Piezoelectric transducer

Abstract

Some embodiments in the present disclosure relate to a piezoelectric transducer and methods for a piezoelectric transducer. The piezoelectric transducer includes a phonon waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of the phonon waveguide. Each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be actuated by an electric field. At least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are actuated in phase.

Description

[0001] Piezoelectric Transducer

[0002] TECHNICAL FIELD

[0003] Embodiments of the present invention relate to the field of piezoelectric transducers for generating acoustic waves in a phonon waveguide.

[0004] BACKGROUND

[0005] Coherent transduction of single excitations, squeezed states, entangled states and other quantum states between different carriers, such as microwave and optical-frequency photons, as well as single phonons will play a key role in interfacing quantum information between different technologies. In particular, transducing between microwave and optical frequency photons will allow for realising scalable interconnects between remote microwave-frequency quantum processors.

[0006] SUMMARY

[0007] It may be desirable to minimise the coupling rates between the waveguide mode with other unwanted parasitic modes in the piezoelectric transducer.

[0008] In some embodiments, this is achieved by obtaining constructive interference for a desired (selected) mechanical mode of excitation in the waveguide.

[0009] The invention is defined by the scope of independent claims. Some of the advantageous embodiments are provided in the dependent claims.

[0010] According to an embodiment, a piezoelectric transducer is provided. The piezoelectric transducer includes a phonon waveguide, a plurality of piezoelectric transducer units, arranged along at least a part of the phonon waveguide, wherein each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be actuated by an electric field, and at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are actuated in phase. For example, at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that an enhanced coupling rate may be obtained for the mechanical mode of excitation.

[0011] In an exemplary implementation, at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged periodically along the phonon waveguide.

[0012] For example, a shape and / or a wavelength of the mechanical mode of excitation is based on one or more of a distance between consecutive piezoelectric transducer units, a size of a piezoelectric transducer unit, and an acoustic velocity within the waveguide between consecutive piezoelectric transducer units.

[0013] In an exemplary implementation, the phonon waveguide includes a first region, a second region and a third region, at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged along the first region of the phonon waveguide, the mechanical mode of excitation in the first region corresponds to an acoustic standing wave, and the second region is adjacent to the first region, the third region is adjacent to the second region and the second region is adapted to couple the acoustic standing wave to a moving wave in the third region.

[0014] For example, one or more piezoelectric transducer units are arranged in the second region in an aperiodic pattern adapted to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide.

[0015] In an exemplary implementation, one or more piezoelectric transducer units are arranged in the second region in a pattern tapering the sizes and / or distances of said one or more piezoelectric transducer units in said second region.

[0016] For example, one or more piezoelectric transducer units are arranged in the second region, and said one or more piezoelectric transducer units in the second region are adapted to be actuated out of phase to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide.

[0017] In an exemplary implementation, the phonon waveguide in the second region includes a pattern of holes tapering towards the first region.

[0018] For example, the phonon waveguide in the third region comprises an array of identical holes. In an exemplary implementation, at least two piezoelectric transducer units are arranged in distance and / or size to obtain the constructive interference for a mechanical mode of excitation in the phonon waveguide.

[0019] For example, the plurality of piezoelectric transducer units are arranged in a linear array along the phonon waveguide.

[0020] In an exemplary implementation, the piezoelectric transducer further comprises a plurality of acoustic shields, wherein at least two acoustic shields out of the plurality of acoustic shields are located at opposing sides of the phonon waveguide at sections of the phonon waveguide at which a piezoelectric transducer unit is arranged.

[0021] For example, a piezoelectric transducer unit out of the plurality of piezoelectric transducer units includes a piezoelectric slab, and a pair of metal electrodes.

[0022] In an exemplary implementation, the piezoelectric slab is contacted by metal electrodes, and the piezoelectric slab is coupled to a respective section of the phonon waveguide.

[0023] In another exemplary implementation, all of the piezoelectric slabs are connected to a single pair of electrodes or a plurality of electrode pairs.

[0024] For example, the piezoelectric slab includes a piezoelectric material.

[0025] In an exemplary implementation, the piezoelectric material includes at least one of the following materials:

[0026] Lithium niobate, LiNbCh,

[0027] - Aluminium nitride, AIN, Barium titanate, BaTiCh.

[0028] For example, the phonon waveguide includes a dielectric or a semiconducting material. The waveguide may also have piezoelectric material on top.

[0029] In an exemplary implementation, the dielectric material is a silicon-on-insulator (SOI) substrate.

[0030] According to an embodiment, a microwave-to-optics transducer is provided. The microwave- to-optics transducer comprises a piezoelectric transducer according to any of the exemplary implementations and examples above, the piezoelectric transducer adapted to couple a microwave mode to a mechanical mode, and an optomechanical cavity adapted to couple the mechanical mode to an optical mode. According to an embodiment, a method for a piezoelectric transducer is provided. The piezoelectric transducer includes a mechanical waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of a mechanical waveguide. The method comprises controlling at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units such that constructive interference is obtained for a mechanical mode of excitation in the mechanical waveguide, when the at least two piezoelectric transducer units are actuated in phase, wherein each of the piezoelectric transducer units is coupled to the mechanical waveguide, and actuated by an electric field.

[0031] BRIEF DESCRIPTION OF DRAWINGS

[0032] An understanding of the nature and advantages of various embodiments may be realized by reference to the following figures.

[0033] Fig. 1 is an exemplary illustration of a coupling of an electromechanical system to mechanical modes and a coupling of said mechanical modes to an output waveguide;

[0034] Fig. 2a is an exemplary top view of a piezoelectric transducer;

[0035] Fig. 2b is an exemplary perspective view of a piezoelectric transducer;

[0036] Fig. 2c is an exemplary illustration of a piezoelectric transducer unit coupled to a phonon waveguide section;

[0037] Fig. 3 is an exemplary illustration of a piezoelectric transducer including a periodic region and an apodization region;

[0038] Fig. 4 is an exemplary illustration of a coupling of a piezoelectric transducer including two periodic regions and an aperiodic region.

[0039] DETAILED DESCRIPTION

[0040] In the following description, reference is made to the accompanying figures, which form part of the disclosure, and which show, by way of illustration, specific aspects of embodiments of the invention or specific aspects in which embodiments of the present invention may be used. It is understood that embodiments of the invention may be used in other aspects and comprise structural or logical changes not depicted in the figures. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0041] It is understood that the features of the various exemplary embodiments and / or aspects described herein may be combined with each other, unless specifically noted otherwise.

[0042] For purposes of the description hereinafter, the terms “end,” “upper,” “lower,” “right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” “lateral,” “longitudinal,” and derivatives thereof shall relate to the disclosed subject matter as it is oriented in the drawing figures. However, it is to be understood that the disclosed subject matter may assume various alternative variations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are simply exemplary embodiments or aspects of the disclosed subject matter. Hence, specific dimensions and other physical characteristics related to the embodiments or aspects disclosed herein are not to be considered as limiting unless otherwise indicated.

[0043] No aspect, component, element, structure, act, step, function, instruction, and / or the like used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more” and “at least one.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, and / or the like) and may be used interchangeably with “one or more” or “at least one.” Where only one item is intended, the term “one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based at least partially on” unless explicitly stated otherwise.

[0044] Transduction of quantum states

[0045] Coherent transduction of single excitations, squeezed states, entangled states and other quantum states between different carriers, such as microwave and optical-frequency photons, as well as single phonons will play a key role in interfacing quantum information between different technologies. In particular, transducing between microwave and optical frequency photons will allow for realising scalable interconnects between remote microwave-frequency quantum processors. The conversion process required for this may be realised by using a mechanical excitation as an intermediary. Integrated piezo-optomechanical devices fabricated from stacked piezoelectric and dielectric thin-films are a promising approach to achieve high efficiency and low noise microwave-to-optics transduction. However, devices demonstrated in the literature have been limited by the low efficiency of electric-to-mechanical transduction (e.g. Chiappina, Piero, et al. "Design of an ultra-low mode volume piezo-optomechanical quantum transducer." arXiv:2303.03664v1).

[0046] One key element of any high efficiency transducer is the simultaneous realisation of interfaces with both microwave frequency and optical frequency radiation. Owing to the 100,000 fold difference in frequency and wavelength between optical and microwave photons, an intermediate mechanical mode may be used to mediate the transduction between the two regimes. In turn, this requires different physical coupling mechanisms and materials, for instance piezoelectricity and superconducting waveguides for the electromechanical interface, and photoelasticity and dielectric waveguides for the optomechanical interface. As a result of this diversity, coupling both interfaces to a single mechanical mode is challenging, in particular balancing the coupling strengths of each interface against mechanical impedance mismatch between the interfaces. As a result of these impedance mismatches, or due to various other reasons, parasitic mechanical modes may be formed that result in loss channels for the signal to be converted, limiting the efficiency of the transduction process.

[0047] A major barrier to improving efficiency are parasitic mechanical modes that may exist in the piezoelectric transducer and the coupling rates of the resonant mechanical mode to the optomechanical section of the device. In order to improve the selectivity of mechanical modes periodic arrays of acoustic sources may be used, leveraging constructive and destructive interference of their individual mechanical excitations to allow for propagation of selected mechanical modes. An example of such devices are interdigital transducers (IDTs) where two interlocking arrays of electrodes are deposited on a piezoelectric material to generate surface acoustic waves (SAW) (e.g A. V. Mamishev, K. Sundara-Rajan, Fumin Yang, Yanqing Du and M. Zahn, "Interdigital sensors and transducers," in Proceedings of the IEEE, vol. 92, no. 5, pp. 808-845, May 2004, doi: 10.1109 / JPROC.2004.826603). However, control over the mechanical mode structure of the device remains challenging due to the acoustic impedance mismatch that occurs between regions with different material stacks. This impedance mismatch causes acoustic wave reflections that reduce coupling between the piezoelectric transducer and the optomechanical region of the device and may lead to multi-modes coupling which is detrimental to the microwave-to-optics transduction process.

[0048] A schematic of the bosonic modes involved in a general electromechanical system are shown in Fig. 1 , which illustrates an example electromechanical system coupled to a mechanical waveguide including multiple coupled bosonic modes: the electrical field mode with frequency a>e, the mode manifold of the piezoelectric transducer consisting of a multitude of modes with frequencies , 0 < n < oo, and the mechanical mode of the output waveguide with frequency (n)m. The coupling efficiencies with the external environment are given by g, while the coupling rates between modes is g.

[0049] An electrical field mode o)eis coupled to the mechanical modes of a piezoelectric transducer with rates gemand to the external environment with efficiency ge. In general the system will present a manifold of mechanical modes, here identified by the index n, with frequencies . Due to impendence mismatch these modes couple with rates g^mto a mechanical waveguide (assumed to be single mode) used to transfer the mechanical energy to other parts of the device, such as for example an optomechanical cavity, with efficiency gm. The rates g^mmay differ from each other by large amounts, and each mechanical mode may have its own loss rate, resulting in an inefficient transfer of mechanical excitation from the manifold to the waveguide.

[0050] Piezoelectric transducer

[0051] To obtain efficient transduction, the mechanical energy in the waveguide mode may ideally be transferred to a mode in the microwave resonator (and vice versa) with high electromechanical coupling gem. Therefore, it is advantageous to develop a transducer architecture that minimises the coupling rates between the waveguide mode with other unwanted parasitic modes in the piezoelectric transducer.

[0052] In an exemplary embodiment, a piezoelectric transducer is provided. The piezoelectric transducer includes a phonon waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of the phonon waveguide. Such a plurality of piezoelectric transducer units may include two or more. Each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be actuated by an electric field. At least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are actuated in phase.

[0053] As it is explained above with respect to Fig. 1 , the electrical field (mode) is coupled to (modes) of) a piezoelectric transducer unit. Fig. 1 illustrates a bidirectional coupling of modes, as indicated by the bidirectional arrows in Fig. 1. In other words, a mode of the electric field may be coupled to the modes of the piezoelectric transducer unit, as well as modes of the piezoelectric transducer unit may be coupled to the electric field (mode). Moreover, a mechanical mode of excitation in the mechanical waveguide may be coupled to the modes of the piezoelectric transducer unit, as well as modes of the piezoelectric transducer unit may be coupled to the mechanical mode of excitation. Thus, for the exemplary piezoelectric transducer described above, each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be coupled to an electric field. At least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are coupled in phase to an electric field. More specifically, a piezoelectric transducer unit may be actuated by an electric field by such a coupling to the electric field.

[0054] Such a mechanical mode of excitation may be an acoustic standing wave in the waveguide.

[0055] In the following, the terms “phonon waveguide”, “mechanical waveguide” and “acoustic waveguide” are used interchangeably.

[0056] For example, at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged periodically along the phonon waveguide. For example, a periodic placement of sources includes that each two consecutive sources have a same distance from each other.

[0057] In other words, to tackle the challenge of realising efficient mechanical wave routing in spite of different material stacks, a possible approach is to reduce the size of the piezoelectric transducer while arranging multiple transducers into a periodic pattern. This architecture has the advantage of exploiting constructive interference of the periodic placement of identical sources to ensure single-mode operation of the transducer, while at the same time impendence mismatch between different regions of the device is minimized due to the small size of each source.

[0058] Such a system architecture for the generation of acoustic waves in a wavelength-scale dielectric device may include a plurality (i.e. including 2 or more units) of piezoelectric transducers displaced in an array which may be either quasi-1 -dimensional or quasi-2- dimensional. For the purposes of this disclosure, a quasi-n-dimensional system has extent approximately equal or below the mechanical wavelength in additional dimensions.

[0059] For example, the plurality of piezoelectric transducer units are arranged in a linear array along the phonon waveguide.

[0060] A piezoelectric interface may be realised through a thin-film dielectric featuring a piezoelectric layer on top or below. For example, the piezoelectric material and the second layer may also be identical and the dielectric may also be another material. The piezoelectric layer may be actuated via an electric field, which may result from electrodes contacted directly to the layer, or through the field resulting from nearby electrodes. The piezoelectric layer may be patterned by etching of a pre-existing thin film, by sputtering of the piezoelectric material in well-defined areas, by growth of the piezoelectric material in well-defined areas, by placing the patterned piezoelectric layer on another material, or some combination of the processes. Additional steps may be required to result in the piezoelectric layer. In some cases, the piezoelectric layer and the thin-film dielectric may be suspended.

[0061] By driving the array of piezoelectric transducers in phase with each other, a periodic acoustic standing or travelling wave is generated in the interface, which is then coupled to a mechanical waveguide patterned in the dielectric layer. The selected acoustic wave is generated through constructive interference between the piezoelectric sources.

[0062] For example, a shape and / or a wavelength of the mechanical mode of excitation is based on one or more of a distance between consecutive piezoelectric transducer units, a size of a piezoelectric transducer unit, and an acoustic velocity within the waveguide between consecutive piezoelectric transducer units.

[0063] For example, the wavelength of the mechanical mode of excitation may be based on the sizes and distances of all piezoelectric transducer units out of the at least two piezoelectric transducer units that are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide. A mechanical mode of excitation for which constructive interference is obtained may be selected by adapting one or more of a distance between consecutive piezoelectric transducer units, a size of a piezoelectric transducer unit and / or an acoustic velocity within the waveguide between consecutive piezoelectric transducer units.

[0064] The shape and wavelength of the mode that is generated may be controlled by the geometric parameter of the sources, such as the distance between consecutive mechanical sources, their sizes and the acoustic velocity between the sources, the latter being controlled by the geometry of the mechanical link between the sources. Such a geometry of sources may be achieved by patterning the dielectric layer, the piezoelectric layer or both. The patterning may be performed by controlling the shapes of the layers and / or an addition of holes in the layers. In addition, the relative phase and strength of the driving signal can also be adjusted. For example, the at least two piezoelectric transducer units, which are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, are arranged in distance and / or size to obtain the constructive interference for a mechanical mode of excitation in the phonon waveguide.

[0065] In an exemplary implementation, a phonon waveguide includes a first region, a second region and a third region. In said exemplary implementation, at least two piezoelectric transducer units out of the plurality of piezoelectric are arranged along the first region of the phonon waveguide, wherein the mechanical mode of excitation in the first region corresponds to an acoustic standing wave. The second region is adjacent to the first region, the third region is adjacent to the second region. The second region may be adapted to couple the acoustic standing wave to a moving wave in the third region. For example, the second region is an apodization region for acoustic impedance matching.

[0066] As mentioned above, in some cases the dimensions and distances between the electromechanical sources is periodic. For example, at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units may be arranged periodically along the first region of the phonon waveguide.

[0067] For specific applications, the dimensions of and distances between electromechanical sources may be aperiodic. For example, to facilitate mechanical impedance matching with the mechanical waveguide the apodization region may be present to either end of the piezoelectric interface.

[0068] As a result the system realises acoustic impedance matching between the piezoelectric interfaces and an acoustic waveguide, allowing for efficient transfer of mechanical excitations through the system.

[0069] In a first example for an apodization region, one or more piezoelectric transducer units may be arranged in the second region in an aperiodic pattern adapted to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide.

[0070] In some cases, such a matching region in the second region may be formed by tapering the sizes and distances between electromechanical sources. A modulation of sources sizes may be used to introduce specific harmonics in the generated mechanical wave. In some cases, by changing the size and spacing of one or more sources at the centre of the array, a confined mode within the extended structure may be realized.

[0071] In other words, in a second example for an apodization region, one or more piezoelectric transducer units may be arranged in the second region in a pattern tapering the sizes and / or distances of said one or more piezoelectric transducer units in said second region. The first example and the second example for an apodization region may be combined. In particular, the second region may include piezoelectric transducer units arranged in an aperiodic pattern and said transducer units may be arranged in the second region in a pattern tapering the sizes and / or distances of said one or more piezoelectric transducer units.

[0072] In a third example for an apodization region, one or more piezoelectric transducer units are arranged in the second region, and said one or more piezoelectric transducer units in the second region are adapted to be actuated out of phase to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide. The first example, the second example and the third example for an apodization region may be combined.

[0073] The phase of each emitter (piezoelectric transducer unit) may be controlled by either directly driving each of them out-of-phase from the others or by controlling the physical distance between sources during the fabrication process. Driving the emitters out-of-phase may be implemented by driving each emitter phase independently. In other words, an emitter may be driven with a phase offset to one or more of the remaining emitters.

[0074] The array may be engineered in such a way that the collective wavefront focuses mechanical energy at specific angles or at specific locations on the sample surface. This feature may be used to efficiently couple the mechanical transducer to other nanostructures, such as for example a nanobeam optomechanical cavity or other quasi-one or quasi-two dimensional designs, or to maximise surface strain in a specific region, which may contain strain-sensitive quantum systems such as, for example, spin-defect quantum dots.

[0075] For example, the phonon waveguide in the second region may include a pattern of holes tapering towards the first region.

[0076] In some cases, impedance matching and control over the mechanical wave may be obtained by patterning the dielectric layer with, for example, a periodic array of holes or by adding acoustic shields on either side of the piezoelectric interface to provide support and isolation from unwanted mechanical vibrations. This architecture may, in principle, be used to generate an arbitrary mechanical wave-front thanks to the interference of multiple wave-fronts generated by single emitters.

[0077] For example, the phonon waveguide in the third region may comprise an array of holes. For example, the array of holes may be an array of identical holes. In this specific example, the piezoelectric transducer may be coupled to an optomechanical cavity (OMC) via a phonon waveguide formed by such a patterning of an array of identical holes. A waveguide unit cell may be designed to support a travelling wave at the same frequency.

[0078] Figs. 2a to 2c show an exemplary piezoelectric transducer. In this exemplary case, the transducer is formed by a periodic 1 D array of piezoelectric slabs (such as slab 210), contacted by metal electrodes (such as electrode 220), and coupled to a phonon waveguide formed by patterning periodic holes in the dielectric layer 250. Fig. 2a provides a top view of the exemplary piezoelectric transducer, where some of the geometrical parameters that define the transducers have been highlighted: the spacing between consecutive sources a, the length L and width w of each source, which in general is different from the width of the mechanical waveguide in dielectric layer wsi. Fig. 2b provides a perspective view of the exemplary piezoelectric transducer. Fig. 2c illustrates a piezoelectric transducer unit. The exemplary piezoelectric transducer unit in Fig. 2c, which is a piezoelectric transducer unit out of the plurality of piezoelectric transducer units, includes a piezoelectric slab 210, and a pair of metal electrodes 220. The piezoelectric transducer unit is arranged on the phonon waveguide 240.

[0079] For example, the piezoelectric slab 210 is contacted by metal electrodes 220, and the piezoelectric slab 210 is coupled to a respective section of the phonon waveguide 240. The piezoelectric slab 210 may include a piezoelectric material. For example, the piezoelectric material may include at least one of the following materials: Lithium niobate LiNbOa, Aluminium nitride AIN, and / or Barium titanate BaTiOa.

[0080] For example, the phonon waveguide includes a dielectric material. For example, such a dielectric material may include a semiconducting material. Such a dielectric material may be a silicon-on-insulator (SOI) substrate or any other suitable substrate. The dielectric material may feature piezoelectric material on top.

[0081] The piezoelectric transducer may include a plurality of acoustic shields, wherein at least two acoustic shields out of the plurality of acoustic shields are located at opposing sides of the phonon waveguide at sections of the phonon waveguide at which a piezoelectric transducer unit is arranged. Each of Figs. 2a to 2c illustrates such acoustic shields. In Fig. 2c, the acoustic shields 230 to 235 are arranged at opposing sides of the phonon waveguide. In this example, the three acoustic shields 230, 232 and 234 and the three acoustic shields 231 , 233 and 235 are located at the opposing side of the waveguide 240. However, the present invention is not limited to three acoustic shields at each side of the waveguide. In general, there may be more than three acoustic shields at each side of the waveguide or there may be less than three acoustic shields at each side of the waveguide. In an exemplary implementation, the piezoelectric transducer according to any of the Figs. 2a to 2c may be a piezoelectric transducer device for the generation of symmetrical horizontally- polarized breathing waves (symmetric lamb waves) in a suspended quasi-1 D nanostructure (nanobeam).

[0082] The material used for these devices may include a thin film piezoelectric material (PE), such as LiNbOa (LN), AIN, BaTiCh, or the like bonded on a silicon-on-insulator (SOI) substrate or other suitable substrates (DS). After patterning the PE, DS and electrode layers (which will typically include a superconducting or normal metal), the device may be suspended by selective removal of a sacrificial layer. In the exemplary implementation, a series of rectangular slabs is patterned on the PE layer to form a linear array. A thin (e.g. 50 nm) film of metal may be deposited on either side of each rectangular slab on both the PE and DS layer to provide electrode connections for the transducers. The device may contain additional features to ensure that strain is appropriately distributed and released during the removal of a sacrificial layer.

[0083] Although the electrical contact of interest is only on the PE layer, the metal may be deposited also on the DS layer as this acts as support for routing of the electrical connections.

[0084] Each PE slab may be connected with quasi-2D acoustic shields patterned on the dielectric layer to provide support to the structure and acoustic isolation of the whole device. By carefully choosing the dimensions of the acoustic shields masses an acoustic band gap centered around the frequency of resonance for the piezoelectric transducer can be achieved. Spacing between sources is designed to select the mechanical mode wavelength, which may resonate inside the piezoelectric device. As mechanical waves from different sources interfere, constructive interference is guaranteed only for those wavelengths which are integer multiples of the sources interspacing. Only mechanical modes with proper periodicity may present high overlap between the piezoelectrically-induced electric field and the field from the metal electrodes. The high overlap between the two fields allows for the efficient transduction of microwave signals to mechanical excitations (and vice versa).

[0085] In this specific exemplary implementation, the piezoelectric transducer may be coupled to an optomechanical cavity (OMC) via a phonon waveguide formed by patterning an array of holes in the silicon layer. For example, the array of holes may be an array of identical holes. The waveguide unit cell is designed to support a travelling wave at the same frequency as the resonance frequency of the piezoelectric transducer. An impedance matching region may be formed, as explained above, by tapering the phonon waveguide holes nearest to the piezoelectric transducer; this region ensures that the standing wave of the periodic piezoelectric array is coupled to the moving wave in the phonon waveguide. The complete device, as illustrated in Figs. 2a to 2c, couples the single mode waveguide to an optomechanical defect confining both optical frequency electromagnetic and mechanical excitations, allowing for the transduction of signals between microwave and optical-telecom frequencies. As a result of the periodic array of sources, the device minimizes the energy loss due to coupling to parasitic mechanical modes in the piezoelectric transducer region, allowing for efficient transduction between microwave and optical frequencies.

[0086] As mentioned above, a way to improve impedance matching between the phononic waveguide and the piezoelectric transducer is to introduce an apodization region. Fig. 3 shows an exemplary implementation of an apodization region 350, where the distances and sizes of the piezoelectric transducer units 320 to 324 have been tapered. In other words, in a direction along the quasi-1 D waveguide 330 towards the periodic region 340, the slabs in the apodization region 350 may, for example, increase in width and the distance between adjacent slabs may increase towards the periodic region 340. This region ensures that the mechanical mode in the periodic region 340 is coupled efficiently into the waveguide 330, by matching the wavevector of the excited phononic (mechanical) mode. The slabs, such as slab 310, in the periodic region 340 have a same size and each two consecutive slabs in the periodic region have a same distance from each other.

[0087] In another exemplary implementation, is shown in Fig. 4, where with an aperiodic region 420 is placed in between two periodic regions 410 and 430. In other words, an aperiodic region 420 is interlaced between two periodic regions forming a quantum well. These more complicated structures may be of use, for example, to increase the lifetime of the mechanical mode in the piezoelectric transducer.

[0088] In the exemplary implementation according to Fig. 4, at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units may be arranged periodically along the first region of the phonon waveguide, which is a first periodic region 410. Adjacent to the first periodic region 410 there is the second region, which is an aperiodic region 420. In the example according to Fig. 4, the third region adjacent to the second region is a second periodic region 430. A periodic region includes at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units arranged periodically along said region of the phonon waveguide, i.e. the piezoelectric transducer units in said periodic region have a same size and are arranged equidistantly along the waveguide. An aperiodic region includes at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units arranged aperiodically along said region of the phonon waveguide, i.e. the piezoelectric transducer units in said aperiodic region may have different sizes and / or may be arranged non-equidistantly along the waveguide. The piezoelectric transducer as explained in detail above may be part of a microwave-to-optics transducer. In particular, a microwave-to-optics transducer may comprise a piezoelectric transducer according to any of the examples described herein. The piezoelectric transducer adapted to couple a microwave mode to a mechanical mode. The microwave-to-optics transducer may further comprise an optomechanical cavity adapted to couple the mechanical mode to an optical mode.

[0089] It is noted that although implementations and examples of the present disclosure were provided above in terms of an apparatus, i.e. the piezoelectric transducer, the corresponding method for said piezoelectric transducer providing the functionality described by the apparatus is also provided.

[0090] The method for said piezoelectric transducer including a mechanical waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of a mechanical waveguide, comprises controlling at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units such that constructive interference is obtained for a mechanical mode of excitation in the mechanical waveguide, when the at least two piezoelectric transducer units are actuated in phase, wherein each of the piezoelectric transducer units is coupled to the mechanical waveguide, and actuated by an electric field.

[0091] Implementations in software and hardware

[0092] It is noted that any of the steps of the method described above may be included as code instructions in a program, which may be executed by one or more processors.

[0093] For example, a controller may control the actuation of one or more piezoelectric transducer units. Such a controller may include memory, processing circuitry, and possibly a transceiver and a user interface. The device may be, for instance a (part of) a computing device or any other suitable device.

[0094] The memory may store the program, which may be executed by the processing circuitry to perform steps of any of the above-mentioned methods. The processing circuitry may comprise one or more processors and / or other dedicated or programmable hardware. The transceiver may be configured to receive and / or transmit (controlling) signals. The device may further include a user interface for displaying messages or status of the device, or the like and / or for receiving a user’s input. A bus interconnects the memory, the processing circuitry, the transceiver, and the user interface. It is noted that the controller may be implemented by any hardware means, apart from using a general purpose processor, it can be implemented as a micro-controller, by means of a programmable hardware such as field programmable gate array (FPGA) or as a specialized hardware such as an application-specific integrated circuit (ASIC). Any combination of the above-mentioned hardware and possibly a software may be used.

[0095] The embodiments and exemplary implementations mentioned above show some non-limiting examples. It is understood that various modifications may be made without departing from the claimed subject matter. For example, modifications may be made to adapt the examples to new systems and scenarios without departing from the central concept described herein.

[0096] Summarizing, some embodiments in the present disclosure relate to a piezoelectric transducer and methods for a piezoelectric transducer. The piezoelectric transducer includes a phonon waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of the phonon waveguide. Each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be actuated by an electric field. At least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are actuated in phase.

Claims

CLAIMS1 . A piezoelectric transducer for a coupling between a microwave-frequency photon mode and a mechanical mode including a phonon waveguide, a plurality of piezoelectric transducer units, arranged along at least a part of the phonon waveguide, wherein each of the piezoelectric transducer units is adapted to be coupled to the phonon waveguide, and be coupled to an electric field, and at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged such that constructive interference is obtained for a mechanical mode of excitation in the phonon waveguide, when the at least two piezoelectric transducer units are coupled in phase to the electric field.

2. The piezoelectric transducer according to claim 1 , wherein at least three piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged periodically along the phonon waveguide.

3. The piezoelectric transducer according to any of claims 1 or 2, wherein a shape and / or a wavelength of the mechanical mode of excitation is based on one or more of a distance between consecutive piezoelectric transducer units, a size of a piezoelectric transducer unit, and an acoustic velocity within the waveguide between consecutive piezoelectric transducer units.

4. The piezoelectric transducer according to any of claims 1 to 3, whereinthe phonon waveguide includes a first region, a second region and a third region, at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units are arranged along the first region of the phonon waveguide, the mechanical mode of excitation in the first region corresponds to an acoustic standing wave, and the second region is adjacent to the first region, the third region is adjacent to the second region and the second region is adapted to couple the acoustic standing wave to a moving wave in the third region.

5. The piezoelectric transducer according to claim 4, wherein one or more piezoelectric transducer units are arranged in the second region in an aperiodic pattern adapted to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide.

6. The piezoelectric transducer according to claim 4, wherein one or more piezoelectric transducer units are arranged in the second region in a pattern tapering the sizes and / or distances of said one or more piezoelectric transducer units in said second region.

7. The piezoelectric transducer according to any of the claims 4 to 6, wherein one or more piezoelectric transducer units are arranged in the second region, and said one or more piezoelectric transducer units in the second region are adapted to be actuated out of phase to perform the coupling of the acoustic standing wave to the moving wave in the phonon waveguide.

8. The piezoelectric transducer according to claim 4, whereinthe phonon waveguide in the second region includes a pattern of holes tapering towards the first region.

9. The piezoelectric transducer according to any of the claims 4 to 8, wherein the phonon waveguide in the third region comprises an array of identical holes.

10. The piezoelectric transducer according to any of the claims 1 to 9, wherein at least two piezoelectric transducer units are arranged in distance and / or size to obtain the constructive interference for a mechanical mode of excitation in the phonon waveguide.11 . The piezoelectric transducer according to any of the claims 1 to 10, wherein the plurality of piezoelectric transducer units are arranged in a linear array along the phonon waveguide.

12. The piezoelectric transducer according to any of the claims 1 to 11 , further comprising a plurality of acoustic shields, wherein at least two acoustic shields out of the plurality of acoustic shields are located at opposing sides of the phonon waveguide at sections of the phonon waveguide at which a piezoelectric transducer unit is arranged.

13. The piezoelectric transducer according to any of the claims 1 to 12, wherein a piezoelectric transducer unit out of the plurality of piezoelectric transducer units includes a piezoelectric slab, and a pair of metal electrodes.

14. The piezoelectric transducer according to claim 13, wherein the piezoelectric slab is contacted by metal electrodes, and the piezoelectric slab is coupled to a respective section of the phonon waveguide.

15. The piezoelectric transducer according to claim 13, wherein the piezoelectric slab includes a piezoelectric material.

16. The piezoelectric transducer according to claim 15, wherein the piezoelectric material includes at least one of the following materials:Lithium niobate, LiNbCh,- Aluminium nitride, AIN,Barium titanate, BaTiCh.

17. The piezoelectric transducer according to any of the claims 1 to 16, wherein the phonon waveguide includes a dielectric material.

18. The piezoelectric transducer according to claim 17, wherein the dielectric material is a silicon-on-insulator (SOI) substrate.

19. A microwave-to-optics transducer comprising a piezoelectric transducer according to any of the claims 1 to 18, the piezoelectric transducer adapted to couple a microwave mode to a mechanical mode, an optomechanical cavity adapted to couple the mechanical mode to an optical mode.

20. A method for a piezoelectric transducer for a coupling between a microwave-frequency photon mode and a mechanical mode, the piezoelectric transducer including a mechanical waveguide and a plurality of piezoelectric transducer units, arranged along at least a part of a mechanical waveguide, the method comprising controlling at least two piezoelectric transducer units out of the plurality of piezoelectric transducer units such that constructive interference is obtained for a mechanical mode of excitation in the mechanical waveguide, when the at least two piezoelectric transducer units are coupled in phase to an electric field,wherein each of the piezoelectric transducer units is coupled to the mechanical waveguide, and coupled to the electric field.

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