Distance scaling and polarization of electric-field noise in a surface ion trap

We probe electric-field noise in a surface ion trap for ion-surface distances d between 50 and 300 {}m in the normal and planar directions. We find the noise distance dependence to scale as d^-2.6 in our trap and a frequency dependence which is consistent with $1/f$ noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 {}m at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry.