A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory

We derive the spectral dispersion law for the virtually imaged phased array (VIPA) based on paraxial wave theory using the Fresnel diffraction analysis. The validity of the dispersion law is verified by comparison with experiments. This spectral dispersion law is compared to a previous law based on plane wave theory. At small incident angles where the VIPA provides its largest spectral dispersion, the paraxial wave law provides a much better fit to the data than the plane wave law does.