Theoretical formulation to shape versatile propagation characteristics of three-layer-tubular waveguides: sub-wavelength and asymptotic study

This theoretical study introduces an analytical formalism to shape the quantification of the photonic modes taking place in three-layer-tubular waveguides, including hollow cylindrical structures. Solving Maxwell's equations in such tubular structure families allowed us to determine the electromagnetic field components in each media of the tube as well as the analytical eigenvalue equations. Thereby we have established an overall frame to be implemented for bound modes focusing on two studies: (1) the internal radius a of the tube is fixed and the external radius b ranges around]a, 10a], with a = [λ/10;λ/2;λ], encompassing then the sub-wavelength dimensional aspect; (2) the external radius b is fixed and the internal radius a ranges around]0, b[, with b = [λ/2;λ;10λ] at λ = 670 nm. The asymptotic behaviour of such optical mode quantification schemes in particular is discussed and demonstrated: indeed, as the internal radius a tends to zero, our prior tubular formalism predicts propagation characteristics identical to those of the well-known fibre theory by way of analytical and numerical strong evidence. We also focus on the cutoff limits of optical bound modes: a map of the different areas related to both monomode and multimode aspects has been dressed as a function of the internal and external radii normalized to the wavelength for versatile dimensional tubular structures. Finally, we discuss the propagation below cutoff in such tubular void structures and propose, for a future investigation, two methods to quantify leaky modes