Integration path in complex plane

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Given this integral $$I=\int_\gamma e^{-jk\rho \cos(\alpha-\phi)}d\alpha$$

and given that $k_x=k\cos\alpha $ is such that $k_x \in(-\infty, +\infty)$ and $\phi \in [o, \pi]$

how can I obtain this picture?What's the meaning of the y-axis?

($\alpha$ is complex)

enter image description here