15 June 1999 Ž . Optics Communications 164 1999 307–316 www.elsevier.comrlocateroptcom Full length article Comparison between copropagative and counterpropagative non-degenerated cascaded parametric interactions P. Baldi a, ) , J. Pruvot a , M.P. De Micheli a , G. Bellanca b , A.C. Cino c a Laboratoire de Physique de la Matiere Condensee, UniÕersite de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France ` ´ ´ b Dipartimento di Elettronica Informatica e Sistemistica, UniÕersita di Bologna, Viale Risorgimento, 2, 40136 Bologna, Italy ` c CRES, Optoelectronics Laboratory, Via Regione Siciliana, 49, 90046 Monreale, Italy Received 16 December 1998; received in revised form 9 April 1999; accepted 14 April 1999 Abstract We show that, in a x Ž2. material, a backward injected signal beam undergoes an automatic p phase shift in a phase-matched cascaded parametric interaction in the presence of a forward injected pump beam. This type of interaction, compared with the previously proposed copropagative cascaded parametric interaction configurations, is shown to have more flexibility for signal processing. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.65 Wi; 42.65 Ky; 42.65 Vh; 42.65 Yj Keywords: Backward or counterpropagative parametric interactions; Cascading; Nonlinear phase shift 1. Introduction There have been extensive efforts during the past decade in the search for large n materials for 2 all-optical signal processing, which ideally requires applying a p phase shift on the signal. The nonlin- Ž . ear phase shift of the fundamental signal beam during a cascaded x Ž2. : x Ž2. process in the second Ž . wx harmonic generation SHG configuration 1 has w x been shown to be of interest 2,3 since this leads to a large effective nonlinear refractive index n eff . Nev- 2 ertheless, this configuration does not satisfy the es- sential demands of a general switching protocol which requires the treatment of low power signals ) Corresponding author. Tel.: q33-4-92-07-67-52; Fax: q33- 4-92-07-67-54; E-mail: baldi@naxos.unice.fr and the possibility of signal power independent packet switching. wx Hutchings et al. 4 have proposed a slightly different scheme based on two non-degenerate dif- Ž . ference-frequency generation DFG processes where an injected pump beam is used to control the phase of the signal beam of interest. Provided that the pump power is large enough compared to the signal power, the signal phase shift is proportional to the pump power and independent of the signal power, which allows processing very weak signals as op- posed to the SHG scheme. Moreover, DFG gain can compensate the signal injection and propagation losses which are present in an actual device. For these reasons, the DFG scheme appears to be more promising than the SHG scheme for all-optical pro- cessing. The first experimental observation of such a 0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0030-4018 99 00188-1