LOSS IN MICROSTRUCTURED FIBRE WITH A SHORT TAPER J.T. Lizier and G.E. Town School of Electrical & Information Engineering, University of Sydney, NSW 2006, Australia. towng@ee.usyd.edu.au Abstract Losses in tapered microstructured fibres have been calculated as a function of shape and length using finite-difference time-domain calculations. Minimal losses are incurred even in non-optimally shaped tapers shorter than 100 micron. The results have important implications for splice losses and device applications. 1. INTRODUCTION Tapered microstructured optical fibres are of interest for applications in spot size conversion [1]. It has previously been shown using finite-difference time-domain modeling that significant changes in the guided mode diameter and numerical aperture may be obtained with minimal loss in optimally-shaped tapers as short as 50μm [2]. Here we present details of loss calculations in microstructured fibres with tapered transitions of varying length and non- optimal shape. We show that even relatively short non-optimally shaped tapers may still be highly adiabatic, and hence provide low loss transitions. 2. ADIABATICITY IN TAPERED WAVEGUIDES The adiabaticity, α, of the mode transition through the taper may be defined in terms of the local taper angle (with respect to the fibre axis), θ t , and local diffraction angle, θ 0 , [3]. t θ θ α 0 = (1). Using the effective index approximation [4] and the Gaussian beam approximation for SIFs, the diffraction angle in regularly microstructured optical fibre may be expressed in terms of the fibre parameters as ρ π λ θ ′ = eff V ln 0 (2), in which the effective core radius is ρ'=0.64Λ [5], Λ is the spacing of a hexagonal lattice of holes in the HF cladding, and V eff is the effective normalized frequency parameter, given by ( 29 2 2 / ' 2 cl co eff n n V - = λ πρ (3), where n cl is the effective index in the HF cladding, and n co the refractive index of the background material. Eq. (2) is consistent with experimental measurements of the diffraction angle from HFs for the range of parameters tested [6]. Large adiabaticity is desirable throughout the taper to minimise radiation and reflection losses from the transition. In a tapered fibre both the taper angle and diffraction angle, and hence the adiabaticity, vary with position through the transition. A figure of merit to compare the overall adiabaticity of differently shaped tapers may be defined as the integral of 1/α, or non-adiabatic integral (NAI). We have previously derived an optimal taper shape in which the adiabaticity is constant, hence maximising the minimum adiabaticity for a given taper length [2]. By contrast, in this work we consider the performance of a non-optimally shaped taper, with radius         - + - - - + ) .( 2 ] 2 ) ( .[ 3 tanh 2 2 1 2 2 1 2 1 2 1 z z z z z R R R R π (4), i.e. a hyperbolic tangent taper, in which R 1 and R 2 , and z 1 and z 2 , refer to the radii and positions at the start and end of the taper. Whist the taper described by Eq. 4 is unlikely to