CN100410704C - Method for configuring air-core photonic-bandgap fibers free of surface modes - Google Patents

Abstract

Coupling of core modes to surface modes in an air core photonic-bandgap fiber (PBF) can cause large propagation losses. Computer simulations analyze the relationship between the geometry and the presence of surface modes in PBFs having a triangular hole pattern and identify ranges of core characteristic dimensions (e.g., radii) for which the fiber supports no surface modes (i.e., only core modes are present) over the entire wavelength range of the bandgap. In particular, for a hole spacing and a hole radius = 0.47 , the core supports a single mode and supports no surface modes for core radii between about 0.7 and about 1.05 , which suggests that such fibers should exhibit a very low propagation loss. The existence of surface modes can be predicted simply and expediently by studying either the bulk modes alone or the geometry of the fiber without requiring a full analysis of the defect modes.

Description

Method and photonic-bandgap fibers that the air-core photonic-bandgap fibers of free of surface modes is configured

Related application

[0001] according to the regulation of the 35th piece of the 119th (e) money of United States code, the application requires the preference of following U.S. Provisional Patent Application: No. the 60/502nd, 329, the U.S. Provisional Patent Application of submitting on September 12nd, 2003; No. the 60/502nd, 390, the U.S. Provisional Patent Application of submitting on September 12nd, 2003; No. the 60/502nd, 531, the U.S. Provisional Patent Application of submitting on September 12nd, 2003; And on April 23rd, 2004 No. the 60/564th, 896, the U.S. Provisional Patent Application submitted to, incorporate them into this paper at this with way of reference.

Background of invention

Technical field

[0002] the application relates to the optical field fiber of propagates light, particularly relates to photonic band-gap (photonic-bandgap) field fiber, and described photonic-bandgap fibers has the hollow fibre core, or refractive index is lower than the fibre core of clad material.

Background technology

[0003] in recent years, air-core photonic-bandgap fibers (PBF) has caused the very big interest of people because of its distinct advantages that is better than traditional fiber.Particularly, the propagation loss among the air-core PBF can't be subjected to core material and limit, and propagation loss be expected can be very low.Nonlinear effect among the air-core PBF is very little, and available liquid or gas are filled fibre core to produce desired light-material interaction.Verified recently, these advantages make many new application become possibility.For instance, following document is described these application: BurakTemelkuran et al., Wavelength-scalable hollow optical fibres with largephotonic bandgaps for CO ₂Laser transmission, Nature, Vol.420,12December 2002, pages 650-653; Dimitri G.Ouzounov et al., Dispersionand nonlinear propagation in air-core photonic band-gap fibers, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2003, Baltimore, USA, 1-6June 2003, paper CThV5,2pages; M.J.Renn et al., Laser-Guided Atoms in Hollow-Core Optical Fibers, Physical ReviewLetters, Vol.75, No.18,30 October 1995, pages 3253-3256; F.Benabidet al., Particle levitation and guidance in hollow-core photonic crystalfiber, Optics Express, Vol.10, No.21,21 October 2002, pages 1195-1203; And Kazunori Suzuki et al., Ultrabroad band white light generation from amultimode photonic bandgap fiber with an air core, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2001, paper WIPD1-11, pages 24-25 incorporates them into this paper at this with way of reference.

[0004] calculating of the selected properties of PBF basic schema or mode (mode) also is reported in the following document for instance: R.F.Cregan et al., and Single-Mode Photonic Band GapGuidance of Light in Air, Science, Vol.285,3 September 1999, pages1537-1539; Jes Broeng et al., Analysis of air guiding photonic bandgapfibers, Optics Letters, Vol.25, No.2, January 15,2000, pages 96-98; And Jes Broeng et al., Photonic Crystal Fibers:ANew Class of OpticalWaveguides, Optical Fiber Technology, Vol.5,1999, pages 305-330 incorporates these documents into this paper at this with way of reference.

[0005] surface modes (surface mode) (not having surface modes in the traditional fiber) is the defect mode that is formed at the boundary between air-core and photon-crystal covering.When the unlimited photonic crystal of unexpected termination, promptly surface modes can appear, and this situation for example occurs in the edge of limited dimension crystal.Clearing end can be introduced one group of new boundary condition, and the surface modes that they cause satisfying these conditions and being confined to this clearing end forms.For instance, please referring to F.Ramos-Mendieta et al., Surface electromagnetic waves in two-dimensionalphotonic crystals:effect of the position of the surface plane, Physical Review B, Vol.59, No.23,15June 1999, and pages 15112-15120 incorporates it into this paper at this with way of reference.In photonic crystal, the existence of surface modes depends primarily on the position of clearing end.For example see also A.Yariv et al., Optical Waves in Crystals:Propagation and Control of Laser Radiation, John Wiley﹠amp; Sons, NewYork, 1984, pages 209-214, particularly at page 210; And J.D.Joannopoulos et al., Photonic Crystals:Molding the flow of light, PrincetonUniversity Press, Princeton, New Jersey, 1995, pages 54-77, particularly atpage 73; Incorporate them into this paper at this with way of reference; In addition for example also can be referring to the F.Ramos-Mendieta et al. that had above quoted, Surface electromagnetic waves intwo-dimensional Photonic Crystals:effect of the position of the surfaceplane.For example, in the photonic crystal of in air, making, only when stopping end-grain cutting (cut through) rod, just can bring out surface modes by the dielectric rod.The clearing end of only cutting air too a little less than, can not bring out surface modes.For example please referring to the J.D.Joannopoulos etal. that had above quoted, Photonic Crystals.Molding the flow of light.

[0006] recent checking shows that surface modes plays a part particular importance in air-core PBF, and the evidence demonstration is installed, and surface modes has brought serious restriction in air-core photonic-bandgap fibers.For example see also Douglas C.Allan et al., Surface Modesand loss in air-core photonic band-gap fibers, in Photonics CrystalsMaterials and Devices, A.Adibi et al. (eds.), Proceedings of SPE, Vol.5000,2003, pages 161-174; Wah Tung Lau et al., Creating large bandwidthline defects by embedding dielectric waveguides into photonic crystal slabs, Applied Physics Letters, Vol.81, No.21,18 November 2002, pages3915-3917; And Dirk M ü ller et al., Measurement of Photonic Band-gapFiber Transmission from 1.0 to 3.0 μ m and Impact of Surface ModeCoupling, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2003, Baltimore, USA, 1-6June 2003, paper QTuL2,2pages incorporates them into this paper at this with way of reference.And for example also can be referring to the J.D.Joannopoulos et al. that had above quoted, Photonic Crystals:Molding the flow of light; The A.Yariv et al. that had above quoted, Optical Waves in Crystals:Propagation andControl of Laser Radiation; And the F.Ramos-Mendieta etal. that had above quoted, Surface electromagnetic waves in two-dimensional photonic crystals:effect of the position of the surface plane.Unless it is suitable to design, optical fiber will be supported a lot of surface modes.

[0007] different with surface modes, fibre core pattern (for example basic fibre core pattern) is the pattern that a kind of peak value of mode intensity is arranged in fibre core.In most of the cases, most of energy also will be included in the air-core.The propagation constant of surface modes approaches usually, even may equal the propagation constant of basic fibre core pattern.For example see also the Dirk M ü lleret al. that had above quoted, Measurement of Photonic Band-gap Fiber Transmission from 1.0 to3.0, μ m and Impact of Surface Mode Coupling.Strong analysis of experiments evidence shows, basic fibre core pattern is coupled to one or more in these surface modes.For example, the random perturbation in the cross section of optic fibre can cause such coupling.Because of its high-energy-density in fiber medium, surface modes has inherent loss, so such coupling is exactly a propagation loss source.And because surface modes occurs on the whole band gap, the neither one part can avoid this loss mechanism on the usable spectrum.Recent discovery is verified, and in the 13-dB/km air-core PBF that Corning makes, surface modes is a reason that reduces transmission bandwidth.For example see also N.Venkataraman et al., Low loss (13dB/km) air core photonicband-gapfibre, Proceedings of European Conference on OpticalCommunication, ECOC 2002, Copenhagen, Denmark, PostDeadlineSession 1, PostDeadline Paper PD 1.1, September 12,2002; And C.M.Smith, et al., Low-loss hollow-core silicalair photonic bandgap fibre, Nature, Vol.424, No.6949,7 August 2003, pages 657-659 incorporates them into this paper at this with way of reference.This effect it is believed that it is the source of the residual loss (about 13dB/km) in this air-core photonic-bandgap fibers.For example see also the Douglas C.Allan et al that had above quoted, Photonic Crystals Materials and Devices.Therefore in the research of ongoing low-loss PBF, it is important understanding the physics cause of surface modes and determine all not have the optical fiber structure of this pattern on whole band gap.

Summary of the invention

[0008] embodiment disclosed herein is based on the information of such acquisition: utilizing numerical simulation, the information that is obtained in the research that the character of the fibre core pattern of PBF and surface modes is carried out.Above-mentioned research focuses on modal PBF geometric configuration, the optical fiber that promptly has the cylindrical airport of periodicity triangle pattern and have the circular core that obtains by introducing air defective in clad material.Such optical fiber for example is described in the following document: the R.F.Cregan et al. that had above quoted, Single-Mode Photonic Band Gap Guidance ofLight in Air; The Jes Broeng et al. that had above quoted, Analysis of air-guidingPhotonic Band Gap; And the Jes Broeng et al. that had above quoted, PhotonicCrystal Fibers:A new class of optical waveguides, Optical FiberTechnology.These achievements also can be applicable to large-scale airport pattern (as hexagon pattern, square pattern etc.), hole shape, reach in the core shape.Above-mentioned achievement also can be applicable to other photonic-bandgap fibers, the optical fiber that promptly has similar geometric, the optical fiber of these similar geometric is according to identical photonic band-gap principle work, (for example fibre core is with another kind of gas but its fibre core must not filled with air, vacuum, the filling of liquid or solid), its clad material hole also needn't be filled with air and (for example filled another kind of gas, vacuum, the clad material hole of liquid or solid), and the solid portion of this covering needn't make (for example clad material can comprise another kind of solid or multiple solid) by silica.In this manual, used term hole or not referred to herein as it with the fibre core of solid or liquid filling be hollow.Here it should be understood that constitute fibre core, clad material hole, and the material refractive index separately of clad material solid portion should be selected to and make optical fiber structure pass through support guiding of photonic band-gap effect or waveguide mode (guidedmode).This just means that the refractive index in the refractive index of fibre core and hole should be lower than the refractive index of clad material solid portion, and the difference between these refractive indexes should be enough big.

[0009] for air-core optical fiber or wherein fiber core refractive index be lower than the optical fiber of clad material solid portion refractive index, recommend several new geometric configuratioies at this.The scope of the fibre core characteristic dimension that these geometric configuratioies had (it is a fiber core radius when fibre core is circle for example) makes supports free of surface modes on the whole wavelength coverage of fiber core at band gap, and only has the fibre core pattern.Especially for radius between about 0.7 Λ to the circular core between about 1.05 Λ (wherein Λ is that the hole of triangle pattern is to pitch of holes), have the fibre core of recommending new geometric configuration and support single-mode, and do not support any surface modes.The loss that means the optical fiber in this configuration scope without surface modes will be starkly lower than existing fiber.Further illustrate as following, to the research of volume mode, perhaps even more simply prove, can easily predict the existence of surface modes in the defect sturcture by direct how much according to separately.Because this structure is actually periodically, the therefore method that hereinafter will describe of the basis existence that comes the caluclate table surface model, will comparing defect mode, to carry out multianalysis more quick, and complicacy is less.

[0010] method disclosed herein can be used to predict whether support surface pattern of specific fibre geometry, so that optical fiber can be designed and manufactured as not support surface pattern.Especially, described in the detailed description, can avoid the existence of surface modes by selecting fiber core radius or other characteristic dimensions, so that the circle in any PBF of being inscribed within lattice texture (for example solid intersecting area) can not cut in the edge of fibre core as following.This technology is effective to large-scale geometric configuration and hole dimension.

[0011] for avoiding surface modes, technical scheme described herein is used to design core shape, so that fibre core does not intersect (for example fibre core only intersects with the section that combines PBF lattice texture) with any PBF lattice texture.Follow this general criterion, PBF can be designed to free of surface modes.

[0012] aspect according to the embodiment of the invention is a kind of method of making photonic-bandgap fibers.This method has been utilized a kind of photonic-bandgap fibers, and this photonic-bandgap fibers comprises such material: wherein be formed with zone map, to form photonic crystal lattice.Described material has first refractive index.Described zone map has second refractive index less than described first refractive index.Described method comprises the intensity profile of determining near the highest frequency volume mode in described zone.Described method forms a central fibre core in described photonic crystal lattice.This fibre core has an edge, and it intersects in such position and described zone map: in described position, the intensity of described highest frequency volume mode is low to moderate is enough to make described optical fiber to support free of surface modes.Preferably, the described zone in the described material is circular; And described zone map is periodic, and is arranged to triangle of every group of three adjacent areas formation; This triangle has the first of the correspondence of described material, and this first is between every pair of zone, and has the corresponding second portion of described material, and this second portion forms a middle body in every group of three adjacent areas.Described central fibre core is formed in the described photonic crystal lattice, thereby makes the edge of described central fibre core only pass the first of described material.In a particular embodiment, the described zone in the described material is the hole, and it has the wall that is limited by material around.Advantageously, these holes in the described material are hollow.Available air, gas or liquid with second refractive index is filled these holes in the described material.Perhaps, described border circular areas comprises a kind of solid with described second refractive index.In certain embodiments, described material is a dielectric, for example silica.

[0013] according to the present invention-another aspect of embodiment is a kind of photonic-bandgap fibers, it comprises a kind of photonic crystal lattice.Described lattice comprises first material with first refractive index.Described first material has the pattern that wherein is formed on second material.Described second material has second refractive index that is lower than described first refractive index.Described photonic crystal lattice has a plurality of first areas and a plurality of second area, and wherein the intensity lobe (intensity lobe) of highest frequency volume mode is supported in the first area, and second area is not supported the intensity lobe of described highest frequency volume mode.A central fibre core is formed in the described photonic crystal lattice.Described central fibre core has an edge, and this edge only passes the second area of described dielectric lattice.Preferably, the pattern of described second material is periodic, and comprises a plurality of geometric areas.Each geometric areas has center separately, and adjacent geometric areas is isolated by center to center Λ.Each geometric areas of described second material is circle, and has radius ρ, and wherein said radius ρ is less than 0.5 Λ.Preferably, described pattern is a triangle, and described first area comprises and is inscribed within three circles between the adjacent geometric areas.In certain embodiments, each inscribe radius of a circle α equals

In addition preferably, the radius ρ of each geometric areas is about 0.47 Λ.In certain embodiments, described fibre core is roughly circle, and the radius that the edge had of described fibre core is within one of them radius of a plurality of radius.In described a plurality of fiber core radius scope first is to the radius that is about 1.05 Λ from the radius that is about 0.68 Λ.In described a plurality of fiber core radius scope second is to the radius that is about 1.43 Λ from the radius that is about 1.26 Λ.In described a plurality of fiber core radius scope the 3rd is to the radius that is about 1.97 Λ from the radius that is about 1.64 Λ.In particularly preferred embodiment, in described a plurality of fiber core radius scope first is to the radius that is about 1.047 Λ from the radius that is about 0.685 Λ, in described a plurality of fiber core radius scope second be radius from about 1.262 Λ to the radius that is about 1.420 Λ, and in described a plurality of fiber core radius scope the 3rd be from for the radius of about 1.635 Λ to the radius that is about 1.974 Λ.

[0014] according to the embodiment of the invention be a kind of method of geometry of selecting core size on the other hand, in order to make the photonic-bandgap fibers of free of surface modes.Described photonic-bandgap fibers has the photonic crystal lattice that comprises first material, and described first material has first refractive index.Described material surrounds the periodic patterns of second material area.Described second material has second refractive index that is lower than described first refractive index.Each zone of described second material is spaced apart by an adjacent area of barrier film of described first material and described second material, and each intersection of barrier film forms a texture of described first material.Described method is included in and limits an inscribe middle body in described each texture of second material, so that the outer perimeter of the adjacent area around the outer perimeter of described inscribe middle body and the described texture is tangent.Described method further comprises a plurality of fibre core characteristic dimension scopes that limit, and wherein the size that is had is in any fibre core of described a plurality of scope within one of them and has an edge, and this edge does not pass any described inscribe middle body.Described method further comprises selects a kind of fibre core, the size that it had to be in described a plurality of fibre core characteristic dimension scope within one of them.Preferably, each zone has a respective center, and adjacent geometric areas is isolated by a center to center Λ.Equally preferably, each zone of described second material is circular, and has radius ρ, and described radius ρ is less than 0.5 Λ.In certain embodiments, described pattern is leg-of-mutton, and described inscribe middle body is circular.Preferably, described radius of a circle α equals

In a particular embodiment, the described radius ρ in each zone is about 0.47 Λ.In such embodiments, the characteristic dimension of described fibre core is a radius of a circle, and in described a plurality of fibre core characteristic dimension scope first for from the radius of about 0.68 Λ to the radius that is about 1.05 Λ.In described a plurality of fibre core characteristic dimension scope second for from the radius that is about 1.26 Λ to the radius that is about 1.43 Λ.In described a plurality of fibre core characteristic dimension scope the 3rd for from the radius that is about 1.64 Λ to the radius that is about 1.97 Λ.In particularly preferred embodiment, in described a plurality of fibre core characteristic dimension scope first is from about 0.685 Λ radius to about 1.047 Λ radiuses, second is from the radius of about 1.262 Λ to about 1.420 Λ radiuses in described a plurality of fibre core characteristic dimension scope, and in described a plurality of fibre core characteristic dimension scope the 3rd be from for the radius of about 1.635 Λ to the radius that is about 1.974 Λ.

[0015] another aspect according to the embodiment of the invention is a kind of photonic-bandgap fibers of supporting free of surface modes.Described photonic-bandgap fibers comprises a photonic crystal lattice zone, and its included material has first refractive index.Described material has a periodic regions pattern that is formed on wherein.Each zone has second refractive index that is lower than first refractive index.Each zone is spaced apart by a barrier film and the adjacent area of described material.Every group of adjacent area be formed on described material middle body around.Described middle body in every group of adjacent area is limited by an incircle, and this incircle has one and the tangent circumference of circumference of described adjacent area.One fibre core is formed in the described photonic-bandgap fibers.Described fibre core has a selected characteristic dimension, so that the edge of described fibre core only passes in the described material not those parts in arbitrary incircle of described middle body.Preferably, described material is a dielectric substance, for example silica.Equally, preferably, described pattern is a triangle, and every group of adjacent area comprises three zones.In particularly preferred embodiment, described fibre core is roughly circle, and described characteristic dimension is the radius of described fibre core.

[0016] be the not method of the photonic-bandgap fibers of support surface pattern of a kind of manufacturing on the other hand according to the embodiment of the invention.Described method comprises that selection one has the photonic-bandgap fibers of photonic crystal lattice, and described photonic crystal lattice comprises having first refractive index materials.Described material has a periodicity delta region pattern that is formed at wherein.Each regional refractive index is lower than described first refractive index.Described material comprises the first between the adjacent holes, and only comprises the second portion between two adjacent holes.Described second portion and the interconnection of described first.Described method further is included in and forms a fibre core in the described photonic crystal lattice.Described fibre core has a selected characteristic dimension, so that the edge of described fibre core is only crossing with the second portion of described photonic crystal region.Preferably, described material is a dielectric substance, for example silica.In addition preferably, described pattern is a triangle, and every group of adjacent area comprises three zones.In particularly preferred embodiment, described fibre core is roughly circle, and described characteristic dimension is the radius of described fibre core.

Description of drawings

[0017] below in conjunction with appended accompanying drawing embodiments of the invention are described, wherein:

[0018] Fig. 1 shows the partial cross-section of the air-core photonic-bandgap fibers (PBF) of an exemplary triangles pattern, and wherein fiber core radius is 1.15 Λ, and pore radius ρ is about 0.47 Λ.

[0019] Fig. 2 is the enlarged drawing of partial cross-section among Fig. 1, and it provides extra details to the spatial relationship between the texture (turning) of the section (barrier film) between airport, adjacent vacant pore and these section intersections;

[0020] Fig. 3 shows the level line of expression typical surface pattern isophote for the air-core PBF of Fig. 1;

[0021] Fig. 4 shows the level line of the basic fibre core pattern isophote of expression for the air-core PBF of Fig. 1;

[0022] Fig. 5 shows the level line of representing typical volume pattern isophote for the triangle pattern air-core PBF of Fig. 1, but air-core PBF wherein also is not removed central construct to form air-core 106;

[0023] Fig. 6 shows the dispersion curve of defect mode for the air-core photonic-bandgap fibers (PBF) of Fig. 1, wherein this air-core photonic-bandgap fibers has the hole of triangle pattern, its have one-period (being that pitch of holes is arrived in the hole) Λ photon-crystal structure and-the pore radius ρ of Yue 0.47 Λ, be in about 1.15 Λ of radius R air-core around, the shade among this figure (cross hacures) part is represented the photonic band-gap of crystal;

[0024] Fig. 7 shows the dispersion curve of defect mode for the air-core PBF of about 1.8 Λ of fiber core radius R;

[0025] Fig. 8 has described a partial cross-section, and it shows sectional hole patterns and the air-core shape of the PBF that therefrom obtains Fig. 7 dispersion curve;

[0026] Fig. 9 shows fibre core pattern (rhombus) and surface modes (triangle) and the curve map of air-core radius at normalization frequencies omega Λ/2 π c=1.7 places;

[0027] Figure 10 A, 10B and 10C are respectively fiber core radius 0.9 Λ, and 1.2 Λ and 2.1 Λ show core shape, and the information of Fig. 9 is from wherein obtaining;

[0028] the diagrammatic representation air-core radius shown in Figure 11, they support single fibre core pattern (non-shade ring) and fibre core and surface modes (shade ring);

[0029] Figure 12 shows the partial cross-section of Fig. 1 triangle pattern air-core PBF, and wherein forming radius in photonic crystal lattice is R ₁Fibre core, and the surface of this fibre core and lattice turning intersect, and the support surface pattern;

[0030] Figure 13 shows the partial cross-section of Fig. 1 triangle pattern air-core PBF, and wherein forming radius in photonic crystal lattice is R ₂Fibre core, and the surface of this fibre core and lattice turning are non-intersect, and support surface pattern not;

[0031] Figure 14 is that highest frequency volume mode maximum intensity on the circle of R shows its curve map (dashed curve) as the function of R with radius according to Fig. 9, and the surface modes maximum quantity is shown its curve map (solid-line curve) as the function of R;

[0032] Figure 15 A and 15B show the intensity contour map of two double degeneration volume mode of highest frequency under the band gap at I point place, wherein R ₁Be an example of fiber core radius, it had both supported also support surface pattern of fibre core pattern, and R ₂Be an example of fiber core radius, it only supports the fibre core pattern;

[0033] partial cross-section of the diagrammatic representation triangle pattern air-core PBF shown in Figure 16, the black circles that wherein is positioned at each dielectric corner is represented the dielectric rod, and what wherein non-shade ring was represented fiber core radius can be with (band), for it, does not intersect with the dielectric rod on the surface of fibre core;

[0034] Figure 17 shows the curve (dash line) of the numerical simulation results of surface modes quantity, and show the geometric model that utilizes Figure 16 and calculate the curve (solid line) of the surface modes quantity that the excellent quantity that intersects with the fibre core surface predicts, wherein the quantity of surface modes is marked and drawn with respect to normalization fiber core radius R/ Λ in every curve;

[0035] Figure 18 has illustrated the graph of relation of normalization fiber core radius R/ Λ with normalization pore radius ρ/Λ, the influence of optical fiber air-filling rate when having surface modes to illustrate;

[0036] xsect of the air-core photonic-bandgap fibers of the schematically illustrated replacement of Figure 19, it has non-circular (for example, hexagon) core shape, and free of surface modes; And

[0037] Figure 20 A and 20B are two kinds and can compare in the fibre core pattern of the photonic-bandgap fibers of having bought on the market and the effective refractive index of surface modes.

Embodiment

[0038] Xia Mian description is based on a kind of photonic-bandgap fibers (PBF) with covering photonic crystal region, this covering photonic crystal region comprises triangular lattice, this lattice comprises a plurality of circular ports that are filled with gas (for example air) in silica or other solids again, and wherein these holes are separated with periods lambda.PBF based on silica for example is described in the R.F.Cregan et al. that had above quoted, Single-Mode Photonic Band Gap Guidance ofLight in Air; The Jes Broeng et al. that had above quoted, Analysis of air-guidingphotonic bandgap fibers; And the Jes Broeng et al. that had above quoted, PhotonicCrystal Fibers:ANew Class of Optical Waveguides.For simplicity's sake, in this instructions such optical fiber is called airport optical fiber; Yet, as discussed above, below discussion and result also can be applicable to such photonic-bandgap fibers: it has fibre core and/or all or some clad material holes and is filled with other materials (for example another kind of gas, vacuum, liquid outside the deacration, and have a solid portion of the clad material of making by the material that is different from silica (for example a kind of different solid or multiple solids) or solid).And these results also are applicable to other sectional hole patterns (for example hexagon pattern, square pattern etc.).

[0039] Fig. 1 shows the partial cross-section of the air-core photonic-bandgap fibers PBF100 of an exemplary triangles pattern.As shown in the figure, optical fiber 100 comprises a solid dielectric lattice 102, and it comprises a plurality of airports 104 that are in around the air-core 106.Illustrate in greater detail three exemplary adjacent holes 104 among Fig. 2.The part that is in the solid lattice 102 between any three adjacent holes 104 is called as texture (or turning) 110, and the thinner region (being the zone between any two adjacent holes) that connects two adjacent textures is called as section (or barrier film) 112.In an illustrated embodiment, each airport 104 has radius ρ.The center to center spacing of adjacent vacant pore 104 is called as the periods lambda of photonic crystal.

[0040] as below discussing in more detail, each texture 110 can be approximate by the incircle 114 of radius α, and wherein the circumference in three holes 104 around the circumference of incircle 114 and the texture 110 is tangent.Can show that by simple geometric calculating the radius α of incircle 114 is relevant, as follows with the radius ρ and the periods lambda of airport 104:

$\mathrm{\α}=(\mathrm{\Λ}/\sqrt{3})-\mathrm{\ρ}$

[0041] as shown in Figure 1, by introduce at fiber optic hub radius be R than great circle cylindricality airport, can advantageously generate the air-core 106 of PBF 100.The position of this right cylinder (being shown a dash line circle among Fig. 1) is called as the edge of fibre core 106 in this article.Radius R is called as the characteristic dimension of air-core 106 in this manual.In circular core example shown in Figure 1, radius R is the radius of circular core.Below discussion be applicable to and have other shapes and characteristic dimension the fibre core of (for example from the center to the bee-line on the nearest border of polygon fibre core).In PBF illustrated in figures 1 and 2 100, radius R is selected to 1.15 Λ, and the radius ρ of each airport 104 is selected to 0.47 Λ.For instance, advantageously selecting radius is the air-core 106 of 1.15 Λ, because the pairing fibre core of this fiber core radius is actually (for example, remove effectively between these seven right cylinders glass structure) by removing from the center of PBF prefabrication that seven right cylinders form.This structure is generally used, and is described in J.A.West et al. for instance, Photonic Crystal Fibers, Proceedings of 27 ^Th European Conference on Optical Communications (ECOC ' 01-Amsterdam), Amsterdam, The Netherlands, September 30-October 4,2001 paperThA2.2, pages 582-585 incorporates the document into this paper at this with way of reference.

[0042] as mentioned above, surface modes is formed at the defect mode of the boundary between fibre core 106 and the photon-crystal clad material 102.Fig. 3 shows a kind of typical surface pattern of the triangle pattern air-core PBF 100 that is used for Fig. 1 and Fig. 2.Fig. 4 shows a kind of representative basis fibre core pattern of the PDF 100 that is used for Fig. 1 and Fig. 2.In Fig. 3 and Fig. 4, level line is represented isophote.The normalization intensity of outmost intensity line is 0.1 in each group, and the normalization intensity of innermost intensity line is 0.9, and each intervenient intensity line represents that normalized step-length recruitment is 0.1.

[0043] when lacking fibre core, PBF only supports volume mode.Fig. 5 shows an example of volume mode.The volume mode of Fig. 5 is to design for the identical triangle pattern air-core PBF 100 (but not removing central construct to form air-core 106) that is shown among Fig. 1.As shown in Figure 3 and Figure 4, the level line of Fig. 5 is represented isophote.

[0044] designated volume pattern shown in Figure 5 comprises a series of narrow intensity lobes, and it is positioned at each center than thick dielectric turning 110 of photon crystal 1 02.Other volume mode can have different lobe distribute (for example all lobes can be placed in the center of barrier film 112, but not the center at turning 110).

[0045] as discussed above, unless optical fiber is designed to eliminate all surface modes rightly, otherwise this optical fiber will be supported many surface modes.As top further discussion, the propagation constant of surface modes approaches or equals the propagation constant of basic fibre core pattern usually, therefore, the fibre core pattern can (for example easily be coupled to surface modes, by carrying out random perturbation at cross section of optic fibre), this will cause the propagation loss of basic fibre core pattern to increase.When optical fiber was not single-mode, this problem existed equally for other fibre core patterns except that basic schema.

[0046], can systematically study the influence of fiber core radius on the fibre core pattern and the influence that surface modes performance upper surface cuts off by changing the radius R of air-core 106.Such research is based on emulation or the simulation that the AMD Linux of University of Michigan at parallel Athlon 2000MP processor that utilizes full vector plane-wave extended method troops and carries out on the machine.A kind of exemplary full vector plane-wave extended method for example is described in Steven G.Johnson et al., Block-iterative frequency-domain methods for Maxwell ' s equations in aplanewave basis, Optic Express, Vol.8, No.3,29January 2001 pages173-190 incorporate the document into this paper at this with way of reference.

[0047] grid resolution used of this emulation is Λ/16, and the super cell is of a size of 8 Λ * 8 Λ.The solid portion of supposing clad material is a silica, and institute porosely is circle and is filled with air.When utilizing 16 parallel processors to move this emulation, the complete modeling of all fibre core patterns of a given optical fiber and the Electric Field Distribution of surface modes and dispersion curve need expend 7 hours to 10 hours usually.

[0048] simulation result for triangle pattern shows, the photonic band-gap that is fit to the air waveguide only exists the airport radius ρ greater than about 0.43 Λ.The maximum circular airport radius that can make in the practice (for example, thereby enough silicas are remained in the barrier film 112 between the adjacent vacant pore 104, so that a supporting construction to be provided) is slightly larger than 0.49 Λ.This research in, by the airport radius ρ of simulation architecture between these two ultimate values.Especially, ρ is selected as about 0.5 Λ.Though these emulation described herein are carried out ρ=0.47 Λ, but to any ρ value between 0.43 Λ to 0.5 Λ, also obtained similar result, and qualitative conclusion described herein all is effective for any airport size among scope 0.43 Λ to 0.5 Λ.

[0049] Fig. 6 has illustrated the theoretic ω-k of the fibre geometry of being studied that produces for fiber core radius R=1.15 Λ (for example referring to Fig. 1) _zFigure.Among Fig. 6, the longitudinal axis is that (be optics angular frequency or the visual angle frequencies omega=2 π c/ λ of Λ/λ), wherein λ is the free space wavelength of light signal, and c is a light speed in a vacuum, and Λ is photon-crystal structure cycle to 2 π c/ Λ in normalization.Thereby the longitudinal axis is represented ω Λ/2 π c=Λ/λ, and it is a dimensionless amount.Transverse axis among Fig. 6 is the propagation constant k along fiber axis (z direction) _z, it is normalized to 2 π/Λ (is k _zΛ/2 π).

[0050] first photonic band-gap supported of the no limit structure of Fig. 1 emulation optical fiber 100 is by shade (cross hacures) region representation.The size and dimension of first photonic band-gap depends on the radius value (its shown in equal 0.47 Λ in the emulation) of airport 104, but the size of this band gap and fibre core 106 is almost irrelevant.Dash line among Fig. 6 is represented light, and regardless of core size and core shape, can there be the fibre core pattern in it down.Shadow region part on this dash line shows, and in emulation optical fiber 100, the normalization frequency range of the light that air-core can be guided is about 1.53 to about 1.9.

[0051] solid-line curve among Fig. 6 is represented the dispersion relation of fibre core pattern and surface modes.In fact this air-core has two kinds of basic schemas.Each pattern is all by polarization linearly almost, and the polarization orthogonal of the polarization of each pattern and another pattern.It is (degenerate) of degeneracy or degenerative that these two kinds of patterns approach.In other words, these two kinds of patterns have almost completely identical dispersion curve in this band gap.In fact uppermost curve comprises two dispersion curves among Fig. 6, corresponds respectively to this two kinds of basic schemas; But because these two curves are almost completely identical, so that can not pick out in the figure.At k _zThe correlation intensity profile of the selected pattern in Λ/2 π=1.7 places, corresponding to one of them be plotted among Fig. 4 of these two kinds basic fibre core patterns, and being plotted among Fig. 3 corresponding to a kind of exemplary table surface model.These profiles show that the highest frequency pattern in this band gap is exactly these two kinds basic fibre core patterns.Other patterns in this band gap are surface modes, and its intensity is positioned at fibre core-clad material boundary, as shown in Figure 3.For fibre core pattern and surface modes, the intensity that overlaps with the space of optical fiber silica part is different.Difference on the intensity causes the group velocity of fibre core pattern near light velocity c, and the group velocity of surface modes is lower, as shown in Figure 6.

[0052] Fig. 6 also shows another distinguishing characteristics of fibre core pattern and surface modes.Especially, the curve of surface modes is always in band gap and ray intersection.On the contrary, the curve of fibre core pattern in band gap with optics from non-intersect.

[0053] by fiber core radius R being changed to 2.2 Λ from 0.6 Λ, the performance of fibre core pattern and surface modes is studied as the function of flaw size with step-length 0.1 Λ.ω-k shown in Figure 7 _zFigure institute at fibre geometry identical with the fibre geometry that is used for producing Fig. 6 information, but fiber core radius (R=1.8 Λ) greatly.Shown as the local cross section of optic fibre among Fig. 8, bigger fiber core radius is formed, for example, by the extra crystalline network outside seven right cylinders removing prefabrication central authorities, so that the intersecting than thin membrane 112 of fibre core 106 surface and 104 in hole, and crossing with thicker dielectric turning 110.As expected, be used for the quantity of the fibre core pattern that appears at Fig. 7 of Fig. 8 embodiment greater than the quantity that is used for Fig. 1 embodiment.In addition, all patterns are all and are used for this fibre core pattern than long radius.In one group four kinds or more modes (for example being 4 kinds in Fig. 7), along with the low-frequency cutoff value of frequency from this band gap begins to increase, five-star fibre core pattern at first occurs.This feature depends on and core size and mode degeneracy degree.For example see also the Jes Broeng et al. that had above quoted, Analysisof air-guidingphotonic bandgap fibers.Along with frequency further increases, pattern quantity reaches certain maximum quantity (being 14) at about 1.7 places of normalization frequency (ω Λ/2 π c) in example shown in Figure 7.On normalization frequency about 1.7, pattern quantity descends gradually up to being 2 (two kinds of basic schemas) at this band gap high-frequency cut-off value place.The maximum quantity of fibre core pattern appear near the frequency that light and lower band edge intersect or among.In the described embodiment of Fig. 7, light is located with crossing than the edge, low-energy zone in a normalization frequency (ω Λ/2 π c), and the value of this normalization frequency (ω Λ/2 π c) is about about 1.67.Note, a plurality of patterns of many curve representations among Fig. 7, these patterns be degeneracy and be overlapping in the figure therefore.

[0054] Fig. 9 shows fibre core pattern maximum quantity (promptly this pattern quantity is marked in ω Λ/2 π c=1.7 places) and R dependence.The quantity of surface modes also is shown among Fig. 9.In addition, the core shape for representative radius R=0.9 Λ, R=1.2 Λ and R=2.1 Λ is shown in respectively among Figure 10 A, Figure 10 B and Figure 10 C.As mentioned above, the grid resolution that is used for producing data point among Fig. 9 is Λ/16.But, producing extra point in the fiber core radius scope between more interested 1.1 Λ to 1.3 Λ, size of mesh opening is reduced to Λ/32 in this scope.Therefore, the ratio of other parts and inequality among the absolute quantity of the surface modes of in this scope, estimating and this figure.This is inessential, is in order to determine the border in surface modes zone because produce the fundamental purpose of data point.

[0055] PBF neutralization has surprising similar based on the performance of the fibre core pattern of the traditional fiber of general internal reflection.Basic schema is (as LP ₀₁Pattern) be (referring to Fig. 6 and the Fig. 7) that doubles degeneracy, it is by polarization linearly almost, and shows class gaussian intensity profile.For example see also the Jes Broeng et al. that had above quoted, Analysis of air-guiding photonicbandgap fibers.Below four kinds of patterns also be degeneracy, and the Electric Field Distribution of these four kinds of patterns is very similar to the HE of traditional fiber ₂₁ ^Odd, HE ₂₁ ^Even, TE ₀₁And TM ₀₁Pattern.In these fibre core patterns many patterns are arranged, particularly rudimentary pattern shows dual degeneracy in the polarization on the major part of this band gap.Along with fiber core radius increases, the quantity of fibre core pattern is increased to 6 (promptly 2 kinds of basic schemas add 4 kinds of degenerate modes above-mentioned) with discrete steps (referring to Fig. 9) from 2 (i.e. 2 kinds of basic schemas), then to 14 (because 8 kinds of patterns of back reach cutoff at much at one radius just) etc.

[0056] Fig. 9 has also illustrated these patterns on the other hand.Specifically, in the time of in R falls into some bounded scope, find that all patterns are the fibre core pattern.First three bounded scope is: scope 1 is from about 0.7 Λ to about 1.1 Λ; Scope 2 is from about 1.3 Λ to about 1.4 Λ; Scope 3 is from about 1.7 Λ to about 2.0 Λ.

[0057] Fig. 7 has illustrated that R equals the situation of 1.8 Λ, and this is the specific example of free of surface modes PBF in the scope 3.Figure 11 schematically shows the free of surface modes scope of being determined by Computer Simulation.In Figure 11, circular background patterns is represented unlimited photon crystal structure, 4 shades (cross hacures) annular section expresses support for the fiber core radius scope of surface modes, and three non-shade annular sections (being denoted as can be with 1, can with 2 and can be with 3) first three radius of expression free of surface modes.Notice that for the radius (for example, the central non-shaded portion of Figure 11) less than 0.5 Λ, fibre core is not supported the fibre core pattern by photonic band-gap effect guiding.

[0058] Figure 11 only is the another kind of mode with diagrammatic representation free of surface modes shown in Figure 9 zone.Thereby, three radius of support free of surface modes among Fig. 9, it is illustrated by the empty triangle that falls within on the bottom level axle, is patterned into three white rings (non-shade) zones (can be with 1,2 and 3) among Figure 11.White can interband complementation (shade) can be with corresponding to Fig. 9 intermediate cam shape and be in radius on the transverse axis, thereby it expresses support for the radius of surface modes.

[0059] in the shade of first in Figure 11 scope (for example, from about 0.7 Λ to about 1.1 Λ can be with 1), fibre core is supported single fibre core pattern on the whole wavelength coverage of band gap, and does not support any surface modes, promptly this PBF is real single-mode.In existing document to the design of single-mode total silicon stone PBF without any record.Note, can be with 2, can and represent that long radius more every other can band with 3, optical fiber no longer is single-mode.

[0060] equal 0.9 Λ for R, an example that stops surface configuration has been shown among Figure 10 A, it falls into this monotype scope (for example, scope 1).The little glass tip that utilization is made fibre core by pressing method or other known manufacturing technologies can be made into these customized configurations.

[0061] quantity of surface modes also depends on fiber core radius to a great extent, although be in a kind of high non-dull mode.For the fiber core radius about about 0.6 Λ, about 1.2 Λ, about 1.6 Λ and about 2.1 Λ, introduced many surface modes, thereby caused surface modes quantity spike to occur.These spikes are shown among Fig. 9.And near these fiber core radius, surface modes quantity changes rapidly with R.The manufacturing of model experiment PBF is by removing central authorities' 7 right cylinders (R approximates 1.15 Λ) or 19 right cylinders (R approximates 2.1 Λ) to form fibre core 106 from prefabrication; Yet, though can making, make simply these particular values of R, also can cause the geometric configuration of support surface pattern, for example, as shown in Figure 9.

[0062] based on the aforementioned result of Computer Simulation, after deliberation the pacing items that occurs of surface modes, and recommended to have the new construction of free of surface modes.Pacing items has caused such observed result, and promptly when intersected at one or more dielectrics turning 110 of the surface of fibre core 106 and photonic crystal lattice 102, surface modes formed.According to this observed result, obtained quick and easy geometric criterion, in order to estimate whether support surface pattern of specific fiber configuration.As discussed below, be applied to having the triangle pattern PBF 100 of circular air-core 106, resulting quantitative forecast of this approximate geometry model and computer artificial result basically identical recited above when this geometric criterion.

[0063] as discussed above, when unlimited photonic crystal stops suddenly, surface modes can occur, for example appear at the edge of limited dimension crystal often.For example, the photonic crystal of being made by the dielectric rod in air is only when stopping can causing surface modes when rod is crossed in end-grain cutting.And the clearing end of only cutting air is too weak and can not produce surface modes.

[0064] in air-core PBF 100, fibre core 106 has also served as the defective of perturbed lattice 102, thereby can cause surface modes in the edge of fibre core 106.Whether surface modes what occur, occurs and depend on all how photonic crystal is terminated, and this has determined the disturbance size that defective is introduced.When lacking air-core, PBF only has volume mode, discusses with reference to Fig. 5 as top.

[0065] as Fig. 1, Fig. 3 and shown in Figure 4 when introducing air-core 106, the dielectric substance of lattice 102 has been replaced in fibre core 106 parts with air.Cut the surface portion of the fibre core 106 of clad material airport 104 among Fig. 1 and replaced air with air.Thereby, as (it for example is described in the J.D.Joannopoulos et al. that had above quoted in the example of a planar photonic crystal, Photonic Crystals:Molding tge flow of light), those parts on fibre core surface can not cause tangible disturbance.It is to replace dielectric with air that the fibre core surface portion of cutting lattice 102 dielectric turnings 110 or dielectric diaphragm 112 among Fig. 1 is only arranged, thus the volume mode of disturbance Fig. 5.This disturbance will be discussed below whether be enough to cause potentially surface modes (surface modes for example shown in Figure 3).

[0066] because the fibre core 106 of virtually any size and shape was always cut some dielectric substance, so fibre core 106 is always introduced certain disturbance.The performance of this disturbance is such, and promptly in ω-k figure, the frequency of all volume mode is upwards moved by the frequency from them entirely in their positions of being undisturbed separately.For silica/air PBF 100, a little less than this disturbance relatively, and this frequency displacement is less, so that nearly all disturbance volume mode is present in during a volume mode can be with.Remove recited above outside, pattern can be with (after this being referred to as " HFBM ") from the highest frequency volume mode than the low-energy zone.Because such pattern just in time is positioned under the band gap in ω-k figure, so this disturbance moves into band gap with them as surface modes.For example see also the J.D.Joannopoulos et al. that had above quoted, Photonic Crystals:Molding the flow oflight.

[0067] always surface modes can be described as the expansion of volume mode.For weak disturbance considered here, what can show is that the main project in this expansion is HFBM, as considers that the origin of these surface modes is desired.This HFBM is a volume mode shown in Figure 5.As shown in Figure 5, the lobe of these patterns all is centered at the turning 110 of crystal 102, and this will produce two important results.At first, because surface modes is to be introduced by the disturbance of this volume mode, so the lobe of surface modes also is centered on the turning 110, for example, and as shown in Figure 3.The second, for will and producing the HFBM of surface modes by disturbance, disturbance is bound to appear in photonic crystal lattice 102 dielectric area that have quite big HFBM intensity, for example, and in the zone that is arranged in 110 places, photon crystal 1 02 turning.These observed results show that on HFBM, the disturbance size that surface modes and air-core 106 are introduced is closely related.If (radius R in for example, as Figure 12 is intersected at 110 places, turning of dielectric lattice 102 and the lobe of HFBM in the surface of fibre core 106 ₁Fibre core shown in), this disturbance is bigger, thereby causes surface modes.Thereby surface modes quantity is proportional as the maximum intensity that intersects with fibre core 106 in the dielectric 102.On the contrary, if (for example, shown in the fibre core of radius R among Figure 13 2) do not intersected with any lobe of this volume mode in the surface of fibre core 106, then form free of surface modes.

[0068] aforementioned content is shown among Figure 14, and its surface modes quantity with ω Λ on the circle of radius R/2 π=1.7 places (value on the longitudinal axis of left side) curve is reproduced as a solid-line curve, and this surface modes quantity is as standardizing to the function of the R of Λ (transverse axis).Figure 14 also comprises the curve (dashed curve) of the maximum intensity (value of arbitrary unit on the longitudinal axis of right side) of highest frequency volume mode.Figure 14 clearly show that the relation between maximum intensity and the surface modes quantity.Two curves of among Figure 14 this are clearly closely-related, and this just confirms, surface modes occurred for radius R, so that the high strength lobe of highest frequency volume mode was cut at the edge of described fibre core.Based on this principle, just disclosed first approximate dependence of surface modes quantity and fiber core radius.By the result of more accurate emulation, aforementioned content shows that the result who utilizes the HFBM criterion to obtain has predicted quite exactly whether surface modes exists.Certainly, the disturbance of many other kinds can cause surface modes in photon crystal 1 02, so that the aforementioned condition that is used to the to lack surface modes condition that necessitates, but is not adequate condition always.

[0069] a criterion that is used for determining whether to exist surface modes, the electromagnetism intensity of highest frequency volume mode is integrated along the fibre core edge.It is enough that these two kinds any that double in the degenerate mode are carried out such integration, because the integration of these two kinds of patterns is equated, desired as symmetry.

[0070] calculates the method that unlimited fibre cladding material volume mode intensity distributes according to a kind of numerical value ground, can realize the aforementioned definite of air-core radius R.According to this method, the intensity distributions of highest frequency volume mode of the optical fiber interested of no air-core will be determined at first.Thereafter, the circular air-core of stack or stacked radius R on this intensity distributions.Shown in Figure 15 A and Figure 15 B, change fiber core radius R and can cause the edge of described fibre core to pass the zones of different of field distribution.According to these computing method, when intersected in the high lobe zone of the edge of described fibre core and this field distribution, optical fiber was with the support surface pattern.At Figure 15 A and Figure 15 B, radius R=R ₁Fibre core be the example of fiber core radius of passing the high strength lobe of 7 (being 6 in this embodiment) highest frequency volume mode.These computing method have predicted that the fibre core with this radius is with the support surface pattern.Extreme at another, as fiber core radius R=R ₂The time, shown in Figure 15 A and Figure 15 B, the fibre core edge does not pass any high strength lobe of this volume mode, thereby radius R ₂Fibre core support surface pattern not.

[0071] though preceding method is described in conjunction with circular port, it should be understood that preceding method is not limited in circular port, it can be applied to any core shape.

[0072] as mentioned above, these computing method are qualitatively.According to this method, if the high strength lobe of the edge of the fibre core of selected radius R and volume mode intersects, the optical fiber that has this radius fibre core so is with the support surface pattern.As so far described, what surface modes are this method do not guarantee to support.And this method does not specify the fibre core edge (promptly being supported) to occur before at surface modes, and how high the intensity that intersects with the fibre core edge have, perhaps must be crossing with what high strength lobes.

[0073] the intensity lobe of recognizing HFBM almost is symmetrical on the position angle, can advantageously simplify the HFBM criterion, as shown in Figure 5.Thereby the part that is limited in each lobe in the dielectric turning 110 can be approximately the circle 114 that is inscribed within turning 110, as shown in Figure 2.As discussed above, the radius α of incircle 114 is relevant with radius ρ with the periods lambda in the hole 104 of triangle pattern, promptly $\mathrm{\α}=(\mathrm{\Λ}/\sqrt{3})-\mathrm{\ρ}.$

[0074] part that is limited to dielectric HFBM is approximated to the two-dimensional array that is centered at the circle 114 on all photons-crystal turning 110, and as shown in figure 16, this figure draws at triangle pattern and ρ=0.47 Λ.This approximate making for surface modes, a kind of new better simply criterion that exists can be expressed as: when one or more crossing in 114 justified with these in the surface of and if only if fibre core 106, have surface modes.Certainly, many other kind disturbances can cause surface modes in photon crystal 1 02, and the aforementioned condition that therefore lacks surface modes is a necessary condition, but it is not an adequate condition always.

[0075] utilize coupled-mode theory also can obtain identical geometric criterion.Consideration is than the symmetry of low-energy zone volume mode, and each turning 110 can be approximated to the dielectric rod that is inscribed within turning 110, the length of wherein should rod having extended PBF 100.Center on by air around the rod of each isolation, thereby constitute dielectric waveguide.This dielectric waveguide is supported a kind of basic schema that has high field (strong fields) in this rod, and high field will dribble in the surrounding air, so this seems the more HFBM independence lobe shown in the image pattern 5.Thereby this periodic excellent array has the pattern of circle shown in Figure 16 114.These independently excellent waveguide modes are because of the approaching weak coupling each other of adjacent rod, thus the formation volume mode.

[0076] HFBM just in time is that of independent wave guide is specific overlapping.If introduce the air-core 106 of the one or more rods of incision, the volume mode that so dielectric removal will in the opposite direction become forming with the waveguide mode disturbance.Then, coupled to each other with this circle that intersect on the surface of fibre core 106 by the waveguide mode of the rod of disturbance, thus form a surface modes.This surface modes supported by this circle rod, thus have each rod outer reduce, shown in the exemplary table surface model of Fig. 3.If barrier film 112 rather than turning 110 were only cut in the surface of fibre core 106, these rods are intact so, and these patterns are coupled to each other must not have fibre core 106 as them.Thereby, form free of surface modes.According to this description, when intersect with rod on the surface of and if only if fibre core 106, there is surface modes.This is with top to be similar to the criterion that the HFBM lobe obtained with incircle 114 be identical.

[0077] in order to verify the correctness of new geometric criterion, this criterion is applied among the air-core of the classification the most widely PBF that is studied, just has as shown in figure 16 in the optical fiber of circular airport of triangle pattern.Fibre core 106 is that a radius that is in optical fiber 100 centers is the bigger circular airport of R.In addition, this analysis supposition is intersected when R is selected to the surface and the one or more rod (for example circle among Figure 16 114) that make fibre core 106, will have surface modes so, and the quantity of surface modes will be with proportional by the quantity of the rod that intersects.This ratio rule is desired just, because along with being increased by the quantity of the rod that intersects, the disturbance size increases thereupon, the quantity of surface modes also increases thereupon.On the contrary, when does not intersect with any rod on the surface of fibre core 106, free of surface modes can appear.A sketch of cross section of optic fibre, for example, sketch as shown in figure 16 makes this criterion can be applied to any fibre geometry easily.

[0078] for triangle pattern, the result of aforementioned geometric analysis is illustrated among Figure 16 graphically.Shade among Figure 16 (cross hacures) thus ring expression and rod intersect the fiber core radius scope of support surface pattern.As above with reference to Figure 11 discussed, non-shade ring between the shade ring (can with 1 to can be with 6) expression is not intersected with any rod thereby the radius of support surface pattern not.By Figure 16 being used basic trigonometry method, can directly calculate the dependence of surface modes quantity and fiber core radius, thereby determine the crossing excellent quantity in surface of the fibre core 106 of a given radius.This quantity is plotted as the solid-line curve among Figure 17, and (for example, R/ Λ) fiber core radius, and the excellent quantity that wherein the left side longitudinal axis is represented and intersect on the fibre core surface is as predicting by geometric criterion wherein to be normalized to the crystal periods lambda during transverse axis of this figure.

[0079] important results shown in Figure 17 has been predicted in this simple supposition, and the some radiuses that promptly are used for such PBF 100 can be with on whole band gap and support free of surface modes.For the radius R of 3.5 Λ nearly, 6 such can take out of in the scope that present Figure 17 covers, and wherein Λ promptly is the crystal cycle as defined above.Scope among Figure 17 does not comprise can be with under the R=0.47 Λ, because such radius is too little, can not support the fibre core pattern.Although not shown in Figure 17,, there are 8 other energy bands for radius greater than 3.5 Λ.Last can be with and be in R and approximate 8.86 Λ.

[0080] table 1 has been listed the border and the width of 14 energy bands.As shown in table 1, first can be with the wideest.For most of purposes, first to be with also be most important because first can be be the single-mode scope that falls into PBF 100 (for example, ρ equals 0.47 Λ for the airport radius, R less than about 1.2 scope in) unique can band.Every other can band (remove the 3rd can be with outside) all narrower basically.One ground supports that being with of free of surface modes will narrow down along with the increase of fibre core 106 radiuses.Notice that because the intrinsic property of excellent approximate value, these values are independent of the refractive index of lattice dielectric 102.

Table 1

Can the band numbering	Scope (unit: Λ) from geometric criterion	Scope (unit: Λ) from the HFBM criterion	Scope (unit: Λ) from emulation	Bandwidth (unit: Λ)
					1	0.685-1.047	0.68-1.05	0.65±0.05-1.05±0.05	0363
2	1262-1.420	126-1.43	1.27±0.01-1.45±0.05	0158
					3	1.635-1974	1.64-1.97	1.65±0.05-2.05±0.05	0339
4	2.189-2.202			0013
					5	2.624-2779			0155
6	3.322-3405			0083
					7	3619-3679			0059
8	3.893-3934			0071
					9	4.271-4402			0131
10	5239-5400			0161
					11	6.218-6.244			0.026
12	6.914-6916			0.0022
					13	7.875-7914			0039
14	8.844-8.856			0.0113

The position of 14 energy bands of the fiber core radius of support free of surface modes in the triangle PBF of ρ=0.47 Λ

[0081], can on supercomputer, utilize full vector plane-wave extended method to carry out the numerical simulation of identical category PBF surface modes, as discussed above in order to estimate the accuracy of aforementioned quantitative forecast.Dielectric is defined as silica, and the radius ρ of airport 104 is restricted to and equals 0.47 Λ.Simulation result is plotted as the empty triangle that combines dash line in Figure 17, wherein the right side longitudinal axis is represented the surface modes quantity predicted by this numerical simulation.Notice that the curve of the curve of this triangle form point and Fig. 9 triangle form point is identical.Very good with the consistance of geometric criterion prediction (in Figure 17, being plotted as solid-line curve).By the information in table 1 the 4th row of the information in table 1 the 2nd row of representing the boundary value that first three free of surface modes that this geometric criterion generates can be with and the expression boundary value that these emulation produced is compared, this consistance will be more obvious.The value that this geometric criterion produces be value that emulation produces 5% in.Note, because these emulation are very consuming time (for example, about 6 hours of each radius), therefore the exact boundary radius that emulation produced (for example calculates in limited number, calculate comprising the radius that first three free of surface modes can be with), and be to utilize the digit of limited number to calculate.On the contrary, geometric criterion can provide much more information in a small amount of time.Be also noted that, the exact magnitude (referring to Figure 17) of surface modes although geometric criterion does not calculate to a nicety, geometric criterion has presented correct trend.Especially, this geometric criterion dopes, and surface modes meeting usually becomes many more along with the increase of the radius R of fibre core 106, and this is consistent with original hypothesis.

[0082] utilizes above-mentioned geometric criterion to recomputate the border radius simply, also can estimate the influence that optical fiber air-filling rate exists surface modes apace by different value to pore radius ρ.Result of calculation as shown in figure 18, it marks and draws on the longitudinal axis on the normalization border fiber core radius R/ Λ from R/ Λ=0.6 to R/ Λ=2.0 and transverse axis from ρ/Λ=0.43 to ρ/Λ=normalization pore radius ρ/Λ of 0.50.The probable value of ρ is limited at about 0.43 Λ between about 0.50 Λ, and as ρ during less than about 0.43 Λ, photonic crystal does not have band gap, and ρ is during less than about 0.50 Λ, and the thickness of barrier film 112 will become 0.The fiber core radius scope of support surface pattern and pore radius are shade (cross hacures), and the fiber core radius scope of support surface pattern is not non-shade.Figure 18 shows that the free of surface modes than macropore 104 generation broads with big air-filling rate can be with, because increase the radius ρ of airport 110 the radius α of rod (by incircle 114 expressions) is reduced.Because excellent size is less, the scope of the fiber core radius R that intersect with these rods is narrower, and the free of surface modes radius can be with and will become wideer.

[0083], can obtain other interested observed results according to the result of above-mentioned research.At first, in experimental PBF 100, fibre core 106 normally 19 pipelines of 7 pipelines by removing central authorities from prefabrication or central authorities forms.These configurations correspond respectively to the fiber core radius R of about 1.15 Λ and about 2.1 Λ.Defined herein geometric criterion has confirmed the prediction of accurate emulation, i.e. these two kinds of configurations all show surface modes, for example shown in Figure 17.The high propagation loss that has had to the explanation of small part most of photonic-bandgap fibers of making up to now of surface modes.

Simulation curve among [0084] the second, Figure 17 shows that a little variation in the fiber core radius can make free of surface modes PBF be transformed into the PBF of support surface pattern.Emergentness during these change is consistent with the disturbance treatment that forms surface modes, thereby has supported the confidence level of excellent approximate value discussed above.

[0085] the 3rd, the trend in the table 1 that utilizes simple physics demonstration to explain not long ago to be discussed.Along with fiber core radius increases, adjacent concentric each layer rod will be more close to each other, as shown in figure 16.For than long radius, just more embarrass circular radius to find and to avoid all excellent spaces.Equally, trend towards intersecting than long radius, thereby the quantity of surface modes is increased with more rod.Can easily find out the form of expression of this influence in the 5th layer and the 6th layer of rod, it is in can be with 4 can be with between 5 among Figure 16.The 5th layer and the 6th layer are radially overlapping, thereby are merged into the fiber core radius district of the single broad of support surface pattern.In other words, promptly be between the 5th layer and the 6th layer of rod, not exist free of surface modes to be with.Same affect also can occur for the the 7th, the 8th and the 9th layer, and it can be with 5 and can be with between 6 Figure 16's, thereby has caused the table 1 can be with 5 maximum radius (R=2.779 Λ) and can be with bigger numerical value difference between 6 least radiuses (R=3.322 Λ).On the contrary, along with fibre core 106 radius Rs increase, free of surface modes can be with and will become narrow further, as can find out that it is that unit has listed the width that each free of surface modes can be with Λ in table 1 the 5th row.

Can reckon with intuitively that [0086] radius is greater than certain critical value R _cFibre core 106 all with the support surface pattern, thereby only to have the free of surface modes of limited quantity to be be available.This expectation directly perceived is consistent with the result of table 1.Especially, for the estimated structure of hole 104 radius ρ that is 0.47 Λ herein, the quantity that free of surface modes can be with is limited (promptly only 14 energy bands), and has a critical radius R _c(promptly about 8.86 Λ), surface modes is at this critical radius R _cOn form a continuum.As indicated in the numerical value in the table 1, it is so narrow (for example Δ R is several percentages of Λ) that back four free of surface modes can be with, so that back four energy bands are likely obsolete for most of practical applications.The inevitable inference of this observed result is exactly, and has geometry in particular described herein and meets with the surface modes problem possibly greater than the multi-mode PBF of the fiber core radius R of 5.4 Λ.

[0087] l/e of any lobe of actual volume pattern among Figure 15 A and Figure 15 B ²The mean value of radius is about 0.22 Λ.Compare with the intensity lobe, inscribe among Fig. 8 (dash line) radius of a circle α is about 0.107 Λ.The value of equivalent redius α by refining the silica rod, and be suspended in the mean radius of the basic schema of airborne solid bar by calculating can obtain a more accurate accompanying drawing and better quantitative consistance.

[0088] the final observed result that obtains in the described from here research is, for any core size, by selecting a non-circular core shape, makes it have a surface of not intersecting with any rod, can avoid surface modes on principle.Figure 19 shows an illustrative example of non-circular core, and its characteristic dimension is corresponding to the bee-line from the center to the nearest border of fibre core.Utilize the fibre core (it is delineated out by the dash line among Figure 19, so that the visual inspection core shape) of a hexagonal shape, even when core region is big, also can avoid introducing any surface modes.This structure has showed a kind of improvement that is better than above-mentioned circular core structure in the application of expectation multi-mode operation.

[0089] geometric criterion described herein is not limited to have the specific triangles geometric configuration of circular clad material hole and circular core.Also be suitable for for other profiles and geometric configuration.

[0090] according to the description of front, whether simple geometry criterion Fast estimation air-core PBF exists surface modes.The result of geometric criterion and numerical simulation results compared have been proved, when geometric criterion being applied in the optical fiber with triangle pattern clad material and circular core, whether the limited quantity of its fiber core radius of supporting free of surface modes of calculating to a nicety can be with and exist.For enough big circular core (promptly for surpass these can with in the radius that can be with of maximum), this optical fiber is for the equal support surface pattern of any fiber core radius.This Common Criteria provides a kind of favourable new tool, so that analyze in the photon-crystal optical fibre with any crystal structure and any fibre core profile whether have surface modes.

[0091] Figure 20 A and Figure 20 B show the effective refractive index of these patterns their curve map as the function of wavelength.Curve among Figure 20 A shows the effective refractive index of the optical fiber of being made by Crystal Fibre.Curve among Figure 20 B shows the effective refractive index of the optical fiber of being made by Corning.These curves utilize numerical simulation to obtain.Basis fibre core pattern is illustrated by the runic curve, and more weak line is surface modes.The minimal losses that it is the mensuration of 100dB/km that the fibre core pattern of Crystal Fibre (Figure 20 A) has an order of magnitude, and Corning fibre core pattern (Figure 20 B) has the minimal losses for the mensuration of 13dB/km.It is main because the fibre core pattern has been coupled to surface modes that the loss of fibre core pattern is considered to, and this is the inherent loss that produces at the fibre core near surface owing to concentration of energy.Therefore, surface modes has suffered the rayleigh scattering that strengthens.The general power that is coupled to surface modes from the fibre core pattern will be enhanced, if thereby a large amount of surface modes of this fibre core support, dissipating so will be bigger.In addition, be well known that the coupling of two kinds of patterns is coupled in the fibre core pattern under the situation of surface modes according to coupled-mode theory, when the effective refractive index of these two kinds of patterns near the time will be stronger.

[0092] when 1.50 mum wavelength places consider these patterns in Figure 20 A and Figure 20 B, can find out that the surface modes in the Crystal Fibre structure (Figure 20 A) is more much more than the surface modes in the Corning structure (Figure 20 B).And the effective refractive index of Corning surface modes is less than 0.986, and the effective refractive index of fibre core pattern is 0.994, and both differ 0.8%.On the other hand, the effective refractive index of the fibre core pattern in the Crystal Fibre structure is 0.996, and the effective refractive index of immediate surface modes is 0.994, and both only differ 0.2%.Except estimate the fibre core pattern to surface modes be coupling in the optical fiber that Crystal Fibre makes stronger, other aspects are identical, particularly are present in how much level of disruption in these two kinds of fiber cores.Thereby Crystal Fibre optical fiber is supported more surface modes, and surface modes is coupled byer force, and this higher propagation loss with Crystal Fibre optical fiber is consistent.According to preceding as can be known described, have more low-loss air-waveguide PBF in order to design, preferred version is to eliminate surface modes fully, as mentioned above.If can not eliminate surface modes fully, so alternative plan be exactly reduce surface modes quantity (for example, do not cut too many clad material lattice turning by making fibre core), improving the efficient of off resonance between fibre core pattern and the residual surface pattern, and both.

[0093] though above be described in conjunction with specific embodiment of the present invention, it should be understood that the description for these embodiment only is for the present invention that explains, and be not intended to limit the present invention.Do not break away under the situation of true spirit of the present invention that claims limit and scope, those skilled in the art can carry out various modifications and application.

Claims (22)

1. method of making photonic-bandgap fibers, this photonic-bandgap fibers comprises having zone map to form the material of lattice, described material has first refractive index, and described zone map has second refractive index that is lower than described first refractive index, and described method comprises:

Determine intensity profile near the highest frequency volume mode in described zone; And

Form a central fibre core in described lattice, this fibre core has an edge, and described edge is low to moderate the position that is enough to make described optical fiber support free of surface modes in the intensity of described highest frequency volume mode, intersects with described zone map.

2. method according to claim 1, wherein said pattern are periodic.

3. method according to claim 1, wherein:

Described zone in the described material is circular;

Described zone map is arranged to every group of three adjacent area and forms a triangle, this triangle has the first separately of described material between every pair of zone, and has formation second portion separately one middle body, described material in every group of three adjacent areas;

Described central fibre core is formed in the described lattice, so that the edge of described central fibre core only passes the first of described material.

4. method according to claim 3, the described zone in the wherein said material is the hole, described hole has the wall that is limited by material around.

5. method according to claim 4, the described hole in the wherein said material is a hollow.

6. method according to claim 5 wherein utilizes the air with described second refractive index to fill described hole in the described material.

7. method according to claim 5 wherein utilizes the gas with described second refractive index to fill described hole in the described material.

8. method according to claim 5 wherein utilizes the liquid with described second refractive index to fill described hole in the described material.

9. method according to claim 3, wherein said border circular areas comprise that one has the solid of described second refractive index.

10. method according to claim 1, wherein said material are dielectric.

11. method according to claim 1, wherein said material are silica.

12. a photonic-bandgap fibers comprises:

One lattice, described lattice comprises first material with first refractive index, described first material has the pattern that is formed on second material wherein, described second material has second refractive index that is lower than described first refractive index, described lattice has a plurality of first areas, the intensity lobe of highest frequency volume mode is supported in described a plurality of first area, and has a plurality of second areas, and described a plurality of second areas are not supported the intensity lobe of described highest frequency volume mode; And

One central fibre core, it is formed in the described lattice, and described central fibre core has an edge, and described edge only passes the second area of described dielectric lattice, wherein:

The described pattern of described second material comprises a plurality of geometric areas, and each geometric areas has center separately, and adjacent geometric areas is isolated by center to center Λ;

Each geometric areas of described second material is circle, and has radius ρ, and described radius ρ is less than 0.5 Λ; And

Described pattern is a triangle.

Be inscribed within three circles between the adjacent geometric areas 13. photonic-bandgap fibers according to claim 12, wherein said first area comprise, each radius of a circle α equals

14. photonic-bandgap fibers according to claim 12, wherein:

The radius ρ of each geometric areas is about 0.47 Λ;

The radius that the edge had of described fibre core is within the radius fibre core scope, and this fiber core radius scope extends to the radius that is about 1.05 Λ from the radius of about 0.68 Λ; And

Described optical fiber is single-mode.

15. photonic-bandgap fibers according to claim 12, wherein:

The radius ρ of each geometric areas is about 0.47 Λ;

The radius that the edge had of described fibre core is in a plurality of radius within one of them;

In described a plurality of fiber core radius scope first is to the radius that is about 1.05 Λ from the radius that is about 0.68 Λ;

In described a plurality of fiber core radius scope second is to the radius that is about 1.43 Λ from the radius that is about 1.26 Λ; And

In described a plurality of fiber core radius scope the 3rd is to the radius that is about 1.97 Λ from the radius that is about 1.64 Λ.

16. photonic-bandgap fibers according to claim 12, wherein:

The radius ρ of each geometric areas is about 0.47 Λ;

The radius that the edge had of described fibre core is at a plurality of radius within one of them;

In described a plurality of fiber core radius scope first is to the radius that is about 1.047 Λ from the radius that is about 0.685 Λ;

Second is to the radius that is about 1.420 Λ from the radius that is about 1.262 Λ in described a plurality of fiber core radius scope; And

In described a plurality of fiber core radius scope the 3rd is to the radius that is about 1.974 Λ from the radius that is about 1.635 Λ.

17. method of geometry of selecting core size, in order to make the photonic-bandgap fibers of free of surface modes, described photonic-bandgap fibers has the lattice that comprises first material, described first material has first refractive index, described material has surrounded the periodic patterns of second material area, described second material has second refractive index that is lower than described first refractive index, a barrier film and the adjacent area of described second material of each zone of described second material by described first material is spaced apart, and each intersection of barrier film has formed a texture of described first material, and described method comprises:

Limit an inscribe middle body in each texture of described second material, the outer perimeter of adjacent area is tangent on every side to make outer perimeter and the described texture of described inscribe middle body;

Limit a plurality of fibre core characteristic dimension scopes, wherein any have be in one of them the fibre core of size of described a plurality of scope and have an edge, described edge does not pass any described inscribe middle body; And

Select a fibre core, the size that it had is in described a plurality of fibre core characteristic dimension scope within one of them.

18. method of geometry according to claim 17, wherein:

Each zone has a respective center, and adjacent geometric areas is spaced apart by center to center Λ;

Each zone of described second material is circular, and has radius ρ, and described radius ρ is less than 0.5 Λ; And

Described pattern is a triangle.

19. being radius α, method of geometry according to claim 18, wherein said inscribe middle body equal Circle.

20. method of geometry according to claim 18, wherein:

The described radius ρ of each geometric areas is about 0.47 Λ;

The radius that the edge had of described fibre core is within the radius, and described fiber core radius scope extends to the radius that is about 1.05 Λ from the radius that is about 0.68 Λ; And

Described optical fiber is single-mode.

21. method of geometry according to claim 18, wherein:

The radius ρ of each geometric areas is about 0.47 Λ;

Described fibre core is a circular, and the described fibre core characteristic dimension radius that is described fibre core;

In described a plurality of fibre core characteristic dimension scope first is to the radius that is about 1.05 Λ from the radius that is about 0.68 Λ;

In described a plurality of fibre core characteristic dimension scope second is to the radius that is about 1.43 Λ from the radius that is about 1.26 Λ; And

In described a plurality of fibre core characteristic dimension scope the 3rd is to the radius that is about 1.97 Λ from the radius that is about 1.64 Λ.

22. method of geometry according to claim 18, wherein:

The radius ρ of each geometric areas is about 0.47 Λ;

Described fibre core is a circular, and the described fibre core characteristic dimension radius that is described fibre core;

In described a plurality of fibre core characteristic dimension scope first is from being about 0.685 Λ radius to the radius that is about 1.047 Λ;

Second is to the radius that is about 1.420 Λ from the radius that is about 1.262 Λ in described a plurality of fibre core characteristic dimension scope; And

In described a plurality of fibre core characteristic dimension scope the 3rd is to the radius that is about 1.974 Λ from the radius that is about 1.635 Λ.

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