Abstract

Enlightened by the special transformation in our preceding paper [J. Mod. Opt. 56, 1227 (2009) ], we propose a new complex integration transformation corresponding to two mutually conjugate two-mode entangled states $⟨\eta |$ and $⟨\xi |$ that is compatible with $\eta -\xi$ phase space quantum mechanics and can be used to obtain the complex fractional Fourier transformation kernel from the chirplet function. This transformation obeys the Parseval theorem and is invertible.

© 2009 Optical Society of America

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