Why you should not use the electric field to quantize in nonlinear optics
Nicolás Quesada, J. E. Sipe · Optics Letters · 2017
We show that using the electric field as a quantization variable in nonlinear optics leads to incorrect expressions for the squeezing parameters in spontaneous parametric down-conversion (SPDC) and conversion rates in frequency conversion. This observation is related to the fact that if the electric field is written as a linear combination of bosonic creation and annihilation operators one cannot satisfy Maxwell's equations in a nonlinear dielectric.