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Analytical expressions for the vector magnetic fields and Fourier transforms associated with thin film heads are presented. These results are derived from accurate, approximate expressions for the surface field of an asymmetric thin film head determined from conformal mapping solutions. A 2-dimensional Green's function is integrated to yield exact analytic expressions for the fields, which are of no more complexity than the Karlqvist field approximations. In spite of their simplicity, these expressions accurately represent the fields at all corners, both at the gap and at the pole edges. These results are only approximate at spatial distances beyond the head edges and at wavelengths beyond about ten times the total head length. The Fourier transform of the surface field is also given in simple analytic form. As an example of the use of these expressions, it is shown how the effect of pole length to gap length ratio, p/g, on pulse superposition can be easily estimated.