For most lasers, the LaserWavelength is longer than the pump wavelength. This is unavoidable for all pumping schemes where one pump photon can generate one laser photon. However, there are upconversion pumping schemes, where two or more pump Photons are used to get a laser ION to a high excited level, SO that the laser photon energy can be larger than that of the pump. (Sometimes, the label upconversion laser is used when the pumping process involves multiple photons, even when the laser wavelength is not shorter than the pump wavelength.)
Early upconversion lasers were demonstrated with bulk crystals, which often had to be cooled to very low temperatures, making the systems impractical. However, significant advances have been achieved e.g. with Er:LiLuF4 crystals, generating relatively high power green Light at room temperature.
Most currently used upconversion lasers are based on Glass fibers where high pump intensities can be maintained over long lengths, so that the laser threshold can be reached even under otherwise difficult conditions. In most cases, Silica glass is unsuitable due to its high phonon energies, which cause strong multi-phonon transitions and thus lead to too short metastable level lifetimes. Therefore, it is often necessary to use heavy-metal fluoride fibers (e.g. ZBLAN), which tend to be quite fragile and expensive.