1. Introduction

Two dimensional photonic crystal (PhC) structures have been widely studied for future photonic integrated circuit applications. Most studies on PhC slabs have concentrated on planar devices which support in-plane guided modes without coupling to external radiation [1], [2]. Recently, a class of optical modes called guided resonances in PhC slabs, has drawn much attention [3–5]. These are Fano-type resonances in PhC slabs when illuminated from above at normal incidence. Due to the phase matching mechanism provided by the periodic index contrast, these in-plane guided resonances above the light line within PhC slabs can be strongly coupled to out-of-the-plane radiation modes, resulting in asymmetrical line shapes in reflection and transmission spectra [6]. These Fano-shaped peaks show very high quality factors, making them suitable for high Q filters [7, 8] and high reflectivity mirrors [9]. The guided resonance also can be incorporated into MEMS to enable mechanical tenability of the optical response [10]. However, so far devices based on guided resonances have mainly been fabricated in Si and Si₃N₄ membranes, which show low or nonexistent electro-optic coefficients and/or slow response speeds. (Si shows no Pockels effect, so index can be modulated only through other mechanisms such as thermal or carrier-induced index changes.)

A widely used dielectric material, LiNbO₃, is extremely important in integrated and nonlinear optical devices because of its large electro–optic coefficients (r₃₃ = 30.8 pm/V at λ = 633 nm) [11], a large transparency range, and a wide intrinsic bandwidth. It has been used in electro-optical modulators [12, 13], surface acoustic wave (SAW) devices [14], tunable filters (switching time < 50ns) [15], nonlinear wavelength converters [16] and all-optical switches [17]. Due to its ultrafast electro–optic response and nonlinear effects, it would be an attractive prospect to realize a guided resonance in single crystal LiNbO₃. This incorporation of nonlinear materials into photonic crystal slabs is important for enhancing nonlinear light-matter interaction in general, as this can be useful for future quantum information processing tasks and also in optical logic elements. In addition, the birefringence property of LiNbO₃, which means its refractive index depends on the polarization direction of light, will also provide a new platform for polarization selective applications. Since the Fano resonance is a characteristic feature of quantum interference [18], this incorporation can potentially open new opportunities for exploiting physical phenomena in quantum optics as well. However, free-standing PhC slabs are very difficult to fabricate in LiNbO₃ due to its well-known resistance towards standard machining techniques. So far several techniques have been developed to fabricate photonic crystals on LiNbO₃ such as ICP-RIE [19], focused ion beam (FIB) [20] and pulsed laser ablation of LiNbO₃ films on sapphire [21, 22]. Recently ion implantation techniques become a very promising method in fabricating LiNbO₃ based photonic devices. There are various methods to treat LiNbO₃ crystals with ion beam, such as the use of ion implantation to form channel waveguides, crystal ion slicing (CIS), and ion beam-enhanced etching (IBEE). IBEE is a combination of ion implantation and chemical wet etching. After ion implantation, defects in the crystal can be intentionally induced (due to energy transfer to the crystal lattice), forming sacrificial layers where chemical resistance to subsequent wet etching is reduced. As a result, the irradiated regions can be removed by wet chemical etching after surface features such as PhCs have been created. Our group has developed this monolithic technique which allows fabrication of suspended LiNbO₃ slab structures [23]. This method provides a possibility to realize guided resonances on bulk LiNbO₃ substrates.

In this letter we conduct a theoretical and experimental study of the guided resonance of free-standing LiNbO₃ PhC slabs. We first perform a detailed numerical analysis on the transmission characteristics by using the 3D FDTD (Finite-Difference Time-Domain) method. The dependence of slab thickness, of radius of holes, and of lattice type is discussed. Next, the polarization dependence of PhC slabs is analyzed. Then a monolithic approach to fabricate free-standing LiNbO₃ PC slabs is presented. The experimentally measured results agree with the numerical simulation.

2. Numerical analysis

We consider a square lattice of air holes in a LiNbO₃ slab. As LiNbO₃ is a bifringent crystal with an ordinary (y-polarization) and extraordinary (z-polarization) refractive index, we first consider a simple case in which only the ordinary index (n_o) plays a role (n_o = 2.227 at 1200nm wavelength) for a specific polarization in the investigations of slab thickness, lattice type and radius dependence. Then both ordinary and extraordinary indices are considered in the investigation of polarization dependence. The structure studied in this work is shown in Fig. 1 . The inset shows the fabricated PhC slabs on X-cut LiNbO₃ substrate. Our calculation domain includes a single unit cell and the 3D FDTD method was used [24]. Perfectly Matched Layer (PML) boundary conditions were used at the X axis boundaries while periodic boundary conditions were used along the Z and Y axes. A Gaussian source is launched from the top of the PhC slab and two power monitors are used to obtain the time response of reflected and transmitted power. Then the fast Fourier transform (FFT) of the time monitor output is performed to obtain the frequency response. In order to improve accuracy of the simulation results, a convergence study was performed and a 0.01nm grid size was chosen.

 

Fig. 1 Schematic of the free-standing X-cut LiNbO₃ PhC slab with slab thickness (t), radius of air holes (r) and lattice constant (a). The ordinary refractive index (n_o) of the slab is 2.227. The inset shows the fabricated photonic crystal slab on an X-cut LiNbO₃ substrate.

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2.1 The dependence of slab thickness

Figure 2 shows the transmission spectra at normal incidence for LiNbO₃ PhC slabs with thicknesses 300 nm, 700 nm and 1.5 µm. The lattice constant (a) and radius (r) of holes are kept at a = 900nm and a ratio of r/a = 0.28. In Fig. 2, when the slab thickness increases, the Fabry-Perot oscillation background becomes more obvious in the infrared region, indicating increased FP interference inside the slab. Figure 2(a) shows the transmission spectrum of a slab of 300nm thickness with two sharp Fano resonance peaks in the wavelength range of 1200nm to 1400nm. When the slab thickness increases, a stronger Fano resonance occurs, leading to a larger number of modes, as shown in Figs 2(b) and 2(c). As the slab thickness decreases, the resonance moves to a slightly shorter wavelength. It has been reported in [25] that decreasing a slab thickness leads to an increase of the delayed length of the resonance, lowering the effective index. Note that it is worthwhile to analyze the slab thickness dependence because the fabrication method presented in this work allows tunability of slab thickness by changing ion implantation energy. This method provides an effective way to design the functionality of the PhC slabs for different applications such as filters and sensors. For example, a tunable filter working in the mid-infrared region can be created by choosing a large slab thickness which leads to guided resonance modes with lower frequencies.

 

Fig. 2 Simulated normal-incident transmission spectra of PhC slabs with various slab thicknesses (a) 300nm, (b) 700nm, (c) 1500nm. The lattice constant (a) and radius (r) of holes keep the same value: a = 900nm and the ratio of r / a = 0.28.

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2.2 Lattice type dependence

Our reference model is based on square lattice; in this section we also consider the triangular lattice. Figure 3 plots the transmission spectra for triangular and square lattices. We choose two groups of structural parameters for square and triangular lattices: one has slab thickness t = 800nm, r = 80nm and periodicity a = 800nm (Fig. 3(a)), and the other has slab thickness t = 800nm, r = 250nm and periodicity a = 800nm (Fig. 3(b)). It is similar to the calculation domain of the square lattice except for the unit cell geometry. The ðlling factor of the triangular lattice is higher than that of the square lattice. It can be seen that with both groups of structural parameters, fewer resonance modes can be excited at near infrared wavelengths in the triangular lattice compared with the square lattice. In square lattices, as the operating wavelength increases, more spurious high order modes are generated. In addition the line shape of the triangular lattice shows sharp peaks, resulting in a higher Q factor than the square lattice. For example, we estimated the Q factor from the full-width at half-maximum (FWHM) in Fig. 3(b). The calculated Q factor at resonance peak in the wavelength of 1166nm is approximately 51 for the square lattice and 134 for the triangular lattice. By using the triangular lattice, the Q factor has been improved by 62%. Moreover, from Fig. 3(a) it can be seen that there is a sharp resonance peak at a wavelength of 1014 nm with a Q factor of ~218 for a triangular lattice but no peak for the square lattice. These features of the triangular lattice make it more suitable for optical switches and modulators due to the lower number of resonance peaks within a certain wavelength range.

 

Fig. 3 Comparison of simulated transmission spectra of PhC slabs for different lattice types. The transmission spectra of PhC slabs with a square lattice are shown with solid lines, while transmission spectra of PhC slabs with a triangular lattice are shown with dashed lines. (a) The structure consists of a slab thickness t = 800 nm, lattice constant a = 800nm and the ratio of r / a = 0.1, (b) The structure consists of a slab thickness t = 800 nm, lattice constant a = 800nm and the ratio of r / a = 0.31.

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2.3 Radius dependence

The dimensions of the PhCs will influence the performance of the devices significantly. In addition, the designed radius may be altered during the fabrication process. Consequently it is worthwhile to study the radius dependence. To demonstrate this, we plot the transmission spectra with ratio r/a varying from 0.1 to 0.31, as shown in Figs. 4(a) -4(d). The other parameters are identical (a triangular lattice with slab thickness t = 800nm). From Fig. 4 we can see that as the radius increases, more Fano resonances are generated and the smooth FP oscillation feature splits into more sharp peaks. Compared with Fig. 4(a), four more Fano resonance peaks are generated in the wavelength range 900nm to 1200nm in Fig. 4(d). Note that the resonance modes have a blue shift as the radius increases. For example, in Fig. 4(a) it can be seen there is a resonance peak at the wavelength of ~1020nm (highlighted with an arrow). As the radius increases, the wavelength of this peak shifts to the region of ~850nm. Furthermore, it is evident that the decrease in the radius leads to the line shape becoming sharper, resulting in a higher Q factor. For the resonance with the arrow in Figs. 4(a)-4(d), the Q factor varies from approximately 218 at r/a = 0.1, to 78 at r/a = 0.31.This is because the lifetime of guided modes in the slab increases as the radius decreases. Consequently one can realize filters with a very high Q factor by simply decreasing the radius of air holes. On the other hand, a broadband reflector with high reflectivity could be realized by enlarging the radius of air holes, as reported in [9].

 

Fig. 4 Comparison of simulated transmission spectra of triangular lattice PhC slabs with a radius of (a) r / a = 0.1, (b) r / a = 0.153, (c) r / a = 0.26, and (d) r / a = 0.31. The lattice constant (a) and slab thickness (t) are kept at: a = 800nm, t = 800nm.

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2.4 Polarization dependence

In silicon and other common materials, due to rotational symmetry at normal incidence, the transmission spectra would be independent of polarization. However, the LiNbO₃ crystal (X-cut), which has negative uniaxial anisotropy, does not show rotational symmetry at normal incidence. In addition, when the rotational symmetry of the structure is reduced in LiNbO₃, many unique polarization dependent devices can be created. Consequently, it is worthwhile to study the polarization dependence of LiNbO₃ PhC slabs. In LiNbO₃, the birefringence creates an index difference between y-polarized and z-polarized light of 0.0762 at 1064nm wavelength [26]. In the coordinate system of the crystal slab, light polarized in the Y direction (y-polarized) will see the ordinary refractive index while light polarized in the Z direction (z-polarized) will see the extraordinary refractive index. In calculation we use the ordinary index (n_o = 2.227) for y-polarized light modeling and extraordinary index (n_e = 2.149) for z-polarized light modeling.

Figure 5(a) shows a comparison of the transmission spectra of polarized light normally incident on a LiNbO₃ PhC slab. The structure we simulated consists of a square lattice with a slab thickness t of 800nm, a lattice constant a of 800nm, and a radius r of 150nm. The coordinate system of the slab is shown in Fig. 5(b). A significant shift (~25nm) for difference polarizations can be observed in Fig. 5(a). Two modes at around 870nm wavelength range are observed for y-polarized light while nearly 100% transmission is observed for z-polarized light. It is concluded that y-polarized light will lead to more resonance modes than z-polarized light. This is also in agreement with [27] that lowering the slab refractive index will reduce the number of modes in a PhC slab. This is predicted by the empty lattice approximation. In order to confirm the phenomenon of polarization dependence in LiNbO₃ PhC slabs, we simulated another structure with difference parameters (a triangular lattice with slab thickness of 800nm, lattice constant of 800nm and radius of 250nm), as shown in Fig. 5(c). The result also shows good correspondence with the previous one. This unique property of LiNbO₃ PhC slabs has many potential applications such as polarization selective filters.

 

Fig. 5 (a) Comparison of simulated transmission spectra of polarized light normally incident on a LiNbO₃ PhC slab. The transmission spectra of y-polarized light are shown with solid lines, while the transmission spectra of z-polarized light are shown with dashed lines. The structure consists of a square lattice with a slab thickness t of 800nm, a lattice constant a of 800nm, and a radius r of 150nm. The inset (b) shows the coordinate system of the slab. The inset (c) also shows the comparison of simulated transmission spectra of polarized light on a different structure, which consists of a triangular lattice with a slab thickness t of 800nm, a lattice constant a of 800nm, and a radius r of 250nm.

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3. Experimental verification

The LiNbO₃ samples used in our experiments were X-cut with two sides polished. Ion implantation is firstly applied to form a buried lattice-damage layer (the damage is quite low near the surface and increases sharply at a certain range, so it’s called the “damaged layer”) at a specified depth in bulk LiNbO_3. Subsequently a focused ion beam (FIB) was used to pattern 2D PhCs. The PhC pattern consists of a square array of air holes with a lattice constant of around 1µm and a radius of average 150nm, as shown in Fig. 6(a) . The beam current used in our experiment was 100pA and the acceleration voltage was 30 kV. Before milling, a 20nm Au layer was evaporated on top of the LiNbO₃ substrate to avoid charging effects. This coating layer was removed after FIB milling by aqua regia. Wet etching of the damaged layer was performed by immersing the sample into a mixed acid consisting of 48% HF and 69% HNO₃ (HF:HNO₃ = 1:2). The damaged layer becomes chemically reactive due to the lattice defects. The top layer with minimal damage shows a very low etching rate. We carefully control the wet etching time in order to avoid over-etching, which could crack the suspended membrane. Consequently, a suspended PhC membrane was successfully formed after wet etching, as shown in Fig. 6(b). The LiNbO₃ membrane had 800nm thickness and was suspended 250nm above the substrate. It can be seen that this suspended LiNbO₃ PhC slab as illustrated in Fig. 6 was fabricated without serious structural defects. One advantage of this fabrication technique is that a vertical PhC profile can be achieved because the bottoms of the milled cones are truncated by the air gap. Ion-induced lattice damage can later be annealed away if necessary.

 

Fig. 6 SEM images of the fabricated free-standing X-cut LiNbO₃ PhC slab. (a)Top view: square lattice with lattice constant a = 1000nm and radius of r / a = 0.15. (b)Side view: the free-standing PhC slab with a slab thickness of 800nm and suspended 250nm above the substrate.

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Optical characterization of the suspended PhC slab was performed using a microspectrophotometer (CRAIC Tech Ltd.) The measured reflectivity for normal incidence is plotted in Fig. 7 (the solid line). The reflectivity spectrum shows a smooth slope instead of a sharp peak because of the small air gap between the membrane and substrate. FDTD simulation is performed to compare with the measured data (the dashed line in Fig. 7). The structural parameters for simulation were estimated from the SEM image after fabrication, which consist of a square lattice of air holes with a lattice constant a = 1000nm and r/a = 0.15, a slab thickness t = 800nm and an air gap g = 250nm above the substrate, which can increase accuracy for modeling the structure proposed in this work. In experiment an X-cut sample and an un-polarized light source were used. Consequently we calculated the reflection spectrum by using the ordinary and extraordinary indices for the same structure respectively and averaging the spectra. From Fig. 7 it can be seen that the calculated spectrum agrees with the measured one. Because the spectra shift for different indices, it seems the guided resonance peaks are “smoothed” and broadened in the average spectrum. In addition two Fano resonance peaks can be observed in the wavelength range 1400nm to 1500nm. It shows excellent agreement with the two wide dips in measured spectra.

 

Fig. 7 Reflection spectra of un-polarized light normally incident on the fabricated PhC slab. Red solid line—measured reflection spectra. Blue dashed line—simulated reflection spectra.

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4. Conclusion

In conclusion, the transmission characteristics of a monolithic free-standing LiNbO₃ photonic crystals slabs based on Fano resonances have been systematically numerical analyzed and experimentally demonstrated for the first time. The simulation results show that the optical properties of photonic crystal slabs are very sensitive to geometrical variations like slab thickness, radius of air holes and lattice type. We demonstrate that by decreasing the slab thickness or using a triangular lattice, a lower number of modes will be generated, leading to better performance for filter and modulator applications in LiNbO₃. In addition, the quality factor of these resonances can be improved by decreasing radius of holes. Furthermore, polarization-dependent transmission properties were also investigated and the results show that in X-cut LiNbO₃ similar spectra can be obtained for different polarizations but there is around a 25nm blue shift for z-polarized light. In summary, we have demonstrated that a monolithic fabrication method in LiNbO₃ can reliably be used to create PhC suspended slabs with predictable optical properties, and is evident that the LiNbO₃ PhC slab has great potential for polarization selective devices using these geometries. These investigations will give guidance in the design of PhC slabs in LiNbO₃.

The 2D PhC slabs was fabricated on a X-cut LiNbO₃ substrate by ion beam enhance etching (IBEE) technology. Our ability to form such structures as reported here is important not only for traditional photonics applications, but for potential quantum optical information processing applications. Excellent agreement was obtained between measurement results of the reflection spectra and simulation analysis results from 3D FDTD. Our results shows that free-standing LiNbO₃ photonic crystals slabs based on Fano resonance have potential applications for various photonic devices like tunable optical filters, sensors, and quantum optics applications where high quality, single crystal LiNbO₃ is needed.