  We propose an efficient approach to improve few-cycle soliton compression
with cascaded quadratic nonlinearities by using an engineered multi-section
structure of the nonlinear crystal. By exploiting engineering of the cascaded
quadratic nonlinearities, in each section soliton compression with a low
effective order is realized, and high-quality few-cycle pulses with large
compression factors are feasible. Each subsequent section is designed so that
the compressed pulse exiting the previous section experiences an overall
effective self-defocusing cubic nonlinearity corresponding to a modest soliton
order, which is kept larger than unity to ensure further compression. This is
done by increasing the cascaded quadratic nonlinearity in the new section with
an engineered reduced residual phase mismatch. The low soliton orders in each
section ensure excellent pulse quality and high efficiency. Numerical results
show that compressed pulses with less than three-cycle duration can be achieved
even when the compression factor is very large, and in contrast to standard
soliton compression, these compressed pulses have minimal pedestal and high
quality factor.
