INTRODUCTIONPolymers containing fluorine atoms (fluorinated polymers) exhibit increased thermal stability, hydrophobicity, improved chemical resistance and decreased intermolecular attractive forces in comparison with their hydrocarbon analogs. These properties are derived from the fundamental atomic properties of fluorine, such as high ionization potential, low polarizability and high electronegativity. 1 The high ionization potential, combined with the low polarizability, leads to weak intermolecular interactions, which in turn leads to low-surface energy and low refractive indices of fluorinated polymers. Recently, fluoropolymers have received considerable attention as high-performance materials for applications in optoelectronic fields. Specifically, the refractive index is a very important property of polymers for photonic applications, for which highly fluorinated polymers such as Teflon (DuPont, Wilmington, DE, USA) and CYTOP (ASAHI GLASS CO., LTD., Tokyo, Japan) are well known and widely used in optical communication networks. Current optical communication networks are based on silica optical fiber and devices. To integrate with these devices and materials, and to reduce the optical loss, polymer materials with refractive index values close to that of the silica materials (1.46) are desired. 2 Therefore, materials with a controllable refractive index are required for the successful design and fabrication of photonic devices. For example, the widely used fluorinated polyimides usually have relatively low refractive indices 3 and this value can be easily manipulated by introducing polar groups and copolymerizing with comonomers containing heavier atoms, such as bromine to give high refractive indices. However, it appears difficult to lower the refractive index. We have modified fluoropolymers with the simple polyaddition of bis(epoxide)s with dicarboxylic acids and diols in the presence of quaternary onium salts and they exhibited a linear relationship between refractive indices and fluorine contents of the polymer. 4,5 Similar investigations have been conducted with fluorinated aromatic-aliphatic copolyethers, 6 fluorinated poly (phthalazinone ether)s 7 and hyperbranched fluorinated polyimides. 8 The relationship between the refractive index (n D ), density (r g cm À3 ), molecular weight (M g mol À1 ) and molecular refraction (R cm 3 mol À1 ) of a polymer is described by the Lorentz-Lorenz equation (Equation 1). 9According to the Lorentz-Lorenz equation, the polymers with low r give low n D . That is, hyperbranched polymers (HBPs) are good candidates for the production of low-density polymers because of their three dimensional globular architecture with higher branched structure. 10 Recent study has indicated that hyperbranched structures have an increasingly important role in reducing crystallinity, to avoid significant optical loss. For example, we have observed and reported that the HBPs show no birefringence due to their highly branched globular structure, preventing their polymer orientation. 11 On t...