Dependence of stimulated scattering in semiconductor microcavities on pump power, angle, and energy R. Butte ´ , 1 M. S. Skolnick, 1 D. M. Whittaker, 1 D. Bajoni, 1,2 and J. S. Roberts 3 1 Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom 2 INFM and Dipartimento di Fisica ‘‘A. Volta’’, Universita ` di Pavia, I-27100 Pavia, Italy 3 Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom Received 10 April 2003; revised manuscript received 7 July 2003; published 29 September 2003 The dependence of stimulated polariton-polariton scattering in InGaAs/GaAs/AlGaAs microcavities on pump power, angle, and energy is investigated. We show that contrary to much previous belief there is no ‘‘magic angle’’ for stimulated scattering under continuous-wave conditions, the process being shown to be a rather general phenomenon, occurring over a wide range of pump angles. Close analogies with optical para- metric oscillator behavior are found, but also aspects which can only be explained by inclusion of the polariton nature of the quasiparticles. The first physical explanation of why the optical parametric oscillator picture leads to the observed square root dependence of signal power on laser intensity is provided. The asymmetric nature of the tuning curve for excitation of the stimulated scattering process is explained in the framework of the renormalization of the lower polariton branch. DOI: 10.1103/PhysRevB.68.115325 PACS numbers: 78.67.-n, 71.36.+c, 42.65.Yj The strong coupling between excitons and photons in semiconductor microcavities MC’s has permitted the inves- tigation of a wide variety of new phenomena over the last few years. 1,2 In particular, the nonlinear properties of MC’s arising from the bosonic nature of cavity polaritons, the nor- mal modes of MC’s in the strong-coupling regime, have at- tracted especial interest. Large nonlinearities based on final- state stimulations have been observed both in ultrafast 3,4 and continuous-wave 5,6 cw experiments. The stimulated scatter- ing process occurs above a threshold power ( P th ) once mac- roscopic occupation of the final states the ‘‘signal’’ S at k  =0 and ‘‘idler’’ I at k  =2 k pump , respectively is reached. 5 In the cw regime, the influence of circularly polarized excitation, 7 off-branch scattering, 8 and temperature depen- dence of threshold power and internal loss 9 has been studied. These studies were performed by exciting the lower polar- iton branch LPB close to the point of inflection, where energy (2 E pump =E signal +E idler ) and momentum (2 k pump =k signal +k idler ) are best conserved for pump, signal, and idler states on the LPB. In this paper we show that stimulated scattering phenom- ena have close analogies with behavior characteristic of op- tical parametric oscillators OPO’s but that a full description requires a polariton picture. We show that the signal intensity exhibits a square root dependence on pump power, as pre- dicted for resonantly pumped OPO’s, but in marked contrast to the linear dependence in a laser. We discuss this observa- tion in terms of the fundamental differences in the way that OPO’s and lasers are coupled to the external excitation. We show that, under cw conditions, stimulation can be achieved over a wide range of pump angles  pump from 10° to 24°, with the signal occurring systematically at k  =0. We are able to account qualitatively for the near independence on  pump by taking account of the finite linewidths of the polar- iton modes which relax the resonance conditions for match- ing pump, signal, and idler to the dispersion curves. 11 It is concluded that stimulated scattering under resonant cw pumping is a rather general phenomenon under real sample conditions. Furthermore, an asymmetric variation of the sig- nal intensity versus E pump is observed and ascribed to renor- malization of the LPB above P th . As appropriate, the phenomena are discussed either in terms of a quantum bosonic picture or in the classical lan- guage of an OPO. 5,12 Within the OPO picture, the nonlinear- ity occurs in the strong-coupling regime and is driven by a resonant  3 effect. This is in contrast with the usual  2 OPO’s where a single pump photon splits into a signal and an idler of half the energy. 10 Within the OPO coupled equa- tions, the photon fields of a standard OPO are replaced by polariton fields. Quantization of the polariton fields leads to the bosonic picture with pump polaritons scattering into sig- nal and idler modes due to final-state stimulations. 11 The experiments were performed on a 3  /2 InGaAs/ GaAs/AlGaAs microcavity with a vacuum Rabi splitting of 6 meV. 5 The experiments were carried out in reflection geometry in a bath cryostat permitting angular access up to 33°. Photoluminescence PL was excited by resonant cw radiation from a tunable Ti:sapphire laser at different  pump and collected with angular resolution of 1° by a 200 - m core fiber and detected by a monochromator, charge- coupled device CCD combination. 13 All results were ob- tained at a temperature of 2 K, in superfluid He. A me- chanical chopper with a duty cycle of 2/15 was used to exclude heating of the sample. The measurements were per- formed at a slightly positive detuning  = ca v (  =0°) - exc =+2.3 meV. Figure 1a shows the experimental LPB dispersion in the low-density limit together with the fitted dispersion. The pair scattering is depicted for the angle at which pump, signal, and idler all lie precisely on the low-power LPB at  pump =15.5°, the point of inflection of the LPB. PL spectra above the threshold for stimulation, excited at  pump =12° and collected at the peak of the signal (  det = signal =1°), at the peak of the idler (  det = idler =25°), and at an angle PHYSICAL REVIEW B 68, 115325 2003 0163-1829/2003/6811/1153255/$20.00 ©2003 The American Physical Society 68 115325-1