Asymmetric graded-index (GRIN) inhomogeneous medium is proposed to enable even-to-odd mode conversion. An exponential refractive index profile is implemented to induce an asymmetric refractive index distribution. A two-dimensional photonic crystal structure composed of constant dielectric radii with rectangular unit cells is deployed. Efficient mode transformation in a compact structure may promote the manipulation of light for the creation of other types of higher-order modes in asymmetric GRIN structures. (C) 2013 Optical Society of America