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July 1,1998 / Vol. 23, No. 13 / OPTICS LETTERS 1001 High-intensity nanosecond photorefractive spatial solitons Konstantin Kos and Gregory Salamo Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701 Mordechai Segev Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 Received January 15, 1998 We report the observation of high-intensity solitons in a bulk strontium barium niobate crystal. The solitons are observed by use of 8-ns optical pulses with optical intensities greater than 100 MW/cm2. Each soliton forms and attains its minimum width after roughly ten pulses and reaches e-I of the steady-state width after the first pulse. We find good agreement between experimental observations and theoretical predictions for the soliton existence curve. O 1998 Optical Society of America OCIS codes: 160.5320, 230.1360, 060.5530. Optical spatial solitons1 are currently stimulating much interest because their existence has potential for applications .such as beam steering, optical interconnects, and nonlinear optical devices that use one light beam to control another. Both brightz and dark3 one-dimensional (lD) Kerr-type spatial solitons, along with their ability to guide and switch other light beams, have been dem~nstrated.~,~ For the most part these demonstrations generally require high intensities in the megawatt range. Interestingly, although Kerr solitons form as a result of the presence of a refractive-index change that is proportional to the optical intensity, it is precisely this dependence that prevents the existence of stable two-dimensional (2D) bright Kerr solitons. Recently, a new type of spatial soliton1 based on the photorefractive effect was predicted and observed both in a quasi-steadystate regime2z3 and more recently in the steady-state Compared with those of Kerrl'-l4 spatial solitons, the most distinctive features of photorefractive spatial solitons are that they are observed at low light intensities tin the milliwatts per square centimeter (mW/cm2) range] and that robust trapping occurs in both transverse dimensions. Both of these attributes make photorefractive solitons attractive for applications and for fundamental studies involving the interaction between s~atial soliton^.'^-^^ One transverse-dimension theory of photorefractive screening soliton^^-^ predicts a universal relationship among the width of the soliton, the applied electric field, and the ratio of the soliton intensity to the sum of the equivalent dark irradiance and a uniform background intensity. We refer to this curve as the soliton existence curve. This curve is important because experiments show that considerable deviations (-20% or more) from the curve lead to instability and breakup of the soliton beam,10,22 whereas much smaller deviations are typically tolerated and are arrested by the soliton stability properties. In the case of a low-intensity photorefractive soliton beam, i.e., a beam with an intensity in the mW/cm2 to kW/cm2 range, recent 1D experiments have known good agreement with this universal relation~hip.'~~~' Although the low-intensity feature of photorefractive spatial solitons is attractive for applications, high-intensity (MW/cm2 to GW/cm2) photorefractive solitons are also interesting, since the speed with which the steady-state screening soliton forms is inversely proportional to the optical intensity. As we show below, solitons in strontium barium niobate (SBN) can form at nanosecond speeds for GW/cm2 intensities, which implies that for photorefradive semiconductors, which have mobilities 100-1000 times larger than those of the photorefractive oxides, soliton formation should occur at picosecond time scales for similar intensities. For these intensities, however, the excited free-carrier density is no longer smaller than that of the acceptors, and the space-charge field is due both to the free carrier and to the ionized donor contribution^.^ In this Letter we report what we believe to be the first experimental observation of high-intensity screening solitons, along with a comparison between experimental results and theoretical predictions. To work in the high-intensity regime, one must satisfy the requirement that l/r
3TA DEL NUOVO CIMENTO VOL. 21, N. 6 ilinear optical beam propagation and solitons ~hotorefractive media :ROSIGNANI (I), P. DI PORTO (I), M. SECEV G. SALAMO (9 and A. YARIV (4) )ipa.r-timento di Fisica, Univwsitd dell'Aqaila - 67020 L'Aquila, Italy slitz~to Nazion.ale di Rsicn della Maleria, Ur~itb di Rorna. 1 - Roma, Italy :lectvical Engitzeering Departmen6 Princeto71 University - Princeton, NJ 08544, USA 'llysics Department, Uwivarsit~ of Arkansa,~ - J'ayettcville, Ah! 72701, USA Lpplied Physics Depal-tmmt, California Institute of Technology - Pasadena, CA 91125, USA vuto il 12 Gellnaio 1998) Introduction The photorefractive effect The space-charge field Time dependence of the space-chargc iield Nonlinear optical beam propagation in photorefractive media Photo~.efractive two-beam coupliag Self-trapped beam propagation 7'1. Spatial screening solitons in one transverse dimensiou 7'2. Spatial screening solitons in two tranverse climensions 7'3. Different ltinds of spatial solitone: quusi-steady-state and photovoltai.c solitons Experiments with screeniag solitons 8'1. Observations of bright screening solitons 8'2. Observ'~,tions of dark screening solito~is 8'3. Waveguides induced by screening solitons 8'4. Soliton collisions 8'5. Incoherent solitons: self-trapping of incoherent light beams Conclusions - Introduction I The advent of nonlinear optics, mainly due to the work of Bloembe~gen and ~orkel-s at the beginning of the '60, has opened the way to a number. of fundainental ;cove~ies and applications (11. No matter how sophisticated the microscopic or enomenological approach adopted to deal with this topic, one of the central problems the cornplete understanding of nonlinear processes is always the solution of the sociated wave propagation equation, which is, of course, intrinsically nonlinear. This .cumstance can be consiclered in many cases as an obstacle to a full comprehension of e problem, due to the we]]-]cnown inathemstical difficulties usually encountered len trying to solve this type of ecluation. However, it is precisely the nonlinear. nature the wave equation which gives rise to a wealth of solutions, and thus of possible
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