A three-stage cascade GaSb-based diode laser heterostructure with an enhanced optical gain spectral bandwidth was designed and fabricated. The gain broadening was achieved by varying the thickness of the type-I quantum wells in different stages of the cascade active region from 10 to 14 nm. The structures were processed into bent ridge gain chips with virtually eliminated feedback from the anti-reflection-coated angled facet. The external cavity devices based on a novel gain chip design demonstrated a record wide tuning range from 2.79 to 3.23 μm in a Littrow cavity configuration at 20°C.