1. Introduction

Lithium niobate (LiNbO₃) is a ferroelectric crystal transparent in visible and near-infrared wavelength range and characterized by large piezoelectric, pyroelectric, electrooptic, acoustooptic and nonlinear optic coefficients [1]. The reproducible and easy fabrication of optical waveguides by metal diffusion [2] or proton exchange [3] in bulk LiNbO₃ makes it a widely used material for telecommunication applications [4]. The development of miniaturized LiNbO₃ devices relies on the capability of confining and controlling the light in slab waveguides, i.e. on the potential fabrication and micro- and nano-structuring of thin LiNbO₃ membranes with preserved bulk material properties. The deposition of LiNbO₃ layers with a thickness of a few hundred nanometers by physical vapor deposition techniques is still challenging since it results in polycrystalline layers without the properties of monocrystalline LiNbO₃ [5]. A way to produce thin membranes of single-crystalline LiNbO₃ is to fabricate them from the bulk crystal. In that way, ultra-thin X-cut LiNbO₃ self-suspended membranes have been realized by ion beam enhanced etching (IBEE) technique [6–8 ]. The linear and nonlinear optical properties of such membranes being nano-structured either by IBEE or by focused ion beam milling (FIB) have been demonstrated [9–11 ]. Another common scheme to produce thin LiNbO₃ membranes is to implement the crystal ion slicing technique. It uses ion beam irradiation and selective etching of damaged LiNbO₃ to produce membranes, which are bonded either to semiconductors [12] or, for optical waveguide applications, to dielectric media less refringent than LiNbO₃ like benzocyclobutene (BCB) [13] or SiO₂ [14]. Such LiNbO₃ layers have a thickness of few microns and require afterwards a chemical-mechanical polishing to reach a membrane thickness less than 1 μm [14]. Electro-optic enhancement has been demonstrated in a photonic crystal (PhC) lattice milled in a ridge waveguide structured in a 1 μm thick X-cut LiNbO₃ membrane bonded to BCB [15]. In order to allow for a better interaction between the light and the PhC structure [16], a thinner Z-cut LiNbO₃ layer on SiO₂ has been chosen and a photonic band gap has been measured [17]. In these structures, the light is confined in a slab waveguide where the substrate has a refractive index larger than one. However, a better vertical confinement of the light is obtained in LiNbO₃ membranes surrounded by air. PhC structures have not yet been reported in thin self-suspended Z-cut LiNbO₃ membranes. Suspended micro-disks have been fabricated in thin LiNbO₃ on insulator (LNOI) either by argon plasma etching [18] or by femtosecond laser ablation [19]. These fabrication methods are however demanding since they require many fabrication steps. In addition to the wet etching step that is mandatory for SiO₂ removal, these techniques need extra fabrication steps, either electron beam lithography [18] or further FIB polishing [19].

In this article, we describe a fast micro- and nano-structuring process for LNOI that is based on only two single steps: FIB milling and SiO₂ etching, allowing for the realization of microstructures in thin self-suspended Z-cut LiNbO₃ membranes. Two types of micro-resonators, a PhC cavity and a micro-disk have been fabricated. Their linear and nonlinear optical properties have been measured and compared to analytical and numerical simulations.

2. Fabrication

The micro-resonators were milled in LNOI samples [20,21]. LNOI wafers consist of a 750 nm thick Z-cut LiNbO₃ membrane bonded on a 1200 nm thick SiO₂ layer deposited by plasma enhanced chemical vapor deposition (PECVD) on a LiNbO₃ substrate. The top and bottom surfaces of the LiNbO₃ layer are optical grade polished. The LNOI pieces have been further modified by thinning down the top LiNbO₃ layer by argon ion beam etching. The etching rate of LiNbO₃ is 10.7 nm/min for an Ar⁺ beam with an energy of 400 eV and a current density of 0.3 mA/cm², allowing for precise adjustment of the final membrane thickness. Two types of self-suspended micro-resonators were fabricated: a PhC cavity in a 373 nm thick LiNbO₃ layer and a micro-disk in a 512 nm thick membrane. The nano- and micro-structuring relies on only two single steps: FIB milling and wet etching, as described in the following. The PhC structure was created by scanning the FIB on the LNOI surface according to the hole pattern. In contrast to the PhC cavity, the micro-disk fabrication requires the removal of much larger volumes of material in the vicinity of the disk. Instead of scanning the FIB over a large surface to physically etch the unwanted LiNbO₃ material all around the micro-disk, which would be time consuming, only the contours of the micro-disk and of small pieces surrounding the micro-resonator have been cut using the FIB. The contour shapes milled by FIB for the micro-disk structuring are sketched in Fig. 1(a). During the subsequent wet etching, the etchant removes the SiO₂ starting at the cut lines. The areas whose contours have been cut by FIB are chosen to be small enough to be completely underetched and detached when the underetching of the disk is finalized. The final stage of this fabrication process consists in etching the SiO₂ layer with an ammonium fluoride - hydrofluoric acid mixture to create self-suspended resonators. During this wet etching, the etchant penetrates through the openings in the top LiNbO₃ layer and removes the SiO₂ layer. For the fabrication of PhC cavities, the etching time is chosen in such a way that the whole SiO₂ layer underneath the PhC cavity is removed. For the micro-disk fabrication, the etching time is controlled so that all the SiO₂ layer underneath the LiNbO₃ parts surrounding the micro-disk is removed, whereas an SiO₂ pillar remains underneath the micro-disk in order to maintain the micro-disk suspended above the LiNbO₃ substrate. A positive side effect of the hydrofluoric-based SiO₂ etchant is that it also removes the material that is contaminated by gallium ions from the FIB patterning [8]. Scanning electron microscope pictures of the fabricated micro-resonators are shown in Figs. 1(b)–(e). The micro-disk (Figs. 1(b),(d)) has a diameter of 39.5 μm and a thickness of 512 nm. It is supported by a 1.2 μm high pillar with a conical shape as can be seen in the cross-section view (Fig. 1(d)). The top view (Fig. 1(b)) shows two pieces of LiNbO₃ that have been detached after wet etching and that correspond to the parts marked with a hatching pattern in Fig. 1(a). The PhC resonator was milled in a 373 nm thick LiNbO₃ layer (Fig. 1(e)). The cross-sections views (Figs. 1(d)–(e)) exhibit thin platinum layers that have been deposited before cutting the samples. The PhC structure is a modified L3 cavity consisting of a line of three missing holes in the ΓK direction of an hexagonal lattice of circular holes. The crystallographic orientation of the LiNbO₃ crystal is shown in the top view (Fig. 1(c)). The hole radii are 148 nm and the lattice period is 530 nm. The holes at each line defect extremity are shifted out by 122 nm and their radius is shrunk down to 143 nm in order to obtain a higher quality (Q) factor than for an unmodified cavity [22]. A set of sixteen holes having larger radius of 175 nm has been placed around the defect with twice the period. The role of these holes is to modify the field distribution of the first cavity mode in such a way that the cavity losses radiate vertically rather than at grazing angles [10, 23]. In that way, it is possible to excite efficiently the fundamental TE-polarized mode from the far-field at normal incidence.

 

Fig. 1 (a): Sketch of the contour shapes milled by FIB for the micro-disk fabrication. (b)–(e): Scanning electron microscopy images of a micro-disk (left) and a modified L3 PhC cavity (right) milled in Z-cut LNOI. Top: Top views. Bottom: Cross-sections after (d) and before (e) wet etching.

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The linear and nonlinear optical properties of these structures have been characterized experimentally.

3. Optical characterizations: linear and nonlinear properties

3.1. Whispering-gallery-modes of the micro-disk

The micro-disk supports several transverse-electric (TE) and transverse-magnetic (TM) polarized whispering-gallery-modes (WGMs) that were investigated experimentally. The light was coupled in and out of the micro-disk by a looped tapered optical fiber. A SMF 28 fiber, with a core diameter of 9 μm and a cladding of 125 μm, was adiabatically thinned down to a diameter of around 1 μm by pulling it in a heat source generated with a hydrogen microflame torch [24]. The tapered fiber was then bent to form a loop that was put close to the micro-disk to allow for an evanescent coupling between the modes of the resonator and the cladding guided modes of the tapered fiber [25]. The coupling efficiency depends not only on the spatial and temporal mode overlaps between the whispery-gallery-modes and the fiber modes, i.e. on the spatial and temporal phase matching parameters, but also on the distance between the tapered fiber and the disk that defines the coupling regime. The temporal phase matching was controlled by tuning the wavelength of a near-infrared laser (Agilent 8164A) that was connected to one extremity of the tapered fiber. The coupling regime was adjusted by optimizing the space between the fiber and the disk that gave rise to the lower transmission at the spectral resonance positions. To measure transmission spectra, the other extremity of the tapered optical fiber was connected to an InGaAs detector. The transmission spectrum of the micro-disk measured in the spectral range from 1520 to 1570 nm is plotted on the left part of Fig. 2(a). It exhibits a large number of dips corresponding to several WGMs. The spectral positions of the different WGMs can be calculated analytically. Since the formation of standing waves in the direction perpendicular to the disk plane, the z-direction, is not possible in such a thin membrane, the modes confined in the slab can be described in a two dimensional approximation by using an effective refractive index of the slab. In this configuration, the TE- and TM-polarized fields are decoupled and the z-components of the electric (for the TE-polarized modes) and of the magnetic (for the TM-polarized modes) fields are solutions of a scalar wave equation. This wave equation, written in a cylindrical coordinate system, can be decoupled in three equations, each one describing the dependence of the fields with respect to a specific coordinate, the transversal (z), radial (r) and azimuthal (ϕ) coordinates, respectively. The transversal wave equation allows for the calculation of the effective indices of the modes by solving the eigenvalue problem of a slab waveguide [26]. This effective index is introduced in the set of the two last equations that are solved by introducing the continuity of the tangential component of the fields at the boundaries of the micro-disk. The complex roots of these equations, solved by the Davidensko’s method [27], give rise to the resonance wavelength of the modes. The different TE_nm- and TM_nm-polarized WGMs are identified by their radial n and azimuthal m mode numbers that correspond to the number of nodes in the field distribution in the radial and azimuthal directions, respectively. The resonance wavelength of the first four radial (n =1 to 4) modes have been calculated for a wavelength range from 1.52 μm to 1.57 μm. The reconstructed spectrum (not shown here) is characterized by a pseudo-periodicity related to the spectral WGM distribution. Indeed, the spacings in wavelengths between two WGMs of the same polarization and radial order but with two successive azimuthal mode numbers vary only slowly in a wavelength range of 50 nm although they depend on the effective refractive indices and on the resonance wavelengths of the modes. In order to reveal the pseudo-periodicity of the spectrum, a fast Fourier transform was applied to the calculated spectral data, that were preprocessed by a Hanning windowing followed by a zero padding (Fig. 2(b)). This Fourier transformation, shown in Fig. 2(b), exhibits three main peaks. In order to determine the origin of these peaks, this Fourier spectrum was compared to the Fourier transformations of the spectra containing on one hand only the calculated TE_nm-polarized WGMs and on the other hand only the calculated TM_nm-polarized WGMs. These Fourier transformations are plotted in the inset of Fig. 2(b). Thus, in Fig. 2(b), the peaks at the lower and higher wave numbers are related to the TM-polarized WGMs while the peak in the middle is assigned to the TE-polarized WGMs. A fast Fourier transform was also applied to the experimental spectral data, that were preprocessed by a Hanning windowing followed by a zero padding (Fig. 2(c)). The shape of this Fourier transformation is quite similar to the one of the calculated transmission spectra (Fig. 2(b)). The shift observed between these curves are ascribed to the fact that all the modes are not experimentally excited in the same way which is not taken into account in the calculated transmission spectrum. The fixed diameter of the fiber taper and the constant distance to the micro-disk do not allow the excitation of all different modes with the same strength. With a larger diameter of the tapered fiber it should be possible to excite lower radial order modes more efficiently. But of course there is a trade-off between phase matching and field overlap, and the refractive index of the tapered fiber (fused silica) will be the ultimate limit for the effective index of the modes that are excitable in the LiNbO₃ micro-disks. To confirm the good similarity between theory and experiment, the calculated WGMs have been reported on the experimental spectrum measured between 1.53 and 1.55 μm (right part of Fig. 2(a)). In this wavelength range, all the TE_nm-polarized WGMs calculated for n=1 to 4 have been measured experimentally which is not the case for the TM_nm-polarized modes. This is due to the coupling efficiency which depends on the overlap between the modes of the disk and the tapered fiber. The WGMs of the micro-disk measured experimentally exhibit loaded Q factors larger than 10,000. For example, a Q factor of 12,800 has been assessed for the TE_3,135-polarized WGM by fitting the experimental resonance spectrum with a Lorentzian curve. Much larger estimates of the intrinsic Q factors of the WGMs would be measured in a weak coupling regime where the tapered fiber would be positioned further away from the micro-disk.

 

Fig. 2 (a) Experimental transmission spectra measured from 1.52 μm to 1.57 μm (left) and from 1.53 μm to 1.55 μm (right). (b) Fast Fourier transform of the calculated transmission spectrum. Inset: Fast Fourier transforms of the calculated TE_mn-polarized modes (blue curve) and of the calculated TM_mn-polarized modes (red curve). (c) Fast Fourier transform of the measured transmission spectrum.

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In addition to the study of the WGMs of the micro-disk, the linear and non-linear optical properties of the PhC cavity were investigated.

3.2. Linear and non-linear optical properties of the photonic crystal cavity

The optical properties of the PhC cavity were characterized with a confocal-type microscope. The linearly polarized light from a tunable laser in the near-infrared wavelength range was focused on the cavity and the scattered light was collected by the same microscope objective. The signal collected from the LiNbO₃ was split into two beams by a dichroic mirror [11]. The nonlinear signal arising from the SHG in LiNbO₃ was reflected while the unconverted photons were transmitted through the mirror. The linear signal polarized perpendicularly to the incident light was measured with an InGaAs detector. The detection of the cross-polarized reflection allows to extract efficiently the weak signal of the cavity mode from the large amount of scattered light, especially when the incident polarization is chosen to be 45° with respect to the line defect [28]. The spectrum recorded under these conditions is shown in Fig. 3(a). It exhibits a resonance at 1356.0 nm. Experimental data are well fitted with a Lorentzian function with a width at half-maximum of 2.0 nm corresponding to a cavity mode with a Q factor of 678. 3D-FDTD simulations performed on the cavity reveal the first TE mode at 1362.8 nm with a Q factor of 1550 [29]. The calculated field intensity of this mode is plotted in the inset of Fig. 3(a). The discrepancies between experimental results and simulations can be attributed to fabrication imperfections. As a comparison, we calculated the Q factor of the same cavity geometry patterned in the LiNbO₃ layer deposited on SiO₂ (bulk LNOI) and we found a value of only 245. Removing the intermediate SiO₂ layer of the LNOI piece decreases the losses of the cavity mode and improves its Q factor. The second harmonic (SH) signal was simultaneously acquired by a silicon avalanche photodiode. The weak remaining linear signal reflected by the dichroic mirror was filtered out by a band pass filter inserted in front of the detector. The SH spectrum measured simultaneously with the linear spectrum, i.e. with an incident polarization of 45° with respect to the line defect, is shown in Fig. 3(b). This figure shows that the SHG is enhanced around 678 nm, a wavelength that corresponds to twice the resonance frequency of the first cavity mode. Experimental data have been fitted with a squared Lorentzian function giving rise to a Q factor of 640, a value close to the one measured from linear experiments. It proves that the SHG enhancement is due to the strong field confinement inside the cavity mode. Additionally, SHG was investigated as a function of the incident polarization angle α. The normalized graph is shown in Fig. 3(c). Experimental data are well fitted with a cos⁴ α function, which is consistent with the radiation behavior of the first mode of an L3 cavity. Indeed, this mode mostly radiates with a polarization perpendicular to the line defect (α = 0°) [10]. As a consequence, the coupled intensity in the first cavity mode follows a cos² α rule, and the SHG intensity, that scales as the square of the excitation intensity, is proportional to cos⁴ α. The power dependence of SHG was finally measured (Fig. 3(d)). As expected for a nonlinear optical phenomenon of second order, the experimental data are well fitted with a quadratic function. The process efficiency is lower than the one obtained in an X-cut LiNbO₃ self-suspended membrane [11], which is a direct consequence of the crystallographic orientation. Indeed, SHG intensity is proportional to the sum of the square of the second order polarization components $(P_i^{(2)})$ given by:

 

Fig. 3 (a) Cross-polarized reflectivity spectrum of the fundamental harmonic of the first cavity mode. Inset: Field intensity of the first cavity mode calculated in the middle of the membrane. Points: Experimental data. Solid blue line: Lorentzian fit. (b) Spectrum of the generated second harmonic excited with an input polarization of 45° with respect to the line defect. Points: Experimental data. Solid blue line: Squared Lorentzian fit. (c) Generated second harmonic as a function of the incident polarization α. Crosses: Experimental data. Solid blue line: Fit with a cos⁴ α function. (d) Second harmonic generation power measured as a function of the input coupled power. Crosses: Experimental data. Solid blue line: Quadratic fit.

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4. Conclusion

We have demonstrated a simple two step fabrication scheme to realize suspended micro-resonators in thin Z-cut LiNbO₃ membranes. The fabrication technique consists first in patterning the structure in a LNOI piece with FIB and second in removing the SiO₂ layer by wet etching. Two types of structures have been produced: a micro-disk and a PhC cavity. The WGMs existing inside the micro-disk were investigated experimentally and theoretically. Similarly, the linear and nonlinear optical properties of a self-suspended PhC cavity have been investigated. The SiO₂ substrate was removed in order to improve the field confinement in the membrane plane giving rise to cavity modes with higher Q factor compared to bulk LNOI. Q factors larger than 10,000 and 600 have been measured in a micro-disk and a PhC cavity, respectively. SHG enhancement due to the strong field confinement inside the cavity has been demonstrated. These results prove the possibility of fabricating functional photonic structures in thin Z-cut LiNbO₃ self-suspended membranes. The strongest nonlinear optical coefficient d ₃₃ can be exploited in such kind of substrates for nonlinear processes of second order like parametric downconversion of type II. Z-cut LiNbO₃ self-suspended membranes are also required for the fabrication of miniaturized nonlinear PhCs based on periodically poled LiNbO₃. The possibility of fabricating both X-cut and Z-cut LiNbO₃ self-suspended membranes is promising for the development of all-optical miniaturized devices in LiNbO₃.