Amplitude-squared squeezing of the electromagnetic field

Operators are defined which correspond to the real and imaginary parts of the square of the field amplitude. These operators obey an uncertainty relation. Squeezing with respect to these operators is defined and minimum uncertainty states are discussed. A number of nonlinear optical processes are examined and shown to produce this effect. Interactions which couple one mode amplitude to the square of another convert this type of squeezing into normal squeezing. An example of such an interaction is given.