1. Introduction

Integrated photonics holds great potential for communication, signal processing and quantum network applications [1,2]. Lithium niobate is one of the most versatile and popular photonic material, due to its wide transparent window (0.4-5 µm), excellent electro-optic property and strong second-order nonlinearity. Recently, with breakthroughs in microfabrication techniques, lithium niobate-on-insulator (LNOI) has emerged as a competitive and promising candidate for integrated (nonlinear) photonics platform [3–5]. Thus far, various important functions have been developed on the LNOI platform, including high-performance modulators [6–9], acousto-optic devices [10], efficient nonlinear wavelength converters [11–13] and photon-pair sources [14,15]. Among them, there are several essential components of integrated photonics, such as ridge waveguides [13–18], photonic crystal cavities [19,20], microdisks [21,22] and microrings [23,24].

Optical waveguides, with strong light confinement, are preferred in integrated photonics. However, conventional waveguides, fabricated either with titanium (Ti) in-diffusion or with proton exchange, suffer from low index contrast ($\Delta n\sim 0.02$) between the core and cladding, resulting in large bending radii and large device dimensions, making it challenging for dense integration. These restrictions can be addressed by using LNOI ridge waveguides with much higher index contrast ($\Delta n\sim 0.7$) and stronger optical confinement, which can dramatically enhance nonlinear interactions. Combined with the flexibility in ferroelectric domain reverse, they can achieve ultrahigh conversion efficiencies (∼2600%W⁻¹cm⁻² for SHG at 1550 nm [13]) which are inaccessible in their bulk counterparts or conventional waveguides (∼90%W⁻¹cm⁻² for SHG at 1550 nm in reversed-proton exchange waveguide). However, the output power is restricted due to the small mode field diameter (MFD) of the nanowaveguides and special coupling design is required. The difficulty can be mitigated by using microscale waveguides with large MFD [25,26]. As for nonlinear photonics applications, the goal is to realize high conversion efficiency with high-power continuous-wave laser or pulsed laser at single pass [27], which holds great promise in wavelength conversion and all-optical single processing in optical communication systems. The most feasible approach is the ridge waveguide with large MFD in view of high damage threshold. Recently, the overall SHG conversion efficiency up to 58% is successfully demonstrated at 1550 nm [28]. Besides, large MFD can be efficiently coupled to standard single-mode optical fiber without special design, which is favorable in scalable fabrication and real communication applications.

Cascaded second-order nonlinear processes can induce a large effective Kerr nonlinearity, which could tremendously reduce the pump power as compared with a direct third-order process [29,30]. The emergence and rapid development of the LNOI technology enable various on-chip devices with unprecedented performances. Cascaded second-order processes will inject new vitality and provide exciting possibilities in nonlinear dynamics on the LNOI platform. In LNOI microdisks, cascaded second-order processes, such as second-/third-harmonic generation (SHG or THG) [21,31] and effective four-wave mixing [32], have been reported for a variety of applications. The cascaded electro-optic effect and second-order frequency conversion have been demonstrated in the LNOI ridge waveguide which offers a method of electrically controlling nonlinear conversion [33]. Besides, the multi-octave spanning supercontinuum spectrum in PPLN nanowaveguides [34] and high harmonic generation (up to the 13th harmonic) in a chirped PPLN ridge waveguide [35] have also been realized through a chain of successive cascaded processes.

In this work, we demonstrate efficient second to fourth harmonic generation in a single PPLN ridge waveguide on the LNOI platform pumped by short pulsed laser. Besides, we report a high single-pass SHG conversion efficiency (∼62%) of picosecond pulsed laser in the pump-depletion region, which provides a method to realize high-efficiency frequency conversion.

2. Experiment and results

The PPLN ridge waveguide has a dimension of $10\,\mu \textrm{m}\,\textrm{(W)} \times 5\,\mu m\,(H) \times 20mm\,(L)$. It is fabricated with a z-cut LNOI wafer, which consists of a 5-µm-thick crystalline lithium niobate on top of a 2-µm-thick buried silica buffering layer above a silicon substrate. Periodical poling of the LNOI is performed using an electrical field poling technique. The poling period, Λ, of the waveguide is approximately 18 µm with a duty cycle of (36 ± 1)%, which takes into consideration both the material and waveguide dispersion. Then, the ridge structure of the LNOI waveguide is formed between two parallel grooves with a depth of ∼2.5 µm in the chip by optical grade dicing. For the PPLN ridge waveguide, the QPM grating provides a reciprocal lattice vector (RLV) ${k_{QPM}}$ to compensate the phase mismatch during the nonlinear coupling process in the waveguide, with ${k_{QPM}} = {{2\pi m} / \Lambda }$ and m being the QPM order. The type-0 phase matching scheme is employed to achieve high conversion efficiency. In the z-cut configuration, the transverse-magnetic (TM) polarized modes access the highest second-order nonlinear coefficient ${d_{33}}$ (∼27 pm/V). Figures 1(a) and 1(b) depict the numerically simulated fundamental TM₀₀ mode profiles at the fundamental (∼1556.22 nm) and SH (∼778.11 nm) wavelengths, respectively.

 

Fig. 1. (a) and (b) Simulation of the fundamental TM mode profiles at the fundamental (1556.22 nm) and SH wavelength (778.11 nm) in the ridge waveguide, respectively. The arrows in the upper right corner denote the direction of polarization. (c) Measured SHG efficiency versus the pump wavelength at room temperature. Inset: top-view of scattered SHG light at the output end. (d) SHG power (red) and conversion efficiency (blue) as a function of input pump power.

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Firstly, normalized SHG conversion efficiency using continuous-wave (cw) pump is experimentally measured to evaluate the performance of the PPLN ridge waveguide. Light from a cw tunable telecom-band laser (1520-1600 nm) is amplified by an erbium-doped fiber amplifier (EDFA). The pump whose polarization is controlled by a polarization controller (PC) enters the ridge waveguide through an end-coupling setup. Two single-mode fiber pigtails couple the light in and out of the PPLN ridge waveguide. At the output end, the pump and SH light are separated by a 780/1550 wavelength-division multiplexer (WDM) with a 60-dB isolation ratio, then monitored by an optical spectrum analyzer (OSA) as well as a power meter. The normalized SHG conversion efficiency is defined as ${{{P_{SH}}} / {(P_P^2 \cdot {L^2})}}$ [13], where ${P_P}$ and ${P_{SH}}$ are the powers of the fundamental wave and generated SH wave measured at the output, L is the interaction length. The measured total fiber-chip-fiber transmission of the PPLN waveguide is ∼40% and the propagation loss is 0.8 dB/cm at around 1550 nm by using the Fabry-Perot interference method, comparable to other reports [36,37]. The measured SHG efficiency with respect to the pump wavelength is shown in Fig. 1(c). As shown in the inset, scattered SH light at the output facet is observed when the pump is set to the QPM wavelength of 1556.22 nm. The measured efficiency spectrum is well consistent with the theoretical modelling. The peak normalized SHG efficiency is ∼320%W⁻¹cm⁻² with a QPM bandwidth of about 0.5 nm. This is relatively high for micrometer PPLN ridge waveguides [28,36,37]. The measured conversion efficiency can be improved by using 50% poling duty, but this would eliminate further cascading processes as will be discussed later. The measured SH power and conversion efficiency is plotted in Fig. 1(d). The SH power follows a quadratic response on the pump in the low-conversion limit. When the input power is increased to ∼6 mW, SHG tends to saturate. The measured highest single-pass conversion efficiency is 11.6% with a generated SH power of 1.74 mW at a pump power of 15 mW. The saturation may be due to the photorefractive effect of lithium niobate, which can be circumvented by magnesium doping.

For short pulsed laser input, we utilize a mode-locked pulsed optical fiber laser as the pump source. The laser produces 500 fs-long-pulses centered at 1556 nm at a 60-MHz repetition rate. The laser has a spectral bandwidth of approximately 10 nm. When directly pumped by the femtosecond laser, multiple colored emission is observed as shown in Fig. 2, which involves cascading processes. At the output end, the generated harmonic light is collimated by a long-focus lens and then dispersed by a prism. In Fig. 2(b), the ultraviolet harmonic manifests as a faint blue spot mainly due to the fluorescence of the paper screen. In addition, the output light signals cover three colors (red, green and purple). The discrete peaks are located at around 778, 519 and 389 nm, respectively corresponding to second, third and fourth harmonic generation.

 

Fig. 2. (a) Image of the PPLN ridge waveguide when excited with 1556 nm femtosecond laser. (b) The generated cascaded harmonic light dispersed by a prism.

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To investigate the cascaded mechanism of harmonics generation, a narrow tunable optical filter (its full width at half maximum bandwidth is 0.45 nm) is placed after the mode-locked pulse laser, to generate narrow bandwidth pulsed pump with tunable central wavelength. After the filter, the laser pulses are theoretically stretched to about 8 picoseconds (Gaussian pulse shape assumed). The PPLN ridge waveguide has the specific poling period to satisfy the first-order QPM condition for SHG. Efficient SHG (∼778.11 nm) and FHG (∼389.05 nm) are simultaneously observed when the central wavelength is turned to the QPM wavelength of 1556.22 nm. In this configuration, the FHG is created through the cascaded processes involving SHG ($\omega \textrm{ + }\omega \to 2\omega $) and successive SHG ($2\omega \textrm{ + 2}\omega \to 4\omega $). The spectra of SHG and FHG are analyzed and plotted in Fig. 3(a). The inset displays a top view of the waveguide with scattered red and ultraviolet harmonics. The input pulse power is gradually changed to quantify the SHG conversion efficiency and pump-depletion ratio. As is shown in Fig. 3(b), SHG conversion efficiency saturates at moderate input pulse powers (∼520 µW). The measured highest single-pass conversion efficiency is ∼62% with an input pulse power of only ∼580 µW in the pump-depletion region. As presented in Fig. 3(c), the FH signal has a fitted quartic dependence on the input power in the small signal condition as expected in the nonlinear conversion process.

 

Fig. 3. SHG and cascaded FHG in PPLN waveguide pumped with pulsed laser at 1556.22 nm. (a) Measured spectrum of the SHG (∼778.11 nm) and FHG (∼389.05 nm) (not to scale). Inset: top-view of the waveguide. (b) Measured SHG conversion efficiency (red) and pump-depletion ratio (blue) as a function of input pulse power, showing 62% single-pass conversion efficiency with an input pulse power of 580 µW. (c) Measured FHG power versus the input power and the corresponding quartic fitting. (d) Calculated effective nonlinear coefficient and the SHG phase mismatching of the PPLN ridge waveguide.

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To illustrate the mechanism of QPM for SHG and cascaded FHG in the PPLN ridge waveguide, the RLV of the PPLN waveguide is numerically calculated by making a Fourier transform of the domain inversion structure [29,30]. Figure 3(d) exhibits that the PPLN structure has a series of discrete RLVs with high effective nonlinear coefficients. Each RLV line satisfies a QPM condition for SHG at a specific fundamental wavelength. The non-zero effective nonlinear coefficients of even order QPMs result from the poling duty away from 50:50. The PPLN waveguide can support both first-order and higher-order QPM conversions. Furthermore, we calculate and plot the phase mismatching curve for SHG considering the effective refractive index in the PPLN waveguide. It is evident that the waveguide can achieve first-order QPM for SHG at around 1556 nm with SH wavelength at 778 nm (point A). An eight-order QPM SHG process occurs at approximately 778 nm (point B), which finally leads to the consequent cascaded FHG observed in the experiment.

When the input pulsed laser is scanned to the non-QPM wavelength of 1556.75 nm (still on the QPM condition but slightly away from the perfect point), efficient SH (∼778.37 nm) and cascaded TH (∼518.9 nm) signals are observed, as shown in Fig. 4(a). The inset of Fig. 4(a) shows the image of the scattered SHG and THG from the waveguide. The THG is achieved via cascaded SHG ($\omega \textrm{ + }\omega \to 2\omega $) and sum frequency generation (SFG) ($\omega \textrm{ + 2}\omega \to 3\omega $). To investigate the cascade SFG mechanism, the intensity profiles of the SHG and THG at the output facet are recorded. The SHG has a fundamental mode profile (bottom left), whereas the THG possesses a higher order mode (bottom right). The cascaded process results from higher-order QPM process mixing between these different modes. Figure 4(b) reveals the output SH power varies with the input pulse power with a quadratic fitting of the experimental data. Compared with Fig. 3(b), the output SH power pumped at the non-QPM wavelength is much lower than that at the QPM wavelength under the same input pulse power. Figure 4(c) indicates the cubic dependence of THG power on the input pulse power which matches well with the theoretical expectation. Besides, we notice that the cascaded SFG process in the PPLN waveguide happens not only at the wavelength of ∼1556.75 nm, but also at several other wavelengths in the QPM main lobe. However, the THG intensities at other wavelengths are extremely weak, which probably arises from phase mismatch in the cascaded SFG process.

 

Fig. 4. SHG and cascaded THG in PPLN waveguide pumped with pulsed laser at 1556.75 nm. (a) Measured spectrum of the SHG (∼778.37 nm) and THG (∼518.9 nm) (not to scale). Inset: top-view of the waveguide, the mode profile of SHG (bottom left) and higher-order THG after filtering (bottom right). (b) Quadratic dependence of the output SHG power on input pulse power. (c) The normalized THG power versus the input pulse power and the corresponding cubic fitting.

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3. Conclusion

In conclusion, we demonstrate efficient SHG and cascaded FHG at the QPM wavelength in a PPLN ridge waveguide on the LNOI platform. In addition, SHG and cascaded THG involving cascaded SFG process are also achieved at the non-QPM wavelength. Furthermore, we also report a ∼62% high single-pass SHG conversion efficiency of pulsed laser. These results based on the LNOI waveguide may have potentials in integrated nonlinear frequency conversion process.