  The multimode waveguide bends (MWBs) with very compact sizes are the key
building blocks in the applications of different mode-division multiplexing
(MDM) systems. To further increase the transmission capacity, the silicon
multimode waveguide bends for dual polarizations are of particular interest
considering the very distinct mode behaviors under different polarizations in
the silicon waveguides. Seldom silicon MWBs suitable for both polarizations
have been studied. In this paper we analyze several dual-polarization-MWBs
based on different bending curve functions. These special curve-based silicon
MWBs have the advantages of easy fabrication and low loss compared with other
structures based on the subwavelength structures such as gratings. A comparison
is made between the free-form curve, Bezier curve, and Euler curve, which are
used in the bending region instead of a conventional arc. The transmission
spectra of the first three TE and TM modes in the silicon multimode waveguide
with a core thickness of 340 nm are investigated. The simulation results
indicate that in the premise of the same effective radius which is only 10 in
this paper, the 6-mode MWB based on the free-form curve has the optimal
performances, including an extremely low loss below 0.052dB and low crosstalk
below -25.97dB for all six modes in the wide band of 1500-1600 nm. The MWBs
based on the Bezier and Euler curve have degraded performances in terms of the
loss and crosstalk. The results of this paper provide an efficient design
method of the polarization insensitive silicon MWBs, which may leverage the
researches for establishing complicated optical transmission systems
incorporating both the MDM and polarization-division multiplexing (PDM)
technology.
