Three - University of Arkansas Physics Department
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Three - University of Arkansas Physics Department

Three - University of Arkansas Physics Department Three - University of Arkansas Physics Department

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Materials Research Society Symposium - Proceedings, v 618, p 141-145,2000 Ma, Res. Sa, Symg. Pioc. Vol. 618 O zWO Lhtcrieis Research Sodefy

' CLEO '99. Conference on Lasers and Electro-Optics, p 539-40,1999 FRIDAY MORNING '/ CLE0'99 / 539 111 So'ons Output Probe Beam CFHZ Fig 2. Photographs of the soliton beams (upper row) and photographs and profiles of the probe beams (that are all launched into the left soliton; middle and lower rows) exiting the crystal, for various separation distances between the solitons. Fig. 2, when the separation of the solitons decreases, the coupling efficiency increases, until the two guided probe beams overlap with each other and are almost indistinguishable. In conclusion, two parallel mutuallyincoherent spatial solitons at close proximity can serve as a directional coupler for light at longer wavelengths and the coupling efficiency gets higher when the separation between the solitons is smaller. 'Fondazione Ugo Bordoni, Rome, Italy **Department of Physics and Astronomy, San Francisco State Universify, San Francisco, California 94132 USA 'Physics Depamnent, Taiwain University, Taiper, Taiwan *Physics Depamnent, Technion, Israel Institute of Technology, Haifa, 32000, lsrael I. M. Segev and G.I. Stegeman, Physics Today, August 1998. 2. P.V. Marnyshev, k Villeneuve, G.I. Stegeman and J.S. Aitchison, Elect. Lett. 30, 726 (1994). 3. M. Morin, G. Duree, G. Salamo and M. Segev, Opt. Len. 20,2066 (1995). 4. M. Shih, M. Segev and G. Salamo, Opt. Lett. 21,931 (1996); M. Shih, Z. Chen, M. Mitchell and M. Segev, J. Opt. Soc. Am. B 14,3091 (1997). 5. M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, Z. Chen, M. Segev, T. Coskun and D.N. Christodoulides, Appl. Phys. Len. 69, 4151 (1996); M. Shih, M. Segev and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997). CM3 11:00 am Sollton-type and oeclllatoy behavior of rpatlally Incoherent beam by nonllnear medium V.V. Shkunov, D.Z. Anderson, JIU, University of Colorado, Campus Box 440, Boulder, Colorado 80309 USA; E-mail: shkunov@jilaul.colorado.edu Recent observation of self-trapping white light1 by photorefractive crystals stimulated theoretical discussionz-' of self-focusing effect in application to spatially incoherent beams. Several models of incoherent self-trapping by slow responding optical nonlinearity have been proposed.'-* They explain the effect and provide agreement with experimental data. But they are either limited by searching soliton solutions4 only, or require computer sirnulations2-3 to describe longitudinal evolution of the captured beam. In the report we propose simple model, which generalizes previous results and allows for explicit analysis oflongitudinal dynamics. The model is basedon a radiation transfer approach,= which is modified to take into account slow spatial variations 6~ of dielectric constant in a medium. First, we point out alocal angular spectrum J(r, 0, z) of an incoherent beam as a relevant characteristic for its nonlinear diffraction. It is an observable characteristic of a beam. Beside that, spatial evolution of J(r, 0, z) can be described in terms of a single differential equation of thefirst order that we derived assuming the beam size exceeds much a transverse coherence size: General soliton solution of this equation, Jl/ Jz = 0, for the case of cylindrical symmetry is J(r, 8) = J(u); u = [SE(~)/E,- O2]/0i and E, is a uniform part of€. It means that for any given transverse profile of average intensity I(r), as well as for any type of medium response 6€(D to this average intensity, the beam can propagate as a spatial soliton.' It gives self-similar solution if its local spectrum J(r, 8) rigidly 13s the local pattern of intensity 1(r) according to the law l(8€(r)/E08i) = (q,/n)dl(r)/d(&). If at the input boundaq z = 0 this relation between I(, 8) and I(r) is violated the beam evolution along z is not solitary. The beam can suffer oscillations of these transverse profiles around their soliton shapes. ~hiseffeciis illustrated using simplest model of nonlinear propagation of the double-Gaussian beam l(r, 8,~) = lo exp[-a(z)rl - p(z)(r. 0) - Y(z)~'I. through a logarithmic saturating medium, &(I) = h In(l/l,),' where such oscillations aren't damped over z. Explicit solutionb that corresponds to nonlinear oscillations along z for the beam radius, a-''2(z), and its divergence y-L'2(z) is reported for this model. Our conclusion is that since it is hardly possible to fit properly local spectrum to intensity prorile the real observations of incoherent self-trapping relate to the oscillating beams rather then to precise solitons. I. M. Mitchell, M. Segev, Nature 387, 880 (1997). 2. D.N. Christodoulides, T.H. Coskun, M. Mitchell, and M. Segev. Phys. Rev. Lett. 78,646 (1997). 3. T.H. Coskun, D.N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23,418 (1998). 4. A.W. Snyder, and D.J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998). 5. S.M. Rytov, Yu. A. Kravtsov, V.I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1987-1989). 6. V.V. Shkunov, D.Z. Anderson, Phys. Rev. Lett. 81,2M13 (1998). - - - Coherent cd~lons between optlcal solltons In photomfractlve lndlum phosphlde Scot Hawkins, Renpi Yu, Jeffery Wojtkiewicz, Gregory 1. Salamo, Department of Physics, University of Arhnsas, Fayertwille, Arkansas 72701 USA; E-mail: shawkins@comp.uark.edu Recent experiments demonstrate that photorefractive spatial solitons can be formed in semi-insulating InP:Fell through the formation of self-induced waveguides. This paper reports on the coherent collision between two solitons in InP at the telecommunications wavelength of 1.3 pm to form a y-junction. As shown in Fig. 1, Light from a diodelaser is split into two beams. Cylindrical lenses are used to independently focus each of the beams onto the crystal's entrance face when observing the collision between one-dimensional solitons, while spherical lenses are used to observe the collision between two-dimensional solitons. The light is polarized vertically, along the (110) crystal axis, while the electric field is applied horizontally along the (001) axis. The beams are arranged so that they are parallel in the horizontal plane. The relative phase between the two beams is controlled through the use of a piezoelectric mirror in the one beam. Before observing a collision in InP, each beam is checked independently to verify that it forms a soliton. Both beams are then launched together and the collision between onedimensional solitons is observed (Fig. 2). Figure 2(a) shows the input of the individual beams with a beam width of 23 pm and an input separation of 36 pm, while Fig. 2(b) shows the normally diMacted output of each beam at a width of 50 pm. With an applied field of negative 11.5 kV, the output diameter is reduced to 25 &m[Fig. ~(cI]. The collision of the two solitons, when the beams are in phase [Fig. 2(d)], results in a single peak with a width

Materials Research Society Symposium - Proceedings, v 618, p 141-145,2000<br />

Ma, Res. Sa, Symg. Pioc. Vol. 618 O zWO Lhtcrieis Research Sodefy

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