The bandwidth of titanium sapphire (Ti:Sa) laser amplifiers can be greatly broadened with shaping the spectral gain via engineering the spectral polarization of amplified pulses and using both π- and σ-cross-sections. In a proof-of-principle experiment, an amplification bandwidth exceeding 85 nm at a gain of 200 was demonstrated. The accompanying computer modeling revealed that a polarization-encoded chirped pulse amplification scheme can be scaled to higher energies and thus can produce multijoule pulses with bandwidth close to 200 nm, making few-cycle petawatt Ti:Sa systems feasible.