Generation and detection of elastic modes having a non-zero total angular momentum

Abstract

The invention relates to a magnetoelastic transducer (TME1, TME2) comprising an element made of a single-crystal ferromagnetic material (EFM1, EFM2) having an anisotropic magnetoelastic tensor, said element having a geometric axis (ASG) of cylindrical symmetry aligned with an axis (ASC) of crystal symmetry exhibiting discrete rotational symmetry of order njc>2 and having at least one resonance between a magnetic oscillation mode (MAG) and an elastic oscillation mode (MAL). It also relates to a system for generating or detecting elastic waves having a total angular momentum of non-zero index comprising at least one magnetoelastic transducer according to one of the preceding claims and an antenna (ANT1; ANT2) configured to generate and / or detect, in correspondence with the ferromagnetic element of said transducer, an electromagnetic mode (MEL) suitable for exciting or being able to be generated by said magnetic oscillation mode of the ferromagnetic element.

Description

DESCRIPTION Generation and detection of elastic modes with non-zero total angular momentum

[0001] The invention lies in the general field of devices for transducing and transmitting information-carrying signals, more particularly using elastic waves propagating in a solid, crystalline or amorphous medium. It applies in particular to the fields of classical telecommunications, quantum computing and quantum communication channels.

[0002] Although electromagnetic waves are the most commonly used information vector in current technology, it is well known from the state of the art that the transduction of information-carrying signals in the elastic wave domain is of definite interest due to their propagation speed 10 5 at 10 6times weaker than electromagnetic waves and their rich dispersion properties and in certain cases non-linearity, allowing the creation of multiple essential signal and information processing devices (delay lines, pulse compression, etc.) that are compact and operate in frequency ranges of up to a few tens of GHz.

[0003] Another remarkable property of elastic waves is that they are the system in solid-state physics with the lowest loss coefficient in the GHz frequency range. This is particularly relevant for quantum information, as this is the frequency range where q-bits operate, and very low losses are essential to preserve quantum coherence between q-bits. Thus, if one wishes to achieve communication preserving quantum information between q-bits located at long distances in an integrated system, solid-state physics dictates that the best candidate will be the use of elastic waves.

[0004] Although elastic wave devices generally implement "plane" waves propagating in volume or on the surface of devices with typically millimetric dimensions, recent developments demonstrate the possibility of realizing integrated "phononic" circuits comparable in terms of dimensions and manufacturing technologies, with their optical analogues. It is also possible to consider the use of hollow fibers, possibly derived from a well-established and commercially available class of optical fibers, as elastic waveguides (Nikitov, 2008).

[0005] In the field of electromagnetic waves, recent decades have seen the emergence of a growing interest in exploiting a previously neglected degree of freedom of these waves, namely their angular momentum. Exploiting this additional degree of freedom makes it possible in particular to increase the maximum information transfer rate by implementing multiplexing processes of the "mode division multiplexing" (MDM) type. Indeed, different modes with distinct angular momenta can propagate independently without significant interference, due to their orthogonality, and therefore can be modulated independently, increasing the maximum information rate in proportion to the number of modes. However, this degree of freedom also exists for elastic waves in solids (Bliokh, 2022).The article (Chen, 2020) provides an overview of technologies for generating and detecting waves - radioelectric, optical and elastic - with non-zero angular momentum, and their applications. The article (Wei, 2019) more specifically discloses the propagation of non-zero angular momentum modes in integrated phononic circuits.

[0006] It therefore becomes possible to envisage the realization of integrated or fibered elastic wave circuits (hollow fibers seem particularly suitable due to their cylindrical symmetry and the localization of energy in the inner part of the fiber around its hollow core, minimizing interference with the environment) taking advantage of the angular momentum degree of freedom in multiplexing schemes similar to those implemented in the optical and electromagnetic domain for signal and information processing purposes with a previously unattainable degree of integration. It also becomes possible to exploit high angular momentum localized modes ("elastic whispering gallery modes") of micrometric elastic wave resonators or cavities with cylindrical symmetry as coherent transducers (in the quantum sense of the term) in interconnection schemes between q-bits (Yamazaki, 2020).Such devices could in the future play a major role in the development of quantum computers and quantum communication channels.

[0007] The transduction (emission / detection) between modulated electrical signals, and therefore carriers of information or signal, and propagating or localized elastic waves having a well-defined, and potentially high, angular momentum (i.e. greater than or equal to 2), is however difficult because such waves are characterized by a complex spatial profile in phase and amplitude.

[0008] The most classical scheme for transduction between electrical signals and elastic waves uses the phenomenon of piezoelectricity. However, this approach is unsuitable for the case of elastic waves with high angular momentum, because it would require complex geometries of multiple electrodes, which are difficult to reconcile with a high degree of integration.

[0009] It is also possible to optically excite elastic modes with defined angular momentum in micro-resonators by using opto-mechanical couplings (Schliesser, 2010). However, this scheme is not suitable for the excitation of propagating elastic waves, and does not constitute a direct transduction approach between electrical signals and elastic waves.

[0010] The invention aims to overcome at least in part the aforementioned drawbacks of the prior art. More particularly, it aims to enable simple and efficient transduction between simple electromagnetic modes and elastic modes - propagating or localized - having a potentially high angular momentum.

[0011] According to the invention, this aim is achieved by exploiting the physical phenomenon of magnetoelasticity (and more particularly magnetostriction) in a crystal.

[0012] More particularly, the invention exploits a device combining a radiofrequency antenna, typically of simple geometry, with an elastic resonator consisting of a single crystal of a magnetostrictive ferromagnetic material, preferably with large quality factors (greater than or equal to 10 4 ), magnetic and elastic, having a specific crystallographic orientation relative to the geometry of the device, and in a specific magnetic configuration, possibly controlled by an external magnetic field.

[0013] More specifically, the magnetic part of the oscillating electromagnetic field generated by the antenna excites a magnetic oscillation mode of the resonator, which in turn excites an elastic oscillation mode by magnetostrictive effect. Since the magnetoelastic tensor of a single crystal is anisotropic (Callen, 1963), the elastic oscillation mode can exhibit an angular momentum significantly different from those of the magnetic oscillation mode and the electromagnetic field of the antenna.

[0014] Conversely, an elastic oscillation mode can excite a magnetic oscillation mode, which in turn emits an electromagnetic field that can be picked up by an antenna.

[0015] This approach enables selective and efficient transduction between a modulated electrical signal and an elastic resonance mode with defined and potentially high angular momentum, with high integration potential and through the use of mature materials and micro-fabrication technologies.

[0016] An object of the invention is therefore a magnetoelastic transducer comprising an element made of monocrystalline ferromagnetic material having an anisotropic magnetoelastic tensor, said element having a geometric axis of cylindrical symmetry.

[0017] This transducer is remarkable in that said geometric axis of cylindrical symmetry is aligned with an axis of crystalline symmetry having a discrete rotational symmetry of order n Jc ^2 and having at least one resonance between a magnetic oscillation mode and an elastic oscillation mode.

[0018] According to particular embodiments: - the element made of monocrystalline ferromagnetic material of the transducer is made of a said material whose elastic constant tensor is substantially isotropic. - said element made of monocrystalline ferromagnetic material has an equilibrium magnetization having a cylindrical axis of symmetry coinciding with said geometric axis. - said element made of monocrystalline ferromagnetic material has, in a majority fraction of its volume, an equilibrium magnetization oriented substantially parallel to said geometric axis of cylindrical symmetry. - said element made of monocrystalline ferromagnetic material has, in a majority fraction of its volume, an equilibrium magnetization having a component in the di- orthoradial section located in a plane perpendicular to said geometric axis of cylindrical symmetry. - said element made of monocrystalline ferromagnetic material is disc-shaped. - said monocrystalline ferromagnetic material constituting the element is a ferromagnetic garnet, preferably comprising in its composition yttrium, iron and oxygen. - the magnetoelastic transducer also comprises a source of a static magnetic field, preferably having an adjustable amplitude, oriented along said geometric axis of cylindrical symmetry in correspondence with said element made of monocrystalline ferromagnetic material.

[0019] The invention also consists of a system for generating or detecting elastic waves having a total angular momentum of non-zero index comprising at least one magnetoelastic transducer as mentioned above and an antenna configured to generate and / or detect, in correspondence with the ferromagnetic element of said transducer, an electromagnetic mode suitable for exciting, or capable of being generated by, said magnetic oscillation mode of the element made of monocrystalline ferromagnetic material of the magnetoelastic transducer.

[0020] According to particular embodiments: - the electromagnetic mode generated or detected by said antenna in correspondence with the element made of monocrystalline ferromagnetic material of said magnetoelastic transducer has a magnetic part having a total angular momentum of index n Ja EZ such that the angular momentum of said elastic oscillation mode has an index n Je = n Jm ± n Jc where n Jm e Z, function of n Ja , is the index of the total angular momentum of the magnetic oscillation mode of the single-crystal ferromagnetic material element. - said antenna is configured so that the magnetic part of said electromagnetic mode has, in correspondence with the element made of monocrystalline ferromagnetic material of said magnetoelastic transducer, a component located in a plane perpendicular to the local magnetization of the latter. - said component of the magnetic part of said electromagnetic mode located in a plane perpendicular to the local magnetization of the element made of ferro-material monocrystalline magnetic field is either substantially uniform in a plane perpendicular to the geometric axis of cylindrical symmetry, or essentially uniform along said axis, or essentially radial or orthoradial. - said antenna is chosen from a straight conductor, a loop conductor or a plurality of such mutually insulated conductors. - the elastic wave generation system also comprises a source of an alternating electric current configured to power said antenna, said alternating electric current having a frequency resonant with said magnetic oscillation mode and said elastic oscillation mode. - It also comprises a detector of an alternating electric current induced in said antenna by an electromagnetic mode generated by said magnetoelastic transducer when it is excited by an elastic mode with total angular momentum of non-zero index. - It also comprises an elastic waveguide mechanically coupled to said magnetoelastic transducer and configured to propagate said elastic oscillation mode of said element made of monocrystalline ferromagnetic material. - It also comprises an elastic wave cavity mechanically coupled to said element made of monocrystalline ferromagnetic material and resonating with said elastic oscillation mode.

[0021] The invention also consists of an optical modulator comprising an elastic wave generation system as mentioned above, in which said ferromagnetic element, or said elastic resonator, is optically transparent, and an optical waveguide is coupled by evanescent wave to said element made of monocrystalline ferromagnetic material or to said elastic wave cavity.

[0022] Other characteristics, details and advantages of the invention will emerge from reading the description given with reference to the appended drawings given by way of example, in which:

[0023] [Fig. 1] illustrates an instantaneous view of the dynamic vector fields of a transverse mode of a cylindrical geometry resonator or waveguide, associated with various values ​​of angular momentum index;

[0024] [Fig. 2A] and

[0025] [Fig. 2B] illustrate two systems for generating, transmitting and detecting elastic waves according to embodiments of the invention;

[0026] [Fig. 3A] and

[0027] [Fig. 3B] illustrate the electromagnetic modes generated by the antennas of the systems of Figures 2A and 2B;

[0028] [Fig. 4A] and

[0029] [Fig. 4B] illustrate the generation of electromagnetic modes having linear and circular polarization, respectively;

[0030] [Fig. 5] illustrates the Larmor precession of the instantaneous magnetization of a ferromagnetic material;

[0031] [Fig. 6A],

[0032] [Fig. 6B] and

[0033] [Fig. 6C] illustrate three possible magnetization states of the ferromagnetic element of the magnetoelastic transducers of the system of Figure 2A and Figure 2B;

[0034] [Fig. 7] illustrates various possible crystal orientations of the ferromagnetic element of the magnetoelastic transducer of the system of Figures 2A and 2B and their orders of symmetry;

[0035] [Fig. 8A] and

[0036] [Fig. 8B] illustrate the operating principle of two magnetoelastic transducers according to respective embodiments of the invention;

[0037] [Fig. 9A] and

[0038] [Fig. 9B], respectively, illustrate the localization of elastic modes at the outer surface of a solid-core waveguide and on the inner surface of a hollow-core waveguide; and

[0039] [Fig. 10] represents a system for generating or detecting elastic waves according to an alternative embodiment of the invention, in which the magnetoelastic transducer couples with an optical fiber to form an optical modulator.

[0040] Figures 1, 4, 6A, 6B, 6C, 8A and 8B illustrate different spatial patterns of the instantaneous configurations of dynamic vectors of the oscillating mode corresponding to modes of a cylindrically symmetric system having different values ​​of angular momentum. The direction of these dynamic vectors evolves in time by rotating around the axis normal to the image plane, either in the counter-trigonometric direction, in the counter-trigonometric direction, or according to a linear combination of these two precession directions. Depending on the physical system considered, the dynamic vector can represent an electromagnetic field, a dynamic magnetization (DM) vector, an elastic deformation field and the mode can be propagating (in a cylindrical waveguide, represented in cross-section) or stationary (in a cylindrical or disk resonator or cavity). As for Figs.6A-C the time evolution of the vector fields is based on the fact that the dynamic magnetization vector MD rotates around the axis defined by the equilibrium magnetization ME.

[0041] The angular momentum is characterized by a relative integer index nj - the modes shown in Figure 1 correspond to nj = [-5,-4,-3,-2,-1,0,-1,+2,+3,+4,+5] - which counts the number of windings of the dynamic vectors along the periphery in cylindrical coordinate systems. Coherent excitation generally imposes the conservation of the angular momentum, and therefore of the index nj.

[0042] In the following, we will consider several types of dynamic vector fields: - We consider the magnetic part HEM of an electromagnetic mode, for example microwave, generated by an antenna. A miniature microwave antenna, straight or loop (also called Q-shaped) in practice only allows the generation of electromagnetic modes whose angular momentum index n Ja is worth 0 or +1. In case n Ja =+1 we distinguish two sub-cases, corresponding to right and left circular polarizations, which can be combined linearly. We note that we are interested here in the total angular momentum of the mode, without distinguishing its "spin" components (associated with the direction of circular polarization) and "orbital" components (associated with the spatial phase). - We also consider the dynamic magnetization, M D , which is the time-varying part and which is added to the equilibrium magnetization, M E , which is constant in the time, to define the instantaneous magnetization, M|, of a ferromagnetic material, see Figure 5. We denote by n Jm the angular momentum index of a magnetic oscillation mode. As an example, not limiting but important for applications, the magnetic modes of an axially saturated disk of indices n (+Jm) and laughed(-j m +2) are quasi-degenerate in frequency. - We still consider elastic deformation in an elastic oscillation mode. We denote by n Je the angular momentum index of such an oscillation mode. The elastic modes of a uniform medium of indices n +Je and n. Je are degenerate.

[0043] According to the invention, the magnetic part of an oscillating electromagnetic field generated by an antenna (typically having an angular momentum index n Jaequal to 0 or +1) excites a magnetic mode in a ferromagnetic material. This magnetic mode has an angular momentum of index n Jm which has the same index n Ja if a resonance condition is satisfied - excites an elastic oscillation mode in the material by magnetostriction effect. However, if the ferromagnetic material has an anisotropic magnetoelastic tensor (notion defined in particular in (Callen, 1963)), magnetostriction will convert - under certain conditions which will be explained later - the magnetic oscillation mode into an elastic mode which can have an angular momentum index n Je significantly different from n Jm. Conversely - also under certain conditions which will be explained later - a mechanical oscillation of the element can excite a magnetic oscillation, which in turn will generate an electromagnetic wave intended to be captured by an antenna. The excitation antenna producing an oscillating field along z is presented as the expression of an excitation n Ja =+0 because the MEM field maintains axial symmetry and the exciter antenna produces an oscillating field along x or y as the expression of an excitation n Ja =+1 because the field is uniform in the plane. As long as the equilibrium texture is invariant by rotation around the axis of symmetry (and this is indeed the case for the textures illustrated in figures 6A-6C), we always have n Jm =n Ja .

[0044] Figure 2A schematically represents a system for generating, transmitting and detecting elastic waves SGD comprising two magnetoelastic transducers TME-i, TME2 coupled to both ends of an elastic waveguide GOE. The first transducer TMEi is used to generate elastic waves- ticks which are transmitted by the GOE waveguide to the second transducer TME2, which detects them.

[0045] The essential element of the TME1 transducer is made up of an element e, a monocrystalline ferromagnetic material EFM (hereinafter we will simply refer to it as a "ferromagnetic element") whose geometry has a cylindrical axis of symmetry ASG. In the example in the figure, it is a disc. The geometric axis of symmetry ASG is aligned (with a tolerance of the order of 9°) with a crystalline axis of symmetry ASC having a discrete rotational symmetry of order n Jc^2. For example, Figure 7 illustrates three crystal planes of a cubic lattice. An axis perpendicular to the (100) plane has a 4-fold symmetry; an axis perpendicular to the (110) plane has a 2-fold symmetry, while an axis perpendicular to the (111) plane has a 3-fold symmetry. Generally speaking, the magnetoelastic tensor of a single crystal is anisotropic and has the symmetry of the crystal lattice; in Figure 7, the reference AME designates each of the principal axes of the magnetoelastic tensor of the crystal for the three section planes considered. For the implementation of the invention, preference will be given to materials having a highly anisotropic magnetoelastic tensor (typically of the order of a hundred kJ / m 3), while possessing elastic properties - quantified by a tensor of elastic constants - as isotropic as possible, for example isotropic to less than 10%. It is possible to use, for example, a ferromagnetic garnet, preferably comprising in its composition yttrium, iron and oxygen, and more particularly yttrium iron garnet (YIG).

[0046] Advantageously, the TMEi transducer also comprises a stationary magnetic field SCM source H o which is preferably aligned (with a tolerance of the order of 9°) with the axes of symmetry ASG and ASC at least in correspondence with the EFM element. The magnetic field source SCM can be for example a permanent magnet or an electromagnet, or even a combination of the two, or even a simple solenoid, as in the case of the figure. Preferably, the intensity of the magnetic field H ois adjustable, which makes the use of an electromagnet or solenoid preferable. The magnetic field H o has a dual function: on the one hand, its intensity determines the equilibrium magnetization configuration of the EFM element, as will be discussed below with reference to Figures 6A, 6B and 6C; on the other hand, it determines the frequencies of the different magnetic modes (oscilla- lations of the magnetization vector), making it possible to match them with those of elastic oscillation modes of said element.

[0047] The SGD system also includes a radiofrequency or microwave antenna ANT which, in the example of Figure 2A, is formed of two loops (elementary antennas in ) perpendicular to each other and to the main plane (xy) of the ferromagnetic element. As illustrated by Figure 3A, each of these loops generates an electromagnetic mode MEM whose magnetic part H EM has, in correspondence with the ferromagnetic element EFM, field lines substantially parallel to each other and to the main faces of the ferromagnetic element (oriented along the xy plane) and perpendicular to the axes of symmetry ASG and ASC (z axis). As illustrated in Figure 4A, if only one of the two elementary loops is excited, the electromagnetic mode has a linear polarization along the y axis or along the x axis. As illustrated in Figure 4B, if the two elementary loops are excited by signals of the same amplitude and 90° phase shift, a circular polarization is obtained in the xy plane. In a manner known per se, other excitation configurations of the loops make it possible to obtain an elliptical or linear polarization along another direction of the xy plane. All these configurations have an angular momentum index n Ja =+1 .

[0048] An alternating current source powers the antenna to enable it to radiate the electromagnetic mode MEM. Advantageously, this source is adapted to allow a variation in the frequency of said alternating current, so as to match it to that of the magnetic mode of the EFM element to be excited.

[0049] The second transducer TME2, located at the opposite end of the GOE waveguide, has essentially the same structure - it comprises a ferromagnetic element EFM2 immersed in a static magnetic field generated by a source (solenoid) SCM2 and cooperates with an antenna ANT2 having the same structure as ANTi. However, the antenna ANT2 is used for reception, and is therefore coupled to an alternating current detector DCA.

[0050] Figure 2B illustrates another system for generating, transmitting and detecting elastic waves which differs from that of Figure 2A in that its antennas each have a single loop arranged in a plane parallel to the main plane of the ferromagnetic element EFM (xy), but spaced from the latter according to the axial direction (z). As illustrated in Figure 3B, the magnetic part H EM of the electromagnetic mode MEM presents, in correspondence with the ferromagnetic element EFM, field lines having a radial component in the xy plane. Such a configuration of the magnetic field presents an angular momentum index n Ja =0.

[0051] A physical phenomenon underlying the operation of the invention is Larmor precession, illustrated in Figure 5. We consider a ferromagnetic material having an equilibrium magnetization represented by a vector M E, whose amplitude and / or orientation can vary from one point to another in the material. When an external magnetic field, oscillating or rotating with an appropriate frequency, called the Larmor frequency (function and equilibrium magnetization, of the applied external magnetic field H o and the geometric shape of the ferromagnetic element EFM) and having an orientation perpendicular to M E , or with a component having such an orientation, is applied to the material, we obtain an instantaneous magnetization M| which forms an angle with respect to the direction of M E and rotates around the latter at the said Larmor frequency. The dynamic magnetization vector M D , given by the vector difference between M| and M E , therefore rotates in a plane perpendicular to M Eat the Larmor frequency. The magnetic oscillation mode of the resonator which, as mentioned above, in turn excites an elastic oscillation mode by magnetostrictive effect, is formed by the different dynamic magnetization vectors in the volume of the ferromagnetic element.

[0052] Figure 6A shows the magnetization configuration of a disc-shaped EFM ferromagnetic element in the presence of an external magnetic field H o (not shown) parallel to the axis of symmetry of the disk (vertical in the figure) of a value significantly higher (by at least 10%) than the saturation value. In this case, in a majority fraction of the volume of the element (more than 50% of said volume, typically of the order of 80% or more) the equilibrium magnetization vectors M Eare substantially parallel (for example, within 9°) to said axis of symmetry. When an electromagnetic mode having a magnetic part oscillating (linear polarization) or rotating (circular polarization) in the principal plane of the ferromagnetic element at the Larmor frequency is applied, the dynamic magnetization vectors M D also rotate in the said plane. Also, an electromagnetic mode- MEM tick with angular momentum index n Ja =+1 induces a magnetic mode MAG with an angular momentum index n Jm =+1 .

[0053] Figure 6B shows the magnetization configuration of a disc-shaped EFM ferromagnetic element in the presence of an external magnetic field H o(not shown) parallel to the axis of symmetry of the disk (vertical in the figure) of a value substantially lower (by at least 10%) than the saturation value, or in the absence of such an external field. In this case, in a majority fraction of the volume of the element (more than 50% of said volume, typically of the order of 80% or more), at its periphery, the equilibrium magnetization vectors VAE are substantially perpendicular (for example to within 9°) of said axis of symmetry and have an orthoradial orientation - or at least have a significant component (of at least 10% of the total amplitude) with a so-called orthoradial orientation. When an electromagnetic mode having a magnetic part oscillating (linear polarization) or rotating (circular polarization) in the main plane of the ferromagnetic element at the Larmor frequency is applied, the dynamic magnetization vectors M Drotate perpendicular to this plane, according to a radial configuration. Also, an electromagnetic mode MEM presenting an oscillating field along z, even spatially uniform, induces a magnetic mode MAG presenting an angular momentum index n Jm =0.

[0054] Figure 6C corresponds to an intermediate situation, in which the external field is close to the saturation value. In this case, the equilibrium magnetization vectors have, at the periphery of the element, an orientation comprising an orthoradial component and a component aligned with the axis of symmetry.

[0055] All three cases, as well as other equilibrium magnetization textures, can be used for implementing the invention. It is noted that in all these cases, due to the symmetry of the EFM element, the MAG magnetic mode has a cylindrical symmetry, with an axis coinciding with ASG and ASC.

[0056] The previous figures have explained how simple antennas (straight or loop) can be used to apply to a ferromagnetic element EFM an oscillating or rotating electromagnetic mode field MEM having an angular momentum index n Ja typically equal to 0 or +1, and how the interaction of this electromagnetic mode field oscillating or rotating with the equilibrium magnetization M E said ferromagnetic element induces, via the Larmor precession phenomenon, the excitation of a MAG magnetic mode - provided that a resonance condition is respected. This MAG magnetic mode has an angular momentum index n Jm which is also typically equal to 0 or +1, and equal to n Ja . Thanks to the magnetostriction effect, this magnetic mode in turn excites (if a frequency resonance condition is satisfied) one or more elastic modes MEL of the EFM element having an angular momentum of index nj e =nja -n jc and n Je =n Ja +nj Ci where n jc is the discrete symmetry order of the magnetoelastic tensor of the material constituting the ferromagnetic element EFM. The value of n jc depends both on the lattice system of this material and on the plane along which it was cut. For example, Figure 7 shows that when a cubic mesh lattice (like that of YIG) is cut along a (100) plane, jc =4 ; when cut along a plane (111) we have jc =3 and when it is cut according to a plane (110) we have jc =2. The possible orders of discrete rotation axes in a crystal are n jc=2, 3, 4 or 6. Furthermore, the harmonics present in the magnetoelastic tensor (or in any other linear response tensor) for a crystal cut in a plane perpendicular to such an axis, are the possible multiples of the order of the axis. So possibly 2, 4 or 6 for an axis of order 2, 3 or 6 for an axis of order 3, 4 for 4 and 6 for 6! This, however, does not reduce to the cubic cell, but covers all possible crystal shapes. We recall that we can always also excite n Jm = n Je .

[0057] Figures 8A and 8B illustrate the operating principle of the magnetoelastic emission transducer of the system of Figures 2A 2B, respectively, when the ferromagnetic element of said magnetoelastic transducer has the magnetization of Figure 6A (equilibrium magnetization vector parallel to the geometric and crystal symmetry axes of the EFM element) and a crystal orientation (111) corresponding to a discrete symmetry of order n jc =3. We denote by z the orientation of the axes of symmetry ASG and ASC (not shown), the EFM element is therefore a disk whose faces are parallel to the xy plane.

[0058] As explained above and illustrated in Figure 8A, the antenna ANT generates an electromagnetic mode MEM having a magnetic part H EM which is locally uniform, with for example a tolerance not greater than 10%, and oriented in the y direction (see Figure 3A), which corresponds to an angular momentum of index n Ja =+1 (here we use only one of the two elementary loops of the antenna, and therefore a linearly polarized electromagnetic field MEM, but the operation would be substantially the same if both loops were used and the polarization was circular). The equilibrium magnetization vector VAE is oriented in the z direction; its interaction with the external magnetic field H E M gives rise to a dynamic magnetization vector M D which rotates in the xy plane. This is a magnetic mode with angular momentum of index n Jm=+1. The instantaneous total magnetization vector M, (which is not shown), is inclined with respect to the z axis and exhibits a precessional motion around it. The excitation of the magnetic mode is possible only if the frequency of the electromagnetic field generated by the antenna is resonant with the precession frequency of the dynamic magnetization vector, which in turn depends both on the properties of the ferromagnetic material from which the EFM element is made and on the intensity of the stationary magnetic field H o .

[0059] By magnetostriction effect, the magnetic mode in turn excites (if a frequency resonance condition is satisfied) one or more elastic modes of the EFM element having an angular momentum of index nje=nj a -njc and n je =nj a -i-nj c. These elastic modes are transmitted to the GOE elastic waveguide; the figure shows the configuration of the MEL elastic displacement vector on the inner surface of a hollow-core GOE elastic waveguide. In the example we an Je =-2 and n Je =+4. In general, these two modes have different resonant frequencies, so only one of them can be resonant with the magnetic oscillation mode and therefore be effectively excited. The mode to be excited can be selected by acting jointly on the intensity of the stationary magnetic field H o and on the excitation frequency of the antenna.

[0060] In the embodiment of Figure 8B, the magnetic part JEM of the electromagnetic field generated by the antenna ANT has a radial component (see Figure 3B), which corresponds to an angular momentum of index n Ja=0. The excited magnetic mode MAG in the ferromagnetic element EFM also has a radial configuration (each dynamic magnetization vector M D rotates in a plane perpendicular to an orthoradial direction) and therefore an angular momentum of index n Ja =0. Due to the discrete symmetry of order n jc =3 of the crystal lattice- of the ferromagnetic element, the excited elastic modes have angular momentum indices n Je =+3 and -3, and are therefore degenerate.

[0061] It is noted that the invention makes it possible to excite several elastic modes having different angular momentum indices. For example, by considering a ferromagnetic material having a cubic crystal lattice oriented (1 10) one can, from n Jm = +1 and access n Je = -3, -1, 1, 3, 5 or from n Jm =0, to n Je =-4,- 2,2,4. For a crystal oriented (100), n Jm=+1 allows access to n Je =-1,3, while n Jm =0 gives access to n Je =-2.2. For a (111) oriented crystal, n Jm =+1 gives n Je =-2.4 and n Jm =0, n Je =-3.3. In summary, the elastic modes n Je =-4,-3,-2,-1, 0, 1, 2, 3, 4 and 5 can be accessed with different antennas depending on the crystal orientation.

[0062] In Figure 8A and Figure 8B, elastic modes propagate along a hollow-core GOE elastic waveguide. This is not essential. Figure 9A and Figure 9B illustrate, for example, how elastic modes of indices n Je =-2 and n Je =+4 can propagate both on the inner surface of a hollow core waveguide (Figure 9A) and on the outer surface of a solid core waveguide (Figure 9B).

[0063] Figure 10 illustrates an alternative embodiment of the invention in which the ferromagnetic material element EFM is a supported micro-disc, for example obtained by etching a magnetic layer deposited on a substrate SUB and carried by a foot P, forming an elastic wave cavity COE resonant at the frequency of an elastic mode MEL which can be excited by magnetostrictive effect as explained above. The antenna ANT is a planar loop deposited on the substrate. The ferromagnetic element EFM / elastic wave cavity COE is transparent at an optical length and at the same time constitutes an optical resonator, coupled by evanescent wave to an optical fiber FO. The excitation of elastic modes of the ferromagnetic element, in particular with non-zero angular momentum index, obtained in accordance with the invention, makes it possible to obtain variable losses in the optical fiber. The system therefore constitutes an optical modulator.Alternatively, a separate COE element, elastically coupled to the EFM ferromagnetic element, can serve as the elastic and optical cavity.

[0064] The invention has been described with reference to certain embodiments, but several variations are possible. For example: - The ferromagnetic element can have a shape other than a disc, provided that it has the desired cylindrical symmetry. - Its equilibrium magnetization may have a configuration different from those illustrated in figures 6A to 6C provided, here too, that it has the desired cylindrical symmetry. - Other types of antenna can be used, possibly generating more complex electromagnetic field configurations. - Other ferromagnetic materials than yttrium, oxygen and iron garnets can be used.

[0065] The invention can find application, for example, in elastic wave communication systems, where appropriate with angular momentum diversity multiplexing, the production of devices such as delay lines, coupling devices between q-bits, etc.

[0066] References

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[0068] (Callen 1963): ER Callen, et al. “Magnetostriction in Cubic Néel Ferrimagnets, with Application to YIG”. Phys. Rev., 1735-1740 (1963).

[0069] (Chen 2020): R. Chen, et al. “Orbital Angular Momentum Waves: Generation, Detection, and Emerging Applications”. IEEE Communications Surveys & Tutorials, 840-868 (2020).

[0070] (Nikitov 2008) : S. A. Nikitov, et al. « Elastic wave propagation in a microstructured acoustic fiber ». IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 1831 -1839 (2008).

[0071] (Schliesser 2010): A. Schliesser, T. Kippenberg « Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators ». In P. e. Berman, Advances In Atomic, Molecular, and Optical Physics (pp. 207-323). Elsevier (2010).

[0072] (Wei 2019): F. Wei, et al. « Phononic integrated circuitry and spin-orbit interaction of phonons >>. Nat. Commun., 2743 (2019).

[0073] (Yamazaki 2020): R. Yamazaki, et al. « Radio-frequency-to-optical conversion using acoustic and optical whispering-gallery modes ». Phys. Rev. A, 053839 (2020)

Claims

CLAIMS 1. Magnetoelastic transducer (TMEi, TME2) comprising an element made of monocrystalline ferromagnetic material (EFMi, EFM2, EFM) having an anisotropic magnetoelastic tensor, said element having a geometric axis (ASG) of cylindrical symmetry, characterized in that said geometric axis of cylindrical symmetry is aligned with an axis of crystalline symmetry (ASC) having a discrete rotational symmetry of order n jc >2 and having at least one resonance between a magnetic oscillation mode (MAG) and an elastic oscillation mode (MEL).

2. Magnetoelastic transducer according to claim 1, the element of monocrystalline ferromagnetic material (EFM-i, EFM2, EFM) of which is made of a said material whose elastic constant tensor is substantially isotropic.

3. Magnetoelastic transducer according to one of the preceding claims wherein said element made of monocrystalline ferromagnetic material (EFM-i, EFM2, EFM) has an equilibrium magnetization (M E ) having a cylindrical axis of symmetry coinciding with said geometric axis.

4. Magnetoelastic transducer according to claim 3 wherein said element made of monocrystalline ferromagnetic material (EFM-,, EFM2, EFM) has, in a majority fraction of its volume, an equilibrium magnetization (M E ) oriented substantially parallel to said geometric axis of cylindrical symmetry (ASG).

5. Magnetoelastic transducer according to claim 3 wherein said element made of monocrystalline ferromagnetic material (EFM-i, EFM2, EFM) has, in a majority fraction of its volume, an equilibrium magnetization (M E) having a component in the orthoradial direction located in a plane (xy) perpendicular to said geometric axis of cylindrical symmetry (ASG).

6. Magnetoelastic transducer according to one of the preceding claims, wherein said element made of monocrystalline ferromagnetic material (EFM1, EFM2, EFM) is disc-shaped.

7. Magnetoelastic transducer according to one of the preceding claims, in which said monocrystalline ferromagnetic material constituting the element (EFM-,, EFM2, EFM) is a ferromagnetic garnet, preferably comprising in its composition yttrium, iron and oxygen.

8. Magnetoelastic transducer according to one of the preceding claims also comprising a source (SCM) of a static magnetic field (H o), preferably having an adjustable amplitude, oriented along said geometric axis of cylindrical symmetry (ASG) in correspondence with said element made of monocrystalline ferromagnetic material (EFMi, EFM2, EFM).

9. System (SGD) for generating or detecting elastic waves having a total angular momentum of non-zero index comprising at least one magnetoelastic transducer (TME-,, TME2) according to one of the preceding claims and an antenna (ANT, ANT-i, ANT2) configured to generate and / or detect, in correspondence with the ferromagnetic element of said transducer, an electromagnetic mode (MEM) adapted to excite, or which can be generated by, said magnetic oscillation mode of the element made of monocrystalline ferromagnetic material of the magnetoelastic transducer.

10. System for generating or detecting elastic waves according to claim 9 in which the electromagnetic mode (MEM) generated or detected by said antenna (ANT, ANT 1 ;ANT2) in correspondence of the element in monocrystalline ferromagnetic material (EFMi, EFM2, EFM) of said magnetoelastic transducer (TME-i, TME2) has a magnetic part (HEM) having a total angular momentum of index n Ja E TL such that the angular momentum of said elastic oscillation mode has an index n Je = n Jm ± n Jc where n Jm GZ, function of n Ja , is the index of the total angular momentum of the magnetic oscillation mode (MAG) of the single-crystal ferromagnetic material element.

11. System for generating or detecting elastic waves according to one of claims 9 and 10 wherein said antenna (ANT, ANT-, ANT2) is configured so that the magnetic part (H EM) of said electromagnetic mode (MEM) presents, in correspondence with the element in monocrystalline ferromagnetic material (EF i, EFM2, EFM) of said magnetoelastic transducer (TMEi, TME2), a component located in a plane perpendicular to the local magnetization of the latter.

12. System for generating or detecting elastic waves according to one of claims 9 to 11 in which said component of the magnetic part (H EM ) of said electromagnetic mode (MEM) located in a plane perpendicular to the local magnetization of the element in monocrystalline ferromagnetic material (EFM!, EFM2, EFM) is either substantially uniform in a plane perpendicular to the geometric axis of cylindrical symmetry (ASG), or essentially uniform along said axis, or essentially radial or orthoradial.

13. System for generating or detecting elastic waves according to one of claims 9 to 12 wherein said antenna (ANTi, ANT2, ANT) is chosen from a straight conductor, a loop conductor or a plurality of such mutually insulated conductors.

14. Elastic wave generation system according to one of claims 9 to 13 also comprising a source (SCA) of an alternating electric current configured to power said antenna (ANTi), said alternating electric current having a frequency resonant with said magnetic oscillation mode (MAG) and said elastic oscillation mode (MEL).

15. Elastic wave generation system according to one of claims 9 to 14 also comprising a detector (DCA) of an alternating electric current induced in said antenna (ANT2) by an electromagnetic mode (MEM) generated by said magnetoelastic transducer when it is excited by an elastic mode with total angular momentum of non-zero index.

16. System for generating or detecting elastic waves according to one of claims 9 to 15 also comprising an elastic waveguide (GOE) mechanically coupled to said magnetoelastic transducer (TME-i, TME2) and configured to propagate said elastic oscillation mode of said element made of monocrystalline ferromagnetic material (EFM).

17. Elastic wave generation system according to one of claims 9 to 15 also comprising an elastic wave cavity (EWC) mechanically coupled to said element made of monocrystalline ferromagnetic material (EFM) and resonant with said elastic oscillation mode (MEL). 18 Optical modulator comprising an elastic wave generation system according to one of claims 9 to 17, wherein said ferromagnetic element, or said elastic resonator, is optically transparent, and an optical waveguide (FO) is coupled by evanescent wave to said element made of monocrystalline ferromagnetic material (EFM) or to said elastic wave cavity (COE).

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