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We report on an integrated acousto-optic filter in domain inverted LiNbO3 using a coplanar electrode configuration, which can achieve complete optical switching at electrical powers as low as 50mW. These values are more than one order of magnitude lower than previously reported results [Opt. Lett. 34, 3205 (2009)]. In order to design the low power consumption devices, we have calculated surface acoustic wave excitation, propagation and acousto-optic interaction in the domain inverted LiNbO3 superlattice using scalar approximation and FEM analysis. Results from both modeling techniques are in good agreement with the experiments, including direct measurement of the acoustic displacement using laser interferometry and acousto-optic performance.
©2010 Optical Society of America
1. Introduction
Lithium niobate (LiNbO3) is widely employed in integrated acousto-optic (AO) filters, primarily for applications in wavelength division multiplexing (WDM) systems [1], spectral slicing of supercontinuum source [2], acoustic modulation [3] and biomedical sensing [4]. The building block of an integrated AO filter based on LiNbO3 is a narrowband polarization converter sandwiched between crossed linear polarizers. The filtering mechanism relies on transverse electric (TE) to transverse magnetic (TM), or from TM to TE, polarization conversion of optical modes due to the rotation of the refractive index ellipsoid that is produced by the acoustic wave. For a wavelength within the filter pass-band, light passes through the input polarizer and it is converted to the orthogonal polarization state. The converted component then passes through the output polarizer. Outside the passband, the filter blocks the input light since the polarization of the light entering the output polarizer is orthogonal to it.
Integrated AO filters typically consist of an acoustic transducer, i.e. usually an interdigitated transducer (IDT) generating Rayleigh surface acoustic wave (SAW), associated with a single mode Ti-indiffused optical waveguide, both being monolithically integrated in a LiNbO3 crystal [5]. An additional acoustic waveguide is usually incorporated to confine the acoustical power density to the immediate vicinity of the waveguide in order to form a so-called doubly confined structure [6–8]. A common technique to fabricate the acoustical waveguide is through indiffusion of a Ti film on the cladding region of the optical waveguide. The acoustic waveguide can also be realized through mass loading effect via thin film deposition on the LiNbO3 substrate as reported in refs. 9 and 10. The aforementioned AO configuration allows for an increase in the polarization conversion efficiency (filter throughput), and reduction of the driving RF power (PRF) requirement to get 100% conversion. Nevertheless, they still suffer from several potential drawbacks, namely a possible leakage of the optical mode into the cladding region doped with Ti can increase the overall optical loss if the separation is not wide enough. This problem can be overcome by replacing the Ti-indiffused SAW waveguides with film-loaded based waveguides, but at the cost of an increase in the overall device length that can reach about 45 mm [9]. A further potential drawback of this configuration lies in the fact that the optical waveguide is usually covered by the metallic electrodes constituting the IDT, thus increasing the overall optical loss.
Acoustic superlattices (ASLs) made of periodically poled ZX-cut lithium niobate (PPLN) have been proposed as an alternative for acoustic wave generation, in particular SAW generation [11]. In an ASL configuration the excited SAW can be in some specific cases localized to and, to a certain extent, guided within the region between the electrodes. This feature makes ASL transducers, when they are integrated with optical waveguides, a good candidate for AO filters. The first demonstration of the use of an ASL transducer in an integrated SAW AO filter has been reported in ref. 12. Yet, the mechanisms of SAW excitation and their modal properties have not yet been discussed in detail. In addition the structures were far from being optimized and required large electrical powers for switching, of the order of watts.
In this paper, we present a detailed analysis of guiding mechanism of the SAW excitation on the ASL transducer with co-planar electrodes. Theoretical modeling based on 2D scalar approximation and full 3D Finite Element (FEM) using COMSOL MULTIPHYSICS is presented. The simulation results are then confirmed by measurements of acoustic transduction and direct detection of displacement using laser interferometry. By optimizing the geometry of the ASL transducer using the presented analysis as a design tool, nearly complete optical switching can be achieved at very low electrical powers (50mW), which results in an improvement by a factor of 20 compared to the previous measurements in similar configuration [12].
2. SAW excitation on ASL transducer with coplanar electrodes
In this section we present the modeling of SAW transduction using both scalar approximation and FEM techniques followed by experimental measurements, which also include direct detection of the mechanical displacement associated to SAW using laser interferometry. We also compare the experimental results with the simulated performance. The schematic of the proposed ASL transducer is shown in Fig. 1 . It includes periodically poled domains on ZX LiNbO3 on top of which two co-planar electrodes are placed.
2.1 Scalar approximation
SAW under a metallic plate (shorted surface case) propagates more slowly than that on the free surface due to the discontinuity of the electric field at the electrode. This condition allows us to simplify the model by representing the structure given in Fig. 2 as an alternation of “slow” (s) and “fast” (f) regions. Each region can be assumed to be a semi-infinite ZX-LiNbO3 substrate covered (region “s”) or not (region “f”) by an infinitely-thin metallic plate. By solving the equation of motion [13] taking the piezoelectricity of ZX-LiNbO3 into account, we can determine the SAW velocity for each region, which will be used in the analysis below, following the model proposed by ref [14]. The 3D geometry can hence be simplified to a 2D problem as shown in Fig. 2.
SAW propagation in both slow and fast regions can be described by scalar potentials Ψs(f) that satisfy the following wave equation
where f 0 is the acoustic frequency of the propagating SAW, and corresponds to the distribution of the SAW velocity in y given bywhere v s(f) is the SAW velocity of the combined material consisting of an alternance between free surface and substrate covered with a metallic layer as described earlier. We impose that the SAW mode propagates along the x-axis with a propagation constant β as illustrated in Fig. 2. The general solution of the Eq. (1) can then be written asNow, by substituting Eq. (3) into Eq. (1) and imposing the corresponding boundary conditions:we can retrieve the SAW modes velocities (v g) and its corresponding mode profile W(y).2.2 Full-vectorial FEM analysis
A full 3D anisotropic and piezoelectric structure was then considered through a FEM analysis and is sketched in Fig. 3 . A few assumptions were made in order to reduce computational time without serious reduction in the accuracy of the final results. In the computational domain, the thickness of the LiNbO3 substrate was taken to be four-wavelengths, since the SAW penetration depth is around one-wavelength from the surface. The structure is periodic in the direction of propagation, so that we can restrict the computational domain in that direction to a unit cell by applying periodic boundary conditions. Furthermore, Perfectly-Matched Layer (PML) was imposed on the bottom face and on the left and right hand side of the electrode to prevent unwanted reflection and its distance to the electrode was kept constant. If a is taken to be the thickness of a positive domain, and b that of a negative domain, the period of the lattice reads .
The spatial piezoelectric constitutive equations and motion equations of the considered problem can be written in the following way:
with and T, S, E, D, and u denote the stress, strain, electric field, electric displacement, and displacement, respectively. e, cE, and εS, are the piezoelectric, stiffness, and permittivity constant in tensor form, respectively and ρ is the mass density. The indices are such that I, J = 1 to 6 and i, k = 1 to 3. Traction-free boundary conditions, i.e. where n refers to a normal component, were assumed on the top of the substrate and periodic boundary conditions were imposed at the boundaries and , so that .With respect to the electrical boundary conditions, a voltage + V(-V) with V = 1V was applied on the left(right) electrodes and zero charge conditions () were imposed on the part of the top surface uncovered by the electrodes. The bottom surface of the substrate was taken as the ground reference by applying a potential V = 0.
2.3 Experimental results for the ASL transducer and comparison with simulations
The modal velocity of all confined SAW modes excited by the ASL transducer was first calculated with the scalar approximation by solving Eq. (1). The electrode width W was a parameter which varied from 30 to 100 μm while the gap GE between the electrodes was equal to the width, i.e. GE = W. The FEM simulation was performed with electrode width stepsize of 10 μm. Material constants of ZX-LiNbO3, e.g. stiffness tensor (cE) and piezoelectric tensor (e), used in the FEM calculation were taken from [15]. The electrode was assumed to be aluminum (Al) with a thickness of 200 nm. The SAW frequency was f 0 = 189.9 MHz corresponding to the lattice period Λ = 20 μm. In order to experimentally validate the model calculated results, 20-μm-period ASL transducers were fabricated. The final ASL structure comprises 500 periods reaching a total length of La = 10 mm. A pair of 200-nm-thick coplanar Al electrodes with different of electrode’s width, (W = 40, 60, 80, and 100 μm) was deposited on the –z face. The samples were electrically characterized with a PNA-X Agilent network analyzer and also with laser-probing technique [17] in order compare the profile of the excited SAW mode with the one from calculation.
In Fig. 4 , the calculated normalized modal SAW velocity from both calculations, e.g scalar approximation and FEM simulation, and measurements as a function of the electrode width are shown. The measured values differ slightly from those obtained with the calculation. This probably related to the fact that the number of periods of the ASL transducer in the experiment is finite as opposed to the infinite number considered in the simulation. The number of measured excited modes and its trend show good agreement with the simulations. We can infer from Fig. 4 that both simulation and experimental results for an electrode width ranging from 30 to about 70 μm, show that the ASL transducer excites two modes: a symmetrical (0th) and an anti-symmetrical (1th) mode as depicted in Figs. 5 . As shown in Fig. 4, these modes tend to get closer when the width is increased. Above 70 μm, higher order mode can also be excited. From the mode profile shown in Fig. 5, the displacement below the electrodes is larger because the acoustic wave tends to propagate on the slow region. Nevertheless it is interesting to note that the symmetrical mode (0th) (Fig. 5(a) or 5(c)) tends to be localized in the central region between the electrodes whereas the anti-symmetrical more is rather located below the electrodes.
Fig. 4 Normalized modal velocity as a function of electrode’s width (W) on a 20-μm period ASL transducer calculated with scalar approximation (solid line) and FEM simulation (triangles), respectively. (Rectangulars) refer to measurement results.
Fig. 5 Mode profiles of the ASL transducer with W = GE = 60 μm calculated with scalar approximation ((a) and (b)), and FEM ((c) and (d)), respectively.
To have a confirmation of the energy distribution of the SAW, the out-plane motion of the substrate surface was imaged using an optical heterodyne interferometer. The setup used is similar to the one described in ref. 17, here only allowing amplitude detection. We show the results in Fig. 6 . The maximum displacement in the z direction is 0.7 nm and the periodic shape reflects the spatial distribution of the PPLN domains using 15 dBm, i.e 31 mW, RF electrical powers. Moreover, by comparison with Fig. 5, the profile of fundamental acoustic mode calculated from simulation agrees well with the measured profile.
Fig. 6 Profile of the fundamental SAW mode excited at frequency 189.8 MHz detected using laser-probing technique on the ASL transducer with W = GE = 60 μm. The inset shows the acoustic beam profile across the electrodes.
3. Surface acousto-optic polarization converters
As discussed in the introduction, the AO filter relies on the conversion between TE and TM modes. The maximum conversion efficiency is obtained when the wavelength of the input beam satisfies the phase-matching condition: , where is the acoustic wave number, λ0 the optical wavelength and NE(NM) the effective refractive index of the TE(TM) mode. Under this condition, the conversion efficiency reads:
where L i denotes interaction length and κ is known as the AO coupling coefficient defined byWith P a/A being the acoustic power density; Pa is the acoustical power and A is the area of acoustic beam. M is a figure of merit of the structure given byIn Eq. (9), p41, ρ, and are the photo-elastic constant, the mass density, and the SAW velocity of ZX-LiNbO3, respectively. Equation (8) shows that κ determines the conversion efficiency and thereby the efficiency of the AO filter. From Eq. (7), it is clear that the theoretical 100% conversion rate can be reached when the condition κLi = π/2 is satisfied. Therefore, in order to improve the efficiency of the AO filter, there are two parameters in accordance with Eq. (8) that need to be taken into account: the figure of merit M and the acoustical power density Pa/A. Since the figure of merit (Eq. (9)) is an intrinsic property of the crystal (ZX-LiNbO3) and we employ an optical waveguide (Ti-LiNbO3) to confine the optical mode, the efficiency of the AO converter will thereby merely depend on the acoustical power density Pa/A. There are then two possible ways to increase Pa/A: either increasing the SAW power Pa or reducing the area of the acoustic beam A.The SAW power Pa radiated by the transducer is proportional to the radiation conductance Ga, that in the case of an ASL transducer is given by
where K2 is the electromechanical coupling coefficient of ZX-LiNbO3; C T is the total static capacitance of the whole transducer; N is a number of lattice periods determined by the transducer length L. Due to the fact that K2, N, and f 0 are usually fixed parameters that are solely determined by the properties of the PPLN structure, it is clear from Eq. (10) that the acoustical power Pa can be increased by increasing the static capacitance of the transducer, C T. The area of the beam (A) can for its part be reduced via lateral confinement of the acoustic displacement that can be accomplished by means of SAW waveguides as explained in the introduction. For that reason, and given the profiles of the acoustic mode calculated and measured in the previous section the full-width-half-maximum (FWHM) of the acoustic beam, can be used as a figure of merit to optimize the AO coupling. Note that Pockels (linear electro-optic) effects might induce coupling between TE and TM polarizations. In particular the y-component of the “static” electric-field through the electro-optic coefficient r51 can induce polarization coupling. This mechanism is actually responsible for the residual modulation that was measured outside the ASL transducer resonance range, but it is independent of the acousto-optic modulation.4. Design and measurement results of optimized AO filter
In order to set an ASL design that would improve the acoustic power density and therefore reduce the RF driving power PRF, we performed numerical calculations by considering the following electrode widths: W = 60, 80, and 100 μm; and for each width W, the gap GE was varied from 20 to 100 μm. A lower limit of 20 μm was imposed to the electrode gap in order to ease the fabrication leaving enough space to allow for the placement of an optical waveguide (around 6 μm width) in the metal-free area. The overall length of the transducer was fixed to 10 mm. A FEM analysis was performed to compute the static capacitance C T and the symmetrical SAW mode, i.e. the fundamental mode, was calculated employing the scalar approximation described in the previous section.
In Fig. 7 we show the calculated capacitance as a function of the electrode gap GE. From the figure we can derive that the optimal values for both C T and A (represented in the plot through FWHM of the acoustic beam) are obtained when the electrode gap is 20 μm.
Fig. 7 Calculated total static capacitance (CT) (left) of the coplanar electrodes on ZX-cut LiNbO3 and the full-width-half-maximum (FWHM) of the acoustic (right) beam as a function of electrode’s gap.
Next, in order to find an optimum configuration for the electrodes for low driving power, we computed the AO coupling coefficient κ as given in Eq. (10) for varying electrode widths (from 40 to 140 μm), while keeping GE fixed at 20 μm. To this aim the electromechanical coupling coefficient K 2 of the ASL transducer was assumed to be around 0.6% obtained from the experimental results presented above. The refractive indices for both TE and TM modes of the 6μm-wide optical waveguide at phase-matched wavelength λ0 = 1455.5 nm are NM = 2.217 and NE = 2.144, respectively. The photo-elastic constant p 41 = 0.05 is taken from [16] and we assumed vR = 3795 m/s. The computed coupling coefficient κ is plotted in Fig. 8 against the electrode width. Now, considering all the simulation results, we infer that the optimal configuration, i.e. maximum AO coupling coefficient κ, is obtained at W = 70 μm at GE = 20 μm.
Fig. 8 Calculated AO coupling coefficient as the electrode width varied from 40 to 140 μm, while keeping GE fixed at 20μm.
To confirm the validity of the theoretical prediction for the optimal device, several ASL transducers with different electrode widths W = 60, 70, and 80 μm and GE fixed at 20 μm were fabricated and the AO measurement was performed using the same setup described in [12]. The measurement results are shown in Fig. 9 . From the figure, we can see that nearly complete optical switching is achieved at low electrical powers (about 50mW) for an ASL transducer having an electrode width W = 70μm and gap GE = 20μm. This result represents an improvement by a factor of 20 compared to previously reported devices using similar configurations [12]. To get an idea of this device performance in terms of power consumption, our AO filter was compared to filter designs reported e.g. in ref. 9. In this paper, the authors demonstrated a very low power AO filter with a 2mW driving power over a 45 mm length. By scaling our own filter down to the same length, the expected driving power of the proposed ASL filter will be of the order of 10 mW, which compares well with the required power for the filters proposed in [9].
5. Conclusion
Surface acoustic wave excitation and propagation is investigated in a domain inverted LiNbO3 based acoustic superlattice and a coplanar electrode configuration. Two modeling techniques, i.e. scalar approximation and FEM analysis, have been used to calculate the acoustic transduction, thus elucidating the SAW mechanism in these novel structures. Both techniques give similar results, which are also in good agreement with the experiments, also including direct detection of the SAW displacement via laser interferometry. Based on these results, we designed and realized an optimized acousto-optic filter that is able to achieve nearly complete optical switching at very low electrical powers (50mW), showing an improvement of a factor of 20 compared to our previous results [12].
Acknowledgments
D. Yudistira acknowledges the support of Generalitat de Catalunya. This work was partially supported by Plan Nacional TEC 2007-60185, Acciones Integradas Hispano-Francesa HF 2008-0033 and by the French Partenariat Hubert Curien (PHC) PICASSO n° 19220SG. The authors thank Vincent Laude for fruitful discussions. We thank Dr. H. Herrmann and Prof. W. Sohler for their collaboration.
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