  We investigate the astonishing physical aspects of Exceptional Points (EPs)
in a 1D planar few-mode optical waveguide. The waveguide hosts four
quasi-guided modes. Here interactions between the selected pair of modes are
modulated by a spatial distribution of inhomogeneous gain-loss profile. Both
the coupled pairs approach two different second-order EPs in parameter plane.
Considering a proper parametric loop to encircle the identified EPs
simultaneously, we establish a specific topological feature where one round
encirclement in parameter space yields the switching between the propagation
constants ({\beta}) of the corresponding pairs of couple modes in complex
{\beta}-plane. Choosing two different patterns of the parametric loop, we
establish the immutable topology in {\beta}- switching phenomena. This robust
mode conversion scheme shall provide a platform to realize selective mode
switching devices or optical-mode converters.
