Orthogonal solutions for asymmetric strongly coupled waveguide arrays: an elegant, analytical approach

Assessment of the orthogonal and non-orthogonal coupled-mode theory for parallel optical waveguide couplers

“…Both κ = κ t and κ = κ t + κ za strongly differ from (38), while an almost perfect overlap exists between the expected results and the CMT ones using the κ = κ t + κ zb . Results obtained with the NO-CMT differ from those obtained using the O-CMT only about 1% for the gap of 200 nm down to almost 0% for the gap of 500 nm (the curves that mutually differ more are those based on (18); those who differ less are those with ( 16)). In this case, there is then no practical difference between the O-CMT and the NO-CMT results, which makes useless the extra computational burden necessary to evaluate (34).…”

“…Differences between the corresponding O-CMT and NO-CMT curves range from about 1% for the gap of 200 nm down to about 0.2% for the gap of 500 nm. Again, curves with differ more are those based on (18); those who differ less are those with (16).…”

“…One can also observe that, if ∆ε ε, the expression of the longitudinal coupling coefficient κ z νµ given by ( 17) simplifies into (18). This has been often done (see, for example, [3]) but does not hold for high index contrast waveguides.…”

“…This has been often done (see, for example, [3]) but does not hold for high index contrast waveguides. Using this approach, (18) is exact. This makes the two approaches independent.…”

“…This value will be compared with the results of the different expressions of the coupling coefficients obtained numerically evaluating the integrals (16)(17)(18) using the fields computed with COMSOL. In particular, three possible values of the coupling coefficient κ will be considered for the O-CMT: i) the transverse coupling coefficient alone, i.e.…”