Method for analysing trapezoidal optical waveguides by an equivalent rectangular rib waveguide

Trapezoidal waveguides: first-order propagation equivalence with rectangular waveguides

“…In all of the following, for notational simplicity, we will continue to use the notation T 1 and T 2 to designate the two (sets of) trapezoidal structures under consideration, with the implicit understanding that with the exception of the value of the large basis L of these structures, all the other geometrical and physical properties of these structures remain unchanged and have the values mentioned earlier. 3 The results are presented in figures 9 and 10 and very much like in the case of the dispersion curves, the curves of the equivalent rectangular structures are in excellent agreement with the corresponding curves of the trapezoidal structures T 1 and T 2 respectively. For each of the modes under consideration, the overlapping precision/relative error per data point is illustrated in figure 11.…”

“…As was mentioned in section 1, it is possible to construct for any given trapezoidal waveguide, an equivalent rectangular waveguide that has to the first order of perturbation the same propagation constant as the original trapezoidal waveguide. The method underlying this construction was first developed in [3], and was briefly investigated numerically for the case of rib-waveguide structures 1 . In this section, we apply this method to the study of strip-loaded waveguide structures, and we show that in this latter case it yields a very simple geometrical criterion that allows one to construct the equivalent rectangular waveguide without recourse to any numerical calculations.…”

“…It should be mentioned that one could have used a different perturbative approach [3] to the construction of a trapezoidal waveguide from a 'fundamental' rectangular waveguide that involves the calculation of fewer correction terms. Such a method is illustrated in figure 5, and in a certain sense it represents the inverse of the method we have used so far.…”

“…In the present paper we will present in detail a simple perturbative treatment of trapezoidal cross-section waveguides that allows one to construct an equivalent rectangular cross-section waveguide that has-to the first order of perturbation-the same propagation characteristics as the original trapezoidal waveguide. The idea of reducing a trapezoidal waveguide to an equivalent rectangular waveguide is by no means new and was originally proposed by Clark and Dunlop [3] in 1988 for rib waveguide structures. In our present work, we apply this idea to the study of strip-loaded waveguide structures, and we derive for this type of structures a very simple and intuitive geometrical method to construct the equivalent rectangular waveguide corresponding to a given trapezoidal waveguide.…”

Quasi-Axial GRIN Lens Implemented in Wedge-Shaped Fiber Coupling With InP-Based PLC

“…For mth (m = 1 ∼ N) ERA waveguide, effective index method can be applied [10], assuming that κ represent the propagation constants for the eigen mode field φ pq,m along the x-and y-directions for core and cladding layers; A pq,m , β pq,m , B pq,m , γ pq,m , N m x , and N m y represent the amplitude of the forwardly guided wave, propagation constant, amplitude of the reflected wave, phase of the reflected wave, number of total guided modes in x-and y-directions, respectively; the suffixes 1 and 2 stand for core and cladding layers; p and q stand for guided-mode order in x-or y-directions; κ 0 is the wave number in vacuum.…”