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Second-harmonic generation (SHG) in the limit of large phase mismatch, given by Deltabeta=beta2-2beta1 effectively induces a Kerr-like nonlinear phase shift on the fundamental wave (FW). The phase mismatch determines the sign and magnitude of the effective Kerr nonlinearity, making large negative phase shifts accessible. This self-defocusing nonlinearity can be used to compress a pulse when combined with normal dispersion, and problems normally encountered due to self-focusing in cubic media are avoided. Thus, having no power limit, in bulk media a self-defocusing soliton compressor can create high-energy near single-cycle fs pulses (Liu et al., 2006). However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH), given by the inverse group velocity difference d12=1/Vg,1 - 1/Vg,2, limits the pulse quality and compression ratio. Especially very short input pulses (<100 fs) experience a Raman-like effect with a characteristic time TR,SHG=2|d12|/Deltabeta [1c]. Here we address the limits imposed by GVM by using thermally-poled silica photonic crystal fibers (PCFs) for cascaded quadratic (chi(2): chi(2)) soliton compression. In standard silica fibers strong effective quadratic nonlinearities around 1 pm/V have been created with poling. PCFs are instead interesting because they have very strong wave-guide dispersion that can be tailored: for SHG index-guiding silica PCFs with a triangular hole-arrangement can have zero GVM for any FW wavelength lambda=780 nm by adjusting the PCF hole pitch A and hole diameter d (Bache et al., 2006). The paper presents a simulations predict that high-quality compression to few-cycle pulses in poled PCFs is possible. Such a waveguided geometry can extend the compression technique to lower-energy pulses and produce uniformly compressed beams.