Does there exist a 2D harmonic function which never goes to ∞ at any point, goes to 0 as r goes to ∞, and isn't f=0?

Question

I need a 2D harmonic function which is always real, never diverges to $\infty$ anywhere, goes to 0 as one goes infinitely far away from the origin, and isn't f=0. $$\begin{matrix}0=\nabla^2f&0=\lim_{r\rightarrow\infty}{f\left(r,\varphi\right)}\\\nexists r,\varphi\ni\left|f\left(r,\varphi\right)\right|\geq\infty&f\left(r,\varphi\right)\in\mathbb{R}\\\end{matrix}$$ Does such a function exist? If so what is it? Polar coordinates are prefered.