2-D AMO operator

When the input offset h₁ is parallel to the output offset h₂, the determinant [equation (24)] of the system (23) is equal to zero. In this case, as we discussed in the main text, the 3-D AMO operator degenerates into a 2-D operator. The fact that the determinant of the system of equations is equal to zero means that the two equations are linearly dependent, and that we are left with only one equation. However, because the operator is two-dimensional, the number of components of the unknown ${\bf k}_{0}$ also goes from two to one. Consequently, another stationary-phase approximation to the AMO operator can be found. The new equation is a quartic, and unfortunately, we have not been able to solve this new equation analytically. However, we have found the solution for the kinematics of the operator with the help of Mathematica; the resulting expression for the 2-D AMO operator is presented in equation (3) of the main text. B