1. Introduction

Microdisk resonators are promising devices in advanced photonic applications due to their unique features, such as small device size, narrow resonant linewidth, and light storage for a long time period. They can confine the resonant lightwave such that the excited whispering gallery modes (WGM) circulate along its circumference. The resonant property of microdisks has been used in various photonic applications, including intensity modulation [1], wavelength filtering [2], laser resonator [3,4], and chemical sensing [5]. In the microdisk resonator, strong light/material interaction due to field buildup in small mode volume and long interaction time enhances nonlinear-optic effect and reduces threshold excitation power. Microdisk resonators with high quality factor (Q factor) and large free spectral range (FSR) have been produced on various material systems, such as Si-based [1,5], III-V [2,3], II-VI [4], and polymer [6] materials, to offer diverse photonic purposes.

Lithium niobate (LiNbO₃) is an important ferroelectric material in photonics due to its excellent physical effects, such as electro-optic effect, nonlinear-optic effect, photoelastic effect, and piezoelectric effect. Utilization of electro-optic effect on microdisk resonators produces fast and effective tuning of the resonant wavelength, and thus the tunability on light intensity and filtered wavelength. The nonlinear frequency conversion response is enhanced by using the microdisk resonator structure. However, limited by the LiNbO₃ microdisk fabrication techniques, the ideal LiNbO₃ microdisk resonators with several μm diameter and smooth surface have not yet been produced. Previously, LiNbO₃ microresonators are produced in the microring form [7,8] by crystal ion slicing [9]. In order to combine the unique WGM properties with electro-optic effect and nonlinear-optic effect, LiNbO₃ disk resonators with diameter 3~6.3mm are produced by mechanical polishing. Their usage finds new photonic applications, such as high-order tunable filter [10], electric field sensor [11], planar coupling to disk resonator [12], frequency doubling at a wide frequency range [13], naturally phase-matched second harmonic generation [14], simultaneous second harmonic and third harmonic generation [15]. Although large-diameter LiNbO₃ disk resonators have smaller radiation loss and thus higher Q factor, the large-disk problems, such as narrow FSR, large device size, and the difficulty in device integration, would restrict the application range.

In this work, we present the first LiNbO₃ microdisk resonator with several μm diameter and smooth surface. The undercut structure of the microdisk is produced by selective ion implantation and chemical etching [16]. By surface tension reshaping, the rough etched surface is smoothed during thermal treatment. The characteristics of resonant modes, such as resonant wavelength, effective index, and field profile, are calculated by finite element method and compared with the experimental results. The resonator measurement demonstrates the large FSR and the high Q factor of the produced LiNbO₃ microdisk resonators.

2. Device fabrication

Figure 1(a) shows the fabrication process of LiNbO₃ microdisk resonators. First, a 120nm-thick Cr film is deposited on the –z face of the LiNbO₃ substrate by RF magnetron sputtering. By photolithography, the 1.2μm-thick photoresist (PR) with a 20μm-diameter circle shape (microdisk pattern) is formed over the Cr film. The Cr film without PR protection is etched by the Cr-7 etchant. After removing the PR, the patterned Cr film is used as chemical-etching mask. Over the circular Cr film, the 2.5μm-thick PR is patterned with a 10μm-diameter circle shape (pillar pattern) and is used as implantation mask. According to the mask deployment in Figs. 1(a)-(4), the substrate is separated into three regions: (I) PR/Cr/LiNbO₃; (II) Cr/LiNbO₃; (III) exposed LiNbO₃. The substrate is implanted by He⁺ ions with the inclination angle 7°. The implantation energy is 350 keV and the implantation dose is 1.3 × 10¹⁶ ions/cm². The implanted He⁺ ions produce the buried lattice damage layer in LiNbO₃, labeled as dot lines in Figs. 1(a)-(5). The SRIM (Stopping and Range of Ions in Matter) program is used to calculate the vacancy concentration distributions after implantation, as shown in Fig. 1(b). In region I, the 2.5μm-thick PR effectively resists the implanted He⁺ ions such that no lattice damage occurs in LiNbO₃. Because the Cr film is thin, the vacancy concentration distribution in region II is 0.12μm shallower than that in region III.

 

Fig. 1 (a) Fabrication process of the LiNbO₃ undercut microdisk; (b) the vacancy concentration distribution in the three regions on LiNbO₃ (LN) labeled in Fig. 1(a)-(4).

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After implantation, the substrate is immersed in the diluted HF solution (HF/H₂O = 1/0.5) for 10hrs with the temperature controlled at 18°C. This etching solution can etch the -z face of LiNbO₃ and the lattice damage layer. Initially, the region without the protection of Cr film is etched. When the etching reaches the depth of the lattice damage layer, the etching would proceed laterally until the entire lattice damage layer is removed. The etching time after removing the entire lattice damage layer determines the gap between microdisk and substrate (or pillar height). After etching, the PR and the underlay Cr film are removed. Because the rough microdisk surface increases the scattering loss, surface tension reshaping is used to smooth the etched surface. As the LiNbO₃ substrate is treated at the temperature approaching the melting point (1257°C), the surface would become slight molten state. Surface tension would modify the substrate surface such that the etched surface becomes smooth. The treatment temperature is chosen at 1120°C, which is smaller than the Curie temperature (1142°C), in order to maintain ferroelectric phase. The slightly melted surface layer re-crystallizes with the seeding of un-melted bulk crystal during cooling and maintains crystalline state after cooling. During thermal treatment, the LiNbO₃ substrate is put in the crucible with LiNbO₃ powder to suppress Li₂O out-diffusion. The heating starts at a rate 5°/min, dwells at 1120°C for 3hrs, and ends with natural cooling. This process is under flowing N₂ gas to avoid contamination.

Figure 2 shows the photographs of undercut LiNbO₃ microdisks without and with thermal treatment. The thermal treatment time is 3hrs, which is far shorter than 50hrs in [17], to avoid microdisk deformation. The scanning electron microscope (SEM) photographs in Fig. 2(a,b) and 2(e,f) demonstrate the thermal treatment effect on enhancing surface smoothness. Not only the entire microdisk surface becomes smoother but also the substrate surface does. It is noted that thermal treatment reshapes the microdisk rim from the angled edge to the round edge. Due to the shadowing effect of implantation mask, the pillar diameter is larger than that of the implantation mask. Comparison of the reflection microscope photographs in Fig. 2(c) and 2(g) shows that thermal treatment makes the microdisk periphery becomes smoother and more like circular. The bottom surface of the microdisk also becomes smoother and uniform. The transmission microscope photographs in Fig. 2(d) and 2(h) display the detailed pillar structure. Because of the hexagonal nature of LiNbO₃ crystal, chemical etching produces a pillar with the hexagonal pedestal. Thermal treatment reshapes the pillar pedestal to the circular shape and makes the pillar near microdisk become vertical, as shown in Fig. 2(f). The atomic force microscope (AFM) measurement shows that thermal treatment reduces the root-mean-square roughness of the etched surface from 1.17nm to 0.41nm, which is close to that of the original substrate surface (0.4nm).

 

Fig. 2 Photographs of the 20μm-diameter LiNbO₃ microdisks (a-d) without thermal treatment; (e-h) with thermal treatment at 1120°C for 3hrs. (a,b,e,f), (c,g), and (d,h) are measured by scanning electron microscope, reflection microscope, and transmission microscope.

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The geometric structure of the produced microdisks has good repeatability as the etching temperature is precisely controlled. The geometry of the LiNbO₃ microdisk can be varied by adjusting process parameters. The diameters of microdisk and pillar are determined by the photolithographic mask pattern. The implantation depth increases with the implantation energy. The level and the range of lattice damage become larger as the implantation dose increases. Therefore, the microdisk thickness increases with the implantation energy but decreases with the implantation dose. The former has the dominant effect. The pillar height increases with the chemical etching time. The microdisk thickness is designed at 0.4μm such that the microdisk has a single vertical resonant mode.

3. Device characterization

Figure 3(a) shows the measurement setup of LiNbO₃ microdisk resonators using the tapered fiber coupling. The tapered fiber is drawn by fiber fuser to the minimum waist radius 2.45μm. The light from the C-band ASE source passes through the polarizer and the polarization controller in order to control the polarization state. It is then input to the tapered fiber for exciting the resonant modes of the microdisk. Under the assistance of two single-tube microscopes with long-working-distance objectives, the three-axis nano-positioning by the XYZ piezo-stage (PI P-611.3) is used to control the distance between microdisk and tapered fiber. The spectrum of the output light is measured by optical spectrum analyzer (OSA). The transmission spectrums of microdisk resonators are normalized with respect to those without coupling to microdisk. The loaded Q factor of the microdisk resonator is determined by Q_L = λ₀/δλ, where λ₀ and δλ are the resonant wavelength and the resonant linewidth. The λ₀ and δλ values are obtained by performing a Lorentz fit to the transmission curve. The coupling parameter K is calculated by $K=(1-\sqrt{T})/(1+\sqrt{T})$, where T is the transmission at resonance. As the Q_L and K values are known, the intrinsic quality factor Q₀ and the external quality factor Q_ex are obtained by solving the equations: 1/Q_L = 1/Q₀ + 1/Q_ex and K = Q₀/Q_ex. Q₀ is the quality factor of microdisk resonator and is related to material absorption, surface scattering, and field radiation. Q_ex is associated with the coupling between microdisk resonator and tapered fiber.

 

Fig. 3 (a) Measurement setup of LiNbO₃ microdisk resonators; (b) photograph of the 20μm-diameter microdisk coupled with the tapered fiber.

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4. Results and discussion

The microdisk resonant modes and the tapered fiber mode are calculated by the full-vectorial mode solver using finite element method in cylindrical coordinates. The microdisk resonant modes for TM and TE polarizations are labeled as TM_p,m and TE_p,m, where p and m are the radial and azimuthal orders. Figure 4(a) shows the comparison of effective index for the first six TE radial modes (TE₁~TE₆) and the first three TM radial modes (TM₁~TM₃) of microdisk resonator, and the fundamental mode HE₁₁ of tapered fiber. The marker positions correspond to the specific resonant modes. Because the ordinary index is larger than the extraordinary index in LiNbO₃, the TE modes have larger effective indices than the TM modes at the same radial order. The effective coupling from tapered fiber to microdisk resonator occurs as the phase matching condition is satisfied. It is found that the tapered fiber coupling mainly excites the TM₁ and TE₄ modes. Figure 4(b) shows the field profiles of the TM_1,57 and TE_4,57 modes for the microdisk resonators with angled edge (without thermal treatment) and round edge (with thermal treatment). Because the TE_4,57 mode has a larger field profile than the TM_1,57 mode, the TE_4,57 mode has smaller field overlap with the tapered fiber mode and larger resonator loss, which result in weaker coupling and resonance.

 

Fig. 4 (a) Comparison of effective index for the microdisk resonant modes and the tapered fiber mode; (b) the simulated field profiles of microdisk resonant modes.

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Figure 5 shows the measured transmission spectrums of the microdisk resonators without and with thermal treatment. The radial and azimuthal orders of the resonant modes are discriminated by comparing the measured resonant wavelength with the one calculated in simulation. The resonant wavelengths of the three main resonant modes (TM_1,56, TM_1,57, TM_1,58) in Fig. 5 are very close to the simulated ones shown in Fig. 4(a). The main resonant mode TM_1,56 of the microdisk resonator without thermal treatment has the FSR of 16.01nm, the T of −3.50dB, the Q_L of 3.09 × 10³, the Q₀ of 3.70 × 10³, and the Q_ex of 1.86 × 10⁴. After thermal treatment, the main resonant mode TM_1,57 has the FSR of 16.43nm, the T of −7.74dB, the Q_L of 1.83 × 10⁴. The Q₀ and the Q_ex are 2.60 × 10⁴ and 6.21 × 10⁴. The blue shift 2.79nm of resonant wavelength is due to the slight shrinkage of microdisk diameter after thermal treatment. It demonstrates that thermal treatment not only enhances surface smoothness but also can be used in tuning the resonant wavelength. The obvious enhancement of the Q₀ after thermal treatment is attributed to the reduction of surface roughness and the smoothness enhancement of microdisk rim. Efficient coupling between microdisk resonator and tapered fiber requires phase matching and large field overlap between microdisk resonant mode and tapered fiber mode. Although the TM₁ and TE₄ modes achieve the similar phase matching level, the TM₁ modes are mainly excited due to its larger field overlap with the tapered fiber mode. The excitation of TM modes in the LiNbO₃ microdisk resonator has the advantage of using the largest electro-optic coefficient r₃₃ and the largest nonlinear-optic coefficient d₃₃ of LiNbO₃. It is noted that the larger pillar diameter increases the leakage loss of high-radial-order modes and facilitates to suppress their resonance. Because a large pillar diameter is used in this work, the first-radial-order TM modes are mainly excited. Elimination of high-radial-order resonant modes effectively extends the FSR of the microdisk resonator. The Q factors of LiNbO₃ microdisk resonators are restricted by small index contrast (compared to semiconductor microdisk), small diameter (compared to LiNbO₃ disk), and non-perfect circular shape. The last can be improved by photoresist reflow during the process of producing chemical-etching mask.

 

Fig. 5 Transmission spectrums of the LiNbO₃ microdisk resonators labeled with loaded quality factor Q and mode order TM_1,m (a) without thermal treatment; (b) with thermal treatment.

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5. Conclusion

LiNbO₃ microdisk resonators with large FSR and high Q factor are demonstrated for the first time. The ultra-smooth undercut microdisk structure with roughness of 0.41nm is successfully produced by selective ion implantation, chemical etching, and surface tension reshaping. The proposed fabrication method has good repeatability and the potential to produce microdisks on the other ferroelectric crystals with good nonlinear-optic effect. The microdisk geometry is designed such that the single vertical modes are excited and the high-radial-order modes are suppressed. This design consideration and the small microdisk diameter effectively extend the FSR of the microdisk resonator. The simulated resonant characteristics by finite element method are well consistent with the experimental results. The produced 20μm-diameter microdisk resonator has the FSR of 16.43nm and the Q factor of 2.60 × 10⁴. The largest FSR value of the LiNbO₃ resonator to date will facilitate new device design. The first produced LiNbO₃ microdisk resonator has the potential to initiates new photonic applications with electro-optic and nonlinear-optic effects.