TECHNICAL FIELD

[0001 ] According to a first aspect, the invention relates to a portion of waveguide. According to a second aspect, the invention relates to a waveguide comprising two (or more) such portions of waveguide. According to a third aspect, the invention relates to a method for making a portion of waveguide.

DESCRIPTION OF RELATED ART

[0002] Waveguides are used in various applications for guiding an electromagnetic wave, see for instance JP2008028468, and in particular its figure 32. A waveguide comprises a cavity where an electromagnetic wave is confined. H Razavipour et al. disclose in a conference proceeding ( 'Ferromagnetic Nanowire (FMNW) Self-biased H-plane Resonance Isolator', in Proceedings of Asia-Pacific Microwave Conference 2010) a special kind of waveguides known as isolators. Isolators are known by the one skilled in the art and allow transmitting power in one direction only. This property is generally named non-reciprocity by the one skilled in the art. Non-reciprocity allows decoupling emission and reception paths of a signal such that they do not interfere. Conventional ferrite isolators present some drawbacks. First, they require a permanent magnet for biaising the ferrite material. Second, they require an external field significantly larger than the effective field, due to demagnetization effects. H Razavipour et al propose in their conference proceeding to replace the ferrite slabs of a ferrite isolator with ferromagnetic nanowire slabs. H Razavipour et al do not disclose how to fabricate such new isolators but rather present calculated performances that could be obtained by replacing the ferrite slabs of ferrite isolators by ferromagnetic nanowire slabs. More specifically, H Razavipour et al calculate such performances for the portions of waveguide shown in figure 1 of this proceeding when the ferrite slabs are replaced by ferromagnetic nanowire slabs. These ferromagnetic nanowire slabs need to be fixed onto the metallic boundary delimiting the cavity of the portion of waveguide. As shown in figure 2 of this proceeding, the ferromagnetic nanowires are embedded into a nanoporous alumina membrane.

[0003] This portion of waveguide that comprises ferromagnetic nanowire slabs presents several drawbacks. First, the mechanical resistance of this portion of waveguide is limited. Second, it is difficult to fabricate different such portions of waveguide with various (or selected) electromagnetic properties.

SUMMARY OF THE INVENTION

[0004] According to a first aspect, it is an object of the invention to provide a portion of waveguide that presents a higher mechanical resistance, and whose electromagnetic properties can be easily varied (or changed). To this end and according to a first aspect, the inventors propose a portion of waveguide for guiding an electromagnetic wave along a main propagation path and between a first and a second extremities of said main propagation path, said portion of waveguide comprising:

- a metallic boundary;

- a cavity for confining said electromagnetic wave, delimited by said metallic boundary, extending along said main propagation path between the first and second extremities of said main propagation path, and presenting a plurality of rectangular cross-sections transverse to said main propagation path;

- a dielectric matrix comprising a plurality of nanopores.

The portion of waveguide according to the invention is characterized in that said dielectric matrix substantially fills said cavity.

[0005] Preferably, the metallic boundary that delimits said cavity has an internal surface whose all cross-sections along said main propagation path present closed contours or closed curves. More preferably, the internal surface of said metallic boundary presents a plurality of rectangular cross- sections transverse to said main propagation path.

[0006] The dielectric matrix substantially fills the cavity. Therefore, if the cavity has a length L along the main propagation path between the first and second extremities, the dielectric matrix substantially fills the rectangular cross-sections of the cavity along said length L. The word substantially means that the dielectric matrix fills at least 90% of the volume of the cavity. Preferably, the dielectric matrix fills at least 95% of the volume of the cavity. More preferably, the dielectric matrix fills at least 99% of the volume of the cavity.

[0007] As the dielectric matrix substantially fills the cavity, the mechanical resistance of the portion of waveguide according to the invention is increased, notably with respect to the waveguides of JP2008028468 and to the waveguides described in Razavipour's publication. The dielectric matrix can indeed support a part of a compression force that would be applied to the metallic boundary delimiting the cavity for instance. This aspect is particularly important when the rectangular cross-sections of the cavity present a large width. When a force of compression parallel to the height of the cavity is applied at the metallic boundary delimiting the cavity, this metallic boundary tends to bend in the absence of a dielectric matrix filling the cavity. The dielectric matrix substantially filling the cavity allows reducing such an effect. Hence, the dielectric matrix strengthens the portion of waveguide or increases its mechanical resistance.

[0008] By filing some nanopores of the dielectric matrix with nanowires of different materials, it is possible to easily modulate or change the electromagnetic properties of the portion of waveguide according to the invention (for instance, one can modulate the relative permeability and the relative permittivity of the portion of waveguide). It is also possible to use a same material but to fill only partially some nanopores, while filling totally other nanopores. Some nanopores can also be maintained empty. The different configurations of filling of the nanopores lead to different electromagnetic properties of the portion of waveguide. Finally, the electromagnetic properties of the portion of waveguide according to the invention can be easily modulated depending on the filling of the nanopores of the dielectric matrix. As the dielectric matrix of the portion of waveguide of the invention substantially fills the cavity, it is possible to obtain the same isolation effects as the ones obtained with the ferromagnetic nanowire slabs of H Razavipour et al's proceeding by filling partially only some nanopores of the dielectric matrix by ferromagnetic nanowires.

[0009] The portion of waveguide according to the invention has other advantages. It does neither need to provide ferromagnetic nanowire slabs, nor to fix them on the walls of the metallic boundary delimiting the cavity of the portion of waveguide. The dielectric matrix can be grown directly from a wall of the metallic boundary, and some ferromagnetic nanowires can be grown in the nanopores by electrodeposition for instance. These techniques are particularly adapted for integration purposes. Therefore, the portion of waveguide according to the invention is more adapted for integration than the portion of waveguide proposed by H Razavipour et al. Integration is of primary importance in microelectronics. The portion of waveguide according to the invention also allows obtaining a portion of waveguide of small dimension. Its thickness can be small, for instance below 1 mm. As the cavity of the portion of waveguide is globally filled with a same filling body (the dielectric matrix comprising nanopores), the process of fabrication of the portion of waveguide according to the invention is still easier. There are not some regions of the cavity filled with air and other regions filled with another material such as slabs of ferromagnetic nanowire material. Hence, the portion of waveguide according to the invention has these further advantages compared to the portion of wave guide proposed by H Razavipour et al. For this last waveguide, one indeed needs to provide the ferromagnetic nanowire slabs and to fix them (by gluing for instance) onto the inner walls of the metallic boundary delimiting the cavity of the portion of waveguide. Decreasing the size of this portion of waveguide (its thickness for instance) is therefore strongly limited for practical reasons of realization and the fabrication of this portion of waveguide is very specific and complicated. H Razavipour et al's portion of waveguide is therefore not adapted for integration. The portion of waveguide according to the invention is well-adapted for high frequency applications as the dielectric matrix comprises nanopores. Moreover, these nanopores can be filled with nanowires.

[0010] The portion of waveguide proposed by H Razavipour et al is not adapted for guiding a wave along a main propagation path that is not linear. This portion of waveguide does indeed use ferromagnetic nanowire slabs that present a main linear direction and it is difficult to make such ferromagnetic nanowire slabs of complex shapes. However, it is often desired to guide an electromagnetic wave along a main propagation path that is not linear. With the portion of waveguide according to the invention, it is possible to easily obtain a portion of waveguide adapted for guiding an electromagnetic wave along a main propagation path that is not linear. Some nanopores of the dielectric matrix can indeed be filled with metallic nanowires that thereafter form a portion of the metallic boundary delimiting the cavity where an electromagnetic wave can be confined. These nanopores can be filled with the metallic nanowires such that such the portion of the metallic boundary constituted by these metallic nanowires is curved, not linear. For instance, one can use a mask presenting curved limits in order to get a boundary between filled and not filled nanopores that is also curved. Finally, the main propagation path is not linear, and the technique for getting such a curved main propagation path is very simple. More generally and for the same reasons, the portion of waveguide according to the invention is particularly well adapted for making portions of waveguide having a complex shape. This is not the case for H Razavipour et al's portion of waveguide.

[0011] The portion of waveguide according to the invention allows confining an electromagnetic wave in the cavity. This is not the case for coplanar transmission lines as depicted in figure 36 of JP2008028468 or in the following publication: Marson et al, "Magnetic Nanowires base Reciprocal & Non-reciprocal devices of Monolithic Microwave Integrated Circuits (MMIC)", NSTI-Nanotech 2008, pages 146-149 (see its figure 2 for instance). Hence, electromagnetic compatibility is improved by using a portion of waveguide according to the invention.

[0012] As discussed below, it is possible to have an isolator by using the portion of waveguide of the invention. Contrary to the coplanar transmission lines depicted in Marson et al's publication, the portion of waveguide of the invention does not require, in order to form an isolator, a permanent magnet for biaising ferrite material. It does neither require an external field significantly larger than the effective field, due to demagnetization effects.

[0013] Preferably, the different rectangular cross-sections transverse to the main propagation path are identical.

[0014] Preferably, the nanopores traverse all the thickness of the dielectrix matrix. [0015] Preferably :

- at least one nanopore of said dielectric matrix is filled with a metallic material, and

- said metallic boundary comprises :

· an upper and a bottom metallic surfaces that are substantially parallel to each other, and

• said at least one nanopore filled with said metallic material, electrically coupling said upper and bottom metallic surfaces.

[0016] Preferably, the nanopores of the dielectric matrix are substantially perpendicular to said upper and bottom metallic surfaces. More preferably, the nanopores extend all along the distance between these upper and bottom metallic surfaces.

[0017] Preferably, said dielectric matrix comprises Al ₂ 0 ₃ . By using Al ₂ 0 ₃ , one can have nanopores of substantially regular size and that are substantially parallel. Another advantage of using an Al ₂ 0 ₃ matrix for the dielectric matrix is that the diameter of the nanopores can be controlled over a wide range, for instance between 10 nm and 200 nm. An Al ₂ 0 ₃ matrix also presents low dielectric losses and physical properties that are weakly dependent on temperature. One can also have a dielectric matrix with a high density of nanopores by using an AI ₂ O ₃ matrix. Moreover, the fabrication of nanopores is facilitated by using an AI ₂ O ₃ matrix, even when the size of the nanopores is very small such as nanopores having a (mean) diameter as small as 10 nm, and preferably lower than 1 nm.

[0018] Preferably, at least one nanopore of said dielectric matrix is at least partially filled with a ferromagnetic material.

[0019] Preferably, at least one nanopore of said dielectric matrix is at least partially filled with a ferroelectric material.

[0020] According to a second aspect, the inventors propose a waveguide comprising two (or more) portions of waveguide as described in the first aspect of the invention. Such a waveguide has the technical advantages of the portion of waveguide of the first aspect of the invention. In particular, such a waveguide presents a higher mechanical resistance, and its electromagnetic properties can be easily varied. Such a waveguide is also particularly adapted for integration. Moreover, it is possible to make a waveguide presenting two (more than two if more than two portions of waveguide are used) main propagation paths of complex shape. Preferably, the main propagation paths of said first and a second portions of waveguide are disposed in series. More preferably, the main propagation paths of said first and a second portions of waveguide are disposed in a parallel electromagnetic configuration. This last preferred example does not mean that the main propagation paths of the first and a second portions of waveguide need to be parallel. That just means that the main propagation paths of the first and a second portions of waveguide are not disposed in series.

[0021] Preferably, the main propagation paths of said first and a second portions of waveguide are substantially parallel to each other along at least a portion of each main propagation path of each said first and a second portions of waveguide.

[0022] Preferably, the cavities of said first and a second portions of waveguide are in communication (or connected) at the first extremities of the main propagation paths of both first and a second portions of waveguide.

[0023] Preferably, the cavities of said first and a second portions of waveguide are in communication (or connected) at the second extremities of the main propagation paths of said first and a second portions of waveguide. With this last preferred embodiment, one can combine, at the junction connecting the two cavities of the two portions of waveguide at the second extremities of the main propagation paths of the two portions of waveguide, electromagnetic waves travelling along the main propagation paths of each portion of waveguide. By changing the length of the main propagation path of a portion of waveguide with respect to the length of the main propagation path of the other portion of waveguide, one can obtain different resultant waves at this junction. Another possibility for changing the resultant waves at this junction is to vary the electromagnetic properties of a portion of waveguide with respect to the electromagnetic properties of the other portion of waveguide. This can be done easily by filling some nanopores of one portion of waveguide with specific materials, while maintaining the nanopores of the other portion of waveguide empty. More preferably, some nanopores of one portion of waveguide are filled at least partially with a ferromagnetic material, and the nanopores of the other portion of waveguide are left empty. Then, one can obtain easily an isolator that is particularly adapted for integration.

[0024] Preferably, the dielectric matrixes of each of said two portions of waveguides are parts of a same body comprising a waveguide dielectric matrix and a plurality of nanopores in said waveguide dielectric matrix. Then, the method of fabrication of this waveguide is facilitated and adapted for integration. Moreover, one can then easily obtain a waveguide comprising two portions of waveguide (or more if the waveguide comprises more than two portions of waveguide) able to guide electromagnetic waves along main propagation paths of complex shapes. For making this preferred embodiment, one can use for instance the following fabrication steps:

- providing one bottom metallic surface;

- thereafter growing on this bottom metallic surface a dielectric matrix comprising a plurality of nanopores;

- thereafter filling some of the nanopores of the dielectric matrix with metallic nanowires in order to define lateral surfaces of the metallic boundaries of the two portions of waveguide; and

- providing one upper metallic surface in electrical contact with the metallic nanowires and substantially parallel to the bottom metallic surface for closing the metallic boundaries of the two portions of waveguide.

This example of method of fabrication is easy, adapted for integration and down-scaling. The cost of fabrication can also be reduced by using this example of method of fabrication. Other methods of fabrication could be used for obtaining this preferred embodiment of the waveguide according to the second aspect of the invention.

[0025] Preferably, at least one nanopore of a dielectric matrix of one of said two portions of waveguides that is located in a cavity of one of said two portions of waveguide is at least partially filled with a ferromagnetic material.

[0026] Preferably, the waveguide proposed by the inventors comprise more than two portions of waveguide according to the first aspect of the invention. For instance, this waveguide can comprise three, four, or five such portions of waveguide. More preferably, the waveguide comprises a plurality of portions of waveguide whose first extremities of their main propagation paths are connected to each other through an input portion of the waveguide, whereas the second extremities of the main propagation paths of the different portions of waveguide are not connected to each other. In this last preferred embodiment, the waveguide therefore presents a single input, and a plurality of outputs that are constituted by the different portions of waveguide. Still more preferably, the waveguide comprises a portion of waveguide according to the first aspect of the invention forming a main cavity having the form of a loop (ie of substantially annular shape) and various input/output portions of waveguide connecting said main cavity and the exterior of the waveguide.

[0027] According to a third aspect, it is an object of the invention to provide a method for fabricating a portion of waveguide that presents a higher mechanical resistance, and whose electromagnetic properties can be easily varied. To this end and according to this third aspect, the inventors propose a method of fabrication comprising the following steps:

i. providing a bottom metallic plate;

ii. forming in a first portion of said bottom metallic plate a dielectric

matrix comprising nanopores while keeping metallic a second portion of the bottom metallic plate;

iii. filling at least partially some of said nanopores with a filling material; iv. providing an upper metallic plate in electrical contact with said second portion of the bottom metallic plate and such that said nanopores are located in between the second portion of the bottom metallic plate and the upper metallic plate, in order to obtain a cavity for confining an electromagnetic wave that is substantially filled with said dielectric matrix comprising said nanopores.

[0028] Preferably, this bottom metallic plate is a metallic film.

[0029] Preferably, said metallic film is deposited on a substrate.

[0030] Preferably, said second portion of the bottom metallic plate comprises at least one lateral metallic bridge for electrically connecting said second portion of the bottom metallic plate and said upper metallic plate.

[0031] Preferably, at least one nanopore is totally filled with a metallic material in step iv. for electrically connecting said second portion of the bottom metallic plate and said upper metallic plate. BRIEF DESCRIPTION OF THE DRAWING

[0032] These and further aspects of the invention will be explained in greater detail by way of example and with reference to the accompanying drawings in which:

Fig.1 shows a perspective view of a preferred embodiment of a portion of waveguide according to the invention and a corresponding rectangular cross-section transverse to a main propagation path of the portion of waveguide;

Fig. 2 shows a cross-section of another preferred embodiment of a portion of waveguide according to the invention;

Fig. 3 shows a cross-section of another preferred embodiment of a portion of waveguide according to the invention;

Fig. 4 shows a cross-section of another preferred embodiment of a portion of waveguide according to the invention;

Fig. 5 shows a cross-section of another preferred embodiment of a portion of waveguide according to the invention;

Fig. 6 shows a top view of a waveguide according to a second aspect of the invention and according to a preferred embodiment;

Fig. 7 shows a cross-section along line AA' of the waveguide of previous figure;

Fig. 8 shows a cross-section of another preferred embodiment of a waveguide;

Fig. 9 shows a top view of another preferred embodiment of a waveguide;

Fig. 10 shows a top view of another preferred embodiment of a waveguide;

Fig. 1 1 shows a top view of another preferred embodiment of a waveguide;

Fig. 12 illustrates the steps of a first example of the method of fabrication according to a third aspect of the invention;

Fig. 13 shows the steps of a second example of the method of fabrication according to a third aspect of the invention;

Fig. 14 shows an exemplary portion of waveguide according to the invention in two dimensions;

Fig. 15 shows simulated S-factors in dB for the portion of waveguide of figure 14;

Fig. 16 shows measured S-factors in dB for the portion of waveguide of figure 14;

Fig. 17 shows measured and simulated differences between S-| ₂ and S ₂ i for the portion of waveguide of figure 14.

The drawings of the figures are neither drawn to scale nor proportioned. Generally, identical components are denoted by the same reference numerals in the figures.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

[0033] The upper part of figure 1 shows a perspective view of a portion of waveguide 1 according to a preferred embodiment. The portion of waveguide 1 is able to guide an electromagnetic wave along a main propagation path 5, between a first 6 and a second 7 extremities of said main propagation path 5. The propagation principle of an electromagnetic wave in a waveguide is known by one skilled in the art. In figure 1 , the main propagation path 5 is linear. However, it could be possible to have a curved main propagation path 5 as it is shown below for the waveguide 100 according to a second aspect of the invention. The portion of waveguide 1 comprises a metallic boundary 20 delimiting a cavity 10 inside which an electromagnetic wave can be confined. The term metallic is known by the one skilled in the art. The cavity 10 extends between the first 6 and second 7 extremities along the main propagation path 5. The cavity 10 presents a series of rectangular cross- sections transverse to the main propagation path 5 (a square cross-section is considered as a specific example of a generic rectangular cross-section; hence, the cavity 10 could have a series of square cross-sections transverse to the main propagation path 5).

[0034] Lower part of figure 1 shows one rectangular cross-section of the cavity 10. The metallic boundary 20 delimiting the cavity has an upper 20u and a bottom 20b metallic surfaces that are substantially parallel. As it can be seen in lower part of figure 1 , the cavity 10 is substantially filled by a dielectric matrix 35 and a plurality of nanopores 40. The rectangular cross-section of the cavity 10 has a height 12 and a width 13, where the height 12 is smaller than or equal to the width 13.

[0035] For all the preferred embodiments of the portion of waveguide 1 according to the invention, the nanopores 40 are preferably elongated prisms. More preferably, the nanopores 40 are elongated circular cylinders. Still more preferably, the nanopores 40 are parallel. Still more preferably, the nanopores 40 are parallel elongated circular cylinders. The nanopores 40 are preferably parallel to the height 12 of the cavity 10. Preferably, all the nanopores 40 have same dimensions. The nanopores 40 have a diameter, or a mean diameter if they are elongated prisms, that is preferably lower than 1 μιη. More preferably, the diameter or the mean diameter of the nanopores 40 is lower than 100 nm, and still more preferably lower than 10 nm. Still more preferably, the diameter or the mean diameter of the nanopores 40 is around 0.5 nm. Preferably, the nanopores 40 form a periodic array, and more preferably a triangular period array.

[0036] For all the preferred embodiments of the portion of waveguide 1 according to the invention, the dielectric matrix 35 can comprise any dielectric material. Preferably, the dielectric matrix 35 comprises Al ₂ 0 ₃ . Preferably, the volume of the nanopores 40 represents 5 to 35 % of the volume of the filling body (dielectric matrix), and more preferably 10 to 25 %. Still more preferably, the volume of the nanopores 40 represents 15 % of the volume of the filling body (dielectric matrix).

[0037] For all the preferred embodiments of the portion of waveguide 1 according to the invention, the height 12 of the cavity 10 is preferably comprised between and 10 and 200 μιτι, and more preferably between 20 and 100 μιτι. Still more preferably, the height 12 of the cavity 10 is equal to 50 μιτι. Nevertheless, the height 12 of the cavity 10 can also be comprised between 1 and 10 μιτι. Preferably, the width 13 of the cavity 10 is comprised between 1 and 50 mm, and more preferably, between 5 and 10 mm. The length of the portion of waveguide 1 along the main propagation path 5 and between the first 6 and second 7 extremities is preferably comprised between 1 and 100 mm, and is preferably equal to 50 mm. [0038] Figure 2 shows a cross-section of a portion of waveguide according to another preferred embodiment. In this preferred embodiment, two nanopores 40 are filled with a metallic material 60. These two filled nanopores 40 electrically couple the upper 20u and the bottom 20b metallic surfaces of the metallic boundary 20, thus forming a portion of the metallic boundary 20 delimiting the cavity 10 into which an electromagnetic wave can propagate. Only one nanopores 40 could be filled with a metallic material 60 in this preferred embodiment. Figure 3 shows a cross-section of a portion of waveguide according to another preferred embodiment. In this preferred embodiment, the two lateral surfaces of the metallic boundary 20 that are parallel to the height 12 are formed by nanopores 40 filled with a metallic material 60. One lateral surface of the metallic boundary 20 is formed by two nanopores 40 filled with a metallic material 60 and another lateral surface of the metallic boundary 20 is formed by one nanopores 40 filled with a metallic material 60. Preferably, the lateral surfaces of the metallic boundary 20 are formed by hundreds or more preferably by thousands nanopores 40 filled with a metallic material 60. The preferred embodiment of figure 3 is particularly well adapted for making portions of waveguide 1 of complex shape, and for making portions of waveguide 1 whose main propagation path 5 is not linear. One can indeed use a dielectric matrix as described above deposited or grown on a bottom metallic surface 20b, and thereafter fill some nanopores 40 with a metallic material 60 in order to shape the required propagation path 5. The metallic material 60 has to fill all the height of the filled nanopores 40 in these preferred embodiments. Preferably, this metallic material 60 is copper, and more preferably aluminum; such a choice is adapted for integration. Finally, an upper metallic surface 20u has to be deposited on top of the layup formed by the bottom metallic surface 20b and the dielectric matrix in order to obtain the cavity 10. The nanopores 40 filled with a metallic material 60 form the lateral surfaces of the metallic boundary 20 that are parallel to the height 12 of the cavity 10. In the preferred embodiments shown in figures 2 and 3, the metallic material 60 filling the nanopores 40 preferably forms nanowires.

[0039] As shown in the lower part of figure 1 , and in figures 2 and 3, the nanopores 40 of the dielectric matrix are preferably substantially perpendicular to the upper 20u and bottom 20b metallic surfaces of the metallic boundary 20.

[0040] In another preferred embodiment, at least one nanopore 40 of the dielectric matrix is at least partially filled with a ferromagnetic material 65, preferably nickel, or with a ferromagnetic transition metal 65 such as Ni, Co, Fe and their alloy. A cross-section of this preferred embodiment is shown in figure 4 where three nanopores 40 are filled partially with such a ferromagnetic material 65. This preferred embodiment is an interesting alternative to the portions of waveguide with ferrite slabs discussed in H Razavipour et al's proceeding. By using a dielectric matrix with nanopores 40, some of them being partially filled, it is possible to have devices of smaller size with respect to the portions of waveguide with ferrite slabs.

[0041] With the preferred embodiment shown in figure 4, one can notably obtain a non-reciprocal portion of waveguide or an isolator. These terms are known by the one skilled in the art. Non-reciprocity means that the propagation coefficient of a travelling electromagnetic wave depends on its direction of propagation. This property is based on the Faraday effect that is known by the one skilled in the art.

[0042] Let us assume that an electromagnetic wave having a circular polarization in the plane x, y propagates in an infinite ferromagnetic material with:

1

H ^± = H, +j

0

where the + (respectively -) sign stands for the right (respectively left) circular polarization, and where 'j' is the imaginary number. The relationship between the magnetic induction B and the magnetic field H is then scalar for each of these two circular polarizations:

B ⁺ = μ ⁺ Η ⁺ ,

B ^~ = μ ^~ Η ^~ .

But it can be shown (see for instance "Microwave Engineering" by D Pozar, 2 ^nd Ed, John Willey & Sons, New York 1998) that the permeability values, μ ⁺ and μ ^~ , depend on the direction (or on the + and - signs) of the circular polarizations (the + and - signs therefore refer to left and right directions of rotation here). In particular, the V polarization presents a ferromagnetic resonance, whereas the '-' polarization does not. As a consequence, phase velocity, phase shift and losses depend on the direction of the circular polarization. The inventors propose to use this property in the portion of waveguide 1 according to the invention. The general expression of the dominant mode of the magnetic field in the cavity 1 0 of the portion of waveguide 1 is (see for instance "Microwave Engineering" by D Pozar, 2 ^nd Ed, John Willey & Sons, New York 1 998) :

Ή = A _± (y) [±p s ( ^nx /a) x - j ⁿ / _a cos( ^nx /a) y] = H _x x + H _y y (Eq. 1 ). In this last equation, the '+' and '-' signs indicate the direction of propagation. The '+' sign stands for an electromagnetic wave travelling along positive y- axis, whereas the '-' sign stands for an electromagnetic wave travelling along negative y-axis. A+(y are the amplitudes corresponding to an electromagnetic wave travelling along positive and negative y-axes. The width 1 3 of the cavity 1 0 is denoted by 'a' in last equation, β is the constant of propagation and is known by the one skilled in the art. From this last equation, the inventors have deducted that there are two positions in the cavity 1 0 where the magnetic field presents a circular polarization (circular polarization if \H _X \ = \H _y \). These two positions are: x = x ₀ = ^a / _n a ten ( ⁿ / _a p) (Eq. 2), and

x = a - x ₀ (Eq. 3).

For instance, at x = x ₀ , the magnetic field becomes:

H(x ₀ ) = A _± (y) - _a {±x - j y) (Eq. 4).

At x = a - x ₀ , the magnetic field becomes:

H{a - x ₀ ) = A _± (y) - _a {±x +j y) (Eq. 5).

Hence, at x = x ₀ and at x = a - x ₀ , there is a circular polarization of the magnetic field and the direction of the circular polarization depends on the direction of propagation of the electromagnetic wave. But the permeability values, μ ⁺ and μ ^~ , depend on the direction (or on the + and - signs) of the circular polarizations. Thus, the propagation of the electromagnetic wave that is dependent on the permeability value, will also depends on the direction of propagation. Therefore, it is possible to have a non-reciprocal portion of waveguide 1 . In particular, it is possible to have an isolator due to the strong attenuation that can be obtained for only one direction of propagation of the electromagnetic wave. For obtaining such an isolator, the inventors propose to fill some nanopores 40 of the cavity 10 with a ferromagnetic material 65 such that the mean distance of these filled nanopores 40 from a lateral surface of the metallic boundary 20 that is parallel to the height 12 is equal to x ₀ (see figure 4). The nanopores 40 filled with a ferromagnetic material 65 are preferably permanently magnetized parallel to the z-axis (ie parallel to the height 12 of the cavity 10), thus referring to as a permanent magnet. Preferably, this ferromagnetic material 65 is a ferromagnetic transition metal such as nickel, cobalt or iron or their alloy for instance. More preferably, Nickel nanowires fill the filled nanopores 40.

[0043] Figure 5 shows another preferred embodiment of the portion of waveguide 1 . In this preferred embodiment, some nanopores 40 are at least partially filled with a first filling material 70 and other nanopores 40 are at least partially filled with a second filling material 75. First 70 and second 75 filling materials are ferromagnetic or ferroelectric but first 70 and second 75 filling materials are different in this preferred embodiment. First filling material 70 can be ferromagnetic and second filling material 75 can be ferroelectric and vice versa. It is also possible that both first 70 and second 75 filling materials are ferromagnetic or ferroelectric. One can obtain an isolator with the preferred embodiment shown in figure 5. The heights along z-axis of the filled parts of the nanopores 40 that comprise first 70 or second 75 filling material can be identical or different.

[0044] As shown in figures 1 to 5, some nanopores 40 are preferably not filled (or left empty). This increases the global stability (in particular the mechanical stability) of the portion of waveguide 1 .

[0045] According to a second aspect, the invention relates to a waveguide 100 comprising two (or more) portions of waveguide 1 as described previously. Figure 6 shows a top view of a preferred embodiment of such a waveguide 100. This preferred embodiment comprises a first 1 a and a second 1 b portions of waveguide. Each portion of waveguide (1 a, 1 b) has a cavity (10a and 10b) and is able to guide an electromagnetic wave along a main propagation path (5a and 5b) that is depicted by black arrows for both portions of waveguide (1 a; 1 b) in figure 5. Reference sign 6a (respectively 6b) is the first extremity of the first main propagation path 5a (respectively second main propagation path 5b). Reference sign 7a (respectively 7b) is the second extremity of the first main propagation path 5a (respectively second main propagation path 5b). As shown in this figure, the first 5a and second 5b main propagation paths are not linear but rather curved. First 10a and second 10b cavities of first 1 a and second 1 b portions of waveguide are substantially filled with a dielectric matrix comprising a plurality of nanopores. As shown in the preferred embodiment of figure 6, first 5a and second 5b main propagation paths of first 1 a and second 1 b portions of waveguide are preferably substantially parallel to each other along a portion (horizontal portion of figure 5) of each main propagation path (5a; 5b). As shown in the preferred embodiment of figure 6, the cavities (10a; 10b) of first 1 a and second 1 b portions of waveguide are preferably connected to each other at the first (6a; 6b) and second (7a; 7b) extremities of the main propagation paths (5a; 5b) of first 1 a and second 1 b portions of waveguide. In the preferred embodiment shown in figure 6, these two connections at the first (6a; 6b) and second (7a; 7b) extremities of first 5a and second 5b main propagation paths are preferably obtained through an input 1 in and an output l out portions of waveguide. So, the preferred embodiment of the waveguide 100 that is shown in figure 6 allows guiding an electromagnetic wave through the input portion of waveguide 1 in, said electromagnetic wave being then divided in two sub electromagnetic waves travelling through first 1 a and second 1 b portions of waveguide, said two sub electromagnetic waves interfering at the output portion of waveguide l out for forming a resultant output electromagnetic wave. The preferred waveguide 100 shown in figure 6 can be used as an interferometer.

[0046] Figure 7 shows a cross-section along the line AA' of the preferred embodiment of the waveguide 100 shown in figure 6. As shown in figure 7, first 1 a and second 1 b portions of waveguide have preferably a same bottom 20b and a same upper 20u metallic surfaces. First 1 a and second 1 b portions of waveguide also preferably have a same dielectric matrix 35 comprising nanopores 40. This dielectric matrix 35 is preferably grown onto the common bottom metallic surface 20b before providing the upper metallic surface 20u. As shown in figure 7, the lateral surfaces of the metallic boundaries of first 1 a and second 1 b portions of waveguide that are parallel to the height 12 of said first 1 a and second 1 b portions of waveguide are preferably obtained by filling some nanopores 40 with a metallic material 60. Then, the fabrication and the integration of the waveguide 100 are facilitated.

[0047] As shown in figure 7, some nanopores 40 of the first cavity 10a of the first portion of waveguide 1 a are preferably at least partially filled with a ferromagnetic material 65 (however, in another preferred embodiment of the waveguide 100 shown in figure 6, no nanopore 40 is filled with a ferromagnetic material 65). Preferably these nanopores 40 are at least partially filled with a ferromagnetic material 65 along a portion of the first main propagation path 5a. Then, the electromagnetic properties seen by two electromagnetic waves traveling through the first 1 a and second 1 b portions of waveguide are different. This allows having a waveguide 100 with interesting properties. Preferably, the nanopores 40 that are at least partially filled with a ferromagnetic material 65 are positioned at mean distance x ₀ given by equation (Eq. 2) from a lateral surface of the metallic boundary of a portion of waveguide 10a, as it is shown in figure 7. Parameter 'a' is the width of the first cavity 10a of the first portion of waveguide 1 a. The preferred embodiment of the waveguide 100 shown in figures 6 and 7 can be used for fabricating efficient isolators, differential phase shifters and switches.

[0048] Figure 8 shows a cross-section of another preferred embodiment of the waveguide 100 according to the second aspect of the invention. In this preferred embodiment, at least one nanopore 40 is at least partially filled with a first filling material 70 and at least another one nanopore 40 is at least partially filled with a second filling material 75. First 70 and second 75 filling materials are ferromagnetic or ferroelectric but first 70 and second 75 filling materials are different in this preferred embodiment. First filling material 70 can be ferromagnetic and second filling material 75 can be ferroelectric and vice versa. It is also possible that both first 70 and second 75 filling materials are ferromagnetic or ferroelectric. One can obtain an isolator with the preferred embodiment shown in figure 8. The heights along z-axis of the filled parts of the nanopores 40 that comprise first 70 or second 75 filling material can be identical or different.

[0049] Figure 9 shows another preferred embodiment of the waveguide 100 according to second aspect of the invention. This preferred embodiment comprises first, second, third, and fourth portions of waveguide that are connected to each other through input 1 in and output l out portions of waveguide. These different portions of waveguide are as described in relation to the first aspect of the invention. First portion of waveguide comprises a first cavity 10a; second portion of waveguide comprises a second cavity 10b; third portion of waveguide comprises a third cavity 10c; fourth portion of waveguide comprises a fourth cavity 10d.

[0050] Figure 10 shows another preferred embodiment of the waveguide 100 according to second aspect of the invention. This preferred embodiment comprises first, second, third, and fourth portions of waveguide that are connected to each other through only one input 1 in portion of waveguide. These different portions of waveguide are as described in relation to the first aspect of the invention. First portion of waveguide comprises a first cavity 10a; second portion of waveguide comprises a second cavity 10b; third portion of waveguide comprises a third cavity 10c; fourth portion of waveguide comprises a fourth cavity 10d.

[0051] Figure 1 1 shows another preferred embodiment of the waveguide 100 according to second aspect of the invention. This preferred embodiment of the waveguide 100 comprises a portion of waveguide 1 of substantially annular shape and four input portions of waveguide 1 in. These different portions of waveguide are as described in relation to the first aspect of the invention. Some of the four input portions of waveguide 1 in shown in figure 1 1 can be used as outputs for the waveguide 100.

[0052] For the preferred embodiments of the waveguide 100 that are shown in figures 9 to 1 1 , all the preferred versions of the portions of waveguide 1 that have been described previously can be used. For instance, some nanopores 40 of these different portions of waveguide 1 can be filled with a filling material. Preferably, each of the matrixes of the different portions of waveguide 1 of the preferred waveguides 100 shown in figures 6 to 1 1 is part of a same body comprising a waveguide dielectric matrix and a plurality of nanopores 40 in said waveguide dielectric matrix. More preferably, the preferred waveguides 100 shown in figures 6 to 1 1 comprise an upper and a bottom metallic surfaces that form portions of the metallic boundaries 20 of the different portions of waveguide 1 of these preferred waveguides 100. Then, the fabrication of these preferred waveguides 100 is facilitated. One only need one bottom metallic plate, one material comprising a dielectric matrix 35 and a plurality of nanopores 40, and one upper metallic plate.

[0053] The portion of waveguide 1 and the waveguide 100 according to first and second aspects of the invention are preferably used with electromagnetic waves having a fundamental frequency higher than 1 GHz, more preferably with electromagnetic waves having a fundamental frequency higher than 5 GHz, and still more preferably with electromagnetic waves having a fundamental frequency higher than 10 GHz.

[0054] As it has been discussed above, some nanopores 40 of the portion of waveguide 1 or of the waveguide 100 are preferably filled with a filling material in preferred embodiments. One can take any material for this filling material. This filling material can be for instance ferromagnetic or ferroelectric. Preferably, the filling material is BaTiO ₂ or PZT.

[0055] According to a third aspect, the invention relates to a method for making a portion of waveguide 1 as described above. Figure 12 illustrates a first example of such a method whose different steps are to be carried out along the black arrow. Fist, one has to provide a bottom metallic plate 200. Preferably, this bottom metallic plate 200 comprises at least one portion of aluminum. More preferably, the entire bottom metallic plate 200 is made of aluminum. Preferably, the bottom metallic plate 200 is a metallic film whose thickness 201 is comprised between 1 and 200 μιτι. More preferably, thickness 201 is comprised between 10 and 100 μιτι, and still more preferably, between 1 and 10 μιτι. Still more preferably, thickness 201 is smaller than 1 μιτι. Preferably, the bottom metallic plate 200 that can be in the form of a metallic film is deposited on a substrate. Preferably, this substrate is a silicon substrate. More preferably, this substrate comprises quartz. Preferably, there is buffer layer between the substrate and the bottom metallic plate 200; more preferably, this buffer layer is metallic.

[0056] Second step of the method is forming in a first portion 230 of the bottom metallic plate 200 a dielectric matrix 35 and nanopores 40 while keeping metallic a second portion 240 of the bottom metallic plate 200. Preferably, anodizing is used for forming the nanopores 40 and the dielectric matrix 35. If the bottom metallic plate 200 is aluminum, anodizing allows obtaining an Al ₂ 0 ₃ matrix. Nanopore arrays with ordered hexagonal structures are preferably fabricated by self-organized anodization of aluminium under optimum anodizing conditions (usually involving a two-step anodization process): see for instance H Masuda and K Fuduka in Science 268, 1466 (1995). In the example shown in figure 12, the second portion 240 of the bottom metallic plate 200 that remains metallic comprises two lateral metallic bridges 245. As shown in figure 12, these two lateral metallic bridges 245 are at least as high as the dielectric matrix 35. As shown in figure 12, some nanopores 40 are preferably filled at least partially with a filling material 210. Preferably, this filling material 210 is metallic. More preferably, this filling material 210 is magnetic (ferromagnetic for instance). Preferably, electrodeposition is used for filling at least partially with a filling material 21 some nanopores 40. Preferably, all the nanopores 40 are filled at least partially with a filling material 21 . Last, one has to provide an upper metallic plate 205 in electrical contact with the second portion 240 of the bottom metallic plate 200 that remained metallic. This upper metallic plate 205 closes the cavity 10 of the portion of waveguide 1 and the nanopores 40 are located in between the second portion 240 of the bottom metallic plate 200 and the upper metallic plate 205. In the example shown in figure 12, the electrical contact between the second portion 240 of the bottom metallic plate 200 and the upper metallic plate 205 is ensured by the two lateral metallic bridges 245.

[0057] Figure 13 illustrates another example of the method of fabrication according to the third aspect of the invention. Contrary to the example shown in figure 12, nanopores 40 are formed along the whole width of the bottom metallic plate 200. Then, some nanopores 40 are filled along their all height with a filling material 210 that is metallic in order to ensure an electrical contact between the bottom 200 and the upper 205 metallic plates. In the example shown in figure 13, the nanopores 40 totally filled with the metallic filling material 210 therefore form some portions of the metallic boundary 20 delimiting the cavity 10 of the portion of waveguide 1 . All the preferred parameters and embodiments described with reference to the example shown in figure 12 can be applied to the example of the fabrication method shown in figure 13. [0058] The method of fabrication described above in reference to figures 12 and 13 can also be used for making the waveguide 100 according to the second aspect of the invention. In particular, this method of fabrication can be used for making the preferred embodiments of the waveguide 100 shown in figures 6 to 1 1 .

[0059] Some results are now presented. They were obtained with a portion of waveguide 1 whose geometry is shown in figure 14. This portion of waveguide 1 has a height 12 equal to 50 μιτι. The dielectric matrix 35 comprises Al ₂ 0 ₃ , and the diameter of the nanopores 40 is equal to 100 nm. The porosity of the dielectric matrix 35 is roughly equal to 13%. Some nanopores 40 are filled with a metallic material 60 (Nickel), thus forming parts of the metallic boundary 20, and connecting its upper 20u and bottom 20b metallic surfaces. The width 13 of the cavity 10 is equal to 6.5 mm. Some nanopores 40 are partially filled (along a height equal to 80% of the total height 12 that is equal to 50 μιτι) with a ferromagnetic material 65. This ferromagnetic material 65 is Permalloy that is known by the one skilled in the art. The width 651 of this ferromagnetic part is equal to 1 mm, and distance x ₀ is equal to 2 mm. The portion of waveguide 1 has a length that is equal to 5 mm (this length is perpendicular to the plane of figure 14, and parallel to the y-axis of figure 1 ).

[0060] Figure 15 (respectively figure 16) shows simulated (respectively measured) S-factors in dB for the portion of waveguide 1 of figure 14. The term S-factor, also known as scattering coefficient is known by the one skilled in the art. Indices 1 and 2 refer to input and output of the portion of waveguide 1 , or to first 6 and second 7 extremities along main propagation path 5 (see figure 1 ). We clearly observe a difference between S-| ₂ and S ₂ i for frequencies lying between 1 .25 and 1 .6 ^* 10 ¹⁰ Hz, reflecting a property of non reciprocity of the portion of waveguide 1 . This property can also be deduced from figure 17 that shows measured and simulated differences between Si ₂ and S ₂ i . Hence, one can obtain an isolator by using some preferred embodiments of the portion of waveguide 1 of the invention. From these three figures, we also observe a relatively good agreement between simulations and measurements.

[0061] The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. Those skilled in the art will recognize that many variations are possible within the spirit and scope of the invention as defined in the following claims, and their equivalents, in which all terms are to be understood in their broadest possible sense unless otherwise indicated. As a consequence, all modifications and alterations will occur to others upon reading and understanding the previous description of the invention. In particular, dimensions, materials, and other parameters, given in the above description may vary depending on the needs of the application.

[0062] The invention can also be summarized as follows. Portion of waveguide 1 for guiding an electromagnetic wave along a main propagation path 5 and between a first 6 and a second 7 extremities of said main propagation path 5, said portion of waveguide 1 comprising: a metallic boundary 20; a cavity 10 for confining said electromagnetic wave, delimited by said metallic boundary 20, extending along said main propagation path 5 between the first 6 and second 7 extremities of said main propagation path 5, and presenting a plurality of rectangular cross-sections transverse to said main propagation path 5; a dielectric matrix 35 comprising a plurality of nanopores 40, said dielectric matrix 35 substantially filling said cavity 10.