WO2011161196A1

WO2011161196A1 - Microstructured optical fibres and design methods

Info

Publication number: WO2011161196A1
Application number: PCT/EP2011/060518
Authority: WO
Inventors: Hugo Jean Arthur Thienpont; Tigran Baghdasaryan; Thomas Geernaert; Francis Berghmans
Original assignee: Vrije Universiteit Brussel
Priority date: 2010-06-22
Filing date: 2011-06-22
Publication date: 2011-12-29

Abstract

The present invention relates to an optical fiber structure (100)comprising a core (110) and a cladding region (120) surrounding the core. The cladding region (120) comprises a plurality of longitudinal holes (122), wherein the plurality of longitudinal holes (122) is adapted in configuration for inducing a focusing effect in a direction transverse to the length direction of the optical fiber structure (100). In this way a photonic crystal lens can be embedded in the optical fiber for efficient transverse coupling in or out of the core (110) area of the fiber. Such fibers may especially be suitable for fiber Bragg grating inscription. The present invention also relates to corresponding methods.

Description

MICROSTRUCTURED OPTICAL FIBRES AND DESIGN METHODS

Field of the invention

The invention relates to the field of optics. More particularly, the present invention relates to optical fiber technology, optical fiber, methods of using them and methods of manufacturing and/or designing them.

Background of the invention

Philip Russell was the first to propose the concept of photonic crystal Fibers (PCFs) in 1991. The possibility of fabricating an optical fiber with holes all along its length became feasible, allowing an unprecedented design freedom to the optical guiding properties of optical fibers. Nowadays PCFs are finding applications in various fields of science and industry and even appear as key components in commercially available devices. The main function of the photonic crystal structure is guiding light along the fiber. The optical guiding properties of such fibers are fully determined by the photonic crystal structure in the cladding. The freedom to design the cladding results in various peculiar properties, which are not achievable by conventional step-index fiber designs. The ability to support single mode guidance within a remarkable broad spectral range or the tailored dispersion of the fiber are among the most notable achievements of PCFs.

Nevertheless, the problem of light propagation in directions perpendicular to the fiber is also studied for particular reasons. First, the main interest in transverse coupling of (laser) light to the core of a PCF lies in the field of grating inscription in PCFs. Conventionally the photosensitivity of doped silica allows the fabrication of gratings by an interference pattern of UV light via a single-photon absorption, but more recent methods are based on a change of the refractive index via multi-photon absorption. For the latter case high intensity laser pulses need be tightly focused in the core of the fiber to provide the necessary optical power densities. In PCFs this is a challenging task because of the numerous air-silica interfaces in the microstructured cladding that tend to aberrate the transversely propagating wavefront. Thus, the efficiency of transverse coupling to the core is becoming a hot topic in this field. Besides grating inscription, several other domains may benefit as well from a more rigorous study of transverse light coupling to the core of a PCF. For instance, fluorescence originating from a biological or chemical sample in a lab-on-a fiber device can carry important sensing information about the nature of the sample.

Also orientation alignment of PCFs is a very important problem, when specific types of PCFs (e.g. birefringent PCFs) need to be installed at a particular orientation for industrial purposes. The fiber orientation could be verified by transverse illumination. Photonic crystal fibers (PCFs), also referred to as microstructured, or holey fibers, are optical fibers wherein the cladding of PCFs consists of air holes all along the fiber axis. The transverse propagation of a laser beam to the core of the fiber (through the microstructure) is not straightforward, as the beam's wavefront will be disturbed by the air silica interfaces in the microstructured cladding, which is detrimental for its proper propagation.

One of the most popular type of fiber optical sensors are fiber Bragg gratings. A fiber Bragg grating is a periodic variation of the refractive index (on the wavelength scale) inscribed in a segment of the fiber core (typically a few millimeter long, with a period that is of the order of magnitude of the considered optical wavelength). The Bragg grating acts as a wavelength-specific mirror. This reflection occurs as coupling between the forward and backward propagation modes at a certain wavelength. The coupling coefficient of the modes is maximal when a special condition (Bragg condition) between the wave vectors of light and the vector number of the grating is satisfied. A fiber Bragg grating is able to sense stress and temperature changes. These external exposures are changing the parameters of the grating, which is being detected in the spectra of the propagating light, i.e. in a wavelength shift of the reflected peak or in a separation of reflected peaks for two guided modes in a highly birefringent optical fiber. Inscription of fiber Bragg grating is usually performed by transverse illumination of the core with an interference pattern or with a short intense laser pulse. Fiber Bragg gratings are widely used elements in optical telecommunication, where they are used for wavelength division demultiplexing, dispersion compensation, laser stabilization, erbium-doped amplifier gain flattening, used as cavity end-mirrors, etc. The two major fiber Bragg grating inscription methods are based on doping using the single-photon photosensitivity of doped silica to UV light, as used in both step-index fibers and germanium or phosphor doped PCFs, and based on inscribing using a multi- photon absorption process (by high intensity femtosecond laser pulses) in doped or undoped silica fibers. With the latter method gratings can be inscribed in non- photosensitive (undoped) fibers and (in some cases) without removing the protective coating, which increases the strength of the sensor element. Additionally, refractive index changes by multi-photon absorption tend to be much more stable up to high temperatures, which makes them especially suited for high temperature sensing applications (~1000°C). In both single-photon and multi-photon techniques laser light is transversely propagating through the cladding to reach the core. In the few demonstrations of fiber Bragg grating inscriptions in PCFs up to now, the coupling efficiency problems arising from the microstructured cladding are recognized. Several approaches and methods for obtaining an increased coupling efficiency exist. The most popular approach is doping the core region by Germanium. Ge-doped silica has a higher photosensitivity to the UV light. Although the array of air holes in the microstructure is distorting the beam shape on its way to the core, the increased (single photon) photosensitivity will result in the possibility to inscribe a grating even when only a smaller amount of optical power is coupled to the core. This method is widely used, but is applicable only for single photon inscription methods. In addition, since PCFs do not require doped regions to be able to confine and guide light, the presence of a such doped regions limits the design freedom, complicates the fabrication and is sometimes even highly unwanted, e.g. in the case of temperature insensitive PCFs. Another method to overcome the detrimental influence of the microstructures is filling the air holes with index matching liquid. This method is considerably reducing the amount of light scattered and reflected from the microstructured cladding, resulting in a more efficient inscription of the grating. Even though the results of liquid filling of air holes were quite promising, it has many disadvantages and difficulties. Especially this process is quite advanced and time consuming in order to be used for industrial grating inscription and liquid filling (and unfilling) of long lengths of PCF is problematic. Still another method to overcome the influence of the microstructure is to apply fiber tapering. Among the disadvantages of this method can be mentioned that this is a rather complicated and time-consuming technique to inscribe a single grating. Additionally, the optical waveguide properties inside such a taper are far from the properties of the original PCF, which makes it difficult to control the sensing properties of such devices. In some studies, also the effect of orienting the fiber in a particular direction to improve the coupling efficiency for inscribing is discussed, indicating that certain orientations of the PCF provide more efficient coupling and thus more favorable inscription conditions.

Summary of the invention

It is an object of the present invention that optical photonic crystal fibers can be provided having a good coupling efficiency for transversal coupling into the fiber core area and that corresponding methods for designing and/or producing and/or using them can also be provided.

It is an advantage of embodiments of the present invention that the optical photonic crystal fibers can be fiber grating inscription assisting fibers.

It is an advantage of embodiments of the present invention that during the design stage of the PCF, the transverse coupling efficiency is taken into account.

It is an advantage of embodiments according to the present invention that microstructured optical fibers can be provided that support transversal coupling, e.g. during fiber Bragg grating inscription, rather than having a detrimental effect. More particularly, in some embodiments, a focusing unit is provided able to assist the grating inscription process, e.g. when multi-photon absorption processes are used. It thus is an advantage of embodiments of the present invention that fibers can be obtained assisting fiber grating inscription. It is an advantage of embodiments according to the present invention that also fiber Bragg grating fabrication by multi-photon absorption can be efficiently performed as the methods can provide better focusing in the PCF core and/or cladding region. The possibility of multi-photon inscription nevertheless provides, amongst others, the possibility to inscribe the gratings in non-photosensitive fibers, inscription through the protective coating and a grating's high thermal stability.

It is an advantage of embodiments of the present invention that fibers with a microstructure can be provided having good functionality. Where in embodiments of the present invention reference is made to photonic crystal fibers, reference also may be made to fibers with a microstructure or microstructured fibers.

It is an advantage of embodiments according to the present invention that the microstructure design can be exploited for adding a particular functionality to the fiber.

It is an advantage of at least some embodiments of the present invention that the optical fibers can be used in an active alignment system e.g. for application areas that require control over the angular orientation of the fibers. It is an advantage that the fibers provide the possibility of transversely coupling light into the fiber.

It is an advantage of at least some embodiments of the present invention that fibers are provided allowing capturing a large amount of radiation. The latter is advantageous in all applications where the signal-to-noise ratio should be high or increased, e.g. for a biophotonic lab-on-a-fiber device. The provision of the fibers therefore may result in more accurate techniques for detecting low concentrations of species, e.g. biochemical species.

The present invention relates to an optical fiber structure comprising a core and a cladding region surrounding the core, the cladding region comprising a plurality of longitudinal holes, wherein a configuration of the plurality of longitudinal holes forms a focusing unit inducing a focusing effect in a direction transverse to the length direction of the fiber structure, and wherein a predetermined variation occurs of a parameter of longitudinal holes in a direction perpendicular to the length direction of the optical fiber structure and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure. The fiber structure may be a photonic crystal fiber. It is an advantage of embodiments according to the present invention that an efficient transversal coupling into the fiber can be obtained, using the focusing effect. It is an advantage of embodiments according to the present invention that the microstructure of the fiber structure can be designed such that an increased efficiency is obtained for coupling from or to the fiber in a transverse direction, rather than a detrimental effect.

The focusing effect may be an effect resulting, upon transverse incoupling radiation in the fiber, in a optical power density higher than would be the case without microstructure cladding being present.

The focusing effect may be a focusing effect providing a transverse coupling efficiency larger than 1.

The predetermined variation of a parameter of the longitudinal holes may be a symmetric variation around the radial direction.

The predetermined variation of a parameter of the longitudinal holes may be a variation according to any of a quadratic function or a cosine hyperbolic function. It is an advantage of embodiments according to the present invention that a lensing effect can be induced for transverse coupling. The variation may be a hyperbolic function according to the formula of refractive index variation in a Mikaelian lens. The predetermined variation may be a predetermined variation of a diameter of the longitudinal holes. It is an advantage of embodiments according to the present invention that by varying the diameter or a characteristic size of the longitudinal holes, a good or increased coupling efficiency can be obtained for transverse coupling.

The predetermined variation may be a variation in distance between neighbouring longitudinal holes. It is an advantage of embodiments according to the present invention that by inducing a change in pitch or in arrangement of the longitudinal holes, a good or increased coupling efficiency can be obtained for transverse coupling.

The variation in distance to a neighbouring longitudinal hole may be a pitch. The predetermined variation may be such that the envelope for the cross-sections of the plurality of longitudinal holes has a plano-concave geometric shape. It is an advantage of embodiments according to the present invention that fiber structures are provided that can easily be manufactured, as only the positioning of the longitudinal holes needs to be adapted.

The plurality of longitudinal holes may be adapted in configuration for inducing a gradient refractive index in a direction transverse to the length direction of the fiber structure and transverse to the radial direction in a cross-section of the fiber structure.

The fiber structure may be polymer based.

The unit may provide focusing of transverse incident radiation on the core, and the fiber structure furthermore may comprise a fiber grating, inscribed on the core. It is an advantage of embodiments according to the present invention that photonic crystal fiber structures with good and/or accurately written fiber gratings can be obtained.

The present invention also relates to the use of an optical fiber structure as described above, for a sensing application, for optical particle trapping or for solar energy applications wherein transverse coupling in or out the optical fiber structure is used. The present invention further relates to the use of an optical fiber structure for fiber grating inscription.

The present invention also relates to a method for producing an optical fiber structure, the method comprising fabricating a core and a cladding region surrounding the core, the cladding region comprising a plurality of longitudinal holes, wherein a configuration of the plurality of longitudinal holes forms a focusing unit inducing a focusing effect in a direction transverse to the length direction of the fiber structure, and wherein a predetermined variation occurs of a parameter of longitudinal holes in a direction perpendicular to the length direction of the optical fiber structure and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure. The method furthermore may comprise, inscribing a fiber Bragg grating in the optical fiber structure using an inscribing irradiation beam, whereby the inscribing irradiation beam is being focused on the core by the configured plurality of longitudinal holes. The present invention also relates to a computer-implemented method for designing an optical fiber structure, the method comprising defining a core and a cladding region surrounding the core, the cladding region comprising a plurality of longitudinal holes, determining parameters for the plurality of longitudinal holes so as to define a predetermined configuration of the plurality of longitudinal holes forming a focusing unit inducing a focusing effect in a direction transverse to the length direction of the fiber structure, wherein a predetermined variation occurs of a parameter of longitudinal holes in a direction perpendicular to the length direction of the optical fiber structure and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure, wherein said determining parameters comprises determining a power or power related parameter for a variation of at least one of the parameters for the plurality of longitudinal holes and selecting the parameter value corresponding with the optimum power or power related parameter determined. At least one of the parameters thereby may comprise one of cross-sectional size or diameter of the longitudinal holes, location of the longitudinal holes, pitch between the longitudinal holes or presence of the longitudinal holes.

The present invention also relates to a computer program product for, if implemented on a processing unit, performing a method for designing as described above.

The present invention furthermore relates to a data carrier storing such a computer program product and/or the transmission of such a computer program product over a network.

In one embodiment, the present invention relates to an optical fiber structure comprising a core region and a cladding region surrounding the core region. The fiber structure comprises a central microstructure comprising a first plurality of longitudinal air holes, wherein the central microstructure is adapted for guiding optical radiation. Additionally, in some embodiments, the fiber structure comprises a side microstructure comprising a second plurality of longitudinal holes, wherein the side microstructure is at least partly surrounding the central microstructure. The latter may be adapted for providing a non-constant optical density.

The system advantageously is adapted for focusing radiation, such as e.g. light waves. Focusing radiation may for example be focusing radiation that propagates off-axis. Off-axis thereby may be at 90° with respect to the axis, under an angle larger than 0°and smaller than 90°, under a plurality of angles with respect to the axis, etc.

In some embodiments, a focusing unit, element or function may be provided by an arrangement of longitudinal air holes forming a gradient index lens, e.g. a Mikaelian lens.

In some embodiment the arrangement of longitudinal air holes may be one or more longitudinal air holes having a tailored diameter, the air holes spaced at a constant distance with respect to neighboring air holes.

In some embodiments, the arrangement of longitudinal air holes may be a plurality of longitudinal air holes having a tailored distance in between the air holes, the air holes having a constant air hole diameter.

In some embodiments, a combination of tailoring of the air hole interdistance to neighbouring air holes and of the air hole diameter can be performed.

In some embodiments an arrangement of a focusing unit, element or function may be provided by an arrangement of longitudinal air holes that form a lens by tailoring the pattern of the air holes. In one embodiment the focusing is achieved by a photonic crystal in a standard hexagonal lattice in a shape of a plano-concave lens.

In some aspects, the present invention also relates to a method for grating inscribing in a fiber structure. By way of illustration, further optional and/or standard features of such systems are shown below.

It is an advantage of embodiments according to the present invention that optical fibers with enhanced coupling can be obtained, which may result in an increased sensitivity when used in a sensing system or optical system. Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims. These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

Brief description of the drawings

FIG. la and FIG. lb illustrate an example of a PCF and characteristic parameters, as can be used in embodiments according to the present invention.

FIG. 2 illustrates an example of microstructure-assisted Bragg grating inscription according to an embodiment of the present invention.

FIG. 3 to FIG. 5 illustrate parameters for a variety of implementations of a photonic crystal fiber according to embodiments of the present invention.

FIG. 6 illustrates an example of a refractive index variation according to the Mikaelian formula, as is used or is to be approximated in a photonic crystal fiber according to an embodiment of the present invention.

FIG. 7 illustrates the hole radii of a photonic crystal Mikaelian lens calculated by two different approaches, as can be used in methods according to embodiments of the present invention.

FIG. 8 illustrates the photonic crystal Mikaelian lens and its ID approximation, as can be used in embodiments of the present invention.

FIG. 9 illustrates the transmittance dependence on grating period for 800 nm incident wavelength. Cosine modulated ID grating with 12 periods, illustrating features and advantages of embodiments of the present invention.

FIG. 10 illustrates the parameters of a photonic crystal Mikaelian lens, as can be used for optimizing a design according to embodiments of the present invention.

FIG. 11 illustrates the hole radius dependence of row (ring) number in case of different values for the central hole diameter (curve 1104 - 700 nm, curve 1106 - 500 nm, curve 1108 - 300 nm), illustrating features and advantages of embodiments of the present invention.

FIG. 12 illustrates a photonic crystal Mikaelian lens with different values of the central hole diameter, as can be used in embodiments of the present invention.

FIG. 13 illustrates a photonic crystal Mikaelian lens with different length, illustrating features and advantages of embodiments of the present invention.

FIG. 14 illustrates a photonic crystal Mikaelian lens with removed holes around the focus point, illustrating features and advantages of embodiments according to the present invention.

FIG. 15 illustrates a photonic crystal with longitudinal holes at variable pitch, illustrating features and advantages of embodiments according to the present invention.

FIG. 16 illustrates a photonic crystal Mikaelian lens with longitudinal holes at variable pitch distance, illustrating features and advantages of embodiments according to the present invention.

FIG. 17 illustrates a photonic crystal Mikaelian lens with longitudinal holes at variable pitch distance but with some holes removed around the focus point, illustrating features and advantages of embodiments according to the present invention.

FIG. 18 illustrates a photonic crystal fiber design based on highly birefringent PCF design and variable hole diameter photonic crystal Mikaelian lens, illustrating features and advantages of embodiments according to the present invention.

FIG. 19 illustrates simulation results for a photonics crystal fiber with a photonic crystal Mikaelian lens with variable hole diameter indicating the intensity distribution along optical axis (ID), illustrating features and advantages of embodiments according to the present invention.

FIG. 20 illustrates a photonic crystal fiber design based on highly birefringent PCF design and variable pitch distance photonic crystal Mikaelian lens, illustrating features and advantages of embodiments according to the present invention.

FIG. 21 illustrates simulation results for a photonic crystal fiber with a photonic crystal Mikaelian lens with variable pitch distance indicating the intensity distribution along optical axis (ID), illustrating features and advantages of embodiments according to the present invention.

FIG. 22 shows photonic crystal plano-concave lenses with different thickness (balance with a cost), illustrating features and advantages of embodiments of the present invention.

FIG. 23 shows a ID power distribution along optical axis of the photonic crystal planoconcave lens for thick and thin designs, illustrating features and advantages of embodiments of the present invention.

FIG. 24 shows a step-index fiber with photonic crystal lens for transverse coupling assistance, according to an embodiment of the present invention.

FIG. 25 shows simulation results for a step-index fiber with embedded photonic crystal lens in the cladding intensity distribution along optical axis of photonic crystal lens, illustrating features and advantages of embodiments of the present invention. The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes.

Any reference signs in the claims shall not be construed as limiting the scope.

In the different drawings, the same reference signs refer to the same or analogous elements. Detailed description of illustrative embodiments

The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not correspond to actual reductions to practice of the invention.

Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

Moreover, the terms top, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.

It is to be noticed that the term "comprising", used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.

Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.

Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

Where in embodiments of the present invention reference is made to transverse coupling, reference is made to the coupling of radiation in or out of the core of the optical fiber structure (e.g. from free space), whereby the radiation to be coupled into the optical fiber system or the radiation coupled out from the optical fiber system travels in a direction not parallel with the longitudinal direction of the optical fiber system, e.g. in a direction substantially perpendicular thereto.

Where in embodiments of the present invention reference is made to transverse coupling efficiency, reference is made to the ratio of the measured physical quantity (optical power density or intensity) in the core of a PCF in case of presence of a microstructured cladding to the same physical quantity in case of absence of microstructured cladding. Such efficiency may be indicated using the symbol ξ. For instance when the intensity value at the centre of the PCF core is under investigation, two simulations are performed: one with the original PCF, while in the second one the microstructured cladding is removed. Afterwards the ratio of these two intensities can be considered as the efficiency of the transverse coupling to the core. It should be mentioned that often the integrated power over the core region is used rather than the power at one particular point.

Where in embodiments of the present invention reference is made to longitudinal holes, reference is made to holes extending substantially longer in the direction of the length of the fiber than in the other direction.

Embodiments according to the present invention are based on a design of the cladding region of photonic crystal fibers (PCF). By way of illustration, a photonic crystal fiber is illustrated in FIG. la, whereby characteristic parameters of the PCF are indicated. In FIG. la a photonics crystal fiber 100 is indicated having a PCF diameter 102, whereby the PCF comprises a core 110 and a cladding region 120. The cladding region comprises a set of air holes 122. In the example shown in FIG. la, a second row of air holes 124 and a pitch distance 126 is illustrated.

In a first aspect, the present invention relates to an optical fiber structure 100 comprising a core 110 and a cladding 120 surrounding the core 110. The cladding 120 region comprises a plurality of longitudinal holes 122. Such optical fiber structures 100 also may be referred to as photonic crystal fibers, or microstructured fibers, or holey fibers. Typical examples of photonic crystal fibers may be made of any suitable material, such as for example silica materials or polymer materials. The longitudinal holes 122 thereby typically extend in the longitudinal direction of the optical fiber structure and are surrounding the core 110. They typically may be in an ordered arrangement, e.g. in a set of rows or rings. According to embodiments of the present invention, the configuration of the plurality of longitudinal holes forming a focusing unit inducing a focusing effect in a direction transverse to the length direction of the fiber structure. In other words, the microstructure, i.e. the presence of the longitudinal holes 122, is used advantageously for inducing a focusing effect for coupling radiation in or towards the core, rather than having a detrimental effect thereon. The focusing unit can be established in a plurality of manners. According to embodiments of the present invention, a predetermined variation occurs of a parameter of longitudinal holes in a direction perpendicular to the length direction of the optical fiber structure and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure. Such a variation can be made explicit in a plurality of manners. The variation may be a dimensional or distance related parameter. A first way of providing such a focusing unit may be through providing a configuration wherein for the longitudinal holes a diameter or pitch or interdistance varies. By varying for example the diameter (more generally a characteristic size of the cross-section of the longitudinal hole) of the longitudinal holes, or the interdistance or a combination thereof, a focusing effect in a direction transverse, i.e. substantially perpendicular, to the longitudinal direction of the optical fiber system can be obtained. A second way of obtaining a focusing unit is through a change in arrangement of the plurality of longitudinal holes. The latter is as also a variation of a parameter of the longitudinal holes, more particularly a variation in the presence of the longitudinal hole or a variation in size wherein for some positions the size of the longitudinal hole is zero or a variation in interdistance between the longitudinal holes. In this way, the focusing unit may be obtained by a particular arrangement, whereby the arrangement is such that a focusing effect in a direction perpendicular to the longitudinal direction of the optical fiber structure is obtained. The focusing effect obtained also is at least perpendicular to the radial direction in the cross- section of the optical fiber structure. The envelope for the arrangement of the longitudinal holes may take a plano-concave shape, a plano-convex shape, a shape comprising at least one concave surface, a shape comprising at least one convex surface, etc. It may take the form of a Mikaelian lens. The plurality of longitudinal holes according to embodiments of the present invention may be adapted in configuration for inducing a gradient refractive index in a direction transverse, also referred to as perpendicular, to the length or longitudinal direction of the optical fiber structure and transverse to a radial direction r in a cross-section of the optical fiber structure. The focusing effect thus may be introduced by a GRIN lensing effect, induced by an adapted configuration of the longitudinal holes. By way of illustration, FIG. lb indicates the direction 130 wherein the focusing effect at least may occur, in the present illustration indicated (dashed lines) by a set of radiation rays incident in a transversal direction on the fiber. As indicated above, the focusing unit may be introduced using a variation of a parameter of the longitudinal holes. Such a variation may occur in a direction perpendicular to the longitudinal direction of the optical fiber structure and perpendicular to the radial direction r in a cross-section of the optical fiber structure, or in other words along the direction 130. The variation may be a variation according to a predefined function, e.g. a symmetric function, symmetric with respect to a radial direction in the fiber. The predefined function also may be a quadratic function or a cosine hyperbolic function. The variation in some embodiments of the present invention may mean that a symmetric, quadratic or cosine hyperbolic functional variation occurs of the one or more parameters of the longitudinal holes occurring along the direction 130. Embodiments of the present invention may comprise a fiber grating, e.g. a fiber Bragg grating, typically inscribed in the core of the fiber. Further features and advantages will become apparent from the examples discussed below.

In one aspect, the present invention also relates to a method for designing and/or producing an optical fiber structure. The method for designing typically comprises defining, for a photonic crystal fiber, a core and a cladding region surrounding the core, the cladding region comprising a plurality of longitudinal holes. The method, which typically is computer-implemented, further comprises determining parameters for the plurality of longitudinal holes so as to define a configuration of the plurality of longitudinal holes forming a focusing unit inducing a focusing effect in a direction transverse to the length direction of the fiber structure, wherein a predetermined variation occurs of a parameter of longitudinal holes in a direction perpendicular to the length direction of the optical fiber structure and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure. Determining parameters thereby comprises determining a power or power related parameter for a variation of at least one of the parameters for the plurality of longitudinal holes and selecting the parameter value corresponding with a good or the optimum power or power related parameter determined. The one or more parameters of the plurality of holes that may be considered for optimization may be similar as those described in the first aspect. Such a design method may be an automated or automatic process, performed according to predetermined algorithms, or parts of such a process may be automated or automatic. Alternatively or in addition thereto, the present invention also relates to a method for manufacturing an optical fiber structure, e.g. designed using a method as described above. The method of producing comprises fabricating a core and a cladding surrounding the core, whereby the cladding region comprises a plurality of longitudinal holes. The longitudinal holes thereby have such a configuration that these form a focusing unit inducing a focusing effect in a direction transverse to the length direction of the optical fiber structure.

Embodiments of the present invention are not limited to design of photonic crystal fibers as described above, but the methods also may comprise the actual manufacturing. Photonic crystal fibers can be made using any suitable technique available to the person skilled in the art.

Fabrication by a stack-and-draw process proves to be the most convenient. During this fabrication process silica capillaries are stacked and fused together to form a preform which is then drawn down to a PCF. Even though most of the PCFs are made out of silica materials, new types of PCFs fabricated from polymer materials are also available. These kinds of fibers are often referred to as microstructured Polymer Optical Fibers (mPOF) and were first fabricated from polymethylmethacrylate (PMMA). The losses in polymers are quite huge (~0.15 dB/m at 650 nm) compared with silica used in conventional fibers (~0.2dB/km), but mPOFs have a significant potential given the range of available polymers and processing methods. Also the possibility to fabricate them in low temperatures allows organic and inorganic dopants to be used. The fabrication of mPOF can also be done via the same stack- and-draw process, even though the first mPOF preforms were fabricated by drilling all necessary holes in one rod of PMMA. The important advantage of this method is that the hole positions are not restricted to the typical hexagonal (or rectangular) lattice arrangement of stacked performs. The flexibility of drilling thus made it suitable for research purposes and resulted in its wide use, however it is currently limited by the limited height of the produced performs.

By way of illustration, embodiments of the present invention not being limited thereby, an example of a manufacturing technique is discussed here. The method is discussed for high silica glass and taking into account particular features, but it is to be understood that this is for the ease of explanation. In an exemplary manufacturing technique, the method may comprise the following steps. The method comprises obtaining high silica glass rods and tubes, whereby for example the glass material may be synthetic silica glass, commercially known as Heralux S. The method also may comprise calibrating the tubes to achieve adequate thickness or collapsing the tubes to create glass rods. The method also may comprise fabricating a first preform with germanium doped core by means of an MCVD method. The method also may comprise scaling down the dimensions of purchased glass rods and tubes as well as the first preform using a fiber drawing tower with a graphite resistance furnace in clean room conditions (class 10000). Another step may be stacking the capillaries, rods and doped rod manually in clean room conditions (class 1000). The method also may comprise heating the stacked capillaries and rods at temperatures between 400°C - 800 °C in a chlorine atmosphere to eliminate impurities and heating the stacked capillaries and rods at temperatures that stick them together to obtain the first stage of a micro-structured perform. Zone heating under controlled pressure for precisely merging the stacked capillaries and rods in the graphite furnace may be performed and, afterwards, scaling down the first preform to get the second stage of a micro-structured preform by means of a drawing tower may be performed. The method may comprise inserting the second stage micro-structured preform into an adequately large glass tube to allow correcting the fiber lattice constant, holes diameters and outer fiber diameter, also referred to as overcladding process. The method furthermore may comprise drawing the designed fiber and adding the protective jacket made of UV curing polymers on the drawing tower.

According to a further aspect, the present invention also relates to the use of a photonic crystal fiber as described above for producing a fiber brag grating inscribed fiber. It thereby is an advantage of embodiments according to the present invention that good fiber brag grating inscription can be performed, despite the presence of the air holes in the photonic crystal fiber. Surprisingly it has been found that the efficiency for inscribing can even be larger when a photonic crystal fiber as described above is used. As described in embodiments of the present invention the photonic crystal fiber may be especially designed for assisting in the fiber brag grating inscription process. By way of illustration, embodiments of the present invention not being limited thereto, an example of a grating inscription using a photonic crystal fiber according to an embodiment of the present invention and thus allowing for microstructure assisted inscription is shown schematically in FIG. 2. This configuration has special importance for grating inscription by the multi-photon absorption or for draw tower gratings, when the laser pulse should be tightly focused into the core of the PCF. With a photonic crystal Mikaelian Lens in the PCF, it is no longer required to focus the pulse via external optical elements only, because the microstructure is going to contribute to that task. This facilitates the complicated procedure of fiber alignment in X and Y directions and introduces stability for grating inscription along those axes. The fibers further can eliminate the necessity of accurate fiber alignment into two directions, i.e. only orientation alignment is to be taken into account.

In still other further aspects, the present invention relates to the use of a photonic crystal fiber as described above for sensing applications, for particle trapping, for solar cell applications, etc. For these applications, efficient transversal coupling may be obtained towards or away from the core of the fiber. Consequently, whereas the examples shown in the present application are mainly describing focusing radiation from outside the fiber to the core, also focusing radiation stemming from the core onto a position outside the fiber may be envisaged. Overall, systems and methods according to the present invention allow for an efficient transversal coupling of radiation into or out of an optical fiber, more particularly a photonic crystal fiber. An increased coupling efficiency, may result in a higher light yield, a higher sensitivity, the possibility of better trapping a particle in a fiber by illumination sideways with an illumination source, etc. Photonic crystal fibers as described above also may be used in lab-on-a-fiber applications.

In one aspect, the present invention relates to a design method for designing an optical fiber. The method may be a computer implemented method. The method comprises defining a core and a cladding region surrounding the core, the cladding region comprising a plurality of longitudinal holes. Such a fiber typically is a photonic crystal fiber. The method also comprises determining parameters for the plurality of longitudinal holes so as to define a predetermined configuration inducing a focusing effect in a direction transverse to the length direction of the fiber structure, wherein said determining parameters comprises determining a power or power related parameter for a variation of at least one of the parameters for the plurality of longitudinal holes and selecting the parameter value corresponding with the optimum power or power related parameter determined. Features and advantages of the methods as illustrated in the examples may be used for these purposes.

In still another aspect according to the present invention, the design method as described above may be a computer-implemented method for performing a method for designing an optical fiber. Such a computer-implemented method may be implemented on a processing system that includes at least one programmable processor coupled to a memory subsystem that includes at least one form of memory, e.g., RAM, ROM, and so forth. It is to be noted that the processor or processors may be a general purpose, or a special purpose processor, and may be for inclusion in a device, e.g., a chip that has other components that perform other functions. Thus, one or more aspects of embodiments of the present invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The processor may be adapted for performing a method for designing a photonic crystal optical fiber or may comprise instructions for performing such a method. The processing system may include a storage subsystem that has at least one disk drive and/or CD-ROM drive and/or DVD drive. In some implementations, a display system, a keyboard, and a pointing device may be included as part of a user interface subsystem to provide for a user to manually input information. Ports for inputting and outputting data also may be included. More elements such as network connections, interfaces to various devices, and so forth, may be included. The various elements of the processing system may be coupled in various ways, including via a bus subsystem. The memory of the memory subsystem may at some time hold part or all of a set of instructions that when executed on the processing system implement the steps of the method embodiments described above. While a processing system as such is prior art, a system that includes the instructions to implement aspects of the methods as described above is not prior art.

The present invention also includes a computer program product which provides the functionality of any of the methods according to the present invention when executed on a computing device. Such computer program product can be tangibly embodied in a carrier medium carrying machine-readable code for execution by a programmable processor. The present invention thus relates to a carrier medium carrying a computer program product that, when executed on computing means, provides instructions for executing designing a photonic crystal fiber according to any of the methods as described above. The term "carrier medium" refers to any medium that participates in providing instructions to a processor for execution. Such a medium may take many forms, including but not limited to, non-volatile media, and transmission media. Non volatile media includes, for example, optical or magnetic disks, such as a storage device which is part of mass storage. Common forms of computer readable media include, a CD-ROM, a DVD, a flexible disk or floppy disk, a tape, a memory chip or cartridge or any other medium from which a computer can read. Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution. The computer program product can also be transmitted via a carrier wave in a network, such as a LAN, a WAN or the Internet. Transmission media can take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise a bus within a computer. By way of illustration, different parameter conditions that advantageously may be used for designing and producing photonic crystal fibers as described above are discussed below. All the values for the parameters below are provided with the incident wavelength evaluated in the host material, i.e. λ/η, whereby λ is the wavelength in vacuum and n is the refractive index of the material.

Examples of parameters for the photonic crystal fiber according to embodiments of the present invention can be found in Table 1. For the different parameters, ranges are provided through their minimum and maximum values, as well as advantageous typical values that may be used. With respect to the outer shape of the optical fiber that can be used, any suitable shape can be used, such as for example a D-shape like shape, an elliptical or circular shape, a hexagonal-like shape, etc.

Table 1

Parameters for the implementation of a photonic crystal Mikaelian lens implemented in the cladding region of the photonic crystal fiber, whereby a varying hole size is used are provided in table 2. The characteristic parameters described are indicated in FIG. 3. The pitch distance thereby is the distance between the centers of two neighbouring holes. The hole columns and hole rows also are indicated in FIG. 3. Besides the ranges provided by minimum and maximum values, also advantageous typical values that may be used are indicated.

Table 3

Parameters for the implementation of a photonic crystal Mikaelian lens implemented in the cladding region of the photonic crystal fiber, whereby a varying pitch between the longitudinal holes is used are provided in table 3. The characteristic parameters described are indicated in FIG. 4. The vertical pitch distance thereby is the distance between the centers of two neighbouring holes in two neighbouring hole rows and the horizontal pitch distance thereby is the distance between the centers of two neighbouring holes in two neighbouring hole columns. The hole columns and hole rows also are indicated in FIG. 4. Besides the ranges provided by minimum and maximum values, again also advantageous typical values that may be used are indicated.

The resulting variation of the average refractive index in the direction of the variation of the parameter of the longitudinal holes advantageously follows the formula of Mikaelian, which can be written for the gradient index change along X axis:

where 7¾ ^iS the effective refractive index at the centre of the lens and L is the length of the lens necessary to change the wave front from cylindrical to plane. An example of a possible refractive index variation according to the Mikaelian formula is shown in

FIG. 5.

Parameters for the implementation of a plano-concave photonic crystal lens implemented in the cladding region of the photonic crystal fiber are provided in table 4. The characteristic parameters described are indicated in FIG. 6. The pitch thereby is the distance between the centers of two neighbouring holes. Furthermore the hole columns en hole rows also are indicated. Besides the ranges provided by minimum and maximum values, again also advantageous typical values that may be used are indicated. Parameter Minimum Maximum Typical

Wavelength range (λ) 300 nm 2000 nm 800-1600 nm J

Material refractive index (n) 1 5 1.45 1

Pitch distance (Λ) Λ/(λ/η) 0.1 3 1 - 2 I

Holes diameter (d) d/Λ 0.1 0.99 0.4-0.5 1

Number of hole rows 5 50 10-20 1

Number of hole columns 5 50 15-20 1

Table 4

By way of illustration, embodiments of the present invention not being limited thereby, examples will further be discussed illustrating features and/or advantages of at least some embodiments of the present invention. The examples provided are numerical examples, based on Finite Difference Time Domain Method (FDTD) simulations. In the examples, fabrication limitations are taken into account. The FDTD software available from LUMERICAL FDTD Solutions was used. The software is able to perform 2D and 3D simulations and has a user-friendly CAD editor to design the required structure.

In FDTD Maxwell equations are solved in the time domain with finite steps in time and space, whereby non-magnetic materials are implied. Besides determination of the differential equations to be solved, discretization of space and time is required, which is performed using a particular meshing scheme, in the present example being the meshing scheme as known in literature. Performing a simulation using LUMERICAL FDTD Solutions is done by introducing information about the physical structures, sources in the present example being a Gaussian beam source and plane wave source, monitors for recording the electromagnetic fields obtained in the present example being a power monitor and time monitor, and details with the simulation parameters. The power monitordetermines the power flow across a user-defined surface or along an axis within the simulation region with high accuracy. The spectral dependence of the power flow may be normalized to the source power. Time monitors record and store the values of the electric and magnetic field components at user-defined intervals during the simulation, at user-defined points in the simulation region. The accuracy of the simulation was tested using reference fibers, and a mesh accuracy of 62 points/wavelength was selected being a compromised choice between time and accuracy. A higher number of mesh points will not add much accuracy, but will increase the simulation time significantly. Further some automation tools were implemented and post processing was done in a separate calculation program.

In one set of examples, embodiments of the present invention not being limited thereby, new designs for photonics crystal fibers and the effect on the transverse coupling efficiency are illustrated, more particularly on the microstructure-assisted grating inscription. The examples of the new PCF designs comprise a design based on a gradient index lens implementation of the photonic crystal structure, e.g. using a photonic crystalMikaelian Lens (PCML) and a design based on a photonic crystal plano-concave lens.

In the first example, the photonic crystal structure is designed with the objective to achieve a high coupling efficiency inside the core of the PCF by carefully tuning the microstructure. The new microstructure design will be based on Mikaelian lens implementation by photonic crystal structure. The designs of the microstructure of a PCF is adapted, e.g. in the present example in order to assist Bragg grating inscription. The photonic crystal mikaelian lens is a lens wherein the focusing effect is obtained by an gradient index medium with parallel plane surfaced optical element. Application of the Mikaelian lens in the photonic crystal is in the present example performed by, instead of varying the refractive index of the material, varying the diameter of the air holes in the photonic crystal, resulting in variable effective refractive index. The approximation of gradient index medium by photonic crystal structure implies that the diameter of the holes should be changing by some specific formula, which can for example be derived from the formula for the Mikaelian lens. In one example, the following approach could be used : the optical path along the central part of the holes was considered to be the same in an ideal gradient index Mikaelian lens. The calculated dependence for the hole diameter in this case is then the following:

whereR is the hole diameter, d is the pitch distance, L is the lens thickness, 7¾is the refractive index in the centre and n the refractive index at the edge. The variation of the refractive index is along the Y-axis. The length L mentioned in the formula is the length necessary to have the focus directly after the lens.

An important aspect to be mentioned is the refractive index in the centre of the PCML

At the state of the design of the PCML a minimal hole diameter at the centre of the structure should be fixed, while the maximal hole diameter is limited by the pitch distance. This minimal diameter in turn is determining the refracting index at the centre of PCML and can be calculated by the following formula: n. [2]

d wherec/ is the pitch distance (hole diameter at the edge) and d_min is the diameter of the hole in the centre of the lens.

An example of a second approach for the calculation of the air hole diameters based on average refractive index at every hole unit cell, as indicated in FIG. 7. For this particular case of PCML (when the pitch distance is constant) a unit cell of the PCML is a square with the side d equal to the pitch distance of the photonic crystal. If the hole radius is r, then the average refractive index for one cell will be the following: m²+(d² -m²)n

n avg [3]

J²

In order to find the formula that describes the radius of the hole in function of the coordinate along which the refractive index is changing (in this case y axis), this equation needs to be defined equal to the formula of the Mikaelian lens. By solving the identity we get the following expression for the hole radius:

This formula [3] and the formula [2] are equivalent and both can be applied for the calculation of hole diameters. The comparison of these formulas is presented in the FIG. 7 in case of PCML with a pitch distance of 250 nm, a minimal hole diameter of 180 nm and a refractive index 1.5.

As can be seen from FIG. 7 there is only a small difference between the values of calculated radii. The curve 702 with the smaller values is the curve based on formula [4], whereas the curve 704 with the higher values corresponds with formula [1]. The simulations on the PCML show no significant difference in the characteristics of the focused beam. But the latter approach is under particular interest as it can be applied for the designs of a Mikaelian lens with variable pitch distance.

In the current example, the lens is introduced in PCFs in order to assist transverse coupling of the laser radiation to the core. As the dimensions of the airholes in the available PCFs are different from those in the PCML, it is necessary to perform further investigation on the PCML to increase the allowed dimensions for being used in PCFs. Since a PCML is an approximation of a gradient index medium by periodic structure (photonic crystal) the first thing to be taken into account is the behaviour of periodic media under illumination with laser radiation. There should be especially careful not to design a PCML that would reflect the incoming laser beam resonantly. As one is also targeting to have high intensities after the lens (focussing effect), the PCML should have high transmittivity. In order to investigate the reflection of the incoming beam depending on pitch distance, the PCML was approximated with a ID grating and the numerical analysis was performed. This ID analysis is reasonable in the sense that only limited angles around the perpendicular direction to the photonic crystallens are going to be used during transverse illumination. The periodicity of the lens is governed by the pitch distance of the photonic crystal, in turn the pitch distance is limiting the possible values for the hole diameter. In FIG. 8, the PCML and its approximation by a ID periodic structure are presented. The investigation of the transmission dependence on the equivalent grating period (equal to the pitch distance) is going to be performed by the Method of Single Expression (MSE), known from prior art. .The structure under investigation is illustrated in FIG. 8. The modulation was chosen such that at the maximum refractive index is n and at the minimum is 1, which corresponds to glass in between holes and air at the centre of the hole. MSE is calculating the field and Poynting vector across the structure and the reflection coefficient at the beginning can be calculated by the following formula: _{r =} ^_{e =} ^²(0) - F(0) - ^(0) - (0)

E_inc U²(0) + iY(0) - U(0) + P(0)

The algorithm was implemented in MATLAB and numerical integration was performed by the Runge-Kutta method. For the above mentioned structure the simulation was made for the transmittance coefficient dependence on the modulation period, which corresponds to the pitch distance of the photonic crystal lens in our case. The cosine modulation with the peak value of refractive index 1.45 and minimum value 1 was modelled under illumination by infrared light at 800 nm. The results are illustrated in FIG. 9.

From the result of simulation it can be clearly seen that for some values of grating period the transmittance is very low and it is important to be aware about it during design process. The occurrence of these minimums in transmission spectra is due Bragg reflection. In FIG. 9one can see several Bragg resonances (marked as A, B and C). In the present example, it seems advantageous to design photonic crystals with a pitch distance (period of the ID grating) as large as possible and from FIG. 9it can be derived that it is reasonable to chose a pitch distance in the region after the second Bragg resonance (region C) where transmittance is above 90%. At the same time it should be emphasized that the diameter of the air holes cannot be increased much, since the approximation of the gradient index medium by a photonic crystal with variable hole diameter will not be valid anymore. Further enlargement of holes will also result in the necessity to consider the interaction of the hole and the wave with the laws of ray optics, i.e. the electromagnetic wave will 'feel' every hole as an independent structure. In order to make sure that the PCML with a pitch distance much larger than the one used in literature will focus the incident light, several PCMLs were designed with the pitch distance around Ιμιη to check whether they are indeed focusing light. The simulations were performed by the LUMERICAL FDTD Solutions software and it was found that in the present example PCML with a pitch distance lower than Ιμιη should be selected. As for higher pitch distance the approximation of gradient index by variable hole diameter is no more applicable. In the present example, a pitch distance of 900 nm was chosen for the further design, since it is both functional and suitable for possible fabrication. By fixing the pitch distance we are also fixing the biggest possible diameter of the hole, at the edge of the PCML. Diameter of the hole at the centre of the PCML is going to be investigated further. The diameters of the holes are increasing via the cosine hyperbolic law, and at the edge and they are limited by the pitch distance. So the smaller the hole diameter at the centre of the PCML, the wider the size of the lens that can be designed. On the other hand the smaller hole diameters is limited by fabrication. Next designs of PCML with the minimal diameter of 300 nm, 500 nm and 700 nm will be presented and compared.

FIG. lOillustrates the main parameters of the PCML. In FIG. lithe dependence of the hole diameter on the number of the hole row is presented in case of different central hole diameter values mentioned above (curve 1104 : 700nm, curve 1106 : 500nm, curve 1104 : 300nm). As can be seen from the figure, PCML is thicker in case of smaller central hole. In case of 300 nm central hole diameter, PCML can have a maximum of 6 rows, so the width of the grating can be 13x0.9 μιη = 11.7 μιη (6 on each side + one central row). The line 1102 in FIG llindicates the limitation of the hole diameter by the pitch distance (900 nm).ln FIG. 12the actual designs of the lenses discussed above are presented. All the lenses are designed with a length of 14.4 μιη (or 16 rows of holes). Because of the limited pitch distance the lenses are having different widths: 17.1 μιη (9 rows), 15.3 μιη (8 rows) and 11.7 μιη (6 rows). The structures are fully designed inside the glass with the refractive index 1.45 and for 125 fs pulse incidence with plane wave front at 800 nm with TE polarization. The lenses were designed to have the same focal length, but the real focal lengths of the photonic crystallenses are higher than expected and are not identical for the current designs. For the one with the central hole of 300 nm the focal point is at a distance of 9.8 μιη from the end of the structure; for 500 nm this value is 8.3 μιη and for the one with 300 nm the distance is 6.5 μιη. Next the power distributions simulated by a frequency domain power monitor in the front part of the lens were determined. The focal points are quite prolonged along the propagation direction which can be a result of the rough approximation of a gradient index media by photonic structure with variable hole diameter. This investigation was aiming to determine how the central hole diameter affects to focusing characteristics. The simulations indicated that it is evident that the design with 300 nm central hole diameter is focusing to the highest intensity, hence highest efficiency, can be observed in focal point in this case. In order to quantify the effect time domain intensity monitors were placed in the focal points. In the simulations by LUMERICAL FDTD Solutions the intensity was normalized to incident beam. The following table presents the peak intensity for above considered designs. Central Hole Diameter 300 nm 500 nm 700 nm

Normalized peak intensity

6.9 6 4.5

(e.g. efficiency ξ)

Table 5

From the results it is becoming obvious that the peak intensity and coupling efficiency is higher when the diameter of the central hole is the smallest (300 nm). This can be explained by the fact that the lens was wider in case of the 300 nm central hole diameter, hence it was able to focus the light from the bigger volume (or surface in case of a 2D simulation) than the others. So in order to have a high transverse coupling efficiency the PCML with higher width, i.e. smaller centre hole diameter, should be preferred.

As the function of photonic crystal cladding is light confinement, it is determining the core area. Hence the focal point is desired to be just after the structure, i.e. in the core region. In the designs presented above the focal point was quite far from the surface (about 7-10 μιη) and we will try to adapt the PCML with the focus just after the structure. As a reference design the one with the central hole diameter of 500 nm will be taken and the next designs with a longer photonic crystal structure will be investigated. The length of the reference structure was 14.4 μιη (16 vertical rows of holes) and the others will have lengths of 18 μιη (20 rows), 19.8 μιη (22 rows) and 21.6 μιη (24 rows). The values for peak intensity for the simulation results by frequency domain power monitor are presented in Table 5. photonic 14.4 μιη 18 μιη 19.8 μιη 21.6 μηι crystallength (16rows) (20 rows) (22 rows) (24 rows)

Normalized peak

intensity 6 3.9 3.7 2.8

(e.g. efficiency ξ)

Table 6

The results of the simulation give important information about the peculiarities of the PCML. Mainly the self distorting property of this lens could be clearly observed from the simulation and the values of the peak intensity (Table 6). In case when the lens is designed to have a length of 21.6 μιη (the longest PCML) the focal point is supposedly inside the lens, but the hole structure is distorting the focusing radiation much. Even for the other designs where the focal point is outside but close to the surface, a photonic crystal structure is partially distorting the cylindrical wave front of the focusing light before reaching the actual focal point. An alternative example, suffering less from this problem is shown in FIG. 14, wherein the wave front of the focusing light will not be affected by the hole structure by removing some selected holes, at the location of the focal point. The peak intensity at the focal point calculated by the time domain intensity monitor is 6, which is the same as for the shorter PCML in FIG. 13. This kind of design with removed holes is also convenient to be used for the design of PCF, as removed holes can be used to form the core region of the PCF.

In another example, another approximation of the Mikaelian lens is used in the photonic crystal fiber by varying of the pitch distance along the direction perpendicular to the optical axis. Above two methods to design PCML with variable hole diameter were presented. For the variable pitch design we will use a method similar to the second approach, which was proposed by us and was based on an approximation of the refractive index by an average refractive index at every 'unit cell' of the photonic crystal. In a PCML with variable pitch distance the average refractive index will change only due to the change of the cell dimensions (pitch distance change) and not the hole diameter as it was before. This kind of PCM L is schematically illustrated in FIG. 15, where the unit cell is indicated with the parameters a andb. According to the definition the parameter b, i.e. the width of the cell, is the only variable in the PCM L with variable pitch distance and during design of the structure the position of the hole along the X axis can be calculated only.

The investigation shows that it is not possible to have a straightforward formula for this type of PCM L structure and the position of the hole along the X axis should be calculated for every row separately. Let us consider the first row and indicate the method of the pitch distance or hole position calculation. The variation of the average refractive index along the X-axis should follow the formula of the Mikaelian lens, which can be written for the gradient index change along X axis:

At the same time the average refractive index for the first row depends on the pitch size (b parameter) or the position of the hole along X-axis. It is also important to note that for the first unit cell the position of the hole is half of the b parameter. This results in the following formula for the average refractive index of the first row, where the parameter b is presented by 2x: , 7iR² + (2x - a - 7iR²)

n _pitch (*) = [7]

2χ · a I n order to find the Xi position of the hole for the first unit cell n_pitch (x) should be equal to _r , _ , , . . . . . It is important to know that these two

Error! Bookmark not defined. ^

formulas are having gradients with opposite sign, so the equation ⁿmik ^x) ^{= n}pitch ^x) '^s having ^{a root}- A solution for both requirements can be obtained using numerical calculation. In order to calculate the pitch distance or the position of the hole for the second cell the same scheme should be used by only shifting the x axis in the formula 7 for n_pitch (x) by the length of the cells used before.

According to this method of the calculation of the pitch distance and hole diameter, the PCML with variable pitch distance was designed. The parameter a (cell length) was chosen to be 900 nm as in previous designs and the hole diameter was also selected to be the same. The parameter b (cell width) for the first cell was designed to be around 1400 nm. The structure in case of illumination by plane wave with the wavelength of 800 nm from above the structure is presented in FIG. 16. The frequency domain power monitor was placed in the front part of the PCML and the focusing of the plane wave with the focus in front of the structure could be distinguished clearly. The peak intensity in the focal point was calculated by time domain intensity monitor and was equal to 4.2 (normalized). This value is a bit lower than that in the previous designs of PCML. In order to increase the intensity the same strategy of removing the holes at the front part could be applied. An example thereof, albeit with an additional row of holes was added, is shown in FIG. 17. The calculated peak intensity in this case is already 5.2, which is smaller, but already comparable with the previous results.

Using variable pitch, a highly localized light intensity is obtained, while in case of variable hole the intensity is more spread around the high intensity point.

The resulting PCFs based on the PCML are now further discussed for a number of reference PCF structures, using the two types of PCML based on variable hole diameter and variable pitch distance presented. First PCF to be presented here is based on combination of highly birefringent design and optimized PCML with variable hole diameter. The design is presented in the FIG. 18. The diameter of the PCF was chosen to be 80 μιη.

The PCF was illuminated from above by TE polarized 125 fs length pulse at 800 nm. Simulation results from the frequency domain 2D power monitor placed at the core part of the PCF were obtained as well as data from the ID intensity monitor along the optical axis of PCF is illustrated, the latter being indicated in FIG. 19. One of the differences between current simulation and the one performed with only PCML illustrated above is the presence of the outer cladding. It is obvious that circular cladding is changing the wave front of the plane wave and can be considered as additional focusing element. From FIG. 19it can also be seen that the peak intensity is about 6.2 (normalized) which was expected. Current design indicates the ability of PCML to be used in PCFs and focus the incident light to the core.

The second design of PCF is based on PCML with variable pitch distance. The same highly birefringent PCF was considered to be reference for the future design. The diameter of the fiber was also taken to be 80 μιη and the structure was illuminated from above by TE polarized 125 fs length pulse at 800 nm. PCF design with variable pitch distance is presented in the FIG. 20. The effect of the outer cladding results in the focusing of the light inside the PCML cladding and for that reason two rows of holes were removed compared to the design presented for optimizing the PCML. It can be seen that this design is having much shorter microstructure, which can mean also fewer scattering centres. The simulation results for the last design of PCF are presented in the FIG. 21. Again frequency domain 2D power monitor placed at the core area were determined together with ID intensity monitor placed along optical axis, the latter being illustrated. As one can see in this case the joint effect of outer cylindrical cladding and PCML with variable pitch distance results in the maximum peak intensity reaching to 8, which is better than for the previous design. Also highly localised focusing is achieved comparing to the design with variable hole diameter.

The designs of PCFs based on PCML are showing high transverse coupling efficiency. This can be considers as main conclusion of the current Section.

The above set of examples illustrates that the use of photonic crystal mikaelian lens is a possible solution for transverse coupling enhancement by a focusing effect. The parameters of PCML were for the above example adapted to be used in PCFs and structures with reasonable airhole diameter were presented. The possibility of having PCML with variable hole diameter and variable pitch distance was illustrated. Additionally a method for calculation of airhole positions in variable pitch distance PCML is illustrated. Designed PCML were investigated and optimized for maximal power coupling ability. The solution of focusing the laser light by PCML shown with the example illustrates the possibility for use in Bragg grating inscription by multi- photon absorption.

In another example, designing the photonic crystalstructure in the fiber in a shape of a lens is illustrated. It is an advantage of embodiments according to the present invention that it allows for easy fabrication process as standard hexagonal lattice can be used. In the present example, the possibility of approximating standard refractive index lens by photonic crystal structure is explored.

The holes of the photonic crystal structure will influence the optical path along the optical axis is shorter than at the edges, where more material with higher refractive index is present. While the same structure fabricated or engraved in glass (imagine glass with the air hole in a shape of plano-concave lens) will focus the light as inverse effect will take place, i.e. optical path along optical axis will be shorter than at the edges. In a same way the holes of photonic crystal forming similar to plano-concave 'air' lens structure (like in FIG. 22) will focus the incident light.

The example shows a photonic crystal structure for focusing of the light was designed in glass by hexagonal lattice of holes in a shape of plano-concave lens. The pitch distance of the photonic crystal was chosen to be 1 μιη with the diameter of holes equal to 900 nm. The radius of the curvature was about 9 μιη. Two designs with different thickness are presented in FIG. 22. The simulations were performed for the TE polarized pulse at the wavelength of 800 nm. Incidence from above the structure was considered in all the simulations.

Simulation results were determined by frequency domain power monitor in 2D and by ID monitor along the optical axis, the ID results being shown in FIG. 23. It is worth to mention that the light is propagating on the negative direction along Y axis and the end of the structure is in the coordinate -4. The focal points of the lenses were in a distance of 22.5μιη from the end of the structures. From the monitors we clearly see that the peak intensity for the thick lens is higher and equal to 5.4, while for the thin lens it is 3.8 (the results are normalized). This is result can be considered to be contra intuitive, as big number of holes are supposed to scatter light more. As we see from the simulations the focal point of these photonic crystal lenses are quite big and prolonged, which is similar to effect from spherical aberrations. The longer focal point can be also the consequence of very rough approximation of cylindrical shape by photonic crystal structure.

Because the focal point of the structure is quite far from it, the structure can for example be used to assist transverse power coupling to the core in conventional step- index fiber, where guiding properties are governed by only refractive index difference of the core and the cladding. This kind of fiber with photonic crystal structure will exclude the necessity of careful focusing of the laser beam at the core and will make Bragg grating inscription process more stable. Taking into account the fact that in the cladding propagation mode is exponentially decaying, photonic crystal structure placed in reasonable distance from the core will not affect the guiding properties of the fiber. In FIG. 24 such a design of step index fiber together with the photonic crystal lens in the cladding is presented. The diameter of the fiber is 126 μιη, while the core has the diameter of 10 μιη. photonic crystal lens is in a distance of about 20 μιη from the centre of the fiber. It worth to note the from above designs of photonic crystal lenses the thick one was chosen in this design as it was having higher focusing efficiency.

The simulations for this fiber were made for the wavelength of 800 nm and TE polarized 125 fs pulse incidence from above the structure is considered. Again 2D power monitor simulations and ID power distribution along the optical axis of the photonic crystal lens was determined, the latter being shown in FIG. 25. The photonic crystal lens was placed in a specific distance from the centre in order to focus the light just to the core. It can be seen that the focal point is indeed situated in the core of the fiber. The intensity peaks before the focal point can also be seen, which are not desired and arose mainly due to the presence of the outer cladding. Meanwhile this peak can be used in some cases, as it has the same intensity value and has much smaller spot size.

The above example illustrates that a focusing structure based on photonic crystal in a shape of a plano-concave lens can be used for focusing the incident light. Focusing characteristics of a thicker lens seem advantageous.

Claims

An optical fiber structure (100) comprising a core (110) and a cladding region (120)surrounding the core (110), the cladding region (120) comprising a plurality of longitudinal holes (122), wherein a configuration of the plurality of longitudinal holes (122) forms a focusing unit inducing a focusing effect in a direction transverse to the length direction of the optical fiber structure(lOO) , and wherein a predetermined variation occurs of a parameter of longitudinal holes (122) in a direction perpendicular to the length direction of the optical fiber structure (100) and in a direction perpendicular to a radial direction in a cross- section of the optical fiber structure (100).

An optical fiber structure (100) according to claim 1, wherein the predetermined variation of a parameter of the longitudinal holes (122) is a symmetric variation around the radial direction.

An optical fiber structure (100) according to claim 2, wherein the predetermined variation of a parameter of the longitudinal holes (122) is a variation according to any of a quadratic function or a cosine hyperbolic function.

An optical fiber structure (100) according to any of the previous claims, wherein the predetermined variation is a variation of the diameter of the longitudinal holes (122).

An optical fiber structure (100) according to any of the previous claims, wherein the predetermined variation is a variation in distance between neighbouring longitudinal holes (122).

An optical fiber structure (100) according to claim 5, wherein the variation in distance between neighbouring longitudinal holes (122) is a pitch.

An optical fiber structure (100) according to any of the previous claims, wherein the predetermined variation is such thatthe envelope for the cross-sections of the plurality of longitudinal holes (122) has a plano-concave geometric shape. An optical fiber structure (100) according to any of the previous claims, wherein the plurality of longitudinal holes (122) is adapted in configuration for inducing a gradient refractive index in a direction transverse to the length direction of the optical fiber structure (100) and transverse to the radial direction in a cross- section of the optical fiber structure (100).

9. - An optical fiber structure (100) according to any of the previous claims, whereinthe optical fiber structure (100) is polymer based.

10. - An optical fiber structure (100) according to any of the previous claims, wherein the focus unit provides focusing of transverse incident radiation on the core (110), and wherein the optical fiber structure (100) furthermore comprises a fibergrating, inscribed on the core (110).

11. - Use of an opticalfiber structure (100) according to any of claims 1 to 10, for a sensing application, for optical particle trapping or for solar energy applications wherein transverse coupling in or out the core (110) of the optical fiber structure (100) is used.

12. - Use of an opticalfiber structure (100) according to any of claims 1 to 9 for fibergrating inscription.

13. - A method for producing an optical fiber structure (100), the method comprising fabricating a core (110) and a cladding region (120) surrounding the core (110), the cladding region (120) comprising a plurality of longitudinal holes, wherein a configuration of the plurality of longitudinal holes (122) forms a focusing unit inducing a focusing effect in a direction transverse to the length direction of the optical fiber structure (100), and wherein a predetermined variation occurs of a parameter of longitudinal holes (122) in a direction perpendicular to the length direction of the optical fiber structure (100) and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure (100).

14. - A method according to claim 13, wherein the method furthermore comprises, inscribing a fiber Bragg grating in the optical fiber structure (100) using an inscribing irradiation beam, whereby the inscribing irradiation beam is being focused on the core (120) by the configured plurality of longitudinal holes (122).

15. - A computer-implemented method for designing an optical fiber structure (100), the method comprising - defining a core (110) and a cladding region (120) surrounding the core (110), the cladding region (120) comprising a plurality of longitudinal holes (122)

- determining parameters for the plurality of longitudinal holes (122) so as to define a predetermined configuration of the plurality of longitudinal holes (122) forming a focusing unit inducing a focusing effect in a direction transverse to the length direction of the optical fiber structure (100), wherein a predetermined variation occurs of a parameter of longitudinal holes (122) in a direction perpendicular to the length direction of the optical fiber structure (100) and in a direction perpendicular to a radial direction in a cross-section of the optical fiber structure(lOO), wherein said determining parameters comprises determining apower or power related parameter for a variation ofat least one of the parameters for the plurality of longitudinal holes and selecting the parameter value corresponding with the optimum power or power related parameter determined.

A computer program product for, if implemented on a processing unit, performing a method according to claim 15.

A data carrier storing the computer program product according to claim 16.

Transmission of a computer program product according to claim 16, over a network.