Sources of photon pairs based on the spontaneous parametric down conversion process are commonly used for long distance quantum communication. The key feature for improving the range of transmission is engineering their spectral properties. Following two experimental papers [Opt. Lett., 38, 697 (2013)] and [Opt. Lett., 39, 1481 (2014)] we analytically and numerically analyze the characteristics of a source. It is based on a $beta$-barium borate (BBO) crystal cut for type II phase matching at the degenerated frequencies 755 nm $rightarrow$ 1550 nm + 1550 nm. Our analysis shows a way for full control of spectral correlation within a fiber-coupled photon pair simultaneously with optimal brightness.
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