CHROMATIC DISPERSION CONTROL IN GERMANIUM-DOPED PHOTONIC CRYSTAL FIBER USING FINITE-ELEMENT APPROACH A.R. Erfan * , A. Kamkar, A. Najafi, R. Karimi Azari, M. Jalalkamali, M.A. Bolorizadeh Photonics Dept., Int. Center for Sci. and High Tech. and the Environ. Sciences, Kerman, Iran. * alirezaerfan.ph79@gmail.com Abstract: In order to control the chromatic dispersion and confinement loss of germanium-doped Photonic Crystal Fiber (PCF), a full-vectorial finite-element method with anisotropic Perfectly Matched Layer (PML) boundary condition is used. Also we have used a state-of-the-art dispersion controlling technique in PCFs to introduce a dispersion flattened germanium doped photonic crystal fiber. 1. INTRODUCTION Germanium-doped PCFs consisting of a central doped defect surrounded by multiple air holes, run- ning along the fiber length, have been widely used in many applications; e.g. enhancing nonlinearity, designing functional devices for fiber communica- tion and sensing the temperature and strain. Control of chromatic dispersion in Ge-doped PCFs is a very important issue for practical applications to optical communication systems, dispersion compensation and nonlinear optics. In this work we have employed a full-vector fi- nite element method, contrary to other methods, is an all-purpose method [4] incorporated with aniso- tropic PMLs for controlling the dispersion by changing the clad holes diameter. It is shown nu- merically that it is possible to design a four-ring germanium doped PCF with flattened dispersion of ) nm km ( ps 10 461 . 2 0 8 ⋅ × ± - in a wide wavelength range while the confinement loss is reduced to km dB 5571 0. at the wavelength m 45 . 1 μ . 2. ANALYSIS METHOD Let’s consider a germanium doped PCF which is surrounded by anisotropic PML regions 1 to 8 with the same thicknesses. The PCF cross section is shown in Fig.(1) where x and y are the transverse coordinates and z is the direction of propagation. The dielectric permittivity, 0 N r ε εε = t t , and the magnetic permeability, 0 N r μ μμ = t t , are defined as reducible tensors where: 0 0 N 0 0 0 0 y z x x z y x y z ss s ss s ss s ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ t For s x , s y and s z as the PML parameters given in table(1) for all regions. We start from Helmholtz vectorial equation: 0 ȝ k ) ε ( 2 0 1 = - × ∇ × ∇ - H H t t (1) where H is the magnetic field, while the z compo- nent could be separated as z) i y)exp( (x, β - = H H due to the z symmetry in the fiber. The dielectric permittivity reducible tensor is decomposed as a 2 2 × matrix, r ε t , and a column vector, zz ε r [4]. The magnetic permeability reducible tensor may also be decomposed similarly. However, the mag- netic permeability is assumed to be scalar and unity for a non magnetic medium. The wave number in the vacuum is defined as λ π 2 0 = k for Ȝ being the wavelength of the propagated wave. Table 1. PML parameters PML regions PML parameter 8 7 6 5 4 3 2 1 2 s 1 s 2 s 1 s 1 1 2 s 1 s x s 4 s 4 s 3 s 3 s 4 s 3 s 1 1 y s 1 1 1 1 1 1 1 1 z s i 1 s s s s 4 3 2 1 - = = = = . Fig. 1. Transverse cross section of fiber surrounded by PML regions. Ge PHOTONICS-2008: International Conference on Fiber Optics and Photonics December 13-17, 2008, IIT Delhi, India