Local error analysis arising from the conventional scalar approximation in wide optical fields

The scalar approximation which is used to represent the optical fields in free space causes large error in large angles due to the neglected longitudinal component of the vector electric field. A short space Fourier transform (STFT) based space-frequency analysis method is proposed to analyze the local error in wide extent optical fields. The error measure is quantitatively defined as the ratio of the local power of the longitudinal component to the local power of the total electric field. The error is analyzed on both parallel and tilted planes with respect to the display that produces the optical field. Moreover, a simulation result for a scalar wave that includes different frequency components at different locations shows that the local error becomes high at the locations where high frequency components exist. The proposed method can be used to analyze the local error, if the the scalar approximation is to be used for the optical field to be generated.