We present a general formulation for quantum macroscopic nonlinear optics, which can be considered as a fully quantized version of its semiclassical counterpart in which the electric field is treated as the classical variable. Our formulation begins with the fundamental minimal-coupling Lagrangian, which is then transformed into the multipolar Lagrangian. After a quantum preservative expansion by using a Hamiltonian decomposition proposed in this paper, we have found the formal relations between the Heisenberg operators of macroscopic polarization density and macroscopic electric field. Finally, the linearized quantum effects for nonlinear optics are also discussed.
© 2009 Optical Society of America
Original Manuscript: August 29, 2008
Revised Manuscript: February 13, 2009
Manuscript Accepted: March 4, 2009
Published: April 3, 2009
Shifeng Jiang and Philippe Gallion, "General formulation for quantum macroscopic nonlinear optics," J. Opt. Soc. Am. B 26, 902-909 (2009)