We report operation of what we believe is the first continuous-wave laser which relies exclusively on cooperative upconvcrsion by coupled ion trios to achieve population inversion. The first laser to operate with an output wavelength shorter than that of the excitation was a pulsed erbium laser reported by Johnson and Guggenheim.l Since this early work, a variety of continuous-wave lasers have been reported in which upconversion occurs by different mechanisms, and inversions of upconverted

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... y levels have been sustained by avalanche processes, 2.3 direct pairpumping,4 and muitiphotoll absorption with variable contributions from energy transfer. 5 ,6 To date, cw upconvcrsion lasers have been operated in 1'1'-, Er-, Tm-, and Nddoped solids, exhibiting surprisingly high efficiencies (up to 30%) in simple and robust, monolithic designs. All can potentially be pumped by diode lasers, and furnish wavelengths typically twice as short as diode lasers. With the advent of room-temperature operation these devices should therefore offer attractive alternatives to harmonic generation schemes 7 for short-wavelength source applications. In this letter we show that in addition to the known avalanche, two-atom and multi photon upcollversion mechanisms, steady-state inversions can also be maintained by cooperative transitions of atomic trios. Spontaneous cooperative fluorescence due to weakly coupled trios of rareearth dopants in dielectric crystals has been studied previously.s However, to our knowledge this is the first report of cw stimulated emission sustained by trio-pumping alone. Furthermore the 0.855 ftnl upconversion laser reported here achieves remarkably efficient cw oscillation on a selfterminating transition. A simple, hut realistic picture of the basic dynamics in the current work is obtained with a six-level model oftriVltlent erbium, indicated schematically in Fig. 1 . Here each manifold is represented by a single level and cooperative transitions are permitted only in level two, which is considered to be vcry long lived at low excitation densities. In reality level three of ErJ + is also long lived, but its population arises entirely from level two pair processes. Hence it contributes to effective losses in the erhium pair laser 4 and to quartic upconversion, but not to the cubic upconversion processes of interest here. In our model we draw on earlier results which justify omission of two-photon absorption source terms for level four popu!ation. 4 Howcver we include the possibility of direct absorption of pump photons by ions maintained in level four by cooperative pair upconversion to reach the upper laser level. Diagonal density matrix clements for this nonlinear system are where the spontaneous relaxation rate betwecn level i and .i is given by Yij and Bij is the induced rate between i and}. The pair and trio upconversion coefficients are (1. and (3, 6 5 I 4 5 312 O. 855 1l m I I 4