We numerically investigate a new function modified from Hamming function to apply in weighting the waveguide
structure of a mismatched optical coupler with the characteristics of low crosstalk, short length, and broad C+L-band.
The full factorial design and beam propagation method are being used to seek the optimal structure parameters of
coupling waveguide. This modified Hamming weighting function (M-HWF) is proved to have the superior performances
to Hamming weighting function (HWF) in several ways. In theoretical computation, the M-HWF and HWF waveguides
have the coupling lengths of 11 mm and 16 mm, respectively at crosstalk of -40 dB and operating wavelength of 1.57
μm. After the numerical design of waveguide structure parameters, the M-HWF also obtain a shorter coupling length of
4.50 mm than coupling length of 5.90 mm of HWF at crosstalk of -40 dB and within the C+L-band (1.53~1.61 μm). The
M-HWF waveguide with the shortest coupling length of 4.5 mm can even reach a broader bandwidth between 1.50 and
A mismatched optical coupler with waveguide weighted by the Blackman function is numerically
investigated in the demand of short-length, C+L-band, low crosstalk, and process tolerance. Utilizing the full
factorial design, the structure parameters of coupling waveguide are obtained by beam propagation method. In
the condition of crosstalk of -33.5 dB, the mismatched optical coupler with proper selected waveguide structure
parameters is found to have a coupling length of 2.80 mm in the transmission wavelength ranges of C+L-band
(1.53~1.61 μm). Obviously, the selection and design of waveguide structure are very important to satisfy the
qualities of a mismatched optical coupler for the demand of short-length, bandwidth, and low-crosstalk.