Highly tunable efficient second-harmonic generation in a lithium niobate nanophotonic waveguide

1. INTRODUCTION

Since their invention in the 1960s [1,2], lasers have been the backbone of modern optics, playing fundamental roles in optical sciences and technologies. For a coherent light source, wavelength tunability is one of the most important specifications, crucially underlying many applications including optical communications [3], spectroscopy [4,5], frequency metrology [6], sensing [7], to name some. However, lasing wavebands are naturally limited by gain media. Nonlinear optical parametric processes, such as second-harmonic generation (SHG), sum-frequency generation (SFG), and difference-frequency generation (DFG), with the flexible engineering of the phase-matching condition, are probably the most prominent approaches to achieve tunable coherent radiation at optical frequencies that can hardly be obtained by lasers directly [8–10].

Lithium niobate (LN), with outstanding nonlinear and linear optical properties, is widely employed for this application, where SFG/DFG has been extensively studied over the past decades, particularly in periodically poled lithium niobate (PPLN) waveguides [11,12]. In general, a type-0 configuration is employed to achieve a high conversion efficiency, and temperature tuning is a common technique to vary the operation wavelength of a PPLN waveguide. However, the pump wavelength tunability of the type-0 SHG is fairly limited [11–13], mainly due to the relatively small wavelength dependence of the thermo-optic coefficient (although DFG can exhibit a large wavelength tunability with a third wave involved). In fact, LN exhibits a remarkable thermo-optic birefringence [14–16], significantly greater than most other optical media [17]. This characteristic can be utilized to greatly increase the wavelength tunability of SHG in PPLN by employing a type-I configuration [11,12,18], which, however, inevitably seriously sacrifices the conversion efficiency due to the significantly weaker nonlinearity compared with a type-0 process.

Over the past decade, a variety of integrated material platforms with ${\chi }^{(2)}$ nonlinearity have been developed for efficient nonlinear optical parametric processes [19–25], where the tight confinement of optical modes is able to significantly enhance nonlinear optical interactions. Recent advances in the integrated LN platform have greatly inspired study of nonlinear optics in LN nanophotonic structures [26–35], showing great potential for nonlinear wavelength conversion with even higher efficiencies compared with PPLN and other integrated platforms. This provides an opportunity to achieve a large wavelength tunability by using the type-I configuration while maintaining a high conversion efficiency at the same time.

Here we demonstrate highly tunable efficient on-chip SHG in an LN nanophotonic waveguide. We achieve SHG through type-I intermodal phase matching between orthogonal polarizations, and by utilizing the strong thermo-optic birefringence of LN, we demonstrate temperature tuning of the SHG wavelength, with a measured tuning slope of 0.84 nm/K for a telecom pump, almost 1 order of magnitude higher than that of type-0 SHG in LN [11,12,36]. Meanwhile, our device is designed to exhibit a large mode overlap, resulting in a theoretical normalized SHG efficiency of $22.2\%{\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$, which enables us to experimentally demonstrate a conversion efficiency of $4.7\%{\mathrm{W}}^{-1}$ in a waveguide only 8 mm long. Our device is of great promise for efficient on-chip wavelength conversion to produce highly tunable coherent visible light, which is essential for various integrated photonic applications such as particle and chemical sensing in aqueous environments [37–39], while taking advantage of the mature telecom laser technology.

2. WAVEGUIDE DESIGN

LN exhibits a significant thermo-optic birefringence, with a value of $|\frac{d{n}_e}{dT}-\frac{d{n}_o}{dT}|\sim 4\times {10}^{-5}{\mathrm{K}}^{-1}$ at room temperature [14–16], where $\frac{d{n}_e}{dT}$ and $\frac{d{n}_o}{dT}$ are the thermo-optic coefficients for the extraordinary and ordinary light, respectively. As a result, if SHG occurs in an LN waveguide between optical waves with orthogonal polarizations, a temperature change of the device would result in a considerable variation of the material birefringence, which in turn shifts the phase-matched wavelength of the SHG process significantly. In particular, we can maximize this effect by using a Z-cut LN waveguide, which supports ordinarily and extraordinarily polarized optical modes with high polarization purity [see Figs. 1(a) and 1(b)] [15].

 

Fig. 1. (a) Schematic of our Z-cut LN waveguide. FEM simulations of (b) mode profiles, and (c) effective indices as functions of wavelength, of ${\mathrm{TE}}_{0,\mathrm{tele}}$ in the telecom and ${\mathrm{TM}}_{j,\mathrm{vis}}(j=0,1,2)$ in the visible, where $w_t=1200\mathrm{nm}$, $h_1=460\mathrm{nm}$, $h_2=100\mathrm{nm}$, and $\theta =75°$, at 20°C. Discontinuity in the curve of ${\mathrm{TM}}_{1,\mathrm{vis}}$ is due to its coupling with ${\mathrm{TE}}_{2,\mathrm{vis}}$ (not shown). Zoom-in of the wavelength-dependent effective indices of ${\mathrm{TE}}_{0,\mathrm{tele}}$ and ${\mathrm{TM}}_{2,\mathrm{vis}}$ at (d) 20°C, and (e) 70°C, with black arrows indicating phase matching; (f) simulated phase-matched pump wavelength ${\lambda }_{\mathrm{PM}}$ as a function of temperature. In (c)–(f), the FEM simulations take into account the temperature and wavelength dependence of the material refractive indices, for both ordinary and extraordinary light [14,40].

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We design the geometry of the Z-cut LN waveguide [see Fig. 1(a)] such that the fundamental quasi-transverse-electric mode (${\mathrm{TE}}_{0,\mathrm{tele}}$) in the telecom band is phase matched with the third-order quasi-transverse-magnetic mode (${\mathrm{TM}}_{2,\mathrm{vis}}$) in the visible. Figures 1(c) and 1(d) show the effective refractive indices of the two modes, simulated by the finite-element method (FEM), which gives a phase-matched pump wavelength of ${\lambda }_{\mathrm{PM}}=1540\mathrm{nm}$ at room temperature of 20°C. Of particular interest is that LN exhibits a significant thermo-optic effect for extraordinary light ($\frac{d{n}_{e,\text{vis}}}{dT}\approx 4\times {10}^{-5}{\mathrm{K}}^{-1}$), while it is negligible for ordinary light ($\frac{d{n}_{o,\text{tele}}}{dT}\approx 0$) around room temperature [14]. As a result, when the device temperature increases, the effective refractive index of the ${\mathrm{TE}}_{0,\mathrm{tele}}$ mode remains nearly intact, while that of the ${\mathrm{TM}}_{2,\mathrm{vis}}$ mode increases considerably. Consequently, the phase-matched wavelength moves dramatically towards longer wavelengths. Figure 1(e) shows an example, where ${\lambda }_{\mathrm{PM}}$ shifts to 1574 nm at a temperature of 70°C. Detailed analysis shows that the phase-matched wavelength depends almost linearly on the device temperature, as shown clearly in Fig. 1(f), with a significant tuning slope of 0.69 nm/K.

Phase matching of the two modes indicates potentially efficient SHG in the designed waveguide. For a lossless waveguide without pump depletion, the SHG efficiency is given by the following expression [8,41]:

Equations (1)–(3) show that the SHG efficiency depends essentially on the spatial mode overlap $\zeta$, the effective mode area $A_{\mathrm{eff}}$, and the effective nonlinear susceptibility $d_{\mathrm{eff}}$. Numerical simulation shows that our waveguide exhibits a small $A_{\mathrm{eff}}=1.46{\mathrm{\mu m}}^2$. In particular, our designed waveguide exhibits a large spatial mode overlap, with $\zeta =0.32$. As a result, the waveguide exhibits a normalized conversion efficiency as high as $\eta =22.2\%{\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$. This value is comparable to that of type-0 SHG in typical PPLN [36,42] and LN nanophotonic waveguides [31] that utilize the maximum component of the ${\chi }^{(2)}$ nonlinearity ($d_{\mathrm{eff}}=d_{33}=27\mathrm{pm}/\mathrm{V}$), although a type-I configuration is employed here ($d_{\mathrm{eff}}=d_{31}=4.3\mathrm{pm}/\mathrm{V}$ [43]). In contrast to those type-0 devices, our waveguide is expected to exhibit a significantly larger thermal tuning slope, as we will experimentally demonstrate in the following.

3. EXPERIMENTAL RESULTS

To confirm our simulation results, we fabricated waveguides on a Z-cut LN-on-insulator wafer [see Fig. 2(b)], where the LN thin film has a thickness of $\sim 560\mathrm{nm}$, sitting on 2-μm-thick buried oxide. Figure 2(c) shows the cross section of a fabricated waveguide whose geometry is very close to our design [see Fig. 1(a)]. In particular, as presented in Fig. 2(d), the waveguide sidewall is very smooth, implying a low propagation loss. In order to quantify the propagation and coupling losses, we fabricated waveguides with the same cross section but different lengths, as schematically shown in the inset of Fig. 2(e). Since these waveguides share the same coupling and bending losses, by measuring their transmission as a function of the differential length, we can extract the propagation loss. Figure 2(e) shows the measurement results, where the propagation loss of straight waveguides for the ${\mathrm{TE}}_{0,\mathrm{tele}}$ mode is measured to be 0.54 dB/cm, a small value that represents the state-of-the-art quality of LN nanophotonic waveguides [35,44,45]. Together with the overall fiber-to-fiber transmission of a straight waveguide [for example, see Fig. 2(f)], we obtained a fiber-to-chip coupling loss of about 5 dB/facet.

 

Fig. 2. (a) Experimental setup for device characterization and SHG measurement. Scanning electron microscope pictures showing the waveguide (b) top view, (c) facet, and (d) sidewall. (e) Fiber-to-fiber loss as a function of the differential length $L_d$, relative to that of $L_d=0$, for waveguides schematically illustrated in the inset, where $L_f$ and $R$ are kept as 8 mm and 100 μm, respectively. (f) Telecom-band transmission spectrum of the TE polarization for a straight waveguide with a length of $L\simeq 8\mathrm{mm}$, whose schematic is shown in the inset. VOA, variable optical attenuator; LF, lensed fiber; WDM, wavelength division multiplexer.

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To demonstrate SHG, we employed a straight waveguide with a length of about 8 mm. We launched a telecom-band continuous-wave (CW) laser into the device, with the setup shown in Fig. 2(a). By scanning the laser wavelength, we were able to measure the efficiency spectrum of SHG. One example is shown in Fig. 3(a), which shows a phase-matched pump wavelength of 1559 nm at a temperature of 18.7°C. The main lobe of the recorded efficiency spectrum agrees well with the theoretical expectation from the function ${\mathrm{sinc}}^2(\mathrm{\Delta }L/2)={[\frac{\sin (\mathrm{\Delta }L/2)}{\mathrm{\Delta }L/2}]}^2$. Interestingly, the efficiency spectrum exhibits multiple significant sidelobes, which are likely introduced by potential nonuniformity of the waveguide thickness along its total length, since the phase-matching condition of SHG is very sensitive to the waveguide geometry.

 

Fig. 3. SHG from a straight LN nanophotonic waveguide with a length of 8 mm. (a) Conversion efficiency spectrum at $T=18.7°\mathrm{C}$, with the center wavelength of the ${\mathrm{sinc}}^2$ function aligned to the measured peak; (b) SHG spectrum at a fixed pump wavelength of 1559.06 nm at $T=18.7°\mathrm{C}$; (c) second-harmonic power as a function of pump power, with experimental data compared with a quadratic fitting, exhibiting a conversion efficiency of $4.7\%{\mathrm{W}}^{-1}$.

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By fixing the pump wavelength at 1559.06 nm, where the peak conversion efficiency is located, we observed coherent radiation from its second harmonic at 779.53 nm, as shown clearly in Fig. 3(b). By varying the pump power, we recorded the SHG power that is plotted in Fig. 3(c). The second harmonic shows a quadratic power dependence on the pump that agrees very well with the theoretical expectation. Fitting the experimental data, we obtained an on-chip conversion efficiency of $4.7\%{\mathrm{W}}^{-1}$ [see Fig. 3(c)].

The recorded SHG efficiency is smaller than the theoretical value given by $\eta L^2$ ($=14.2\%{\mathrm{W}}^{-1}$), primarily due to the nonzero propagation losses of the waveguide. The LN waveguide exhibits a propagation loss of 0.54 dB/cm at the pump wavelength [see Fig. 2(e)]. That at the second harmonic, however, is challenging to characterize with the current setup, due to the difficulty in effective light coupling into a high-order waveguide mode. As a rough estimate, we assume it to be $\sim 2.16\mathrm{dB}/\mathrm{cm}$, since the propagation loss is dominated by the Rayleigh scattering from the sidewall roughness that scales with the wavelength as $1/{\lambda }^2$ [46]. As a result, the theoretical conversion efficiency is estimated to be $\sim 9.1\%{\mathrm{W}}^{-1}$ for the 8-mm-long waveguide, after we take into account these propagation losses. On the other hand, the potential nonuniformity in the waveguide geometry might also impact the conversion efficiency to a certain extent. In addition, the coupling loss of the high-order second-harmonic light is likely underestimated due to its large mode mismatch with the focused fiber modes, leading to a conservative estimation of the recorded conversion efficiency. Therefore, the measured conversion efficiency can be improved in the future by reducing the waveguide sidewall scattering loss (say, with an oxide cladding), by increasing the uniformity in the wafer thickness with appropriate chemical mechanical polishing, and by optimizing coupling of the second-harmonic light (say, with a separately designed on-chip coupler [23]).

To show the spectral tuning capability of our device, we varied the device temperature from 18.7°C to 90.0°C and measured the SHG efficiency spectra. The recorded peak efficiencies are similar to that shown at 18.7°C [see Fig. 3(c)]. Figure 4(a) presents the peak-normalized spectra at different temperatures. It shows clearly that the SHG spectrum shifts towards longer wavelengths when the device temperature increases. By mapping the phase-matched pump wavelength as a function of temperature, we obtained Fig. 4(b), showing an experimentally measured tuning slope of $\frac{d{\lambda }_{\mathrm{PM}}}{dT}=0.84\mathrm{nm}/\mathrm{K}$, almost 1 order of magnitude larger than that achieved by type-0 SHG in LN [11,12,36]. The experimental results agree well with our simulations [see Fig. 1(f)]. A slightly larger experimental value of the tuning slope is likely due to positive contributions by pyroelectric [47] and thermal expansion effects [48] in the waveguide cross section, which were not taken into account in the simulations.

 

Fig. 4. Thermal tuning of SHG. (a) Conversion efficiency spectra at different temperatures. Each spectrum is normalized by its peak value for clear comparison. (b) Measured phase-matched pump wavelength ${\lambda }_{\mathrm{PM}}$ as a function of temperature.

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4. CONCLUSION

In conclusion, we have demonstrated highly tunable efficient SHG in an LN nanophotonic waveguide. The LN waveguide exhibits a high optical quality with a propagation loss as low as 0.54 dB/cm in the telecom band, which represents the state-of-the-art quality of LN nanophotonic waveguides reported to date [35,44,45]. In particular, we took advantage of the strong thermo-optic birefringence of LN to achieve thermal tuning of the SHG wavelength, with a tuning slope of 0.84 nm/K for a telecom-band pump, significantly higher than that offered by type-0 SHG in LN. At the same time, thanks to the tight mode confinement and a large spatial mode overlap, our waveguide exhibits a high theoretical normalized conversion efficiency of $22.2\%{\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$, even for the type-I intermodal phase matching, which is comparable to that of type-0 SHG in typical PPLN and LN nanophotonic waveguides utilizing the largest nonlinear term $d_{33}$. Our waveguide design enabled us to experimentally record an SHG efficiency of $4.7\%{\mathrm{W}}^{-1}$ inside a waveguide only 8 mm long.

We have demonstrated large tuning of type-I SHG by exploiting the strong thermo-optic birefringence of LN. In fact, this technique can also be applied to increase tunability of other nonlinear parametric processes in LN, such as DFG and SFG, by employing interband optical waves with different polarizations. Compared with type-0 phase matching widely studied in LN for a higher efficiency, type-I and type-II processes in LN nanophotonic waveguides offer a much larger thermal tunability while maintaining a high efficiency, showing great promise for tunable and efficient on-chip nonlinear wavelength conversion that produces coherent radiation from visible to mid-infrared wavelengths.