What are the most commonly used materials for Laser Diodes ?

Most commonly used materials for semiconductor lasers are the III-V compounds. These are such as GaAs, AlGaAs, InGaAs and InGaAsP depending upon the desired lasing wavelength emission.
Recently, GaN/AlGaN and InGaN/AlGaN are  being used to achieve laser diode emission in the green blue and ultraviolet regions.
InGaN (indium-gallium-nitride) is used for direct green laser diode emission.
Blue Diode Lasers (blue semiconductor laser diodes) are typically fabricated out of aluminum gallium nitride (AlGaN) or aluminum indium gallium nitride (AlInGaN).
Violet 405nm laser diodes and 375 nm UV laser diodes are based on either gallium nitride or indium gallium nitride.