Broadband highly efficient nonlinear optical processes in on-chip integrated lithium niobate microdisk resonators of Q-factor above 10⁸

The LN microdisk resonators were fabricated on the LN thin film wafer prepared by crystal cutting, polishing and bonding. Femtosecond laser direct writing and chemo-mechanical polishing were then utilized in sequence for patterning the LN thin film into free-standing microdisk resonators [details in the fabrication process can be found in the supplemental materials (https://stacks.iop.org/NJP/23/123027/ mmedia)]. As a matter of fact, recent works on LN photonic integrated components and circuits exclusively use the thin film LN on insulator (LNOI) as the material platform [15, 16]. Here, we chose to use the mechanically thinned LN thin film but not ion sliced LNOI for the reason as follow [33]. LNOI is obtained by the ion-slicing of submicron-thickness films from the single-crystalline LN bulk, where the implantation layer of helium ions (He⁺) defines the cleavage plane in the monocrystalline LN [15, 16]. The crystal quality of the ion-sliced LN thin film has been examined using Rutherford backscattering, revealing an inferior quality as compared to the LN bulk crystal [24]. Moreover, the quality of the ion-sliced film can only be partially recovered to the pristine bulk crystal after high-temperature annealing above 1000 °C [24]. In practical photonic applications, the LN thin film is typically bonded on a silica buffer layer for high refractive index contrast and optical isolation. Unfortunately, the annealing temperature at 1000 °C will spoil the bonding between the LN thin film and the underneath silica layer [16, 34]. Therefore, a relatively low temperature of 500 °C is chosen for annealing, leading to inferior optical property of LNOI to the bulk LN crystal. This problem becomes more severe with the development of fabrication techniques to allow for generation of ultra-smooth surface finish like PLACE, because otherwise the Q factor is dominated by the scattering loss at the sidewall surface but not the weak intrinsic material absorption.

The scanning-electron-microscopy (SEM) image of the fabricated LN microdisk resonator with a diameter of 1030 μm is presented in figure 1(a), showing an ultra-smooth surface with an average surface roughness less than 0.5 nm [22, 23]. The wedge angle of the microdisk sidewall is 8°, rendering the thickness of the microdisk resonator being varied from the submicron-scale at the edge to 3.5 μm near the center, as shown in figure 1(b). The fundamental WGM is simulated and plotted in the top inset of figure 1(b), with the center of the mode located 12 μm horizontally from the microdisk edge where the local LN thin film is only 600 nm thick, leading to a mode volume two orders of magnitude smaller than previously reported LN bulk resonators of the same diameter [11–13]. The distance between the SiO₂ pedestal and the microdisk edge was chosen to be 100 μm (see optical micrograph in the bottom inset of figure 1(b)) by controlling the HF acid etching time, which is sufficient to protect the WGMs from the scattering loss induced by the rough SiO₂ pedestal. The UHQ factors combined with the small mode volumes of the fabricated micro-resonators are ideal for efficient frequency conversions as shown below.

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The Q-factor of the LN resonator was first measured by sweeping the wavelength of a tunable laser (linewidth <200 kHz, Model: TLB 6728, New focus Inc.) injected into the resonator using a tapered fiber with a diameter of 0.9 μm. The relative position between the tapered fiber and the resonator was finely adjusted to fulfill the critical coupling condition using an XYZ piezo stage with a positioning resolution of 20 nm, which was monitored in real time by a charge coupled device (CCD) mounted above an objective lens with numerical aperture of 0.3. A low input laser power of only 5 μW was used in the measurement to avoid the thermo-optic and nonlinear optical effects. The signal was coupled out of the resonator by the same tapered fiber, sent into a high-speed photo detector with a bandwidth of 30 GHz, and real-time recorded with an oscillograph. The measured transmission spectrum as plotted in figure 1(c) was fitted with a Lorentzian-shaped resonance profile centered at ∼1551.52 nm as shown in the inset of figure 1(d), indicating a loaded Q factor Q_L of 7.5 × 10⁷ and a transmission T_F of 6%. The intrinsic Q factor Q_i was determined to be 1.20 × 10⁸ by the equation Q_i = 2 × Q_L/(1 + T_F ^1/2). Afterwards, a cavity ring-down measurement was conducted for measuring the Q factor and compared with the Q factor determined by the transmission spectrum measurement. In this way, the uncertainty in the precise measurement of such high Q factors can be safely excluded. The ring-down measurement was carried out by repeatedly scanning the laser with a high-speed Mach–Zehnder modulator into the targeted resonance, and the result is shown in figure 1(d). The retrieved photon lifetime is 64.3 ns, from which the intrinsic Q factor is derived to be 1.23 × 10⁸. The Lorentzian fitting and the cavity ring-down measurement agree very well with each other. Importantly, the mode volume is only 5.2 × 10³ μm³ in the UHQ microresonator. The intrinsic Q factor at 777.6 nm wavelength is measured to be 7.75 × 10⁷, the detail of which is provided in the supplemental materials. Some smaller microdisks with diameters of 130 μm and 240 μm were also fabricated, both showing intrinsic Q factors around 0.9 × 10⁸. (The details of the results and the statistics on the Q factors of microdisks with different diameters from 100 μm to 3 mm are provided in the supplemental materials). Since the bending losses are exponentially inverse proportional to the diameters of the resonators, the tiny variance (<30%) of the Q-factors for microdisk resonators with diameters from ∼1 mm to ∼100 μm indicates that the measured Q factors in the UHQ microdisks are solely determined by the intrinsic material absorption.

Frequency conversions in the UHQ LN microdisk resonators were investigated to explore the new regime of nonlinear interactions facilitated by the UHQ factors and small mode volumes [11–13, 25]. It is well known that phase-matching between the pertinent waves underpins efficient and low-threshold nonlinear frequency conversions in WGM-resonators [2]. Modal phase-matching (MPM) by manipulating geometric dispersions and quasi phase-matching (QPM) are frequently employed for frequency conversions in on-chip micro-resonators [35–40]. However, MPM suffers from a relatively low second order nonlinear coefficient, whereas QPM suffers from extra complexity in the fabrication process as well as the spectral fluctuation and optical loss caused by the imperfection in the domain poling [40–43].

We chose another QPM scheme for our nonlinear frequency conversion experiments, in which X-cut LN microdisk resonators were employed for achieving the natural quasi phase-matching (NQPM) as revealed recently [44]. The inherent cyclic phase-matching for transverse-electric (TE) WGMs circulating along the circumference of the χ⁽²⁾ micro-resonator with in-plane optical axis naturally facilitates broadband and efficient frequency conversions without resting on specific modal dispersion and nonlinearity pattering. By controlling the polarization of the injected pump light to excite the TE mode in the X-cut LN resonator with a diameter of 1030 μm, strong SHG and THG signals were observed when the wavelength of the pump light was set as 1555.2 nm. The spectrum was recorded by an optical spectrum analyzer (OSA, detected wavelength range of 600–1700 nm) and a fiber spectrometer (detected wavelength range of 300–1000 nm) as shown in figure 2(a). The SHG and THG signals were both TE polarized as well. The conversion efficiency of SHG grows linearly with the in-coupled pump power with a very high normalized conversion efficiency T_n of 470%/mW with relatively low pump power, showing a maximum absolute conversion efficiency T as high as 23% at a saturation in-coupled pump power P_sat of ∼0.11 mW, as shown in figure 2(b). The absolute conversion efficiency is also greater than the 15% conversion efficiency of the periodically poled LN (PPLN) microring at similar pump powers [37]. The theoretical value of the absolute conversion efficiency can be calculated by a theoretical modeling considering the pump depletion [37, 45], which is

$$\begin{align} T=\frac{{Q}_{\mathrm{L},\mathrm{F}}}{{Q}_{\mathrm{C},\mathrm{F}}}\frac{{Q}_{\mathrm{L},\mathrm{S}\mathrm{H}\mathrm{G}}}{{Q}_{\mathrm{C},\mathrm{S}\mathrm{H}\mathrm{G}}}=25\%.\end{align} \tag{ 1 }$$

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Here, Q_L,F, Q_C,F, Q_L,SHG, Q_C,SHG are the loaded (L) Q factors and the coupled (C) Q factors of the fundamental wave (F) mode and the second harmonic (SHG) mode, respectively, which can be experimentally extracted from the transmission spectra. The measured Q factors of the fundamental wave are provided in the supplemental materials. And the coupled Q factor of each mode is calculated by an equation Q_C = 1/(1/Q_L − 1/Q_i). Therefore, the experimental result 23% agrees well with the theoretical prediction 25%. And the saturation in-coupled pump power is determined by P_sat = 16T/T_n = 0.85 mW, indicating a higher saturation power than the experimental observation. And such a discrepancy is common in WGM LN resonators [11, 13, 37], resulting from the enhanced photorefractive effect [46] with the high in-coupled power, particularly in UHQ microresonators. Besides, the normalized conversion efficiency of THG was measured to be 30%/mW², outperforming the best reported values as well [39, 44, 47], as shown in figure 2(c).

The ultrahigh conversion efficiencies are a result of synergetic contribution from several critical characteristics in the fabricated on-chip X-cut LN microdisk resonator including the UHQ factor, the small mode volume V, the high nonlinear optical coefficient (d₃₃ for LN) and the implementation of NQPM by choosing the proper polarization configuration. Meanwhile, due to the dense spectral mode distribution of the millimeter–diameter resonator, broadband NQPM can be anticipated for a plethora of WGM pairs. To check this hypothesis, the transient output powers of harmonics were detected by continuously tuning the pump wavelength from 1530 nm to 1570 nm with a tuning rate of 0.5 nm s⁻¹, and the output powers of SHG and THG at each pump wavelength are shown in figure 2(d). The spectral resolution of the measurement curves was limited by the power meter of a sampling rate of 10 Hz. Remarkably, both SHG and cascaded THG were observed in the spectrum spanning over the entire telecom C-band with high and relatively stable conversion efficiencies insensitive to the pump wavelength thanks to the choice of the broadband NQPM scheme.

When the in-coupled pump power raised to more than 0.11 mW, higher-order nonlinearities such as Raman scattering and Kerr effect emerged. These processes impeded the power increase in the harmonics generation. Figure 3(a) shows clearly a visible light emission from the resonator, which was captured by a visible CCD camera. The spectrum ranging from 385 to 1700 nm wavelength recorded by the OSA (red line) and the fiber spectrometer (black line) is plotted in figure 3(b), when the in-coupled power was 3.8 mW. Here, FHG from the microdisk without sophisticated dual-periodically polling [39] was also detected at 388.8 nm wavelength with an output power as high as 3.16 μW. Meanwhile, Raman assisted frequency comb generation was observed around the pump wavelength with a comb line spacing of 7.9 THz with Raman shift of 238 cm⁻¹ [48], as shown in the rectangular box II in figure 3(b). Cascaded Raman assisted frequency comb generation was also detected around second harmonic wavelength for the first time, which is shown in the rectangular box I in figure 3(b). Each comb line in box I was generated by sum frequency generation process between the fundamental light and the comb line in box II. There is also a spectrum of cascaded Raman scattering lines [18, 22] recorded in the spectral range from 388 nm to 1700 nm, where the spectrum beyond 1700 nm was unable to measure as limited by the detection range of the OSA (Model: AQ6370D, Yokogawa Inc.). Thus, with only one pump laser operated at 1555.2 nm wavelength, an ultra-broad spectrum from ultraviolet to infrared can be generated with decent conversion efficiencies, indicating the unique nonlinear characteristics of the UHQ LN microresonator.

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When the pump laser operating at the telecom wavelengths was replaced with a near-visible tunable laser (765–781 nm) above certain threshold power, broadband non-degenerated OPO signals were observed. Figure 4(a) shows such an OPO spectrum detected by the OSA when being pumped at 770.4 nm wavelength with only 20.6 μW in-coupled power. The signal and idler waves at wavelengths of 1517.2 nm and 1565.2 nm were generated thanks to the satisfactory phase matching and triply resonant condition among the signal, idler and pump waves. The detected output power of OPO increases linearly with the increasing pump power above certain threshold power, as shown in figure 4(b). The threshold power was determined to be only 19.6 μW, which is the lowest among all the OPO investigations in on-chip LN micro-resonators, to the best of our knowledge [26]. The gain rate of OPO was determined to be 20% by linear fitting. Since the NQPM scheme allows the broadband phase matching, the degenerated OPO wave was also detected when the pump wavelength was tuned to 777.6 nm at a slightly higher threshold power of 20.0 μW, as evidenced in figure 4(c).

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The versatility of broadband NQPM for a wide range of nonlinear optical processes, including SHG, THG, FHG, and OPO, realized on the same microdisk resonator is quite appealing for further investigations. Previous works have unveiled the indispensable role of the natural 'poling' of the effective nonlinearity in X-cut LN microdisk on mitigating the wave-vector mismatch (Δk) which is also oscillating due to the anisotropic refractive indices along the periphery of the microdisk [44, 49]. Specifically, the oscillation of Δk relaxes the stringent requirement by QPM at unique poling period. Besides, NQPM inherently contains four periods of nonlinearity for QPM, and the periods are determined by the diameter of the microdisk which can be easily controlled (see figure 4(d)). Moreover, since the spectral mode density of the microdisk depends on its diameter as well, the millimeter-scale microdisk employed in this work can provide plenty sets of WGMs with suitable wave-vector mismatches covered by the small momentum (long period) of the nonlinearity poling, as corroborated by the simultaneous observations of efficient and broadband frequency conversions arising from various nonlinear processes with distinct phase-matching criteria. It should be noted that although NQPM entails the use of high-order WGMs which reduces the effective nonlinearity, its advantage in the UHQ micro-resonators can easily compensate for this defect by significantly enhanced resonance and achieve ultrahigh efficiencies for multiple nonlinear optical processes.