Analytical Approach in Finding the Semi-Optimum Hollow-Core Bragg Fiber With Minimum Loss

Since it is quite difficult to analytically optimize hollow-core Bragg fibers to have minimum confinement loss without using the Floquet theorem, which does not hold for cylindrical structures, the cylindrical Bragg mirror is approximated by its planar counterpart. For this reason, first, the optimum planar waveguide formed by sandwiching a hollow layer between 1-D Bragg mirrors is found in this paper. The optimization for the dominant transverse-electric mode is analytically performed by using the pointwise wavenumber closely related to the wave admittance. A closed-form expression is then found to relate the propagation constant of this waveguide to the thickness of the hollow layer. This expression is then modified for the cylindrical structure, and the propagation constant is approximately related to the hollow-core diameter of the Bragg fiber to be optimized. The optimum cladding region is then found as if it were planar and a semi-optimum hollow-core Bragg fiber is proposed. Its superiority over conventional hollow-core Bragg fibers is numerically demonstrated by following a rigorous approach.