Radiation losses of step-tapered channel waveguides

We compute the radiation losses of a rectangular dielectric waveguide (integrated optics channel waveguide) that is tapered so that its wider cross-sectional dimension increases by roughly a factor of three while its narrow dimension remains constant. As the waveguide widens its refractive index decreases to ensure that the waveguide supports only one guided mode. The taper is approximated by a discontinuous staircase curve. A rectangular waveguide taper of 2-microm thickness, tapering from 3- to 10-microm width through fourteen steps of 0.25-microm height, has a minimum loss (at 0.6328-microm wavelength) of 0.13 dB for a 200-microm taper length.