Mathematical Fundamentals of Modern Linear Optics

Figure 2

Direction of the tangent to a path 𝛾_𝑢(𝑧) at a given point 𝑃^∗(𝛾_𝑢(𝜁),𝜁) can be characterized by angles (𝜃,𝜑) of the spherical coordinate system (𝜑∈(0,2𝜋),𝜃∈(0,𝜋/2)), or by “velocities” (𝑥̇,𝑦)̇.