IN THE CLADDING

The following publications are considered relevant for an understanding of the background of the invention:

C. Kittel, Introduction to Solid State Physics, 8 ^th ed., Wiley, 2005.

G. Tao, A.F. Abouraddy and A.M. Stolyarov, "Multimaterial Fibers", Int. J. of Applied

Glass Science 3, 349-368 (2012).

G. Tao et.al., "Infrared Fibers", Advances in Optics and Photonics 7, 379^158 (2015). Sh. Fan and J.D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs", Phys. Rev. B 65, 235112 (2002).

FIELD OF THE INVENTION

The present invention relates to optical fibers, and to devices comprising such fibers. It also relates to the field of photonic crystals. BACKGROUND OF THE INVENTION

An optical fiber is a long, thin strand of transparent material. Its shape is usually similar to a cylinder (when not bent). In the center, it has a core. Around the core is a layer or a layered system called cladding. The core and the cladding are made of different kinds of glass, plastic or other materials. A plastic coating, called the buffer, usually covers the cladding to protect it. Often, the buffered fiber is put inside an even tougher layer, called the jacket. This makes it easy to use the fiber without breaking it.

A single-mode (SM) optical fiber is an optical fiber designed to carry only one optical mode. Modes are the possible solutions of Maxwell's equations with appropriate boundary conditions. These modes define the way the electromagnetic fields are distributed in space. Two or more waves can have the same mode while having different frequencies. In single-mode fibers, there can be waves with different frequencies, but of the same mode, which means that they are distributed in space in the same way.

The light in a fiber is confined not only in the core, but extends also into the cladding. Moreover, its intensity is non-uniformly distributed in the cross-section of the fiber. The effective mode area is defined to provide some characteristic of the area in he cross-section of the fiber, occupied by light. Usually, it is defined as

where / is the light intensity and the integration is over the cross-section of the fiber.

Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications. Fibers are also used for illumination, carrying images (thus allowing viewing in confined spaces, as in the case of a fiberscope) and fiber optic sensors.

Optical fibers (doped with certain rare earth elements such as erbium) are also frequently used as optical amplifiers. For example, this allows an optical signal to travel further distances, without converting the optical signal to an electrical signal and then back to an optical signal. These optical amplifiers are also used in fiber lasers. They can be very powerful, because a long thin fiber is easy to keep cool, and produce a good quality light beam.

For many applications, it is desirable to use optical fibers with large effective mode areas (LMA fibers) and with single-mode guidance. Due to the large mode area, these fibers have reduced optical intensities compared to regular fibers. Therefore, they effectively have lower nonlinearities and a higher damage threshold, which makes them suitable, e.g. for the amplification of intense pulses in fiber amplifiers (e.g. ultra-short pulses), for high-power fiber lasers (which are used, for instance, in material processing such as car manufacturing) and for delivery of intense light. Whereas standard single- mode fibers have an effective mode area below 100 μηι ² , large mode area fibers reach values of hundreds or even thousands of μηι ² .

A photonic crystal is a periodic optical structure that affects the motion of photons in much the same way that ionic lattices affect the motion of electrons in solids. The refractive index in a photonic crystal changes in one, two or three dimensions periodically. A photonic crystal structure can change the wavevector of the light incident on the structure by the addition of a reciprocal lattice vector G (see [C. Kittel]). If the photonic crystal has periodicity in one-dimension, the magnitude of

2π

the reciprocal lattice vector is ±— m , where a is the period and m is an integer, while a

the direction of the reciprocal lattice vector is the direction of the periodicity. SUMMARY OF THE INVENTION

The present invention provides an optical fiber. The cladding of the fiber includes a layer referred to hereafter as the "primary cladding layer". The cladding may include one or more layers or other structures inside the primary cladding layer, i.e. between the core and the primary cladding layer (referred to as "inner cladding" hereafter). The cladding may also include one or more layers or other structures outside of the primary cladding layer (referred to as "outer cladding" hereafter). The refractive indexes of some elements of the primary cladding layer are higher than that of the inner cladding materials, or the core when the inner cladding is absent. The refractive indexes of some elements of the primary cladding are also higher than the refractive index of the outer cladding materials, or the buffer when the outer cladding is absent. The core may be hollow.

The primary cladding layer may have a body made of a high refractive index material and possess a periodic array of holes optionally filled with a lower refractive index material. The holes may be drawn in the longitudinal direction of the fiber while the periodicity of the array is in the azimuthal direction (longitudinal, azimuthal and radial directions hereafter refer to the cylindrical coordinate system relevant to a fiber). The holes may be drilled in the radial direction while the array is periodic in one or two directions perpendicular to the radial direction. For example, the array may periodic in the azimuthal and/or longitudinal directions of the fiber.

The primary cladding layer may have a body made of a relatively low refractive index material and possess a periodic array of intrusions made of a high refractive index material. The intrusions may be drawn in the longitudinal direction of the fiber while the periodicity of the array is in the azimuthal direction. The intrusions may be inserted in the radial direction while the array is periodic in one or two directions perpendicular to the radial direction. For example, the array may be periodic in the azimuthal and/or longitudinal directions of the fiber.

Light confinement is achieved via an anti-resonance in the transmission through the primary cladding layer. Namely, the periodic array of holes or intrusions enables coupling between an optical mode inside the primary cladding layer and the light both in the core part (the core and the inner cladding if present) and in the outer space (outer cladding, buffer etc.). Indeed, the wavevector of the light in the core part can be changed by the addition of any of the reciprocal lattice vectors G of the photonic crystal constituted by the array. Its longitudinal and azimuthal components can then match those of the optical mode inside the primary cladding layer. The wavevector of the light inside the primary cladding layer can be changed by the addition of any of the reciprocal lattice vectors G of the photonic crystal constituted by the periodic array. Its longitudinal and azimuthal components can then match those of the light in the outer space. In this situation, the light in the core sees two channels to penetrate the cladding: direct transmission and the transmission assisted by the optical mode inside the primary cladding layer. A destructive interference between these channels is achieved at an appropriate combination of fiber parameters and leads to an anti-resonance in transmission. This anti-resonance essentially prevents light from escaping the core (and the inner cladding if present).

Thus, in one of its aspects, the invention provides an optical fiber comprising: (a) a core

(b) cladding, the cladding including a primary cladding layer, provided with a periodic array of holes or intrusions, the primary cladding layer confining light to the core by an anti-resonance in transmission.

In the optical fiber of the invention, the primary cladding layer may hold a predetermined optical mode. The primary cladding layer may comprise one or more materials having an index of refraction higher than an index of refraction of one or more layers adjacent to the primary cladding layer. One or more of the materials in the intrusions may have an index of refraction higher than an index of refraction of one or more layers adjacent to the primary layer. The periodic array of holes may optionally contain a substance and one or more of the materials having an index of refraction higher than an index of refraction of one or more layers adjacent to the primary layer are not included in the holes.

In the optical fiber of the invention, the holes or intrusions may extend longitudinally along the fiber and the periodicity of the array of the holes or intrusions may be in an azimuthal direction. The holes or intrusions may extend radially in the fiber and the array may be periodic in one or more directions perpendicular to the radial direction. The array of holes or intrusions may be periodic in a longitudinal direction of the fiber.

The core may be hollow and may be filled with one or more gasses. The optical fiber of the invention may have a predetermined mode type and a predetermined core radius, wherein the core radius fits a zero of a Bessel function appropriate for the mode type. The optical fiber may have a transmission through a direct channel close to 1. For example, this can be achieved when k ^ad h = πη , where k ^ad is the radial wavevector in the primary cladding layer, A is a thickness of the primary cladding layer and n is a predetermined integer.

The period a of the array of holes or intrusions may be selected so that an azimuthal component of a wavevector of a guided resonance in the primary cladding layer is equal to an azimuthal component of a wavevector of the predetermined mode in the core.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carried out in practice, a preferred embodiment will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

Fig. la shows a cross-section of an optical fiber in accordance with one embodiment of the invention;

Fig. lb shows a longitudinal transection of the optical fiber of Fig. la;

Fig. 2 illustrates light confinement in the fiber of Figs, la and lb;

Fig. 3 shows the cross-section of an optical fiber in accordance with a second embodiment of the invention;

Fig. 4 shows an optical fiber in accordance with a third embodiment of the invention; and

Fig. 5 shows a simulated intensity distribution of the TE ₀₁ mode in an exemplary simulation of the optical fiber.

DESCRIPTION OF THE INVENTION

Fig. la shows a cross-section of a fiber 100 in accordance with one embodiment of the invention. Fig. lb shows a longitudinal section of the fiber 100 in the plane A A' shown in Fig. la. The fiber 100 includes a core 101 with refractive index n _core surrounded by a cladding which includes a primary cladding layer comprising a body 102 with refractive index n _prim and a circular array of holes 105 extending longitudinally along the fiber 100. The holes 105 are arrayed with azimuthal periodicity. The holes may be of any shape. The holes may be filled with air, or filled with a material having a refractive index n _hole with n _hole < n _prim . The cladding may also include an inner cladding 103 which may consist of one or more layers or other structures. The cladding may further include an outer cladding 104 which may consist of one or more layers or other structures. The refractive index of the body of the primary cladding layer 102, n _im , is larger than the refractive index of the layers in contact with it. Thus, n _prtm is greater than n _core when no inner cladding 103 is present, and n _prim is greater than the average refractive index of the inner cladding 103, when the inner cladding is 103 is present. Similarly, n _rim . is greater than the average refractive index of the outer cladding 104, when present. The cladding may be surrounded by a buffer, a jacket and/or other structures (not shown in Figs, la and lb) as is well known in fiber technology. The core 101 may be hollow.

The fiber can be fabricated by known fabrication techniques, for example, as disclosed in G. Tao, A.F. Abouraddy and A.M. Stolyarov and G. Tao et.al.

Light entering the fiber 100 is confined in the fiber 100 by means of an anti- resonance in the transmission through the primary cladding layer 102 and 105 as schematically illustrated in Fig. 2. Fig. 2 shows part of the primary cladding layer 102 and 105. Since the refractive index of the body of the primary cladding layer 102, n _prim , is larger than the refractive index of the adjacent layers, the primary cladding layer can hold one or more optical modes 206 which, in the absence of the array of holes 105, would be decoupled from the surroundings. The array of holes 105 can add an amount 2π

of ±— m to the azimuthal components of the wavevectors of the modes, where a is a

the period in micrometers of the array and m is an integer. This couples the optical modes of the primary cladding layer 102 and 105 to the optical modes in the surrounding layers, and turns the optical modes of the primary cladding layer 102 and 105 into "guided resonances ", as disclosed, for example, in Sh. Fan and J.D. Joannopoulos. Referring still to Fig. 2, light 207 coming from the core 101 then sees two routes of penetration through the cladding: a direct transmission indicated by the arrow 208 and transmission assisted by one of the optical modes 206, indicated by the arrows 209. A destructive interference between these channels is achieved by an appropriate combination of fiber parameters and leads to an anti-resonance in transmission. This anti-resonance essentially prevents light from escaping the core.

A combination of fiber parameters leading to destructive interference can be found, for example, via the following process:

1. Given a desired operation frequency (<y ), mode type and core radius, the propagation constant ( β ) of the mode can be determined. For example, when the inner cladding is absent, the radius of the core 101 should fit a zero of the Bessel's function appropriate for the mode type, since the primary cladding layer 102 and 105 is to be constructed as a near perfect mirror with a reflection coefficient very close to 1.

2. Parameters of the fiber are selected so that the transmission through the direct channel 208 is close to 1. This is required to provide a satisfactory spectral shape of the anti-resonance. Perfect transmission through the direct channel 208 can be achieved roughly when k _r ^clad h = πη , where k _r ^clad is the radial wavevector in the primary cladding layer 102 and 105, h is the thickness of the primary cladding layer 102 and 105 and n is an integer. Another exemplary way to achieve near perfect transmission in the direct channel 208 is to maximize losses (imaginary parts of the propagation constants) of the optical modes in the core, h can then be chosen so that this condition would be fulfilled at the working point (ω,β ) found in the first step.

3. The period a of the array of holes is selected so that the azimuthal component of one of the wavevectors of a guided resonance in the primary cladding layer 102 and 105 is equal to the azimuthal component of the wavevector of the desired mode in the core part (the core 101 and the inner cladding 103) at the working point ( ω,β ). (A guided

2π

resonance has a series of wavevectors k ₀ ±— m associated with it.) For example, in the a

case of a TEoi mode in the core, the following relation should be fulfilled: m = 0 , where h is the two dimensional wavevector of the optical mode

in the primary cladding layer 102 and 105.

Fig. 3 shows a cross-section of a fiber 300 in accordance with another embodiment of the invention. The fiber 300 includes a core 101a with refractive index ncore surrounded by a cladding which includes a primary cladding layer comprising a body 102a with refractive index n _im and a circularly periodic array of intrusions 305.

The core 101a may be hollow. The cladding may also include an inner cladding 103a which may consist of one or more layers or other structures. The cladding may further include an outer cladding 104a which may consist of one or more layers or other structures. The cladding may be surrounded by a buffer, a jacket and/or other structures (not shown in Fig. 3) as is well known in fiber technology.

In this embodiment, the body of the primary cladding layer 102a does not necessarily have a refractive index higher than the refractive indexes of the core 101a, the inner cladding 103a or the outer cladding 104a. A periodic array of intrusions 305 has a refractive index higher than the refractive indexes of the core 101a, the inner cladding 103a (when present), the outer cladding 104a (when present), and the body of the primary cladding layer 102a. The intrusions 305 extend in the longitudinal direction of the fiber while the periodicity of their array is in the azimuthal direction. The intrusions may be of any shape.

Light entering the fiber 300 is confined in the fiber 300 by means of an anti- resonance in the transmission through the primary cladding layer 102a and 305 essentially as explained above with reference to Fig. 2. A destructive interference between the direct and periodicity-assisted channels is achieved by an appropriate combination of fiber parameters and leads to an anti-resonance in transmission. This anti-resonance essentially prevents light from escaping the core. A combination of fiber parameters leading to destructive interference can be found, for example, via the process similar to the process described above.

Fig. 4 shows a cross-section of a fiber 400 in accordance with another embodiment of the invention. The fiber 400 includes a core 101b with refractive index n _core surrounded by a cladding which includes a primary cladding layer comprising a body 102b with refractive index n _prim and an array of radially oriented holes or intrusions 405. The array of holes or intrusions 405 is periodic in one or two directions perpendicular to the radial direction. For example, the array may periodic azimuthally and/or longitudinally in the fiber. In Fig. 4, for the sake of illustration, the array of holes 405 is periodic in both the azimuthal and the longitudinal directions. The cladding may also include an inner cladding 103b which may consist of one or more layers or other structures. The cladding may further include an outer cladding 104b which may consist of one or more layers or other structures. The body of the primary cladding layer 102b does not necessarily have a refractive index higher than the refractive indexes of the core 101b, the inner cladding 103b or the outer cladding 104b. The cladding may be surrounded by a buffer, a jacket and/or other structures (not shown in Fig. 4) as is well known in fiber technology. The core 101b may be hollow.

Light entering the fiber 400 is confined in the fiber 400 by means of an anti- resonance in the transmission through the primary cladding layer 102b and 405 essentially as explained above with reference to Fig. 2. A destructive interference between the direct and periodicity-assisted channels is achieved by an appropriate combination of fiber parameters and leads to an anti-resonance in transmission. This anti-resonance essentially prevents light from escaping the core. A combination of fiber parameters leading to destructive interference can be found, for example, via the process similar to the process described above.

As an example, a fiber of the invention was modeled by a computer simulation. A fiber having the cross-section shown in Fig. la with a hollow core of 100 μιη diameter and no inner cladding was simulated. The primary cladding layer was about 0.24 μ ^η ι thick, the refractive index of the body of primary cladding layer 102 was 3.48 while the filling ratio of the primary cladding layer (the ratio of the cross-sectional area of the body of the primary cladding layer 102 to the cross-sectional area of the holes 105 was 5.7 (85%/15%). The period of the array of holes was around 2.15 μηι. The fiber was designed to hold a single TEoi mode and operate at a vacuum wavelength of 1.55 μι ^η . Fig. 5 shows the calculated optical intensity distribution in the fiber. The calculated attenuation constants of the seven first modes are presented in Table 1 (the higher modes have larger attenuations). A very large difference can be seen between the calculated attenuation constant of the TEoi mode for which the fiber was designed, and the calculated attenuation constants of the other modes. Thus, the fiber is essentially a single-mode fiber that will carry the TEoi mode while the other modes decay at short distance. Table 1. Attenuation of seven first modes. (Other modes have larger attenuation) in an exemplary simulation of a fiber of the invention. The fiber was designed to hold the TEoi mode.