New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform**The project supported by National Natural Science Foundation of China under Grant No. 10175057

Abstract

By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.