We employ the recently established basis (the two-variable Hermite–Gaussian function) of the generalized Bargmann space (BGBS) [ Phys. Lett. A 303, 311 (2002) ] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT.
© 2008 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: December 21, 2007
Manuscript Accepted: February 15, 2008
Published: March 26, 2008
Hong-Yi Fan, Li-yun Hu, and Ji-suo Wang, "Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics," J. Opt. Soc. Am. A 25, 974-978 (2008)