  We numerically propose a scheme for realizing an all-optical femtosecond
soliton diode based on a tailored heterojunction Bragg grating, which is
designed by two spatially asymmetric chirped cholesteric liquid crystals. Our
simulations demonstrate that with the consideration of optical nonlinearity,
not only the femtosecond diode effect with nonreciprocal transmission ratio up
to 120 can be achieved, but also the optical pulse evolving into soliton which
maintains its shape during propagation through the sample is observed. Further,
the influence of pulse width and the carrier wavelength to the femtosecond
diode effect is also discussed in detail. Our demonstrations might suggest a
new direction for experimentally realizing the femtosecond soliton diode based
on the cholesteric liquid crystals.
