Rectangular coordinates, also known as Cartesian coordinates, are commonly used to describe electromagnetic waves because they provide a convenient and intuitive framework for analyzing and manipulating the properties of these waves. While spherical coordinates can also be used to describe electromagnetic waves, rectangular coordinates offer several advantages in this context:
Simplicity of representation: Rectangular coordinates involve three orthogonal axes (x, y, and z) that are mutually perpendicular to each other. This orthogonal system simplifies the representation of complex wave phenomena, allowing straightforward analysis of wave propagation, interference, and reflection.
Separation of variables: Rectangular coordinates facilitate the separation of variables in the wave equations. The governing equations for electromagnetic waves, such as Maxwell's equations, are often expressed in terms of partial differential equations, which can be solved more easily using rectangular coordinates due to their separability. This property enables the decomposition of wave equations into independent one-dimensional equations along each coordinate axis.
Uniformity and isotropy: Electromagnetic waves propagate uniformly in all directions, and rectangular coordinates provide a homogeneous representation of space. The Cartesian coordinate system allows for a consistent treatment of waves propagating in any direction, simplifying the analysis and manipulation of their properties.
Practical applications: Many practical applications and engineering systems involving electromagnetic waves, such as antennas, waveguides, and transmission lines, are naturally described and analyzed using rectangular coordinates. The geometry and components of these systems often align well with the Cartesian coordinate system, making it a convenient choice for practical calculations and simulations.
That being said, spherical coordinates can still be useful in certain scenarios, especially when dealing with wave phenomena in radially symmetric systems or when analyzing wave radiation in free space from a point source. Spherical coordinates are particularly effective for calculating the radiation pattern and far-field characteristics of antennas, where the wave properties exhibit spherical symmetry. In such cases, spherical coordinates provide a more natural and concise representation.