Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)A new approach to reduce the bending loss of the fundamental quasi-transverse magnetic mode in optical waveguides is presented. A much lower bending loss is achieved by designing waveguides that use as substrate or cladding an anisotropic metamaterial made of multilayers of thin films of germanium and porous silica instead of a conventional silica substrate or cladding. We numerically demonstrate a reduction in the bending loss of up to similar to 3 dB/90 degrees for a silicon-on-insulator (SOI) waveguide of the standard core size (500x220 nm), as well as, up to similar to 10 dB/90 degrees for a sub-wavelength SOI waveguide of core size (372x186 nm), even considering the high absorption of the germanium layers in the cladding, both designed to operate at 1550 nm.28 872875Brazilian C&T Institute FOTONICOM through National Council of Technological and Scientific Development [574017/2008-9]Fundacao de Amparo a Pesquisa do Estado de Sao Paulo [2008/57857-2]Colombian Agency Enlaza MundosBrazilian Agency Coordenacao de Aperfeicoamento de Pessoal de Nivel SuperiorFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)