Method for manufacturing a robust THz hollow-core waveguide with inhibited coupling and robust THz hollow-core waveguide with inhibited coupling

Abstract

Robust THz hollow-core waveguide with inhibited coupling comprising: a microstructured cladding (SCF1) comprising a plurality of tubular motifs (MCF1) arranged in a ring around a core (C1) so as to confine at least one radiation at an optimal wavelength within said core; an outer cladding (GE1) surrounding the microstructured cladding (SCF1), a waveguide formed by said outer cladding and said microstructured cladding being called the initial waveguide; an inner cladding (GI) disposed between the microstructured cladding and the outer cladding, the tubular motifs being nested within the inner cladding so as to permit their mechanical retention within the waveguide.an index and thickness of the inner cladding being optimized as a function of a core diameter and the optimal wavelength such that a ratio between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 at the optimal wavelength.

Description

Title of the invention: Method for manufacturing a robust THz hollow-core waveguide with inhibited coupling and Robust THz hollow-core waveguide with inhibited coupling technical field

[0001] The invention relates to the field of microstructured hollow-core optical fibers with inhibited coupling. Previous technique

[0002] Hollow-core microstructured fibers can be separated into two main categories: bandgap guided fibers (HC-PCF-PBG for Hollow-Core; Photonic-Cristal-Fiber; Photonic BandGap in English) and inhibited coupling fibers (HC-PCF-IC for Hollow-Core; Photonic-Cristal-Fiber; Inhibited Coupling in English).

[0003] These types of fibers offer numerous advantages for use in gyroscopes, including: they exhibit low losses, and it is theoretically possible to transfer light from the fiber core to a resonant element of the microstructured cladding, or conversely, from the resonant element to a guiding core. Similarly, this type of fiber exhibits light leakage from its core with a very specific azimuthal distribution and polarization dependence.

[0004] Guidance in PCF-PBG fibers is caused by the existence of photonic band gaps created by the periodicity of the microstructured cladding. Guidance in HC-PCF-PBG band gap fibers is achieved in a periodicity defect (the core) whose refractive index is lower than that of the cladding. HC-PCF-PBG fibers have hollow cores (air cross-section, refractive index ni = 1). This guidance is therefore different from that of conventional optical fibers or solid-core microstructured PCF cladding fibers, where the guidance and confinement of light in the core is caused by total internal reflection between the core with refractive index ni and the microstructured cladding having an average refractive index n2eff lower than nb.

[0005] Alternatively, coupling inhibited fibers (or IC fibers) are optical fibers that have negatively curved core walls, offering numerous advantages. They allow for low attenuation, polarization retention, relatively large core modes, very low spatial overlap between the core mode and the silica core wall, and coupling efficiency exceeding 90% (see Debord, B. et al. Hollow-Core Fiber Technology: The Rising of “Gas Photonics”. Fibers 2019, 7, 16). In an IC-type HC-PCF hollow-core fiber, where the core mode and cladding mode have the same effective index, light Propagating in the core could therefore theoretically propagate in the cladding. However, the confinement and guidance of the core mode in these fibers is based on the inhibition (or anti-resonance) between the coupling of the core mode and the cladding mode. This inhibition is achieved by the structure of the microstructured cladding and that of the core contour. In other words, the dot product between the electric field of the core mode (Icore#) and that of the cladding mode (Icladding#) is very small. The coupling term between these two modes can be reduced by having a small spatial intersection between the fields Icore# and Icladding#, or by a large phase shift between the transverse spatial phase of the core mode and that of the cladding mode. Since this confinement only exists for certain wavelength ranges, discontinuities are then observed in the refractive index dispersion curve and therefore in the transmission curve.

[0006] Figure IA shows a propagation loss curve as a function of wavelength for a typical HC-PCF type IC FE fiber known in the prior art and illustrated in Figure IB. More precisely, Figure IB schematically illustrates a cross-section of an FE fiber called HC-PCF-IC-SR-TL because the microstructured cladding GS comprises a plurality of tubular lattice MT motifs—typically made of silica—arranged around the hollow core C in a single ring (Single Ring or SR) within an outer cladding GE. In a manner known per se, in order to achieve confinement and guidance of radiation at a wavelength λop in the core Cl, the tubular MT motifs exhibit a wall thickness tcf and an index ncf such that with 2ÀOp m(m+ï) , 2Àop 4 / h+1 me N*-

[0007] In the illustrated example, the wall thickness of the tubular motifs is tcf = 2 jim. Figure IA shows discontinuities in the propagation loss curve. Wavelengths within the Zcf range exhibit very low losses because there is a small spatial intersection between the lc[)meui fields # and I0cladding# or a strong phase shift between the transverse spatial phase of the core mode and that of the cladding mode. Wavelengths within this Zcf range can therefore be guided within the core C over long distances. The curve in Figure IA illustrates an example of a wavelength 20 that can be guided by the fiber in [Fig. 1B]. Conversely, wavelengths within the Zcp range exhibit much higher losses because there is significant coupling between cladding modes and the core mode, and therefore they cannot be efficiently guided.

[0008] In the terahertz (THz) range, commercially available waveguides have a very high linear attenuation coefficient (from 20 dB / m to 14 dB / m in the 0.22 - 0.33 THz band, from 67 dB / m to 47 dB / m in the 0.5 - 0.75 THz band, or from 130 dB / (m at 88 dB / m in the 0.75 - 1.1 THz band) which does not allow propagation beyond a few centimeters. There are some large-core waveguides that allow propagation with low losses at the expense of extensive multimode guidance. However, in practice, these waveguides are difficult to manufacture because they require etching a micrometric structure along the waveguide, which limits the length of manufactured waveguides to a few tens of centimeters and results in a significant manufacturing cost (several tens of thousands of euros). Similarly, inhibited-coupling hollow-core waveguides appear to be a very promising solution for enabling low-loss guidance of terahertz radiation, given that air is the optimal medium for propagating THz waves.However, in practice, the most effective anti-resonant waveguides are limited to laboratory demonstrations, as they do not incorporate a sheath to mechanically support the dielectric tube assembly. These waveguides exhibit fragility and mechanical instability due to the presence of a microstructured sheath providing anti-resonance confinement.

[0009] The invention aims to overcome certain problems of the prior art by means of an optimized hollow-core THz waveguide with inhibited coupling (and a method for manufacturing this waveguide) which includes, in particular, an inner sheath, disposed between the microstructured sheath and the outer sheath of the waveguide, in which the tubular patterns are interlocked so as to allow their mechanical retention within the waveguide. The inner sheath is optimized so that the linear attenuation coefficient of the robust waveguide at the optimal wavelength to be guided is minimally impacted by the presence of the inner sheath. Thus, this inner sheath ensures mechanical stability and reinforcement of the waveguide without significantly altering the propagation conditions of the THz electromagnetic wave, and even improves propagation performance in certain aspects (described below). Summary of the invention

[0010] To this end, an object of the invention is a method for manufacturing a robust THz hollow-core waveguide with inhibited coupling, said method comprising a design step and a material manufacturing step of the robust waveguide thus designed, said method being characterized in that the design step comprises the following steps: - Selection of an optimal wavelength ^op to be guided in the robust waveguide - Design of a so-called initial THz hollow-core waveguide with inhibited coupling comprising: • a micro-structured sheath comprising a plurality of patterns tubular arrays arranged in a ring around a core so as to confine at least one radiation at the optimal wavelength λop within said core • an outer sheath surrounding the microstructured sheath - Design of an inner sheath in a first dielectric or metallic material and intended to be disposed between the microstructured sheath and the outer sheath of said initial waveguide designed in the second step and thus form the robust waveguide in which the tubular patterns are nested in the inner sheath so as to allow their mechanical retention in the robust waveguide, said inner sheath design step (including a substep of optimization of an index and thickness of the inner sheath as a function of a core diameter and the optimal wavelength ^op so that a ratio arl between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 and preferably less than or equal to 2 at the optimal wavelength ^p.

[0011] According to one embodiment of the manufacturing process of the invention, the physical manufacturing step comprises: - a first sub-step in the manufacturing of the inner and outer sheaths, - a second sub-step in the manufacture of tubular patterns, and - a third sub-step of assembling the tubular patterns and a assembly formed by the inner sheath and the outer sheath.

[0012] Preferably, in the preceding embodiment, the first manufacturing substep is carried out by additive printing.

[0013] Preferably, in the preceding embodiment, the inner sheath is made of an adhesive, for example a UV adhesive, the third manufacturing substep then being carried out by gluing the inner sheath with the tubular patterns.

[0014] Another object of the invention is a robust THz hollow-core waveguide with inhibited coupling comprising: - a microstructured sheath comprising a plurality of tubular motifs arranged in a ring around a core so as to confine at least one radiation at an optimal wavelength λop within said core - an outer sheath surrounding the microstructured sheath, a waveguide formed by said outer sheath and said microstructured sheath being called the initial waveguide, - an inner sheath in a first dielectric or metallic material and disposed between the microstructured sheath and the outer sheath, the tubular patterns being nested in the inner sheath so as to allow their mechanical retention in the robust waveguide, a complex index ngi and a thickness eg' of the inner sheath being optimized as a function of a diameter Dc of the core and the optimal wavelength Àop so that a ratio arl between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 at the optimal wavelength ^op.

[0015] According to one embodiment of the robust waveguide of the invention, the inner sheath is a ring having a thickness egî substantially constant in a plane transverse to the robust waveguide and substantially constant longitudinally.

[0016] According to one embodiment of the robust waveguide of the invention, the inner sheath is arranged discontinuously longitudinally, for example in a plurality of sections of the same length L; separated longitudinally by a distance AL;.

[0017] According to an embodiment of the robust waveguide of the invention, a ratio rt between the thickness of the inner sheath and a radius of the tubular patterns is adapted as a function of the diameter of the core, an absorption coefficient of the material constituting the tubular patterns and the guiding wavelength so that the ratio ar! is less than or equal to 5 at the optimal wavelength ^op.

[0018] Preferably, the ratio rt is between 1 and 2 and preferably between 0.05 and 0.95.

[0019] According to an embodiment of the robust waveguide of the invention, a real part of the ngi index of the inner sheath is between 1.4 and 3, preferably between 1.4 and 2 at the optimal wavelength.

[0020] According to an embodiment of the robust waveguide of the invention, an imaginary part of the ngi index of the inner sheath is between 0.0001 and 0.015. This range is particularly suitable for guiding THz waves with low attenuation.

[0021] According to an embodiment of the robust waveguide of the invention, a ratio rt between the thickness of the inner sheath and a radius of the tubular patterns are adapted to allow a reduction of the peaks of strong attenuations of a transmission spectrum of said robust waveguide.

[0022] According to one embodiment of the robust waveguide of the invention, the first dielectric material is silica, glue or plastic.

[0023] According to a preferred embodiment of the robust waveguide of the invention, the microstructured cladding is formed of tubular patterns having a refractive index The internal cladding is made of silica or a first material having a refractive index ngi with a real part between 1.4 and 2.5 at the optimal wavelength and an egi / rt ratio between the thickness of the internal cladding and the radius of the tubular motifs between 0.05 and 0.75. This embodiment has been identified by the inventors as providing optimal guidance performance in the THz range for both joined and disjointed tubular motifs. The core diameter is preferably between 8 and 12 times the optimal wavelength to allow for better guidance.

[0024] According to an embodiment of the robust waveguide of the invention, a thickness and diameter of the tubular patterns are constant longitudinally and in which the internal sheath is adapted so that a distribution of the tubular patterns in a plane transverse to the robust waveguide varies longitudinally so that the robust waveguide allows, from a first end of the robust waveguide to a second end of the robust waveguide, a transition between a first intensity distribution of a guided fundamental mode to a second intensity distribution of the guided fundamental mode.

[0025] According to an embodiment of the robust waveguide of the invention, a thickness and diameter of the tubular patterns are constant longitudinally and in which the inner sheath is adapted so that a distribution of the tubular patterns in a plane transverse to the robust waveguide varies longitudinally so that the diameter of the core of the waveguide varies longitudinally and so that a cross-section of a fundamental mode undergoes a homothety longitudinally.

[0026] According to one embodiment of the robust waveguide of the invention, the thickness eg< is greater than or equal to 0.01 x rt, with rt a radius of the tubular patterns. Brief description of the drawings

[0027] Other features, details and advantages of the invention will become apparent from the description given with reference to the accompanying drawings provided by way of example, which represent, respectively:

[0028] [Fig. 1 A], a propagation loss curve as a function of wavelength of a typical HC-PCF type IC fiber known from the prior art, illustrated in [Fig.1B]

[0029] [Fig.2], a schematic illustration of a cross-section of a robust waveguide according to the invention,

[0030] [Fig.3A], a schematic illustration of one embodiment of the waveguide robust invention

[0031] [Fig.3B], the evolution of the linear attenuation coefficient of the fundamental mode HEn depending on the radiation frequency, for three different waveguides,

[0032] [Fig.3C], the transmission spectrum of two waveguides, one of which is a waveguide robust according to an embodiment of the invention;

[0033] [Fig.3D], the evolution of the attenuation of the fundamental mode HEn as a function of the radiation frequency, for three different waveguides, including two robust waveguides according to the invention,

[0034] [Fig.4], a schematic illustration of a cross-section of the robust waveguide according to the MR4-MR8 configurations of the invention

[0035] [Fig.5], two different graphs showing the evolution of the linear attenuation coefficient of the fundamental mode in the hollow core of the Ref3, MR5 and MR5 configurations,

[0036] [Fig.6], an embodiment of the invention in which the robust waveguide is adapted to effect, from a first end of the robust waveguide to a second end of the robust waveguide, a transition between a first transverse intensity distribution of a guided fundamental mode to a second transverse intensity distribution of the guided fundamental mode,

[0037] [Fig.7], an embodiment of the invention in which the robust waveguide is adapted to achieve, from a first end of the robust waveguide to a second end of the robust waveguide, a longitudinal variation of the core diameter,

[0038] [Fig.8], a graph showing the evolution of the value of the linear attenuation coefficient of the robust waveguide of [Fig.7], as a function of the core diameter.

[0039] In the figures, unless otherwise indicated, the elements are not to scale and identical references designate identical elements. Description of the implementation methods

[0040] Fig. 2 schematically illustrates a cross-section ST of a robust waveguide 1 according to the invention.

[0041] We will first describe the general structure of the robust waveguide 1 before detailing the different embodiments and their performance. Finally, we will describe a manufacturing process according to the invention for obtaining the robust waveguide 1 of the invention.

[0042] This robust waveguide 1 is a hollow-core terahertz (THz) waveguide with inhibited coupling which comprises a micro-structured cladding GS comprising a plurality of tubular MT patterns (also referred to as MT capillaries hereafter) which can be joined or disjoined, an outer cladding GE and an inner cladding GI.

[0043] More specifically, the MT tubular patterns of the microstructured cladding GS are arranged in a ring around the core C so as to confine at least one radiation at an optimal wavelength λop in the THz range within the core C. The tubular patterns have a diameter (i.e., a maximum dimension in the transverse plane of the waveguide) Dt = 2r( and a wall thickness ei. As mentioned previously, guiding a predetermined wavelength 2λp is made possible by an appropriate choice of wall thickness and MT tubular patterns. The thickness ei is related to the material used to constitute the MT tubular patterns, more precisely the complex refractive index of the material. This material is, for example, silica or a polymer-type material.

[0044] By "THz waveguide", it is meant here that the waveguide of the invention allows to guide at least one radiation having the optimal wavelength 2oP with a frequency between 0.1 THz and 30 THz.

[0045] By way of non-limiting example, the robust waveguide 1 illustrated in the embodiment of [Fig. 2] comprises 8 MT tubular patterns that are disjoint from one another. As is known per se, the distribution of the MT tubular patterns in the microstructured cladding GS in the transverse plane of the waveguide determines the azimuthal distribution of the leakage field of the guided radiation in the core. It is understood that the invention is not limited to this specific example and can be implemented with a different number of MT tubular patterns, of more or less complex topology, which may be joined or disjoint (see, for example, [Fig. 4] described below). An exhaustive description of the various possible arrangements of the tubular patterns, their shapes, and their effects on the guidance would fall outside the scope of the present invention.

[0046] The outer GE sheath surrounds the microstructured GS sheath so as to protect the microstructured GS sheath. This outer GE sheath is typically a dielectric material, such as silica or a polymer. A waveguide formed solely by the outer sheath and the microstructured sheath is hereafter referred to as the "initial waveguide." This initial waveguide is therefore identical to that described in [Fig. 1B].

[0047] Unlike the initial waveguide, the robust waveguide of the invention comprises an inner sheath GI disposed between the microstructured sheath GS and the outer sheath GE, and in which the tubular motifs MT are interlocked so as to allow their mechanical retention within the robust waveguide. This inner sheath GI is made of a first dielectric or metallic material of complex index ngi and is in the form of a layer of thickness egg arranged in a ring around the core C and bonded to the outer sheath GE.

[0048] According to a preferred embodiment, the inner sheath is deposited on the initial waveguide via a "glue gun" for example.

[0049] Preferably, in order to best control the guidance conditions along the entire length of the waveguide, the inner cladding has a thickness eg» that is substantially constant in a plane transverse to the robust waveguide, and substantially constant longitudinally (i.e., along the length of the waveguide). Thus, in this embodiment, the cross-section ST of the waveguide 1 is constant longitudinally.

[0050] Alternatively, according to another embodiment illustrated in Figure 3A, the inner sheath GI is arranged discontinuously along its length, for example, as a plurality of sections of the same length L separated longitudinally by a distance A. This embodiment has the advantage of being more easily manufactured. Indeed, it is then possible to simply encircle the tubular motifs so as to hold them fixed in the waveguide with several ring sections that form the inner sheath sections. By way of non-limiting example, L = 1 cm and A = 10 cm. Alternatively, the sections are not of the same length and / or are not separated by the same distance.

[0051] According to a variant of the embodiment of [Fig.3A], some of the longitudinally distributed sections have different internal sheath materials from each other.

[0052] According to a first embodiment, the inner sheath GI is a separate layer from the outer sheath GE, made of a first dielectric material distinct from that of the outer sheath. Alternatively, according to a second embodiment, the inner sheath GI is a continuation of the outer sheath GE, and is therefore made of the same material as the latter. Generally, in all embodiments of the invention, no portion of the tubular patterns MT is embedded in the outer sheath GE and, by convention, the boundary between the outer sheath GE and the inner sheath GI is defined by the end of the tubular patterns most radially eccentric with respect to the center of the core.

[0053] The inner cladding GI allows the position of each tubular motif MT to be fixed—in the transverse plane of the waveguide and longitudinally—thus ensuring mechanical stability and reinforcement of the robust waveguide relative to the initial waveguide. However, the presence of the inner cladding modifies the complex effective index perceived by the radiation in the robust waveguide. Therefore, it is necessary that the various parameters (complex index ngi and thickness e&) of the inner cladding be optimized so that the linear attenuation coefficient at the optimal wavelength of the robust waveguide is minimally affected by the presence of the inner cladding.

[0054] Through numerous simulations and experiments, the inventors determined that, for a predetermined torque of core diameter Dc and optimal wavelength It was possible to optimize the index ngi and the thickness eg of the inner cladding GI such that the ratio ar / between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 (and preferably less than or equal to 2) at the optimal wavelength λop. Each of these parameters, ngi and egi, influences the linear attenuation coefficient ai of the robust waveguide and depends on the various parameters of the initial waveguide, particularly the various parameters of the MT tubular patterns (e.g., wall thickness, diameter, distribution in the transverse plane, number of patterns), which determine the optimal waveguide wavelength Jap and the associated linear attenuation coefficient. Importantly, however, there is an optimal pair (ngi, egi) for each pair (Dc, Jap).

[0055] The thickness egi of the inner sheath GI must be sufficient to mechanically support the tubular patterns MT. Although the minimum thickness required to support the tubular patterns MT depends on the material of the inner sheath and the dimensions of the tubular patterns MT, through several experiments, the inventors determined that a thickness eg' greater than 0.01 x rt provides mechanical support for the tubular patterns MT. Therefore, preferably, the thickness eg< of the inner sheath GI is greater than 0.01 x rt.

[0056] Figure 3B shows the evolution of the linear attenuation coefficient of the fundamental mode HEn as a function of the radiation frequency, for three different waveguides according to three curves Cl, C2, and C3. The three curves Cl, C2, and C3 are simulation results. Curve Cl corresponds to the evolution of the linear attenuation coefficient of the fundamental mode HEn in an initial waveguide comprising 10 MT silica capillaries with a diameter Dt = 2.6 mm and a wall thickness of 134 µm, forming a hollow core in air with a diameter Dc = 6 mm and an external silica sheath. The complex refractive index of silica at the optimal wavelength, λann / f, is λnt = 1.954 - 0.0047 i Jop — JW [im \ Jop — 1 J HZ] (corresponding to an absorption coefficient of 849 dB / m). Curve C2 corresponds to the evolution of the linear attenuation coefficient of the fundamental mode HEn in a robust waveguide according to the invention, formed from the initial waveguide of curve Cl and comprising an internal silica sheath GI of thickness egi = rt. This configuration will be referred to as MRI hereafter. Finally, curve C3 corresponds to the evolution of the linear attenuation coefficient of the fundamental mode HEn in a robust waveguide according to the invention, formed from the initial waveguide of curve Cl and comprising an internal sheath GI of thickness egi = rt, and in a first material with a refractive index of 1.5 - 0.01*1 over the frequency range studied. This configuration will be referred to as MR2 hereafter. The imaginary part of the index implies that the first material used in the waveguide of curve C3 is absorbent for the optimal wavelength

[0057] Figure 3B shows that the three curves C1, C2, and C3 are virtually identical and indistinguishable from one another, thus indicating no significant variation in the linear attenuation coefficient introduced by the inner sheath. Therefore, the introduction of the inner sheath, even when it is in a first absorbing material for the optimal wavelength λ4λ, does not significantly impact the propagation conditions of the electromagnetic wave THz when the parameters ng1 and λg1 are chosen appropriately.

[0058] This result is also confirmed by Table 1 below, which summarizes the calculations of the effective index f of the linear attenuation coefficient aHEi of the fundamental mode HEn for different configurations Refl, Ref2, MR1-MR3. More specifically, the effective index and the linear attenuation coefficient Ref2 are obtained for the initial waveguide of the Cl curve in Figure 3B. Similarly, the effective index and the linear attenuation coefficient Refl are obtained for the initial waveguide of the Cl curve in Figure 3B, but without the external silica sheath. The MRI and MR2 configurations have been described in Figure 3B, and the MR3 configuration corresponds to a robust waveguide according to the invention, identical to that of configuration MR2 but with an internal sheath made of a first dielectric material having an index ngi such that ngi = 3 - 0.0 l^i. Refl Ref2 MRI MR3 MR3 Effective index neffam 0.999314983 0.999314945 0.999314930 0.999314936 0.999314936 0.10450 Attenuation ta, (dB / m) 1.04263 0.09972 0.10402 0.10334

[0059] These simulation results do not illustrate any significant variation of these values ​​by the introduction of the inner sheath in the MR1-MR3 configurations of the invention compared to the Refl and Ref2 configurations known in the prior art, even when the sheath has a very high real part of the ngi index as in the MR3 configuration or high absorption as in the MR2 and MR3 configurations.

[0060] Figure 3C shows the transmission spectrum of a waveguide according to an embodiment MR2' of the invention (curve C2'). More specifically, the waveguide of embodiment MR2' of the invention has a length of 30 cm and comprises 10 MT silica capillaries with a diameter Dt = 2.6 mm and a wall thickness of 127 µm, forming a hollow core in air with a diameter Dc = 6 mm and an external silica sheath. The complex refractive index of silica at wavelength optimal = 3Q() = 1 TH^ is nt - 1.954 - 0.0047i (corresponding) (with an absorption coefficient of 849 dB / m). In embodiment MR2', the inner sheath was formed by applying glue using a glue gun, without any special precautions. This layer of glue provides mechanical support for the waveguide.

[0061] For comparison, the curve Cl' corresponds to the spectrum of an initial waveguide identical to the waveguide of embodiment MR2', except that it does not include an internal sheath.

[0062] Curve C2' shows that the spectrum of the waveguide in embodiment MR2' is characterized by different transmission windows induced by the antiresonance mechanism. Comparison of curves C1' and C2' demonstrates that there is a very small variation in the transmission spectrum induced by the addition of the inner sheath, which is made here of a highly absorbing material. These results demonstrate that adding an inner sheath results in a negligible increase in the attenuation of the waveguide.

[0063] Figure 3D illustrates the effect of the inner cladding material on the absorption of the robust waveguide. More specifically, Figure 3D shows the evolution of the linear attenuation coefficient of the fundamental mode HEn as a function of the radiation frequency, for three different waveguides, according to three curves C3', C4', and C5', which are simulation results.

[0064] Curve C5' corresponds to the evolution of the linear coefficient of the fundamental mode HEn of the initial waveguide in [Fig. 3C]. Similarly, curve C4' corresponds to the evolution of the linear coefficient of the fundamental mode HEn of the robust waveguide according to embodiment MR2' detailed in [Fig. 3C] with a highly absorbing silica inner sheath (ngi = 1.954 - i*102). Finally, curve C3' corresponds to the evolution of the linear coefficient of the fundamental mode HEn of a robust waveguide according to an embodiment identical to embodiment MR2' detailed in [Fig. 3C], except that the inner sheath is not made of silica but of a highly absorbing polymer-type material (ngi = 1.5 - i*102).

[0065] The ordinate of curves C3', C4', and C5' represents the attenuation, which is given here as a function of the imaginary part of the effective index of the waveguide. Furthermore, it should be noted that the abscissa of curves C3', C4', and C5' is given as a function of the silica absorption, i.e., the imaginary part of the index of the material of the tubular motifs (Im(nt)). This amounts to modeling the waveguide at different frequencies THz, since the refractive index (real part) of silica is constant in this range (nr = 1.954). The attenuation of the inner cladding at different frequencies in the THz range is illustrated by the points in the figure, i.e., _ 4 6 [(y4 13 g iq-3 at 0.6 THz, at 0.1 THz; In^ = ~ L6 10-3 at 0.3 THz, Inin^ = -4.6.10'3 at -1.2 .102 at 2'5THz'

[0066] Finally, Figure 3D shows the curve C6' which traces the evolution of the ratio ar / Uj between a linear attenuation coefficient of the robust waveguides and a linear attenuation coefficient of the initial waveguide

[0067] Figure 3D illustrates, firstly, that the C3' and C4' curves coincide and that there is a reduction in the attenuation of the HEn mode when the absorption of the tube material is reduced, up to a plateau value. Figure 3D also demonstrates that, for a high absorption coefficient of the tubular motifs (Im(nt) > 10⁴ - i.e., in the THz range), the addition of an internal sheath made of silica or a highly absorbent polymer does not have a significant impact on the attenuation of the fundamental HEn mode. For reference, the ratio 2 is 2.30 for = HT4-

[0068] Thus, by these results and other simulations, the inventors determined that a ratio ar / (ij less than or equal to 5 (and preferably less than or equal to 2) at the optimal wavelength ^op was possible in the terahertz domain for an inner cladding having a material such that the imaginary part of the index ngi of the inner cladding is between 0.0001 and 0.015. This characteristic is applicable in the case where the cladding comprises joined and disjoint tubular patterns.

[0069] Since the previous results were obtained with joined tubular patterns, the focus is now on confirming that the inner sheath produces the same effects in a robust waveguide with disjointed tubular patterns. Indeed, it is known that reducing the diameter of the capillaries so that they are disjointed reduces the linear attenuation of the fundamental mode and, under certain conditions, significantly increases the attenuation of higher-order modes, thus enabling effective single-mode propagation.

[0070] The simulation results presented in Table 2 below detail, for 6 different configurations Ref3, MR4-MR8, the calculations of the linear attenuation coefficient aHE\ idu fundamental mode HEn, of the ratio Φ between the coefficient linear attenuation of the TEOi mode and that of the fundamental mode HEn, and the difference Act = urj!El i " aLHEi 1 between the linear attenuation coefficient of the fundamental mode HEn of each MR4-MR8 configuration with that of the reference configuration Ref3. W3; MR4: MRS; MRb MR7 MRS / ] 1.46 ] 1.5 - O.Oîi; 1.5 - 0.0H i.'> - Mil 1.5-0.30 ....... y .......5.77.7............5 0.26 : 04 0.03 Q.stj «XfSU 0.263 i 0.325 dB / tp î 0.390 dB / m 1 0.439 dB / m 0.448 dB / m 0.481 dB / m 23.S: 53 ? 37.5: 31.2 s 3 9 36.0 S i 0.063 08 ] 0.128 68 1 O.i75 d8 0.183 88 0.218 dS ...7...............................1. ..............................L... ........................... ............................... ..............................

[0071] The reference configuration Ref3 corresponds to an initial waveguide comprising six disjointed MT silica capillaries with a wall thickness of et - 100 µm, a core diameter Ds = 2.8 mm, and a core diameter Dc = 4 mm with an outer sheath of refractive index 1. This initial waveguide is suitable for guiding an optimal frequency of 600 GHz. Indeed, through simulations, the inventors determined that an optimum value pq - y of the MT capillary diameter relative to the core diameter increases the attenuation of the TEOi mode by a factor of approximately 40 compared to the attenuation of the Hn mode. This allows for quasi-single-mode waveguide guidance. It is important to note that in the case of a silica waveguide, the variation of the fundamental mode attenuation as a function of the core diameter Dc is relatively small.In the case of a guide composed of 8 capillaries, the diameter of the capillaries has little influence on the attenuation of the HE11 mode, which makes it possible to make waveguides with an A ~ q ratio.

[0072] Figure 4 schematically illustrates a cross-section of the robust waveguide according to the MR4-MR8 configurations. The MR4 configuration corresponds to a robust waveguide according to the invention formed from the initial waveguide of the Ref3 configuration and with an inner silica sheath with an overlap between the inner sheath GI and the tubular patterns MT (corresponding to the rtl ratio, which is 0.25). The MR5 configuration corresponds to a robust waveguide according to the invention formed from the initial waveguide of the Ref3 configuration and with an inner sheath made of a first dielectric material with a refractive index of -1.5 - 0.0l*i and with an overlap between the inner sheath GI and the tubular patterns MT of 0.25. The MR6 configuration is identical to the MR5 configuration, but the overlap between the inner sheath GI and the tubular patterns MT is 0.1. The MR7 configuration is identical to the MR5 configuration, but the overlap between the inner sheath GI and the tubular patterns MT is 0.05. Finally, the MR8 configuration is identical to the MR5 configuration, but the overlap between the inner sheath GI and the tubular patterns MT is 0.01.

[0073] Table 2 illustrates the possibility of adding around the silica capillaries an internal sheath composed of a first absorbing dielectric material (silica or first a dielectric material having a complex refractive index n = 15-0 (0l*i) without significantly altering the attenuation °hea\ of the fundamental mode propagating in the hollow core formed by 6 disjoint capillaries. Indeed, the addition of the inner sheath results in an increase Aa in the attenuation of the fundamental mode HEn of each MR4-MR8 configuration compared to that of the Ref3 configuration less than or equal to 0.218 dB!m. It is noted that the use of a silica inner sheath (MR4 configuration) makes it possible to obtain an increase Aa half as great as the use of an inner sheath in a first dielectric material having a complex refractive index tlgi = 1.5 - 0.01*1 (MR5 configuration).

[0074] Furthermore, Table 2 highlights an optimal value of the e^ / rt overlap of the capillaries with the inner sheath of 0.25 allowing to obtain an attenuation (1he\ i of the fundamental mode of 0.326 dBl m for an inner sheath in silica or of 0.390 dBlm for a first very absorbing dielectric material having a complex refractive index — 1.5 — 0.0 l*i.

[0075] The results in Table 2 are confirmed by Figure 5, which presents two different graphs showing the evolution of the linear attenuation coefficient of the fundamental mode in the hollow core of the Ref3, MR5, and MR5' configurations. The MR5' configuration is a configuration according to the invention identical to the MR5 configuration, except that the first dielectric material of the inner sheath does not exhibit absorption (complex refractive index n — ] 5^

[0076] More specifically, in the lower graph of [Fig. 5], curve C6 represents the evolution of the linear attenuation coefficient of the fundamental mode HEn as a function of the radiation frequency in the Ref3 configuration. Curve C4 represents the evolution of the linear attenuation coefficient of the fundamental mode HEn in the MR5 configuration, and curve C5 represents the evolution of the linear attenuation coefficient of the fundamental mode HEn in the MR5' configuration. Firstly, curves C4 and C5 coincide, which implies that adding an absorption coefficient to the inner cladding has a very small influence on the value of the fundamental mode attenuation coefficient. This result demonstrates the possibility of using absorbing materials for the cladding. Furthermore, adding the absorbing inner cladding eliminates spurious peaks of high attenuation present in the attenuation spectrum of the waveguide without a visible cladding between 0 and 1.45 GHz and 0.55 GHz in curve C6 but not in curves C4 and C5.

[0077] Furthermore, curve C7 of the upper graph in Figure 5 represents the evolution of the ratio ar / a- as a function of the radiation frequency, with ar the linear attenuation coefficient of the fundamental mode HEn in the MR5 configuration and ai the Linear attenuation coefficient of the fundamental mode HEn in the Ref3 configuration. The top graph of [Fig. 5] illustrates that adding the inner cladding results in a small increase, less than a factor of 2 across most of the spectrum, in the linear attenuation coefficient compared to the Ref3 configuration without the inner cladding. For frequencies above 0.8 GHz, a reduction in the linear attenuation coefficient is even observed thanks to the addition of the inner cladding. Similarly, as observed in the bottom graph of [Fig. 5], a reduction in the linear attenuation coefficient is observed at certain frequencies between 0.45 GHz and 0.55 GHz thanks to the addition of the inner cladding, which helps to suppress spurious peaks of high attenuation present in this spectral range.

[0078] The MR4, MR5, and MR5' configurations according to the invention are preferred configurations for guiding radiation at the optimal wavelength corresponding to the 600 GHz frequency in order to efficiently guide over the 560 GHz - 620 GHz range (referenced BTS in Figure 5 below), which corresponds to the emission range of many THz sources. They were developed following numerous simulations and optimizations, particularly regarding the choice of the anti-resonant transmission window and the minimization of the amplitude of spurious peaks related to the capillary wall thickness. The capillary diameter Dt is optimized by calculating the attenuation spectrum of the HE11 mode as a function of the core diameter Dc. These results show that the ratio Dt / Dc = 0.70 provides the best attenuation spectrum (low attenuation and moderately amplitude spurious peaks in the transmission band).

[0079] Furthermore, the core diameter influences the intensity of coupling to the cladding modes. For example, in the preferred MR4, MR5, and MR5' configurations according to the invention, the attenuation spectrum of an initial waveguide composed of a 4 mm diameter core exhibits lower attenuation peaks than for a 3 mm diameter core. Since the peak amplitude is relatively low, at a level acceptable for propagating THz waves, a diameter of 4 mm was chosen as the minimum value. A larger diameter further reduces the peaks and the attenuation coefficient of the HE11 mode. However, this leads to a convergence of the effective indices of the HE11 mode and the higher-order modes, which can make it difficult to excite only the HE11 mode.

[0080] As illustrated in Figure 5 below, the waveguides of the preferred configurations MR4, MR5, MR5' allow the fundamental mode to propagate with a linear attenuation of less than 0.5 dB / m over the considered BTS frequency range. Furthermore, they allow confinement of the HE11 mode with a diameter of 2 mm at half maximum height (in power) and approximately 2.5 mm at 1 / e, at 600 GHz.

[0081] More generally, in order to obtain highly satisfactory waveguide performance with a linear attenuation of less than 0.5 dB / m over the BTS frequency range, the microstructured cladding GS of the robust waveguide is formed of disjoint (or disjoint) tubular patterns having a refractive index nt between 1.4 and 2.5, a thickness between 0.2 and 0.3 times the optimal wavelength, and a diameter Dt between 0.3 and 0.9 times the core diameter, the core diameter being between 6 and 20 times the optimal wavelength (preferably between 8 and 12), the inner cladding being made of silica or a first material having a refractive index ngt with a real part between 1.4 and 2.5 at the optimal wavelength and an egi / rt ratio between the thickness of the inner cladding and a radius of the tubular patterns being preferably between 0.05 and 0.75.

[0082] Thus, the invention consists of adding an internal sheath GI around the hollow core of a THz waveguide with inhibited coupling, without significantly altering the propagation conditions of the fundamental mode in the hollow core. This innovation offers the following advantages: - It ensures mechanical stability and robust mechanical reinforcement of the waveguide - It helps to protect the core of the guide from external contaminants (e.g., dust) - It allows the use of absorbent materials to make the sheath (e.g. glue, supports or guides made by 3D printing, plastic)

[0083] In the illustration of Figures 2 and 4, the MT tubular motifs have a circular cross-section (i.e., circular cylindrical tubes), but it is understood that the invention is not limited to this embodiment. The tubular motifs may, for example, be nested structural motifs, i.e., an interlocking of different concentric tubes with progressively smaller diameters. Alternatively, these tubular motifs may be elliptical tubes, with the major axis of the ellipses oriented radially towards the center of the fiber, or any other shape known to those skilled in the art.

[0084] Figure 6 illustrates an embodiment of the invention in which the robust waveguide is adapted to perform, from a first end E1 of the robust waveguide to a second end E2 of the robust waveguide, a transition from a first transverse intensity distribution II of a guided fundamental mode to a second transverse intensity distribution I2 of the guided fundamental mode. For this purpose, the thickness and diameter of the tubular patterns MT and the thickness egi of the inner sheath are constant longitudinally. Furthermore, the inner sheath is adapted so that a distribution of the tubular patterns in a plane transverse to the waveguide The robust waveguide varies longitudinally so that it allows for the transition of the transverse intensity distribution. Indeed, the position of the tubular patterns in the transverse plane of the waveguide determines the transverse intensity distribution, and the inner cladding determines the position of the tubular patterns in the transverse plane of the waveguide. Thus, the inner cladding allows for a high degree of modularity in the longitudinal distribution of the tubular pattern positions, which enables longitudinal control of the transverse intensity distribution.

[0085] By way of non-limiting example, the waveguide of [Fig. 6] is based on the MR4 configuration according to the invention, modified to allow a transition from a first transverse intensity distribution of Gaussian II in a circular core 4 mm in diameter to a second transverse intensity distribution of substantially elliptical in a rectangular core measuring 5.65 mm x 2 mm (or vice versa). This shape transition results in a slight, but very acceptable, increase in the linear attenuation coefficient from 0.326 dB / m at 0.6 THz.

[0086] This type of robust "transition" waveguide provides an effective solution to problems related to differences in the shape of the THz beam between two structures, such as, for example, injecting a THz beam from a THz horn antenna into a circular beam or into a waveguide with a circular core. Indeed, this rectangular core shape is particularly well suited for coupling a waveguide to a horn antenna of a THz source.

[0087] Figure 7 illustrates an embodiment of the invention in which the robust waveguide is adapted to achieve a variation in the core diameter from a first end E1 of the robust waveguide to a second end E2 of the robust waveguide. This variation is made possible by the inner cladding, which determines the position of the MT tubular patterns in the transverse plane, these patterns determining the core diameter. Thus, by longitudinally varying the position of the MT tubular patterns in the transverse plane of the waveguide while ensuring that the intensity distribution of the fundamental mode remains constant longitudinally, the inner cladding allows a longitudinal variation in the core diameter. To ensure this variation in the core diameter only, it is necessary that the thickness and diameter of the tubular patterns be constant longitudinally.Furthermore, it is preferable that the thickness of the inner sheath be constant longitudinally.

[0088] This type of robust "transition" waveguide makes it possible to provide an effective solution to the problems related to the differences in diameter of the THz beam in free space or confined in a structure, or between two structures, such as for example, the injection of a THz beam propagated in free space into a waveguide whose core is smaller than the diameter of the beam.

[0089] By way of non-limiting example, in the illustration of [Fig. 7], the waveguide of [Fig. 7] is based on the MR5 configuration according to the invention, modified to allow an increase in the core diameter from 4 mm to 9.3 mm without significantly increasing the linear attenuation coefficient of the fundamental HEi b mode

[0090] This result is illustrated in [Fig. 8] where curve C8 plots the evolution of the linear attenuation coefficient of the robust waveguide of [Fig. 7] as a function of the core diameter. For comparison, curve C9 plots the evolution of the linear attenuation coefficient as a function of the core diameter of the initial waveguide of the MR5 configuration (i.e., the robust waveguide of the MR5 configuration without the inner cladding) modified to allow an increase in the core diameter from 4 mm to 9.3 mm.

[0091] [Fig.8] allows us to observe two critical aspects of the embodiment of [Fig.7].

[0092] First of all, on the C8 curve, we note that the reduction of the core diameter from 4 mm to 9.3 mm does not increase the linear attenuation coefficient of the fundamental mode HEI 1 and even reduces it: it goes from a value of less than 0.3 dB / m for a core diameter of 4 mm to a value of less than 0.07 dB / m for a diameter of 9.3 mm.

[0093] Furthermore, by comparing curves C8 and C9, it is observed that the introduction of the inner sheath allows for better confinement of THz waves at the optimal frequency of 600 GHz, given that the linear attenuation coefficient for curve C8 is lower than that of curve C9. This latter result clearly illustrates that, under certain conditions, the inner sheath improves the propagation conditions of THz radiation in the robust waveguide.

[0094] Another object of the invention is a method for manufacturing the robust waveguide 1 according to the invention. This manufacturing method comprises a design step and a material fabrication step of the robust waveguide thus designed.

[0095] The design step includes a first step A of selecting the optimal wavelength to be guided in the robust waveguide. In a step B, the initial waveguide is designed, comprising: - the microstructured GS sheath comprising the MT tubular motifs arranged in a ring around the core C so as to confine radiation at the optimal wavelength within the core - the GE outer sheath surrounding the GS microstructured sheath

[0096] Finally, the design phase includes a final step C for the design of the inner sheath GI intended to be placed between the microstructured sheath and the outer sheath of the initial waveguide designed in step B. Thus, the robust waveguide is conceptually formed in which the tubular patterns are nested within the sheath. internally so as to allow their mechanical retention in the robust waveguide. The design step of the internal cladding GI includes a sub-step of optimizing the index ngi and the thickness eg< of the internal cladding as a function of the core diameter Dc and the optimal wavelength ^op so that the ratio ar! between the linear attenuation coefficient of the robust waveguide and the linear attenuation coefficient of the initial waveguide is less than or equal to 5 (preferably less than or equal to 2) at the optimal wavelength hop.

[0097] Furthermore, preferably, the physical manufacturing step of the manufacturing process of the invention comprises a first substep for manufacturing the inner and outer sheaths. This first substep can be carried out by any method known to those skilled in the art, separately for the inner and outer sheaths or simultaneously for both sheaths. Preferably, it is carried out by an additive manufacturing technique (3D printing) in order to limit costs, the inner sheath being "printed" onto the outer sheath.

[0098] The material manufacturing step includes a second substep for manufacturing the tubular patterns. Here again, this second substep can be carried out by any method known to those skilled in the art. For example, the tubular patterns are manufactured using techniques employed to produce photonic crystal fibers or conventional telecommunication optics, given the similarity in dimensions and materials between the tubular patterns of the waveguides according to the invention and the cores of these conventional optical fibers.

[0099] Finally, the material manufacturing step includes a third substep of assembling the tubular patterns and an assembly formed by the inner and outer sheaths. Preferably, this last substep is carried out by bonding, the inner sheath then being made with an adhesive, for example, a UV adhesive. This embodiment has a clear advantage of ease of implementation.

[0100] The manufacturing process of the invention therefore has the advantage of having a material manufacturing step that can be easily implemented by techniques well known to those skilled in the art.

Claims

Demands

1. A method for manufacturing a robust (1) THz hollow-core waveguide with inhibited coupling, said method comprising a design step and a material fabrication step of the robust waveguide thus designed, said method being characterized in that the design step comprises the following steps: A. Selection of an optimal wavelength ^op to be guided in the robust waveguide B. Design of a so-called initial THz hollow-core waveguide with inhibited coupling comprising: C. a microstructured sheath (GS) comprising a plurality of tubular motifs (MT) arranged in a ring around a core (C) so as to confine at least one radiation at the optimal wavelength λop within said core D. an outer sheath (GE) surrounding the microstructured sheath (GS) E. Design of an inner sheath (IL) in a first dielectric or metallic material and intended to be disposed between the microstructured sheath and the outer sheath of said initial waveguide designed in step B and thus form the robust waveguide in which the tubular patterns are nested in the inner sheath so as to allow their mechanical retention in the robust waveguide, said design step of the inner sheath (IL) comprising a substep of optimization of an index and a thickness of the inner sheath as a function of a core diameter and the optimal wavelength h>p such that a ratio ari between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 and preferably less than or equal to 2 at the optimal wavelength A-op.

2. A manufacturing method according to the preceding claim, wherein the physical manufacturing step comprises: A. A first sub-step in the manufacturing of the inner and outer sheaths, B. a second sub-step of manufacturing the tubular patterns, and C. a third sub-step of assembling the tubular patterns and an assembly formed by the inner sheath and the outer sheath.

3. A manufacturing method according to claim 2, wherein the first manufacturing substep is carried out by additive printing.

4. A manufacturing method according to claim 2 or 3, wherein the inner sheath is made in an adhesive, for example a UV adhesive, the third sub-assembly step then being carried out by gluing the inner sheath with the tubular patterns.

5. Robust (1) THz hollow-core waveguide with inhibited coupling comprising: - a microstructured cladding (GS) comprising a plurality of tubular motifs (MT) arranged in a ring around a core (C) so as to confine at least one radiation at an optimal wavelength λop within said core; - an outer cladding (GE) surrounding the microstructured cladding (GS), a waveguide formed by said outer cladding and said microstructured cladding being called the initial waveguide; - an inner cladding (GI) of a first dielectric or metallic material and disposed between the microstructured cladding (GS) and the outer cladding (GE), the tubular motifs being embedded in the inner cladding so as to permit their mechanical retention within the robust waveguide.a complex index ngi and an inner cladding thickness eg' being optimized as a function of a core diameter Dc and the optimal wavelength h>p such that a ratio ar / between a linear attenuation coefficient of the robust waveguide and a linear attenuation coefficient of the initial waveguide is less than or equal to 5 at and preferably less than or equal to 2 at the optimal wavelength ^op.,

6. Waveguide according to the preceding claim, wherein the inner sheath is a ring having a thickness eg' substantially constant in a plane transverse to the robust waveguide and substantially constant longitudinally.

7. Waveguide according to claim 5, wherein the internal gain is arranged discontinuously longitudinally, for example in a plurality of sections of the same length L separated longitudinally by a distance AL.

8. Waveguide according to any one of claims 5 to 7, wherein a ratio eg;!rt between the thickness of the inner cladding and a radius of the tubular patterns is adapted as a function of the diameter of the core, an absorption coefficient of the material constituting the tubular patterns (MT) and the guiding wavelength so that the ratio arl ai is less than or equal to 5 and preferably less than or equal to 2 at the optimal wavelength ^op.

9. Waveguide according to the preceding claim, wherein the egi / rt ratio is between 1 and 2 and preferably between 0.05 and 0.

95.

10. Waveguide according to any one of claims 5 to 9, wherein a real part of the ngi index of the inner cladding is between 1.4 and 3, preferably between 1.4 and 2 at the optimal wavelength.

11. Waveguide according to any one of claims 5 to 10, wherein an imaginary part of the index ngî of the inner sheath is between 0.0001 and 0.

015.

12. Waveguide according to any one of claims 5 to 11, wherein a ratio e^ / rt between the thickness of the inner sheath and a radius of the tubular patterns are adapted to permit a reduction of the peaks of strong attenuations of a transmission spectrum of said robust waveguide.

13. Waveguide according to any one of claims 6 to 12, wherein the first dielectric material is silica, glue or plastic.

14. Waveguide according to any one of claims 6 to 13, wherein the microstructured cladding is formed of tubular patterns having a refractive index nt of between 1.4 and 2.5, a thickness of between 0.2 and 0.3 times the optimal wavelength, and a diameter Dt of between 0.3 and 0.9 times the core diameter, the core diameter being between 6 and 20 times the length optimal wavelength (preferably between 8 and 12), the inner sheath being made of silica or in a first material having a refractive index ngi with a real part between 1.4 and 2.5 at the optimal wavelength and a ratio e^lrt between the thickness of the inner sheath and a radius of the tubular motifs being preferably between 0.05 and 0.

75.

15. Waveguide according to any one of claims 6 to 14, wherein a thickness and diameter of the tubular patterns are constant longitudinally and wherein the inner sheath is adapted so that a distribution of the tubular patterns in a plane transverse to the robust waveguide varies longitudinally so that the robust waveguide allows, from a first end of the robust waveguide to a second end of the robust waveguide, a transition from a first intensity distribution of a guided fundamental mode to a second intensity distribution of the guided fundamental mode.

16. Waveguide according to any one of claims 6 to 14, wherein a thickness and diameter of the tubular patterns are constant longitudinally and wherein the inner sheath is adapted so that a distribution of the tubular patterns in a plane transverse to the robust waveguide varies longitudinally so that the diameter of the core of the waveguide varies longitudinally and so that a cross-section of a fundamental mode undergoes a longitudinal homothety.

17. Waveguide according to any one of claims 6 to 16, wherein the thickness egi is greater than or equal to 0.01 x with r' a radius of the tubular patterns.

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