Alkeskjold, Thomas Tanggaard

Lægsgaard, Jesper

Petersen, Sidsel Rübner

Intermodal degenerate four wave mixing (FWM) is investigated numerically in large mode area hybrid photonic crystal fibers. The dispersion is controlled independently of core size, and thus allows for power scaling of the FWM process

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Intermodal parametric gain of degenerate four wave mixing in large mode area hybridphotonic crystal fibersPetersen, Sidsel Rübner; Lægsgaard, Jesper; Alkeskjold, Thomas TanggaardPublished in:Nonlinear Optics Technical DigestPublication date:2013Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Petersen, S. R., Lægsgaard, J., & Alkeskjold, T. T. (2013). Intermodal parametric gain of degenerate four wavemixing in large mode area hybrid photonic crystal fibers. In Nonlinear Optics Technical Digest (pp. NW4A.08).Optical Society of America.NW4A.08.pdf Nonlinear Optics Technical Digest © OSA 2013Intermodal parametric gain of degenerate fourwave mixing in large mode area hybrid photoniccrystal fibersSidsel R. Petersen1,∗, Jesper Lægsgaard1, Thomas T. Alkeskjold21DTU Fotonik, Technical University of Denmark, Ørsteds Plads Building 343, 2800 Kgs. Lyngby, Denmark2NKT Photonics A/S, Blokken 84, 3460 Birkerød, Denmark∗srpe@fotonik.dtu.dkAbstract: Intermodal degenerate four wave mixing (FWM) is investigated numerically inlarge mode area hybrid photonic crystal fibers. The dispersion is controlled independently ofcore size, and thus allows for power scaling of the FWM process.© 2013 Optical Society of AmericaOCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (060.5295) Photonic crystal fibers.1. IntroductionControl of the group velocity dispersion (GVD) is the key to control the spectral position of the maximum gain of aFWM process in silica fibers. Tailoring of the GVD is possible in photonic crystal fibers (PCFs), since the zero GVDwavelength (ZDW) scales with core size [1]. However, for power scaling a large mode area (LMA) is needed, which isincompatible with the GVD control in standard PCFs through core scaling, since the material dispersion dominates inlarge core fibers. In this work a hybrid LMA PCF is considered, with a cladding consisting of airholes and high-indexinclusions. A microscope image of such a fiber is seen in Fig. 1a. The high-index inclusions give rise to a photonicbandgap (PBG) effect, and adjustment of the airhole diameters allow for single mode (SM) guidance in a LMA core.The diameter size of the high-index inclusions on one side of the core is reduced with respect to the diameter sizeon the other side of the core, resulting in an asymmetric design, providing control of blue- and red spectral edge ofthe PBGs [2]. In Fig. 1b the calculated overlap integral of the fundamental mode (FM) polarized along the Ge-rodswith the core region is shown. The overlap integral has been calculated in steps of 0.1 nm with a full-vector modalsolver based on the finite element method. In Fig. 1c the calculated group velocity dispersion parameter (D) of thetransmission band 990nm− 1070nm is shown. The Zero Dispersion Wavelength (ZDW) is positioned at 1054.5 nm,shorter wavelengths lie in the normal dispersion regime, while the dispersion is anomalous for longer wavelengths.Near the bandedges the curve diverges substantially. Large values of normal and anomalous GVD is thus experiencedon the edges of the PBGs, providing control of the GVD independently of core size.2. Degenerate four wave mixingDegenerate four wave mixing is a third order nonlinear process. In the process two pump photons are annihilated andone so-called signal and idler photon are created. For the process to take place, two conditions must be satisfied. Thefirst is energy conservation, which is given by 2ωp =ωs+ωi, where ωp is the pump photon, ωs the signal photon, andωi the idler photon. The second condition is phase matching, which has a linear and nonlinear contribution. The linearcontribution is given by ∆β = β (ωs)+β (ωi)−2β (ωp), where β (ωs), β (ωi), and β (ωp) is the propagation constantat signal, idler, and pump frequency, respectively, and the nonlinear contribution arises from the Kerr effect.2.1. Parametric gainThe parametric gain can be calculated from a set of coupled differential equations [3,4]. Overlap integrals of the inter-acting pump-, signal-, and idler- fields are included in these equations. These overlap integrals are typically assumedto be equal, which is a good approximation in e.g. endlessly single mode PCFs, where the spatial mode distributionis approximately the same at all wavelengths. However, when PBG guidance is present, the spatial mode distributiondiffers substantially, and the overlap integrals cannot be approximated by any simple expression.If a pump power much higher than the signal and idler power is assumed, and the pump remains undepleted in theNW4A.08.pdf Nonlinear Optics Technical Digest © OSA 2013(a) (b) (c)(d)Fig. 1: (a) Microscope image of the double-clad large mode area hybrid photonic crystal fiber. The inner claddingconsists of airholes (black circles) with hole-to-hole spacing Λ and seven missing airholes define the core region. Onerow of airholes is replaced with high-index Germanium-doped silica rods of two sizes (white circles). (b) Calculatedoverlap integral of the fundamental mode polarised along the Germanium-doped silica rods with the core region.(c) Calculated group velocity dispersion in the transmission band 995nm− 1065nm. (d) Calculated parametric gain(green curve, y-axis on the left) for the case where the signal and idler are generated in the fundamental mode. Theoverlap integral is also shown (black curve, y-axis on the right).FWM process, an approximate expression for the parametric gain can be obtained. Following a similar approach as inSec. 10.2.2 in [4] the effective phase mismatch, κ , and approximate parametric gain, g, can be found:κ = ∆β +2n2ωpcPp( fsp+ fip− fpp) , (1)g =√(n2ωpcPp fsipp)2−(κ2)2, (2)where n2 is the nonlinear-index coefficient, c is the speed of light, Pp is the pump power, and f jk, ( jk = sp, ip, pp),and fsipp, are the field overlap integrals defined in [4] with the indices representing the pump, p, signal, s, and idler, i.To obtain the field overlap integrals, the modes of the hybrid PCF are calculated with a full-vector modal solver basedon the finite element method, 50 modes for each considered wavelength. In Fig. 1d the gain has been calculated forsignal and idler being generated in the fundamental mode. Similar gain curves for other combinations are considered,and the combination resulting in the largest gain can be found, which allows one to predict which modes the signaland idler will be generated in, in an actual measurement.References1. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell “AnomalousDispersion in Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 12,(7) 807–809 (2000).2. T. T. Alkeskjold, “Large-mode-area ytterbium-doped fiber amplifier with distributed narrow spectral filteringand reduced bend sensitivity,” Opt. Express 17,(19) 16394–16405 (2009).3. J. Hansryd and P. A. Andrekson, “Fiber-Based Optical Parametric Amplifiers and Their Applications,” IEEE J.Sel. Topics Quantum Electron. 8,(3) 506–520 (2002).4. Govind P. Agrawal, “Nonlinear Fiber Optics,” Elsevier, United States of America, Fourth edition, 2007.

Intermodal parametric gain of degenerate four wave mixing in large mode area hybrid photonic crystal fibers

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Intermodal parametric gain of degenerate four wave mixing in large mode area hybrid photonic crystal fibers

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