was 10 µm, and the electrode period was 3.8 µm (Fig. 1(a)). During the electric field poling process, the sample was immersed in silicone oil to avoid air breakdown caused by the high electric field. The ambient temperature and air humidity were kept constant at 24°C and 45% RH, respectively. Multiple electrical pulses (voltage: 190 V, frequency: 10 Hz, duty ratio: 65%, number of pulses: 5) from a pulse power supply were applied to the electrodes. The reversed domain was observed by piezoresponse force microscopy (Bruker Dimension Icon) and by confocal Raman spectroscopy (Horiba LabRAM HR 800). During the PFM measurement, an AC drive signal was applied to the conductive PFM probe tip. Due to the inverse piezoelectric effect, domains with different orientations exhibited different behaviors (expand or contract), thereby distinguishing the inversed and non-inversed domains. As shown in Fig. 1(b), the regions in the red frame were the electrodes, and the black regions outside the red frame were the reversed domains, and the yellow ones were non-reversed domains. The confocal Raman spectroscopy was in the back-scattering $\textrm{X}({\textrm{ZZ}} )\mathrm{\bar{X}}$ configuration by using a 473 nm laser with a power of 3 mW and an ×100 (NA = 0.9) objective [27]. The Raman measurements were taken from the centrals of the reversed and non-reversed domains. In Ref. [28], there was Raman spectrum intensity variation at the domain wall. In Ref. [29], E(TO₁), E(TO₈) and A₁(LO₄) had slight intensity differences between reversed and non-reversed domains. Because A₁(TO₂) phonon related with the Li atom vibration, and the Li atom moved during domain reversion. A₁(TO) Raman line was investigated. The results show that there was no obvious difference. The Raman line appearing at 520 cm⁻¹ was produced by silicon, which was marked with ‘A’ in Fig. 1(c).

Fig. 1. (a) The schematic diagram of periodic poling and measured pulse waveform on the electrodes. (b) PFM phase image of the periodic reversed domains. (c) Raman spectra in reversed domain region and non-reversed domain region.

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The waveguides were defined in the periodically poled region by combining electron beam lithography and reactive ion etching. The detailed process was as follows. The samples were spin-coated with a layer of 800-nm thick HSQ photoresist, and then exposed to electron beam with a beam current of 10 nA. The exposed sample was developed to obtain a photolithography mask. The Cr mask with a thickness of 320-nm was realized by the lift-off process. Finally, the waveguide was realized by etching in a fluorine-containing gas atmosphere. The poling electrodes were not removed before waveguide patterning because it was used for the following photolithography alignment, and it was removed by the etching process of the waveguide. The morphology of the waveguide was characterized by SEM as shown in Fig. 2(b). The cross section of the waveguide was a trapezoid, in which the topline was 1.8 µm, and the baseline was 2.1 µm. And the etch depth of the waveguide was about 234 nm. The schematic diagram was shown in Fig. 2(a). Compared to the designed width of waveguide mask (2 µm), because of the mask erosion during the etching process, the topline of the etched waveguide was narrower than the designed width. Because there was some re-deposition during the etching process, the baseline of the waveguide was wider than the designed value. The designed parameters were chosen by considering the trade-off between the SH conversion efficiency and the waveguide loss. A wide waveguide or a shallow etched depth would result in a poor optical mode confinement. A narrow waveguide width or a deep etched depth would increase waveguide loss. The two end faces of the waveguide were polished for end-face coupling. The length of the waveguide after polishing was about 4 mm. The periodically poled region with a length of 3 mm was located approximately in the middle of the waveguide.

Fig. 2. (a) Schematic diagram of the waveguide cross section. (b) The SEM image of the waveguide end face.

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The linearly polarized light from a tunable laser (TSL-210VF) was coupled into the waveguide through a lensed polarization maintaining fiber (PMF). The pump light was adjusted by rotating the PMF to TE polarization, to use the d₃₃ of x-cut LNOI. The pump light and the second harmonic from the waveguide output were collected by an objective lens (40× / 0.65) and then pass through a beam splitter. The second harmonic power was measured by a Si detector, and the pump light power was measured by an InGaAs detector after passing through a TE polarizer. The TE polarizer was used to filter out unwanted TM noise. The schematic diagram of the measurement system was shown in Fig. 3. The propagation loss of the waveguide was evaluated (3.6 dB/cm) by the Fabry-Perot method at the wavelength of the 1567 nm, and the fiber-to-waveguide coupling loss was 7.2 dB. The propagation loss and output coupling loss at the wavelength of 783.5 nm were 4.5 dB/cm and 1.3 dB, respectively. The normalized conversion efficiency (η_nor) was calculated by the formula:

(1)$$\begin{array}{c} {{\mathrm{\eta }_{nor}} = \frac{{{P_{2\omega }}}}{{P_\omega ^2{L^2}}}} \end{array}$$

P_2ω and P_ω were the second harmonic power and pump power at the output of the waveguide [14], respectively, and L was the length of the periodic reversed domain region.

Fig. 3. Schematic diagram of experimental setup.

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The measured normalized conversion efficiency as a function of pump wavelength was shown in the Fig. 4(a). The phase matching peak split into two peaks with accompanying broadening, corresponding to the wavelengths of 1567 nm and 1577 nm, respectively. This phenomenon had been discussed in quasi-phase matching and birefringent phase matching processes in lithium niobate channel waveguides [30,31]. The mode distributions and effective refractive indices of the pump light and second harmonic were simulated by Lumerical Mode Solutions. In the simulations, the trench at the foot of the etched region was modeled by using the multiple trapezoids. The depth of the trench was about 34 nm, which had some impact on the phase matching wavelength. The electric field (E_z) profiles of pump and SH mode were shown in the Fig. 4(b). The simulated normalized conversion efficiency with the pump wavelength was calculated by the formula:

(2)$$\begin{array}{c} {{\mathrm{\eta }_{nor}} = \frac{{8d_{33}^2}}{{{\varepsilon _0}cn_\omega ^2{n_{2\omega }}\lambda _{2\omega }^2{S_{eff}}}}sin{c^2}\left( {\frac{{\Delta k \cdot L}}{2}} \right)} \end{array}$$

(3)$$\begin{array}{c} {{S_{eff}} = \frac{{{{\left[ {\mathrm{\int\!\!\!\int }E_{z,\omega }^2({x,y} )dxdy} \right]}^2}\mathrm{\int\!\!\!\int }E_{z,2\omega }^2({x,y} )dxdy}}{{{{\left[ {\mathrm{\int\!\!\!\int }d({x,y} )E_{z,\omega }^2({x,y} ){E_{z,2\omega }}({x,y} )dxdy} \right]}^2}}}} \end{array}$$

(4)$$\begin{array}{c} {\Delta k = {k_{2\omega }} - 2{k_\omega } + 2\pi {\Lambda ^{ - 1}} = \frac{{2\pi {n_{2\omega }}}}{{{\lambda _{2\omega }}}} - \frac{{2 \times 2\pi {n_\omega }}}{{{\lambda _\omega }}} + \frac{{2\pi }}{\Lambda }} \end{array}$$

where d₃₃ was the nonlinear coefficient of lithium niobate, ε₀ was the vacuum dielectric constant, and c was the speed of light in vacuum. n_ω and n_2ω were the effective refractive indices of the pump light and the second harmonic, respectively. λ_2ω was the wavelength of the second harmonic. ${E_{z,\omega }}({x,y} )$ and ${E_{z,2\omega }}({x,y} )$ were the z-direction components of the pump light and the second harmonic modes, respectively. $\Delta k$ was the phase mismatch between the pump light and the second harmonic, and L was the length of the periodically poled region. $\mathrm{\Lambda }$ was the poling period. The simulated SHG efficiency was shown in Fig. 4(a).

Fig. 4. (a) The simulated (black line) and experimental value (red line) of the SHG spectrum. (b) The simulated TE electric field profiles (E_z) at 1567 nm (fundamental) and 783.5 nm (second harmonic).

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Compared with the simulated value (4636%W⁻¹cm⁻²), the measured conversion efficiency was smaller (684%W⁻¹cm⁻²), and there was a broadening of the phase matching peak, which showed that the interaction between pump wavelength and second harmonic was not completely phase-matched. Two quantities were used to determine the quality of the waveguide and estimate the contributions of different defects to the second harmonic curve: the maximum second-harmonic power in the wavelength scan and the integral of the generated power with respect to the fundamental wavelength [32]. The measured SH curve could be treated as a result from the simulated SH curve by a two-step transition. The first step was to keep the shape of the simulated SH curve unchanged, but reduce the area (integral) under the simulated SH curve to that of the measured SH curve. The second step was to keep the area unchanged, but change the shape of the SH curve to be the same as that of the measured SH curve [32]. Both steps resulted in a reduction of the conversion efficiency. In our case, the measured maximum second-harmonic power was 8.3 dB lower than the simulation, and it was divided into two parts. One part was a 3.6 dB decrease calculated by the area ratio defined by Eq. (4), and it came from the first-step transition. The area or the integral was defined by the following formula [32]:

(5)$$\begin{array}{c} {\int {P_{2\omega }}d\lambda = \int {\mathrm{\eta }_{nor}}P_\omega ^2{L^2}d\lambda \; } \end{array}$$

The 3.6 dB decrease was mainly caused by waveguide loss, and the irregular shape of the reversed domains. The other part was 4.7 dB, and it came from the second-step transition. It was mainly caused by the inhomogeneities in the effective refractive index along the waveguide. The fabricated device might be improved using the following steps. First, the LN layer should have a good thickness uniformity. Then, in the nano-fabrication process, the linewidths of the photoresist mask and the chrome mask should be strictly controlled. In the subsequent reactive ion etching, the etching conditions should be optimized to reduce the fluctuation of the etching linewidth. In addition, the device should have the ability to shift the phase matching wavelength to compensate for the fabrication errors, such as using the thermo-optic or electro-optic effects. The dimension variation of the waveguide would result in the effective index inhomogeneities, and so the relation between the waveguide dimension and the poling period was simulated, as shown in Fig. 5. Figure 5(a) showed the poling period with the film thickness. When the poling period was fixed at 3.8 µm, a film thickness change of 1.2 nm (from 500 nm to 498.8 nm) would cause a phase matching wavelength shift of 10 nm (from peak 1 (1567 nm) to peak 2 (1577 nm)). To keep this 10 nm phase matching wavelength shift, the waveguide widths should be changed from 2.066 µm to 2.042 µm, which was shown in Fig. 5(b). Similarly, Fig. 5(c) showed that etching depth change of 10 nm (from 234 nm to 244 nm) would cause a phase matching wavelength change of 10 nm. These simulations showed that the phase matching was sensitive to waveguide geometry [33,34].

Fig. 5. For different film thicknesses (a), waveguide widths (b) and etching depths (c), the relationships between poling periods and fundamental wavelengths.

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In order to study the reason of phase-matched spectrum deviates from the ideal sinc² function, the cross section of waveguide was measured by the Atomic Force Microscope (AFM), and it was found that the waveguide width and the etch depth changed at the different position. The results were shown in Table 1. The abrupt waveguide width change from 1.882 µm to 1.922 µm might be caused by the deviations in the chrome mask fabrication and LN waveguide etching. It could be improved by strictly controlling the linewidth of the chrome mask and optimizing etching parameters of LN waveguide.

Table 1. The waveguide width and the etch depth at the different position of the waveguide

View Table

From the measured waveguide geometry (assuming a linear change in the waveguide width and etch depth between two adjacent measurement position), the phase-matched spectrum was reconstructed by the formula [35]:

(6)$$\begin{array}{c} {\eta \propto {{|\phi |}^2}} \end{array}$$

(7)$$\begin{array}{c} {\phi = \frac{{\Delta z}}{L}\mathop \sum \limits_{n = 0}^N {e^{i\Delta z\mathop \sum \nolimits_{m = 0}^n \left( {\Delta {\beta_m} - \frac{{2\pi }}{\Lambda }} \right)}}} \end{array}$$

(8)$$\begin{array}{c} {\Delta {\beta _m} = {k_{2\omega }} - 2{k_\omega } = \frac{{2\pi {n_{2\omega }}}}{{{\lambda _{2\omega }}}} - 2 \times \frac{{2\pi {n_\omega }}}{{{\lambda _\omega }}}} \end{array}$$

where n_ω and n_2ω were the effective refractive indices of the pump light and the second harmonic, respectively. λ_ω and λ_2ω were the wavelength of the pump light and the second harmonic, respectively. L was the waveguide length, and the waveguide was spaced by $\mathrm{\Delta }z$ form a mesh of N points. The measured phase-matched spectrum compared to the reconstructed one as shown in Fig. 6. In the reconstructed phase-matched spectrum, the film thickness was 499.4 nm. We found that the phase-matched spectrum was very sensitive to the waveguide geometry.

Fig. 6. The reconstructed phase-matched spectrum (black line) and the measured phase-matched spectrum (red line)

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3. Conclusion

In conclusion, a periodic poling with a period of 3.8 µm was realized in x-cut LNOI. The SHG was obtained in a dry-etched waveguide. The measured maximum normalized conversion efficiency was 684%W⁻¹cm⁻² at the wavelength of 1567 nm. The waveguide loss, the irregularity of the reversed domain, and the effective index inhomogeneities were analyzed to be the main sources for the decreased conversion efficiency. The SH curve deviated from the simulated curve, which was mainly caused by the inhomogeneities effective index along the waveguide. The simulation results showed that the phase matching was very sensitive to waveguide geometry. These results provided useful information for studying nonlinear process in the LNOI.

Funding

Natural Science Foundation of Shandong Province (ZR2020LLZ007); National Key Research and Development Program of China (2018YFB2201700, 2019YFA0705000).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Position along the waveguide (µm)	Waveguide width (µm)	Waveguide etch depth (nm)
400	1.882	259
1200	1.882	264
1700	1.882	255
2300	1.922	259
2800	1.922	254
3000	1.922	260

Second harmonic generation by quasi-phase matching in a lithium niobate thin film

Abstract

1. Introduction

2. Experiment and result

3. Conclusion

Funding

Disclosures

Data Availability

References

Data Availability

Cited By

Figures (6)

Tables (1)

Equations (8)

Optical Materials Express