End facet of a multimode waveguide

2D simulations of a configuration with the following specification: background refractive index nb = 1.0, refractive index of the guiding layer ng = 3.2, waveguide thickness W = 1.54 µm. All calculations are meant for a vacuum wavelength of 1.532 µm and for TE polarization, i.e. Ey is the single nonvanishing component of the electrical field.

the computational domain

The figures in the table below lead to illustrations of the stationary electric field that is generated by inserting a single guided mode, or a specific superposition of two modes, respectively.

  Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t) Ey(x,z,t)
Order of the input mode: 0 1 2 3 4 5 6 3, 5
Reflected power: 0.31 0.50 0.72 0.80 0.76 0.71 0.27 0.99
Transmitted power: 0.68 0.43 0.20 0.10 0.14 0.15 0.54 < 0.01

The row 'reflected power' shows the relative power that is transferred to the backwards traveling version of the input mode(s), while the 'transmitted power' is the entire relative power that is observed on the free space side of the facet. Hence the two rows do not add to one; the remaining part of the input power is either reflected into other guided modes (in all cases one order of magnitude smaller than the direct reflection), or scattered backwards into nonguided parts of the electromagnetic field.

The last column corresponds to a bimodal excitation, including the 3rd and 5th order mode of the waveguide. Note the high reflectivity that is predicted for this incoming field, compared to the values of columns 3 and 5. The mode amplitudes were selected such that the field at the facet resembles the resonant field in a microcavity with the same parameters …