  In this paper, we calculate the analytical solutions for the radii of planar
and polar spherical photon orbits around a rotating black hole that is
associated with quintessential field and cloud of strings. This includes a full
analytical treatment of a quintic that describes orbits on the equatorial
plane. Furthermore, The radial profile of the impact parameters is studied and
the radii corresponding to the extreme cases are derived. For the more general
cases, we also discuss the photon regions that form around this black hole. To
simulate the orbits that appear in different inclinations, we analytically
solve the latitudinal and azimuth equations of motion in terms of the
Weierstrassian elliptic functions, by considering the radii of spherical
orbits, in their general form, as the initial conditions. The period and the
stability conditions of the orbits are also obtained analytically.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena