Multimode Interference (MMI) device is a useful optical component for optical power splitter/combiner and router
applications. In this paper we present high precision calculation results on the optimum position of self-images in an
MMI and their variation due to wavelengths, for WDM applications. We show that the commonly used MMI self-image
position calculation methods, using the beat length of two lowest order modes or effective MMI width approximation,
lead to significant deviations from the optimum self-image position. We calculate the optimum position of the self-image
by finding the maximum value of overlap integral of total MMI field, comprised of all MMI modes, with the total field at
the input of the MMI device. In addition, for the optimum output power coupling distance for MMI, we calculate the
overlap integral of the total MMI field with the output waveguide field. Both these methods give approximately the same
optimum length. We obtain up to 60 um difference in optimum self-image position for a Si MMI (width =15 ~ 30 um),
and refractive index difference of 0.02 between core and cladding, from the approximations based methods. We also
calculate the variation of this image position in 1.50 um to 1.60 um wavelength region. We show that the optimum image
position is strongly dependent on wavelength, with up to 100 um variations in this wavelength range. In addition, we
show that there is a significant variation in this self image position with MMI widths, at points where a new power
carrying mode is added.
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