Guiding 2.94 µm using low-loss microstructured antiresonant triangular-corefibers

Yang Chen,1 Mohammed F. Saleh,1 Nicolas Y. Joly,2, 3 and Fabio Biancalana11)Scottish Universities Physics Alliance (SUPA), School of Engineering and Physical Sciences,Heriot-Watt University, EH14 4AS Edinburgh, UK2)Max Planck Institute for the Science of Light, Gunther-Scharowsky str. 1, 91058 Erlangen,Germany3)Universitat Erlangen-Nurnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany

(Dated: 6 April 2016)

We introduce a new simple design of hollow-core microstructured fiber targeted to guide mid-infrared lightat a wavelength 2.94 µm. The fiber has a triangular-core supported via silica-glass webs enclosed by a largehollow capillary tube. The fiber specific dimensions are determined by the anti-resonant guiding mechanism.For a triangular-core with side length 100 µm, the fiber has a minimum transmission loss 0.08± 0.005 dB/mand dispersion 2.3 ps/km/nm at the operational wavelength 2.94 µm.

PACS numbers: 42.81.Qb,42.82.Et

I. INTRODUCTION

High-power laser sources such as Er:YAG laser at 2.94µm and CO2 laser at 10.6 µm have influential medicaland technological applications. The delivery of outputintense pulses of these sources in silica-glass step-indexfibers has always been a huge obstacle because of thelow-damage threshold of the glass materials as well asthe high attenuation of silica in the mid-infrared regime.

Hollow-core fibers (HCFs), with their unconventionalguiding properties, seem to be the best solution for thisproblem1–3. These fibers are engineered waveguides thatuse non-traditional methods for transferring light overrelatively-long distances in a low-index core surroundedby a high-index structure. Photonic bandgap (PBG)fibers are periodic microstructures that exploit the anal-ogy with solid-state physics for confining light4. Lightwith optical frequencies lying within a forbidden bandgapis trapped inside the low-index-core due to the prohibitedpropagation inside the fiber-cladding. 1D and 2D PBGfibers have been demonstrated by wrapping a multilay-ered Bragg structure5–7 or stacking a number of capillarytubes in a suitably shaped preform8–11, respectively. Byincreasing the number of cladding layers, the fiber guid-ing loss is dramatically suppressed, albeit over restrictedwavelength bands.

Anti-resonant (AR) HCF fiber is another type of mi-crostuctured fiber, where the guiding mechanism is basedon the anti-resonant modes of Fabry Perot cavities12,13.These fibers have wide transmission windows, but withhigher losses in comparison to the PBG fibers. Also,adding more layers to the cladding has small influenceon decreasing the fiber-losses14. In recent years, a greatdeal of effort has been dedicated to suppress dramaticallythe losses of AR-HCF far beyond that of PBG fibers,by using multi-non-concentric capillary tubes15. Contactpoints between cladding capillaries have to be avoided,since they would break the antiresonance condition andmay lead to additional losses16. Another technique for

FIG. 1. (Color online). Sketch of our proposed hollow-coreanti-resonant triangular-core fiber. t1, t2, and t3 are the thick-ness of the cladding, web, and jacket tube, respectively, s isthe core-side length, and R is the jacket tube radius.

loss reduction is to add an extra outer cladding with anoptimum displacement from the core17. Particular neg-ative curvature cores have been also shown to substan-tially lessen the fiber-losses18–20. In this case, carefuldesign is required to prevent coupling between the coreand cladding modes20. Very recently, broadband single-mode operation have been demonstrated in these fibersby resonant filtering of higher order modes21.

II. FIBER DESIGN

The delivery of the output light emitted by Er:YAGlaser at 2.94 µm was achieved by using tube-leakyfibers with losses 0.85 dB/m22, or hollow-core negative-curvature fibers with losses 0.06 dB/m23. Also as re-cently predicted, transmission losses at this particularwavelength can reach minimal values using AR fiberswith large numbers of nested tubes arranged in a cer-tain order24. In this paper, we present an AR-HCF with

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a simple design for guiding mid-infra red light at 2.94 µmwith only 0.08± 0.005 dB/m losses. The fiber is made ofthree identical adjacent silica-glass capillary tubes encir-cled by a wider capillary with radius R acting as a jackettube with thickness t3. During the fabrication processthe three touching capillaries create a perfect equilat-eral triangle ought to the action of surface tension inabsence of additional external pressure, as shown in Fig.1. This structure is a very simplified version of the rou-tinely made Kagome-lattice HCF, where adjacent tubesstraighten up to create a star-of-David pattern. In thecurrent case, we only use three tubes, resulting in a tri-angle at the center of the structure. The triangle hasa thickness t1 determined by the dimension of the orig-inal capillary, and a length s = R(1 + 2/

√3)−1. The

thickness t2 of the supporting webs is constrained byt2 = 2t1 due to fabrication requirements. It has beenshown recently that a core with a polygon shape willhave lower guiding losses as the number of the poly-gon sides decreases14. Hence, one can conjecture thatour fiber would have lower losses in comparison to an-other one with a hexagonal core, for instance. Thefiber is anticipated to have great impact on the deliv-ery of high-power laser pulses1–3, in gas-based nonlin-ear optical applications25, and medical23,26 and sensingapplications27,28.

The simulations in this paper are done using COMSOLsoftware for three different fibers with core side lengthss =40, 70, 100 µm, which we rename so forth as (a), (b),and (c), respectively. A suitable perfectly matched layer(PML) is used to estimate the attenuation of each fiber.PMLs with enough thicknesses, several times the oper-ating wavelength, have been used for the fibers (a), (b),and (c), respectively. Convergence of losses with PMLthickness for the three fibers has been achieved as de-picted in Fig. 2. For instance, the attenuation of fiber(c) is 0.08±0.005 dB/m at the designing wavelength 2.94µm. The error is deduced from the slight oscillationsduring numerical convergence, observed when increasingthe PML layer to large values. Material absorption losseshave not been included similar to recent studies29. A cap-illary tube that has the thickness of the triangle (c) andthe radius of its inscribed circle has losses 26.86 dB/m,which demonstrates the effectiveness of our design.

The anti-resonant wavelengths λl of an AR-HCF aregiven by13,

λl =4t√n22 − n21

2l + 1, (1)

where t is the cladding thickness, n1 and n2 are the coreand cladding refractive indices, and l ≥ 0 is an inte-ger that defines the order of the transmission window.Whereas the resonant wavelengths that leak outside thefiber-core during propagation are

λm =2t√n22 − n21m

, (2)

where m is another positive integer, which represents the

FIG. 2. (Color online). Loss-dependence of hollow-core anti-resonant triangular-core fibers on the thickness of perfectmatching layers with t1 = t3 = 2.19 µm and λ = 2.94 µm.Blue stars, red circles, green triangles represent the fibers (a),(b), and (c).

FIG. 3. (Color online). Losses of hollow-core anti-resonanttriangular-core fibers with the core-side length s = 40 µm(blue stars), 70 µm (red circles) and 100 µm (green triangles)at the first five anti-resonant modes.

order of the loss peaks. Knowing the operating wave-length, different triangular-core thicknesses t1 can be de-termined using Eq. 1 by replacing t = t1, correspondingto the different values of l ≥ 0. Based on the fact thatthe loss will grow with the rise of anti-resonant order,we have focused our attention on the first few values ofl. The guiding loss of the fundamental mode for fibers(a), (b), and (c) at the design wavelength 2.94 µm forl = 0−4 are depicted in Fig. 3. For these values of l, thecorresponding thicknesses t1 are 0.73, 2.19, 3.64, 5.10,and 6.56 µm, respectively. Based on the results shown inFig. 3, we have chosen the 1st−order anti-resonance witht1 = 2.19 µm thickness, since it results in transmission

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FIG. 4. (Color online). Loss-dependence of hollow-core anti-resonant triangular-core fibers on the jacket tube thickness t3,with t1 = 2.19 µm and λ = 2.94 µm. Straight blue, dashed-dotted red, and dashed green lines represent the fibers (a),(b), and (c) with side lengths s = 40, 70, and 100 µm.

losses < 0.1 dB/m for fiber (c).The effect of the jacket tube thickness on the losses

for the three fibers has been portrayed in Fig. 4 witht1 = 2.19 µm. First, as the core-side increases, the coreeffective area also increases, and the loss will drop dueto better mode accommodation inside the large core. Incontrast to Ref.29, the losses in our fiber have a peri-odic oscillatory dependence as t3 varies. The loss minimaoccurs when the jacket tube thickness also satisfies theanti-resonant condition Eq. 1. Moreover, the loss peaksare positioned at 1.46 , 2.91, and 4.37 µm, which are ex-actly the thicknesses that fullfil the resonant conditionEq. 2 for m = 1, 2, 3. Although light is trapped insidethe triangular-core, satisfying this resonance condition inthe jacket-tube ring allows the confined mode to escapefrom the core towards the jacket.

Our fiber performance measured by the spectral-dependence of its losses and dispersion is displayed inpanels (i,ii) of Fig. 5 for the three fibers under consid-eration with t1 = t3 = 2.19 µm. The loss-dependencebehaves similarly to Fig. 4, however, with slightly de-creasing losses as moving towards shorter wavelengths.The reason is that the modal effective area shrinks whendecreasing the wavelength, hence, the mode is better con-fined and its guiding-loss drops. The loss maxima andminima take place when the wavelength matches Eqs. (1)and (2), respectively. For the fiber (c), with side-length100 µm, the attenuation approaches notably only 0.08dB/m at the designing wavelength 2.94 µm, very close tothat value obtained using the negative curvature fiber26.As demonstrated in panel (ii), the fiber exhibits also flatlow dispersion of about 2.3 ps/km/nm around this wave-length, especially for the case (c), allowing the fiber to beof great interest for nonlinear light-matter applications,especially when the core is filled with gases.

The fundamental mode profiles of the triangular-core

FIG. 5. (Color online). Wavelength-dependencies of (i) lossesand (ii) dispersion of the triangular fibers (a), (b), and (c).The simulation parameters are λl = 2.94 µm, and t1 = t3 =2.19 µm.

fibers are displayed in the first three panels of Fig. 6 us-ing the aforementioned designed parameters. The effec-tive mode areas of the fibers (a), (b) and (c) are 133, 422,and 935 µm2, respectively. In panel (d), we have com-pared the triangular fiber (a) to a hexagonal fiber thathas the criterion of having the same incircle enclosed bythe triangle-core as well as the same jacket tube radiusR. We have found that the losses of the hexagonal fiber is156 dB/m, which is much higher than the triangular-corefiber, as we have anticipated earlier.

We have also explored the possibility of implementingnegative-curvature cores that can reduce the confinementloss more18–20. In designing this type of fiber, we main-tain the locations of the three vertices as in the straightcase via choosing a radius of curvature ρ larger than theside of the triangle, ρ ≥ s. Using this method, the bentwalls are prevented from touching each other, avoidingthe formation of optical resonators that may lead to ad-ditional losses. In Fig. 7, we have scanned the radiusof curvature ρ from 150 to 500 µm, and have calculatedthe losses. In this simulation, the determined values ofthe triangular-core and jacket thicknesses from the abovestudies have been used. Surprisingly, the losses of ourfiber do not follow the tradition by varying the radiusof curvature. For large values of ρ, which in the limitρ → ∞ would correspond to the straight wall case, thelosses approach asymptotically the aforementioned val-ues 0.08 dB/m. With decreasing ρ or in other wordsincreasing curvature, losses start to have strong peaksaround ρ = 160 and 320 µm due to large coupling overlapbetween the core and cladding modes20. The minimumbetween these two peaks is approximately ≈ 0.2 dB/m,

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FIG. 6. (Color online). (i)–(iii) Fundamental-mode profilesof the triangular fibers (a), (b), and (c). The simulation pa-rameters are λl = 2.94 µm, and t1 = t3 = 2.19 µm. (iv)Fundamental mode profile of a hexagonal fiber having thesame incircle enclosed by the fiber (a).

which indicates that negative curvature does not assistin suppressing the guiding losses.

III. CONCLUSION

In conclusion, we have proposed the design of a newsimple anti-resonant triangular-core fiber that can guidelight at the mid-infrared frequency range. The fiberis made of relatively few identical capillary tubes withthickness 2.19 µm. Our fiber has shown remarkably low-loss below 0.1 dB/m as well as low dispersion ∼ 2.3ps/km/nm at the operating wavelength 2.94 µm. Also,we have shown that the thickness of the jacket tube hasa significant role in confining the light inside the core.Moreover, we have found that introducing negativelycurved walls does not work towards loss-suppression. Infact, much higher losses have been obtained for certainvalues of the radius of curvature due to strong overlapbetween the modes of the core and the cladding. Finally,we believe that our design will induce other novel ideasand stimulate new research in the area of guiding far-infrared light for industrial30, medical23,26, and sensingapplications27,28.

M. Saleh would like to acknowledge the support ofhis research by Royal Society of Edinburgh and ScottishGovernment.

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FIG. 7. (Color online). Loss-dependence of negatively-curvedtriangular-core fibers on the radius of curvature ρ with fixeddistance 100 µm between its vertices. The simulation param-eters are the same as in Fig. 5. The inset shows a zoom of thegeometry of the curved core. The jacket tube is still present,but is not shown in the figure.

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