WO2010127676A1

WO2010127676A1 - Hollow-core optical fiber incorporating a metamaterial cladding

Info

Publication number: WO2010127676A1
Application number: PCT/DK2010/050099
Authority: WO
Inventors: Niels Asger Mortensen; Min Yan
Original assignee: Danmarks Tekniske Universitet - Dtu
Priority date: 2009-05-05
Filing date: 2010-05-05
Publication date: 2010-11-11

Abstract

An optical fiber (100, 200, 300) for guidance of electromagnetic radiation with an operational wavelength l, the fiber (100, 200, 300) having a longitudinal direction along a longitudinal axis and a transverse direction in a plane perpendicular to the longitudinal axis, the fiber (100, 200, 300) comprising: - a core region comprising a hollow core (101, 201, 301, 401, 501, 601, 801) extending along the longitudinal axis, and - a cladding (102, 202, 302, 402, 502, 602, 802) comprising a first cladding region (220, 320, 420, 520, 620, 820) surrounding the core (101, 201, 301, 401, 501, 601, 801) region and comprising a dielectric background material (222, 322, 422, 522, 622, 822), the first cladding region (220, 320, 420, 520, 620, 820) having a total cross-sectional cladding area, the first cladding region (220, 320, 420, 520, 620, 820) further comprising a number of longitudinally extending cladding elements located in the background material (222, 322, 422, 522, 622, 822) and having a total cross-sectional element area, wherein the first cladding region (220, 320, 420, 520, 620, 820) has a filling fraction f being defined as the ratio between the element area and the cladding area wherein - the cladding elements (221, 321, 421, 521, 621, 821) are made of metal and are oriented substantially parallel to the core (101, 201, 301, 401, 501, 601, 801) region in a transverse distance from the core (101, 201, 301, 401, 501, 601, 801), and wherein the distance L between neighbouring cladding elements (221, 321, 421, 521, 621, 821) is smaller than half the wavelength l, and wherein the cladding elements (221, 321, 421, 521, 621, 821) are arranged so that transverse magnetic radiation with a wavelength of l can propagate through the core (101, 201, 301, 401, 501, 601, 801) region. The invention further relates to a method relating to and the use of the inventive fiber.

Description

Title: Hollow-core optical fiber incorporating a metamaterial cladding

Technical Field

The present invention relates to an optical fiber for guidance of electromagnetic radiation with an operational wavelength λ, the fiber having a longitudinal direction along a longitudinal axis and a transverse direction in a plane perpendicular to the longitudinal axis, the fiber comprising: a core region comprising a hollow core extending along the longitudinal axis, and a cladding comprising a first cladding region surrounding the core region and comprising a dielectric background material, the first cladding region having a total cross-sectional cladding area, the first cladding region further comprising a number of longitudinally extending cladding elements located in the background material and having a total cross-sectional element area, wherein the first cladding region has a filling fraction f being defined as the ratio between the element area and the cladding area. Furthermore, the present invention relates to the use and a method for the use of the inventive fiber.

Background

Conventional fibers, e.g. as used for telecommunication, rely on the principle of total internal reflection (TIR) to guide light along the core of a fiber. TIR requires that the refractive index of the core is higher than the refractive index of the cladding. This generally prevents TIR-guiding in an air core, since the refractive index of air being unity is lower than any other bulk material. However, if the fiber is to be operated at a wave- length close to an absorption peak, e.g. caused by molecular vibration resonances, in the cladding material, a real part of the refractive index smaller than unity may be achieved, since the material absorpsion may be described as a finite imaginary part of the refractive index. In that way, the physical requirement of the absolute value of the refractive index being larger than unity may be fulfilled, while the real part may be smaller than one. Fibers relying on this principle, known as attenuated total internal reflection (ATR) are well known in the art. However, such fibers are inherently lossy.

It is also known in the art to achieve guidance of visible or infra-red light in a hollow core by the so-called photonic bandgap effect. This effect relies on a highly periodic structure in the cladding of a fiber to provide destructive interference for light attempting to escape from the core out through the cladding, thus reflecting the light back into the core of the fiber. The highly periodic cladding structure needed to achieve low loss guidance by the photonic bandgap effect makes such structures difficult and time consuming to fabricate.

Efficient transmission of transverse-electric (TE) radiation, i.e. radiation having only magnetic field components in the propagation direction, may be achieved in a hollow metallic fiber (HMF). However, such fibers have high losses for transverse-magnetic (TM) radiation, i.e. radiation having only electric field components in the propagation direction.

Disclosure of the Invention

It is an object of the present invention to obtain new optical fiber, which overcomes or ameliorates at least one of the disadvantages of the prior art or which provides a useful alternative.

According to the invention, the object is achieved by ensuring that the cladding elements are made of metal and are oriented substantially parallel to the core region in a transverse distance from the core, and wherein the distance Λ between neighbouring cladding elements is smaller than half the wavelength λ, and wherein the cladding elements are arranged so that transverse magnetic radiation with a wavelength of λ can propagate through the core region. This configuration of a hollow core and a cladding with metallic cladding elements provides a fiber with improved loss performance, especially for the transmission of transverse magnetic (TM) radiation. The arrangement of a number of metallic cladding elements, which extend in the propagation direction of the radiation, in a dielectric background material provides a metamaterial with special optical properties. When both the spacing between cladding elements and the element size are much smaller than the wavelength, the metamaterial may be treated as a homogenized medium with an effective permittivity tensor of the form ε = diag\ε_x , ε_y , ε_z ) , where the subscripts x and y characterize directions in the transverse plane, and z is the fiber axial direction. In the special case of uniformly distributed cladding elements this may be further simplified, since ε_x = ε_y ≡ ε_t . In the transverse plane, the permitivity is positive, but due to the unrestricted electron motion in the longitudinal z-direction, ε is negative. If, at the same time the transverse component of the effective permeability, μ_t , is larger than or equal to unity, the cladding metamaterial will reflect incident transverse magnetic radiation propagating along the z-direction. Since most natural materials are impermeable, i.e. μ_t = l , this requirement is typically trivially fulfilled.

The fiber length is here to be understood as being the length of a fiber in use, not necessarily the full production spool. The fiber may be closed with e.g. a window in one or both ends for termination, without falling outside the scope of the invention. As the fiber may be flexible and thus may bend or twist, the core and cladding elements are typi- cally not kept straight over the full length of the fiber. Thus, by longitudinal direction it is not meant that the fiber is necessarily oriented in one direction but is used to define the substantial direction of propagation of radiation in the fiber. What determines the optical properties is that the fiber is kept straight over lengths on the scale of the wavelength, i.e. that changes are adiabatic.

Definitions: Electromagnetic radiation is here to be understood as comprising vacuum wavelengths in the range from 10nm to 1000μm, e.g. covering the ultra-violet, visible, infra-red, and terahertz range. Throughout this text, the term "wavelength" is to be understood as the vacuum wavelength of radiation with a given frequency.

In a particular embodiment of the invention, the distance between neighbouring cladding elements relative to the wavelength is in the range of 0.05-0.5, or 0.1 -0.4, or even 0.2-0.3.

In a particular embodiment of the invention, designed for guiding light with a wavelength of substantially 10.6μm, the distance between neighbouring cladding elements is in the range of 1 -5μm, or 2-4μm, or even 3 μm.

In a specific embodiment, the cladding elements are arranged so that TM radiation can propagate along the core region with a loss of less than 10 dB/m, or less than 5 dB/m, or even less than 1 dB/m.

In an embodiment of the invention, the fiber comprises at least a second cladding region, wherein the second cladding region comprises a number of second cladding ele- ments, wherein the second cladding elements are made of another metal than the cladding elements.

In another embodiment, the fiber comprises at least a second cladding region, wherein the second cladding region comprises a number of second cladding elements, and wherein the filling fraction of the second cladding region is larger or smaller than the filling fraction of the first cladding region.

In another embodiment, the fiber comprises at least a second cladding region, wherein the second cladding region comprises a number of second cladding elements, wherein the distance between neighbouring second cladding elements A₂ is larger or smaller than the corresponding distance A₁ in the first cladding region.

In an embodiment of the invention, the hollow core has a transverse dimension, such as a diameter, and wherein the transverse dimension relative to the wavelength is lar- ger than 3, or larger than 5, or in the range 10-100. As propagation losses for a circular core scale inversely with the cube of core radius, the proposed values represent suitable compromises between the quality of the beam exiting the fiber, and the propagation loss.

In a specific embodiment of the invention, the hollow core has a transverse dimension, such as a diameter, in the range of 100μm-2mm, or 200μm-1 mm, or even 300μm- 800μm. These values for the core size are especially suitable for fibers designed for a wavelength of around 10.6μm, corresponding to the radiation from a CO₂ laser.

In an embodiment of the invention, the dielectric background material in the first cladding region further comprises a number of longitudinal airholes, which are elongated in the longitudinal direction of the fiber. Such airholes will act to further fine tune the material tensor components of the final homogenized metamaterial. However, the signs of the tensor components usually remain unchanged.

In an embodiment of the invention, the cladding comprises an outer cladding region, the outer cladding region comprising at least a first solid material, and wherein the outer cladding region is a metallic layer arranged outside the first cladding region. Such an arrangement combines the good guiding properties for TM modes provided by the cladding elements, with the good guiding properties for TE modes provided by a metal-coated hollow waveguide. Therefore, the fiber according to this embodiment will guide both pure TE and TM modes with low loss. Furthermore, this fiber will also guide mixed polarization or hybrid modes, such as the MP₁₁ mode (also traditionally known as HE₁₁ mode) with low loss.

In an alternative embodiment, the fiber comprises a layer of the dielectric background material outside the first cladding region for providing a mechanical strength to the fiber. However, other choices of outer cladding materials are also possible.

In an embodiment, the outer cladding region may comprise a second solid material, such as a polymeric coating.

In a specific embodiment, the polymeric coating may be chosen to be an Acrylate coating.

In a further embodiment, the third solid material may be a soft inner coating provided between the dielectric fiber background material and a hard outer coating. Evidently to the skilled person, the fiber may comprise a third, a fourth, a fifth, or even more solid materials.

In an embodiment of the invention, the cladding elements are arranged along one or more concentric circles. This arrangement of cladding elements allows for convenient fabrication of a circular hollow core void.

In a specific embodiment of the invention, the first cladding region comprises a single circle of cladding elements. Even just one circle of cladding elements has surprisingly been found to provide good guidance of TM radiation, especially in embodiments including a metallic outer cladding region.

Alternatively, the fiber may comprise multiple circles of cladding elements, such as two, three, four, five or even more.

In another embodiment of the invention, the cladding elements are arranged in a triangular structure. Arrangement of the cladding elements in a triangular structure is especially convenient when a fiber preform is stacked from a large number of preform ele- ments, e.g. in what is known in the art as the stack-and-draw process. This is due to the fact that the triangular structure is the naturally occuring close-packed structure, and thus a stable geometry.

In an embodiment of the invention, the cladding elements are regularly spaced.

In an embodiment of the invention, the cladding elements are arranged in a random or irregular structure. The fact that the guiding effect does not rely on strict periodicity opens up for using less regular or random structures which may be realised with more ease. In addition, undesired cladding resonances in a regular structure may be suppressed in the presence randomness and irregular arrangements of the metal cladding elements. Such resonances may otherwise give rise to spikes in the transmission and loss spectrum of the fiber. By suppressing these cladding resonances, such spikes are suppressed or avoided, albeit potentially at the cost of a higher overall loss throughout the spectrum.

In an embodiment of the invention, the cladding elements have a substantially circular cross-section. Substantially circular cladding elements are particularly convenient from a production view, since this shape minimizes the interface area between the cladding element and the background dielectric. Furthermore, any sharp edges on the elements could possibly act to initiate formation of cracks in the dielectric, thus leading to re- duced structural stability of the fiber.

In an embodiment of the invention, the cross-sectional dimensions, such as a diameter, of the cladding elements are substantially identical.

In an embodiment of the invention, the cross-sectional dimensions of the cladding elements are in the range of 0.2-5μm, or 0.5-3μm, or even 0.8-2μm.

In another embodiment of the invention, the relative cross-sectional dimensions of the cladding elements to the wavelength are in the range of 0.02-0.5, or 0.05-0.3, or even 0.7-0.2.

In an embodiment of the invention, the fill fraction is in the range of 0.05-0.8, or 0.08- 0.5, or even 0.1 -0.3. Depending on the chosen transverse spacing between the cladding elements, these ranges of the fill fraction results in the lowest loss values.

In an embodiment of the invention, the cladding elements comprises a material chosen from the group of noble metals, i.e. silver, gold, or copper. Noble metals are advantageous for use in the cladding elements as their dielectric function support a large negative real part while the negative imaginary part is not too high.

In an alternative embodiment, the cladding elements comprise a metallic alloy with dielectric properties comparable to those of the noble metals.

In an embodiment of the invention, the dielectric background of the first cladding region comprises a material chosen from the group of: Zinc Selenide (ZnSe), Arsenic Selenide (As₂Se₃), or any other suitable dielectric that is transparent at the operational wavelength. The dielectric background material must be chosen to be compatible with metal of choice for the fabrication method, e.g. softening temperature, viscosity, thermal expansion coefficient, etc, for fiber drawing technique.

The objective is further achieved by a method of transmitting electromagnetic radiation through a fiber according to any of the preceding embodiments, the electromagnetic radiation having a wavelength λ in the range of 1.8-1000 micrometers, or 100-1000 micrometers, or 1 .8-100 micrometers, i.e. in the near infrared, the middle infrared, the far- infrared, or the terahertz range.

The objective is further achieved by the use of a fiber according to any of the above- mentioned embodiments for transmission of light with a wavelength λ in the range of 10.4-10.8 micrometers, or 10.5-10.7 micrometers, or even substantially 10.6 micrometers. Thus, the fiber is used guidance of light from, e.g. CO₂ lasers. Low loss guidance of light from CO₂ lasers with a wavelength of 10.6 μm is challenging due to the few materials available that are transparent at such long wavelengths. Therefore, the inventive fiber may provide a suitable alternative to the fibers already available.

Brief Description of the Drawings

The invention is explained in detail below with reference to an embodiment shown in the drawings, in which

Fig. 1 shows an optical fiber according to the prior art,

Fig. 2 illustrates a fiber according to an embodiment of the invention, Fig. 3 illustrates a fiber according to a second embodiment of the invention,

Fig. 4 illustrates a detail of a fiber according to a third embodiment the invention,

Fig. 5 illustrates a detail of a fiber according to a fourth embodiment of the invention,

Fig. 6 illustrates a detail of a fiber according to a fifth embodiment of the invention,

Fig. 7 shows losses and effective indices as functions of filling fraction calculated for fibers according to embodiments of the invention,

Fig. 8 illustrates a guided mode in a fiber according to an embodiment of the invention,

Fig. 9 shows calculated losses as functions of filling fraction for fibers according to embodiments of the invention, and

Fig. 10 shows calculated losses as functions of core diameters for fibers according to embodiments of the invention.

Detailed description of the Invention

Illustrated in Fig. 1 is a conventional optical fiber 100 as known in the art. The fiber comprises a core 101 and a cladding 102. Light is guided along the core 101 of the fi- ber 100 by total internal reflection. This requires that the refractive index of the material in the core 101 is larger than the refractive index of the material in the cladding 102. Thus guiding of light in an air core may not be achieved in this type of fiber.

Fig. 2 shows an embodiment of the inventive fiber 200. Analogously to the conventional fiber 100 shown in Fig. 1 , the inventive fiber 200 comprises a hollow core 201 and a cladding 202. The hollow core 201 extends substantially throughout the length of the fiber 200. However, for practical purposes, the fiber 200 may be terminated with e.g. a solid window to seal the hollow core from the environment. Surrounding core 201 is the first cladding region 220, in which metallic cladding elements 221 are located in a di- electric background material 222. The cladding 202 may further comprise an outer cladding region (not shown), for adding mechanical strength or otherwise improve han- dling of the fiber 200. The outer cladding region may be made of the dielectric background material or of another material, such as a polymeric coating. In the embodiment shown in Fig. 2, the cladding elements 221 are arranged with a fixed pitch Λ along five concentric rings. Other arrangements of the cladding elements will be discussed below. If both the pitch and the transverse dimensions of the cladding elements are significantly smaller than the wavelength of the light to be propagated through the fiber, the first cladding region may be considered as consisting of a metamaterial. This metama- terial may for the present geometry be approximated by a square unit-cell of edge dimensions of the pitch Λ. For such a unit-cell, the maximum filling fraction, before the cladding elements start to collide is approximately 0.785. Here the filling fraction is defined as the ratio of the cross-sectional area of the cladding elements 221 to the total cross-sectional area of the first cladding region 220.

That the structure shown in Fig. 2 will guide transverse magnetic radiation, with field components of E_r, H_θ, and E_z, may concluded from the following derivation. Assuming that the material parameters of the cladding have the tensor form as

Note that any tensor component can be a negative value. To simplify the analysis, it is assumed that ε_r = ε_θ ≡ ε_t and μ_r = μ_θ ≡ μ_t . The harmonic dependence is taken as exp(- jGX + βz) . Due to cylindrical symmetry, field within the medium is completely characterized by two similar wave equations, one for H₂ and the other for Ez. The H₂ wave equation is c⁾²H- 1 c⁾²H 1 0H μ ₂

Or^{2 '} r² Oθ² 7 dr μ_t where ^T ^~" h)t't^εt ^ . By variable separation ^■"^■- — Φ(r )θ(6')_j ^_{6 wave e}q_ua. tion can be decomposed into two equations. One of them gives rise to angular dependence of the field as ^exf^} v ^ιn"), where m is an integer. The radial dependence of the field is governed by

0

This equation is a Bessel or modified Bessel differential equation, depending on the sign of ft ^f . For electromagnetic radiation confinement in a hollow core, it is neces- ri ^ 1.2 sary for the field to be evanescent in the cladding while ^ ^ ^ho (as the wave should be propagating in the core). Subsequently, if is found that this condition can be fulfilled when

^(k*ε_ιμι - 3²) < 0 βt and the corresponding radial eigen-field in the cladding can be written generally in Bessel functions as

/ . / 11 z. 7 .2 where V f^{t t} . Similar analysis can be carried out for the E, wave equation.

And the resulted condition for E₂ confinement is

^ (k*μ_ts_t - Ϊ²) < O.

The general radial wave solution is the same as the above-stated except with μ changed to ε. Other field components can be written as a function of E, and H,. There- fore once the conditions for the H_z and E_z specified by last and third last equations are fulfilled, confinement of the overall mode is ensured. One such set of solutions for the

TM polarized wave is

Zz < 0, μ_t > I ₁ which is fulfilled by the proposed fiber. However, the fiber as shown in Fig. 2 does not support neither TE polarized waves nor waves with mixed polarization, such as MP or

HE modes.

In Fig. 3 is shown a fiber according to another embodiment of the invention, corresponding to the fiber shown in Fig. 2, where like reference numerals refer to like parts. Therefore, only the differences between the two embodiments are discussed here. In this embodiment, the outer cladding region 323 comprises a metal layer 330. This metal layer acts as a hollow metallic waveguide for TE polarized radiation. Thus, this embodiment combines a first cladding region comprising the metamaterial for guiding TM radiation, and a metallic outercladding for guiding TE radiation. In the shown em- bodiment, the first cladding region comprises cladding elements arranged along just one ring around the core. However, multiple rings of cladding elements may be used, or indeed any other suitable arrangement of the cladding elements. Since the inner cladding is transparent to TE waves, it may give rise to constructive wave resonance in the layer. In turn, such resonances may amplify the loss caused by metal-wire absorption, and should therefore be avoided. This resonance condition is fulfilled when the metamaterial thickness is equal to multiples of half the transverse wavelength for TE light in the medium.

Fig. 4 shows details of an embodiment of the first cladding region 420 according to the invention. The fiber shown in a partial view in Fig. 4 corresponds to the fiber 200 shown in Fig. 2, where like reference numerals refer to like parts. Therefore, only the differ- ences between the two embodiments are discussed here. The first cladding region 420 comprises airholes 440, in addition to the cladding elements 421. Various arrangements of the airholes 440 are concievable and the arrangement shown here is merely to be understood as illustrative and not limiting for the invention. The cladding elements 421 are here shown as arranged along concentric rings, but airholes 440 may be in- eluded in the first or any other cladding region comprising cladding elements 421 arranged in any other geometry as described throughout this document. The airholes 440 being much smaller than the wavelength of the propagating radiation, will effectively modify the optical properties of the background material 422, thus creating an effective medium. This effective medium will have a lower index of refraction than the bulk mate- rial 422.

Fig. 5 illustrates another embodiment of the first cladding region 520. The fiber shown in a partial view in Fig. 5 corresponds to the fiber 200 shown in Fig. 2, where like reference numerals refer to like parts. Therefore, only the differences between the two em- bodiments are discussed here. According to this embodiment, the cladding elements 521 are arranged in a triangular structure or lattice, i.e. that three neighbouring elements 521 are placed in the corners of an equilateral triangle with a side length equal to the pitch Λ. Illustrated in the figure is the simple unit cell 525, from which the full structure of the first cladding region may be constructed. For instance, the filling frac- tion may conveniently be calculated from the unit cell 525.

Fig. 6 illustrates another embodiment of the first cladding region 620. The fiber shown in a partial view in Fig. 6 corresponds to the fiber 200 shown in Fig. 2, where like reference numerals refer to like parts. Therefore, only the differences between the two em- bodiments are discussed here. According to this embodiment, the cladding elements 621 are irregularly arranged in the background material 622. Furthermore, the actual cladding elements 621 as shown here are of varying sizes and shapes. However, substantially identical cladding elements may also be irregularly arranged.

Example 1 : In this example, the properties of a fiber designed for propagation of light with a wavelength of 10.6μm, corresponding to the light from a CO₂ laser, are studied. This wavelength is important especially due to the fact that high-power CCh laser beam can be used for material processing and various medical surgeries. The fiber geometry is as shown in Fig. 2, i.e. a circular hollow core, surrounded by cladding elements arranged in five concentric rings. In the calculations, the cladding only consists of the first cladding region, outside which there is air. The core diameter is 700μm. For the cladding elements the use of silver wires with ε = 2951 + 1654/, imbedded in a host dielectric with a refractive index of 2.5 corresponding to ε = 6.25 is consider. Several transparent materials at this wavelength have an index around this value, such as Zinc selenide (ZnSe) and arsenic selenide (As₂Se₃).

Fig. 7 illustrates calculated losses and effective mode indices as function of the filling fraction for example 1 , where the cladding element spacing Λ is varied. When the size of metal wires is close to the skin depth of the metal (tens of nanometers), Maxwell- Garnett theory (MGT) is valid for deriving the effective permittivity tensor of the homogenized metamaterial

where/d and /_m represents filling ratios of the dielectric and metallic materials (f_d +f_m = 1), respectively; ε_d and ε_m are the permittivity values of the element dielectric and metal- lie materials, respectively. As shown by the above equations, the effective permittivity components are solely determined by/_m. With a homogenized material tensor in MGT limit, the loss and effective mode index (n_eff ) values of the guided TM_Oi mode are derived as /_m varies from ~0 (completely dielectric) to 1 (completely metal). The results are shown in the figure. It is seen from Fig. 7a that, as/_m decreases, the loss value ini- tially remains close to that for the metal-clad fiber, and it drops sharply when /_m becomes less than 0.2. Therefore it is possible for the metamaterial cladding to perform better than a full-metal cladding for confining the TM mode. In practice the limit where MGT is valid is rather difficult to achieve in practical fibers. Therefore, realistic fiber structures are numerically simulated by taking all mesoscopic geometrical features into account. A finite element method (FEM) has been employed for this purpose. Simulations for a number of realistic structures are summarized in Fig. 7, where the loss and n_eff values of the TM_Oi mode are shown as a function of f_m when Λ takes values of 0.125, 0.25, 0.5, 1 , 2, and 4 μm. Notice that FEM simulations for all curves corresponding to realistic microstructured fibers start from f_m = 0.02 and stop at f_m = 0.74. Further beyond that filling fraction, the values (dotted portions of the curves) are extrapolated according to simulated data. It is observed that, when Λ gets larger, the loss curve shifts away from the limiting MGT curve, downwards to smaller values. This is further evidence that the metal-wire based metamaterial makes a superior reflector for TM light compared to plain metal. However, it is noticed that the downward shift in loss curve is not without limit. In particular, when Λ increases to a certain value (after 2 μm in this case), the spacings between two neighboring layers of metal wires become large enough to support resonant modes. These resonances experience relatively high loss due to their proximity to metal wires. The coupling from the TM_Oi core mode to these cladding resonances will result in higher loss to the TM_Oi mode, which is manifested by the loss spikes observed in Fig. 7a. These resonances will become especially severe for a large Λ value. From the figure, it is concluded that one should take a compromise between the propagation loss and the number of cladding resonances in choosing the right Λ (and thereafter the cladding element size, calculated from the desired filling fraction). When Λ = 0.125μm, the metamaterial cladding is as thin as 0.625μm (16 times smaller than 10.6μm). Quite remarkably, such a metamaterial cladding, though very thin, confines TM light exceptionally well.

In Fig. 8, contours of the axial component of the Poyntings vector 880 is shown for the guided TM_Oi mode, corresponding to the power density of the mode. The fiber is simulated for light with a wavelength of 10.6μm, and has a 700μm core diameter, Λ=2μm, and a filling fraction of 0.2. It is noticed from Fig. 8a that the overall mode field is well guided in the core 801 by the metamaterial in the first cladding region 820 of the cladding 802. Shown in the plot with arrows is the transverse electric field 881. The zoom-in plot in Fig. 8b reveals detailed field interaction with the metal-wire medium, in the area indicated on the right side of Fig. 8a. Note that the contours shown in Fig. 8a and 8b do not correspond to the same values. Surface plasmon polariton is partially excited at metal wires adjacent to the interface. However, the field rapidly decays into the clad- ding 802. The plot also quantitatively indicates that a couple of metal cladding element layers would be sufficient to prevent leakage of TM light. In other words, the effective skin depth of the metamaterial cladding for TM light is very small compared to the corresponding bulk metal. The above fiber, though supporting TM modes, does not con- fine TE modes (and also not mixed-polarization or MP modes).

Example 2:

To provide a fiber which supports both TM and TE modes, and thus also MP modes, a fiber with the structure shown in Fig. 3 is studied. Based on the results in Example 1 , the focus is here on a particular metal-wire spacing Λ = 2 μm. First the effect of the metamaterial cladding thickness is investigated by studying two hybrid-clad fibres: one has a metamaterial thickness of 2μm (one layer of metal wires); the other has a metamaterial thickness of 4μm (two layers of metal wires).

Fig. 9 shows the calculated loss values for the TE_Oi and TM_Oi modes guided by the two fibres, expressed again as functions of f_m. Superposed is the loss curve of the TM_Oi mode guided by a fibre with pure metamaterial cladding [i.e. the curve marked with "Λ = 2μm" in Fig. 9]. According to Fig. 9, at a relatively large f_m value the TM_Oi mode loss is hardly affected as compared to the value for the metamaterial-clad fibre, which is true even when the hybrid fibre has only one layer of metal wires. At small f_m, a thin metamaterial cladding layer even helps to reduce the cladding resonance, and therefore to reduce the loss of the TM_Oi mode. It turns out that the lowest loss for the TM_Oi mode is achieved by the hybrid fibre with only one layer of metal wires. In the limit of f_m = 1.0, both hybrid fibres degenerate into a HMF, whose TM_Oi and TE_Oi modes have loss values as indicated by the black and open stars, respectively, in Fig. 9. Clearly it is seen that in such a conventional HMF, the TM mode suffers over 1000 times higher loss as compared to the TE mode. This is the key factor that restricts the usage of such conventional fibre at this operating wavelength. By adding a metamaterial layer as an inner cladding, the TE_Oi mode is found to have a slightly higher loss as compared to that in a HMF of the same core size. However, the loss value of the TE_Oi mode is still below 0.1 dB/m, which is well acceptable for a wide range of applications. No cladding resonances have been found in this particular case which deteriorates the TE propagation. However, as stated above, since the inner cladding is transparent to TE wave, it can give rise to constructive wave resonance in the layer. In turn, resonances can am- plify the loss caused by metal-wire absorption. This resonance condition is fulfilled when the metamaterial thickness is equal to multiple of half transverse-wavelength for TE light in the medium, which is confirmed numerically (not shown here).

In Fig. 10, it is shown how loss values of the TE_Oi and TM_Oi modes guided in a hybrid clad fibre vary with respect to the fibre core size, such as a radius. As the core radius R increases, the losses decrease roughly as 1/R³. Such loss dependence on R is also found for other types of hollow core waveguides, including HMF and the OmniGuide™. For comparison, the loss values of the same two modes guided in a HMF are also shown. By comparison, it is seen that propagation loss for the TM mode is greatly reduced (by more than 100 times when core diameter is moderately large) with the novel hybrid-clad design, whereas the loss for TE mode experiences only a slight increase. MP modes have both TE and TM field components and the two sets of field components are not independent. Through numerous simulations, it has been found that a MP mode with a low azimuthal order number in general has a propagation loss in between that of the TE_Oi and TM_Oi modes. In addition, the loss of a low-order MP mode is somewhat close to that for the TE_Oi mode. For example, for a fibre with a 700 μm core diameter, the MP₁₁ (traditionally known as HE₁₁ mode) has a loss of 0.1 1 dB/m, and the MP₂₁ mode has a loss of 0.28 dB/m. From Fig. 10, the losses for TE₀₁ and TM₀₁ modes are respectively 0.07dB/m and 0.52dB/m. It is worth mentioning that the MP₁₁ mode in a HMF with the same core size experiences a loss of 49dB/m. In practical applications, MP₁₁ mode is of particular importance. Light output from lasers are usually linearly polarized and with a Gaussian beam profile. Such a laser beam matches excellently with the MP₁₁ mode. Therefore the loss value of the MP₁₁ mode almost determines the overall propagation loss of such a fibre.

The examples have been described according to preferred embodiments of the invention. However, the invention is not limited to these embodiments. For example, the cladding elements may have many other cross-sectional shapes, such as elliptical, triangular, square, rectangular, or even be irregular. Furthermore, the shape may vary between cladding elements. Reference list:

Λ cladding element spacing d cladding element dimension

100,200,300,800 fiber 101,201,301,401,501,601,801 core

102, 202, 302, 402, 502, 602, 802 cladding

220, 320, 420, 520, 620, 820 first cladding region

221 , 321 , 421 , 521 , 621 , 821 cladding element

222, 322, 422, 522, 622, 822 background material 323 outer cladding region

225, 525 (approximate) unit cell

330 metal layer

440 airhole

880 axial Poynting vector component 881 transverse electric field

Claims

1. An optical fiber (100, 200, 300) for guidance of electromagnetic radiation with an operational wavelength λ, the fiber (100, 200, 300) having a longitudinal direction along a longitudinal axis and a transverse direction in a plane perpendicular to the longitudinal axis, the fiber (100, 200, 300) comprising:

- a core region comprising a hollow core (101 , 201 , 301 , 401 , 501 , 601 , 801 ) extending along the longitudinal axis, and

- a cladding (102, 202, 302, 402, 502, 602, 802) comprising a first cladding re- gion (220, 320, 420, 520, 620, 820) surrounding the core (101 , 201 , 301 , 401 , 501 ,

601 , 801 ) region and comprising a dielectric background material (222, 322, 422, 522, 622, 822), the first cladding region (220, 320, 420, 520, 620, 820) having a total cross- sectional cladding area, the first cladding region (220, 320, 420, 520, 620, 820) further comprising a number of longitudinally extending cladding elements located in the back- ground material (222, 322, 422, 522, 622, 822) and having a total cross-sectional element area, wherein the first cladding region (220, 320, 420, 520, 620, 820) has a filling fraction f being defined as the ratio between the element area and the cladding area characterised in that

- the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are made of metal and are oriented substantially parallel to the core (101 , 201 , 301 , 401 , 501 , 601 , 801 ) region in a transverse distance from the core (101 , 201 , 301 , 401 , 501 , 601 , 801 ), and wherein the distance Λ between neighbouring cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) is smaller than half the wavelength λ, and wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are arranged so that transverse magnetic radiation with a wave- length of λ can be confined and propagate along the core (101 , 201 , 301 , 401 , 501 , 601 , 801 ) region.

2. A fiber (100, 200, 300) according to claim 1 , wherein the hollow core (101 , 201 , 301 , 401 , 501 , 601 , 801 ) has a transverse dimension, such as a diameter, and wherein the transverse dimension relative to the wavelength is larger than 3, or larger than 5, or in the range 10-100.

3. A fiber (100, 200, 300) according to any of the preceding claims, wherein the dielectric background material (222, 322, 422, 522, 622, 822) in the first cladding region (220, 320, 420, 520, 620, 820) further comprises a number of longitudinal airholes (440), which are elongated in the longitudinal direction of the fiber (100, 200, 300).

4. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cladding (102, 202, 302, 402, 502, 602, 802) comprises an outer cladding region (223, 323), the outer cladding region (223, 323) comprising at least a first solid material, and wherein the outer cladding region (223, 323) is a metal layer (330) arranged outside the first cladding region (220, 320, 420, 520, 620, 820).

5. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are arranged along one or more con- centric circles.

6. A fiber (100, 200, 300) according to any of the claims 1 -4, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are arranged in a triangular structure.

7. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are regularly spaced.

8. A fiber (100, 200, 300) according to any of the claims 1 -4, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are arranged in a random or irregular struc- ture.

9. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) have a substantially circular cross- section.

10. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cross-sectional dimensions, such as a diameter, of the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) are substantially identical.

1 1 . A fiber (100, 200, 300) according to any of the preceding claims, wherein the fill fraction is in the range of 0.05-0.8, or 0.08-0.5, or even 0.1 -0.3.

12. A fiber (100, 200, 300) according to any of the preceding claims, wherein the cladding elements (221 , 321 , 421 , 521 , 621 , 821 ) comprises a material chosen from the group of noble metals, i.e. silver, gold, or copper.

13. A fiber (100, 200, 300) according to any of the preceding claims, wherein the dielectric background material (222, 322, 422, 522, 622, 822) of the first cladding region (220, 320, 420, 520, 620, 820) comprises a material chosen from the group of: Zinc Se- lenide (ZnSe), Arsenic Selenide (As₂Se₃), or any other suitable dielectric that is trans- > parent at the operational wavelength.

14. A method of transmitting electromagnetic radiation through a fiber (100, 200, 300) according to any of the preceding claims, the electromagnetic radiation having a wavelength λ in the range of 1 .8-1000 micrometers, or 100-1000 micrometers, or 1.8-100 micrometers, i.e. in the near infrared, the middle infrared, the far-infrared, or the terahertz range.

15. Use of a fiber (100, 200, 300) according to any of the claims 1 -13 for transmission of light with a wavelength λ in the range of 10.4-10.8 micrometers, or 10.5-10.7 mi- crometers, or even substantially 10.6 micrometers.