“…The linearly graded, parabolic, exponential, Gaussian refractive index profiles, characterized by unique features [3,4], are often used in waveguide devices. The waveguide properties are studied with analytical [5] and numerical methods [6][7][8]. The analytical methods are divided into exact [9][10][11] and approximate (for example, Wentzel-Kramers-Brillouin (WKB), Stevenson-Pade) [12][13][14][15].…”