A novel Er3+-doped honeycomb photonic bandgap fiber for highly efficient amplification Zhi Wang*, Yange Liu, Guiyun Kai, Jianfei Liu, Chao Wang, Chunshu Zhang, Tingting Sun, Xiaoyi Dong Institute of Modern Optics, Nankai University, Tianjin, China 300071 ABSTRACT We present a numerical study of the guidance and amplification properties in an Er3+-doped honeycomb photonic bandgap fiber with down-doped core. Our analysis is based on a full-vector plane-wave expansion method and Runge-Kutta iterative algorithm. Overlap integrals between mode profiles and Er3+-doped region varies from 0.973 to 0.350 in guiding range of the fiber. The highly efficient amplifier can be designed by using this fiber. Keywords: Erbium-doped fibers, fiber amplifier, photonic bandgap, photonic crystal fibers
1. INTRODUCTION Photonic crystal fibers (PCFs) have recently attracted significant attention due to their unusual properties, including tailorable group velocity dispersion [1] and large or small mode areas [2], [3]. These properties have been used to design high-performance rare-earth doped fiber laser and amplifier [4]-[8]. The PCFs used in these applications are commonly based on the guiding mechanism of total internal reflection. Whereas another class of PCF, photonic bandgap fiber (PBGF), is more potential because of its special guiding mechanism. In PBGFs, light is confined in the vicinity of the core by the photonic bandgap (PBG) effect of photonic crystal cladding. T.Sondergaard [9] and A.Cucinotta et al. [10] have analyzed the PBGF laser and amplifier, respectively. The PBGFs considered by them consist of a honeycomb cladding structure and a core defect created by the introduction of an extra air hole in a honeycomb cell. Because of the presence of the central air hole, the fundamental mode profile in the PBGF is a ring-like shape, which makes a difficulty to efficient coupling with standard fibers. In this paper, we investigate the amplifier properties of a novel PBGF. This fiber, firstly introduced by T.P. Hansen et al. [11], composes a honeycomb cladding and a down-doped region as a defect in core. Er3+ ions are uniformly doped in the core region. Using a full-vector plane-wave expansion method, we obtain the frequency range and field profiles of guided mode for the PBGF. Then, the overlap integral between the mode profiles and Er3+-doped region is calculated. Finally, we investigate the gain and noise figure of the Er3+-doped PBGF amplifier by resolving the propagation and population rate equations by using Runge-Kutta iteration algorithm.
2. NUMERICAL METHOD The starting point of full-vector plane-wave expansion method is the vectorial wave equation for magnetic field H(r) as an eigenvalue problem: *
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Passive Components and Fiber-based Devices, edited by Yan Sun, Shuisheng Jian, Sang Bae Lee, Katsunari Okamoto, Proc. of SPIE Vol. 5623 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.576017
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{
}
∇ × ε −1 (r )∇ × H(r ) = (ω c ) H (r ) 2
(1)
where ε(r) represents the dielectric constant, ω and c are the angular frequency and the velocity of light in vacuum, respectively. The eigenfrequencies and eigenfunctions are computed by resolving the equations with periodic boundary conditions using preconditioned conjugate-gradient minimization of the block Rayleigh quotient in a planewave basis[12]. This method allows us to demonstrate the guiding properties of the PBGF. Firstly, we calculate the frequency range of PBG in the honeycomb structure. Then the field profiles and mode index of the guided mode for PBGF are investigated by using this method with a supercell approximation. Er3+-doped fiber amplifiers are modeled using the propagation and rate equations for a homogeneous, two-level laser medium. We assume that the Er3+ ions are uniformly distributed in a disk of radius rd, concentric with the fiber core. Thus the overlap integral between the dopant and optical mode Γ can be derived:
Γ=∫
2π
0
rd
∫0
i (r , φ )rdrdφ
(2)
where i(r,φ) is the normalized optical intensity mode distribution which can be obtained from the field profiles of guided mode. Er3+-doped fiber amplifiers are modeled using the propagation and rate equations for a homogeneous, two-level laser medium. We assume the emission cross section, the absorption cross section, and the spontaneous life-time of the Er3+ ions doped in the PBGF equal to those in the conventional Al/Er-fiber. Although those parameters may be changed by the codoped ions in core and PBG effect, the discussion is valid for analyzing how the amplifier performance is affected by the guiding properties of PBGF. Substituting for the value of Γ at single and pump wavelength in the propagation and rate equations, we employ an iterative process based on Runge-Kutta algorithm to resolve these equations. The ASE from 1430nm to 1630nm is considered with 1nm spacing in our simulation.
Fig. 1. Central part of the PBGF structure showing the doped
Fig. 2. Variation of the effective refractive index for guided
region in gray.
mode with normalized wavelength. The bottom left inset shows photonic band structure of the perfect honeycomb structure.
3. RESULT AND DISCUSSION The PBGF design under consideration is shown in Fig. 1. The air holes are arranged in a honeycomb lattice with a
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down-doped region to form a solid core defect. d and Λ are the diameter and pitch of air holes in cladding, respectively. dc is the diameter of down-doped core region with relative down-doping levels of 0.5%. The ratios of d/Λ=0.6 and dc/Λ=1.4 are fixed in this paper. Er3+ ions are uniformly doped in the down-doped region with the concentration N=1.74×1025ions/m3. The frequency range of PBG in perfect honeycomb structure is calculated firstly. For a fixed normalized out-of-plane wave vector component βΛ=6.28, the photonic band-structure diagram of the perfect honeycomb structure is shown in the inset of Fig.2. The out-of-plane wave vector corresponds to the propagation constant of the fibers. This figure reveals a PBG between the normalized frequency kΛ=4.66 and 4.87, where no mode solutions are found, irrespective of the polarization of the light. The PBG is various with βΛ, as well as the normalized wavelength λ/Λ. We illustrate the PBG edges as a function of λ/Λ in Fig. 2 with dashed lines. Then the field profiles and mode index of the guided mode for PBGF are investigated by using the plane-wave expansion method with a supercell approximation. The effective refractive index for guided mode as a function of the normalized wavelength is reported in Fig. 2. As seen from Fig. 2, the curve of guided mode index locates below of the effective cladding refractive index and inside FBG region, which reveals guided modes are localized by the PBG effect. Because of the limitation of PBG boundaries, the guided mode has cutoffs both in short wavelength and long wavelength. The wavelength range of guided mode is from 0.26Λ to 1.63Λ, in which the fiber remains single mode. Because both pump and signal need to be simultaneously guided in the fiber amplifier, the value of Λ is limited in a range. For example, if the pump is 980nm and the signal ranges from 1525nm to1565nm, we have 0.26Λ1.565µm, which means 0.98µm
