Enhancement of mid-infrared saturable absorption of graphene by compositing with PbSe for ultra-short pulse lasers in the ∼ 2.8 to ∼ 4 μm band

•Graphene/PbSe composite was synthesized by a facile hydrothermal method.•Mid-infrared saturable absorption and modulation depth of Graphene/PbSe have been much enhanced compared with pure graphene.•Mid-infrared saturable absorption mirrors were fabricated by spin-coating Graphene/PbSe on gold-plated silicon substrates.•Stable Q-switched Er:YAP bulk laser was realized at ∼ 2.8 µm with the pulse width 326 ns, repetition rate 107 KHz and the average output power 498 mW.