Guiding 2.94 µm using low-loss microstructured antiresonant triangular-core fibers Yang Chen,1 Mohammed F. Saleh,1 Nicolas Y. Joly,2,3 and Fabio Biancalana1 1Scottish Universities Physics Alliance (SUPA), School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh, UK 2Max Planck Institute for the Science of Light, Gu¨nther-Scharowsky str. 1, 91058 Erlangen, Germany 3Universita¨t Erlangen-Nu¨rnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany (Dated: February 1, 2016) We introduce a new simple design of hollow-core microstructured fiber targeted to guide mid- infrared light at a wavelength 2.94 µm. The fiber has a triangular-core supported via silica-glass 6 websenclosed bya large hollow capillary tube. The fiberspecific dimensions are determined based 1 ontheguidingtechnique,whichisbasedontheanti-resonantmechanism. Foratriangular-corewith 0 side length 100 µm, the fiber has a minimum transmission loss 0.08±0.005 dB/m and dispersion 2 2.3 ps/km/nm at theoperational wavelength 2.94 µm. n a PACSnumbers: 42.81.Qb,42.82.Et J 9 I. INTRODUCTION 2 ] s High-powerlasersourcessuchasEr:YAGlaser at2.94 c µm and CO laser at 10.6 µm have influential medical 2 i t and technological applications. The delivery of output p intense pulses of these sources in silica-glass step-index o fibers has always been a huge obstacle because of the . s low-damage threshold of the glass materials as well as c i the high attenuationof silica in the mid-infraredregime. s y Hollow-core fibers (HCFs), with their unconventional h guiding properties, seem to be the best solution for this p problem [1–3]. These fibers are engineered waveguides [ that use non-traditional methods for transferring light FIG. 1. (Color online). Sketch of our proposed hollow-core 1 over relatively-long distances in a low-index core sur- anti-resonant triangular-core fiber. t1, t2, and t3 are the v rounded by a high-index structure. Photonic bandgap cladding, web, and jacket tube thickness, respectively, s is 4 (PBG) fibers are periodic microstructures that exploit thecore-side length, and R is the jacket tuberadius. 6 the analogy with solid-state physics for confining light 0 [4]. Light with optical frequencies lying within a forbid- 8 0 den bandgap is trapped inside the low-index-coredue to with an optimum displacement from the core [17]. Par- . the prohibited propagationinside the fiber-cladding. 1D ticular negative curvature cores have been also shown to 1 and2DPBGfibershavebeendemonstratedbywrapping substantially lessen the fiber-losses [18–20]. In this case, 0 amultilayeredBraggstructure[5–7]orstackinganumber carefuldesignisrequiredtopreventcouplingbetweenthe 6 1 ofcapillarytubesinasuitablyshapedpreform[8–11],re- core and cladding modes [20]. Very recently, broadband : spectively. By increasing the number of cladding layers, single-mode operation have been demonstrated in these v the fiber guiding loss is dramatically suppressed, albeit fibers by resonant filtering of higher order modes [21]. i X over restricted wavelength bands. r Anti-resonant (AR) HCF fiber is another type of a II. FIBER DESIGN microstuctured fiber, where the guiding mechanism is basedontheanti-resonantmodesofFabryP´erotcavities [12, 13]. These fibers have wide transmission windows, The delivery of the output light emitted by Er:YAG but with higher losses in comparison to the PBG fibers. laser at 2.94 µm was achieved by using tube-leaky fibers Also, adding more layersto the cladding has small influ- with losses 0.85 dB/m [22], or hollow-core negative- ence on decreasing the fiber-losses [14]. In recent years, curvature fibers with losses 0.06 dB/m [23]. Also as agreatdealofefforthasbeendedicatedto suppressdra- recently predicted, transmission losses at this particu- matically the losses of AR-HCF far beyond that of PBG larwavelengthcanreachminimal values using ARfibers fibers,byusingmulti-non-concentriccapillarytubes[15]. withlargenumbersofnestedtubes arrangedina certain Contact points between cladding capillaries have to be order [24]. In this paper, we present an AR-HCF with a avoided,sincetheywouldbreaktheantiresonancecondi- simple design for guiding mid-infra red light at 2.94 µm tionandmayleadtoadditionallosses[16]. Anothertech- withonly 0.08 0.005dB/mlosses. The fiber ismade of ± niqueforlossreductionis toaddanextraoutercladding three identical adjacentsilica-glasscapillary tubes encir- 2 cledbyawidercapillarywithradiusRactingasajacket tube with thickness t . During the fabrication process 3 the three touching capillaries create a perfect equilateral triangleoughtto the actionofsurfacetensioninabsence of additional external pressure, as shown in Fig. 1. The triangle has a thickness t determined by the dimension 1 oftheoriginalcapillary,andalengths=R(1+2/√3)−1. The thickness t of the supporting webs is constrained 2 by t =2t due to fabrication requirements. It has been 2 1 shownrecentlythatacorewithapolygonshapewillhave lower guiding losses as the number of the polygon sides decreases [14]. Hence, one can conjecture that our fiber would have lower losses in comparison to another one with a hexagonal core, for instance. The fiber is antici- patedtohavegreatimpactonthe deliveryofhigh-power laserpulses[1–3]aswellasingas-basednonlinearoptical applications [25]. ThesimulationsinthispaperaredoneusingCOMSOL FIG. 2. (Color online). Loss-dependence of hollow-core anti- software for three different fibers with core side lengths resonanttriangular-corefibersonthethicknessoftheperfect s=40,70,100µm, whichwe renameso forthas (a), (b), matching layers with t1 = t3 = 2.19 µm and λ = 2.94 µm. Bluestars,redcircles,greentrianglesrepresentthefibers(a), and (c), respectively. A suitable perfectly matched layer (b),and (c). (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 PML thickness for the three fibers has been achieved as de- picted in Fig. 2. For instance, the attenuation of fiber (c)is0.08 0.005dB/matthedesigningwavelength2.94 ± µm. Theerrorisdeducedfromtheslightoscillationsdur- ingnumericalconvergence,observedwhenincreasingthe PML layer to large values. Material absorption losses have not been included similar to recent studies [26]. A capillary tube that has the thickness of the triangle (c) and the radius of its inscribed circle has losses 26.86 dB/m, which demonstrates the effectiveness of our de- sign. The anti-resonant wavelengths λl of an AR-HCF are given by [13], 4tpn2 n2 λl = 2− 1, (1) FIG. 3. (Color online). Losses of hollow-core anti-resonant 2l+1 triangular-core fibers with the core-side length s = 40 µm where t is the cladding thickness, n and n are the core (bluestars),70µm(redcircles)and100µm(greentriangles) 1 2 and cladding refractive indices, and l 0 is an inte- at thefirst fiveanti-resonant modes. ≥ ger that defines the order of the transmission window. Whereas the resonant wavelengths that leak outside the (a), (b), and (c) at the design wavelength 2.94 µm for fiber-core during propagation are l=0 4aredepictedinFig. 3. Forthesevaluesofl,the − 2tpn2 n2 corresponding thicknesses t1 are 0.73, 2.19, 3.64, 5.10, λm = 2− 1, (2) and6.56µm,respectively. Basedontheresultsshownin m Fig. 3,wehavechosenthe1st orderanti-resonancewith − wheremisanotherpositiveinteger,whichrepresentsthe t1 = 2.19 µm thickness, since it results in transmission order of the loss peaks. Knowing the operating wave- losses <0.1 dB/m for fiber (c). length,differenttriangular-corethicknessest canbe de- The effect of the jacket tube thickness on the losses 1 termined using Eq. 1 by replacing t =t , corresponding for the three fibers has been portrayed in Fig. 4 with 1 to the different values of l 0. Based on the fact that t = 2.19 µm. First, as the core-side increases, the core 1 ≥ the loss will grow with the rise of anti-resonant order, effective area also increases, and the loss will drop due we have focused our attention on the first few values of to better mode accommodation inside the large core. In l. The guiding loss of the fundamental mode for fibers contrast to Ref. [26], the losses in our fiber have a peri- 3 FIG. 4. (Color online). Loss-dependence of hollow-core anti- resonanttriangular-corefibersonthejackettubethicknesst3, 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. FIG.5. (Coloronline). Wavelength-dependenciesof(i)losses and (ii) dispersion of the triangular fibers (a), (b), and (c). odicoscillatorydependenceast varies. Thelossminima The simulation parameters are λl = 2.94 µm, and t1 = t3 = 3 occurs when the jacket tube thickness also satisfies the 2.19 µm. anti-resonant condition Eq. 1. Moreover, the loss peaks are positioned at 1.46 , 2.91,and 4.37 µm, which are ex- actly the thicknesses that fullfil the resonant condition Eq. 2 for m = 1,2,3. Although light is trapped inside thetriangular-core,satisfyingthisresonanceconditionin the jacket-tube ring allows the confined mode to escape R. Wehavefoundthatthelossesofthehexagonalfiberis from the core towards the jacket throughthe fiber webs. 156dB/m,whichismuchhigherthanthetriangular-core Our fiber performance measured by the spectral- fiber, as we have anticipated earlier. dependence of its losses and dispersion is displayed in panels (i,ii) of Fig. 5 for the three fibers under consid- eration with t1 = t3 = 2.19 µm. The loss-dependence We have also explored the possibility of implement- behaves similarly to Fig. 4, however, with slightly de- ingnegative-curvaturecoresthatcanreducethe confine- creasing losses as moving towards shorter wavelengths. ment loss more [18–20]. In designing this type of fiber, The reasonis thatthe modaleffective areashrinkswhen we maintain the locations of the three vertices as in the decreasingthewavelength,hence,themodeisbettercon- straight case via choosing a radius of curvature ρ larger fined and its guiding-loss drops. The loss maxima and than the side of the triangle, ρ s. Using this method, ≥ minimatakeplacewhenthewavelengthmatchesEqs. (1) the bent walls are prevented from touching each other, and (2), respectively. For the fiber (c), with side-length avoiding the formation of optical resonators that may 100 µm, the attenuation approaches notably only 0.08 lead to additional losses. In Fig. 7, we have scanned dB/m at the designing wavelength 2.94 µm, very close the radius of curvature ρ from 150 to 500 µm, and have to that value obtainedusing the negativecurvaturefiber calculated the losses. In this simulation, the determined [27]. Asdemonstratedinpanel(ii),thefiberexhibitsalso values of the triangular-coreand jacket thicknesses from flat low dispersion of about 2.3 ps/km/nm around this theabovestudieshavebeenused. Surprisingly,thelosses wavelength,especially for the case (c), allowingthe fiber ofourfiberdonotbehavetraditionallybyvaryingthera- to be ofgreatinterestfor nonlinearlight-matterapplica- diusofcurvature. Forlargevaluesofρ,whichinthelimit tions, especially when the core is filled with gases. ρ would correspond to the straight wall case, the → ∞ The fundamental mode profiles of the triangular-core lossesapproachasymptoticallytheaforementionedvalues fibers are displayed in the first three panels of Fig. 6 us- 0.08dB/m. With decreasingρ orinotherwordsincreas- ing the aforementioned designed parameters. The effec- ing curvature, losses start to have strong peaks around tivemodeareasofthefibers(a),(b)and(c)are133,422, ρ = 160 and 320 µm due to large coupling overlap be- and 935 µm2, respectively. In panel (d), we have com- tween the core and cladding modes [20]. The minimum pared the triangular fiber (c) to a hexagonal fiber that between these two peaks is approximately 0.2 dB/m, ≈ has the criterion of having the same incircle enclosed by which indicates that negative curvature does not assist the triangle-core as well as the same jacket tube radius in suppressing the guiding losses. 4 III. CONCLUSION In conclusion, we have proposed the design of a new simple anti-resonant triangular-corefiber that can guide light at the mid-infrared frequency range. The fiber is made of relatively few identical capillary tubes with thickness 2.19µm. Our fiber has shownremarkablylow- loss below 0.1 dB/m as well as low dispersion 2.3 ∼ ps/km/nm at the operating wavelength 2.94 µm. Also, we have shown that the thickness of the jacket tube has a significant role in confining the light inside the core. Moreover, we found that introducing negatively curved walls does not work towards loss-suppression. In fact, much higher losses have been obtained for certain values of the radius of curvature due to strong overlapbetween the modes of the core and the cladding. Finally, we be- lieve that our design will induce other novel ideas and stimulatenewresearchintheareaofguidingfar-infrared light. FIG. 6. (Color online). (i)–(iii) Fundamental-mode profiles of the triangular fibers (a), (b), and (c). 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Loss-dependenceofnegatively-curved triangular-core fibers on the radius of curvature ρ with fixed distance100µmbetweenitsvertices. Thesimulationparam- etersarethesameasinFig. 5. Theinsetshowsazoomofthe geometry of thecurved core. The jacket tubeis still present, but is not shown in thefigure.