In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets of the component polar codes. Moreover, we show how polar codes can be described as irregular product codes. We propose a two-step decoder for long polar codes taking advantage of this dual nature to heavily reduce decoding latency. Finally, we show that the proposed decoding technique outperforms both standard polar codes and state-of-the-art codes for optical communications under latency constraints.