Two-dimensional steady-state photorefractive screening solitons

Shih, Ming-Feng; Leach, Patrick; Segev, Mordechai; Garrett, M. H.; Salamo, Greg; Valley, George C.

doi:10.1364/ol.21.000324

Cited by 179 publications

(80 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In essence, the photorefractive nonlinearity is anisotropic [13], which makes it non-ideal to test our model. However, many experimental results suggest that for a large range of parameters, the anisotropy is fairly small: isolated 3D solitons are almost fully circular [14], and planar collisions between 3D coherent solitons are almost fully isotropic [15], except for a special case, e.g., when the collision plane is normal to the c-axis of the crystal and for a particular initial distance between the solitons [16]. In this respect, even though the photorefractive nonlinearity is not isotropic in 3D, one can still employ it to qualitatively study the predictions of our theory.…”

mentioning

confidence: 99%

Induced Coherence and Stable Soliton Spiraling

et al. 1999

Self Cite

View full text Add to dashboard Cite

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Self-guided optical beams (or spatial solitons) have attracted substantial research interest in the last three decades [1].Although interactions between twodimensional (2D) solitons in Kerr and non-Kerr media have been studied extensively, only the recent discoveries of stable three-dimensional (3D) solitons in different nonlinear bulk media In this Letter we develop, for the first time to our knowledge, a theory of soliton spiraling in a photorefractive-type nonlinear bulk medium. We derive an analytical model describing stable soliton spiraling and predict a number of new effects in soliton interactions, such as an induced coherence and control over 3D interactions, which we verify here experimentally, using experimental setup similar to that reported earlier [3]. Importantly, our analytical model and numerical simulations show that interacting-spiraling solitons conserve angular momentum. We believe that this result is a core foundation for future research on 3D soliton control, resembling the conservation of linear momentum in the interaction of more conventional (1+1)-dimensional solitons [6].We consider incoherent beam interaction in an isotropic saturable nonlinear medium described by two coupled normalized nonlinear Schrödinger (NLS) equationswhere u and w are the beam envelopes, z is the propagation distance; ∇ 2 ⊥ ≡ ∂ 2 /∂x 2 + ∂ 2 /∂y 2 accounts for the diffraction in the transverse (x, y) plane. This system, in the 2D case (i.e., for ∇ 2 ⊥ ≡ ∂ 2 /∂x 2 ), gives rise to incoherently-coupled soliton pairs [7] and to incoherent collisions [8] which have both been demonstrated with photorefractive screening solitons [9].We look for solitary waves of Eqs. (1) in the form u = U (r) exp (iβ u z), w = W (r) exp (iβ w z), where the envelopes U and W satisfy the equationsHere r ≡ x 2 + y 2 is the radial coordinate, and β u and β w are nonlinearity-induced shifts of the propagation constants. System (2) has two families of soliton solutions: U = G u (β u , r), W = 0 and U = 0, W = G w (β w , r), which can be found numerically by solving the equation, where α = {u, w}. These solutions can be characterised by the soliton powers P (β α ) ≡ 2π ∞ 0 G 2 α (β α , r) rdr. In addition to the one-component solitons, at β u = β v ≡ β there exists a family of two-component (vector) solitons defined as: U = G(β, r) cos θ, W = G(β, r) sin θ, where the variable θ characterises a power distribution between the components. Moving solitons of Eqs. (1) can be obtained by a well-known gauge transformation.

show abstract

mentioning

confidence: 99%

Induced Coherence and Stable Soliton Spiraling

et al. 1999

Self Cite

View full text Add to dashboard Cite

show abstract

“…38). However, in practice, by suitably choosing the experimental geometry one can find a crystalline configuration that does not rotate the polarization and which has one electro-optic coefficient much larger than the others (for example, strontium barium niobate 24,27,30,31 ) in such a way that an optical field initially polarized along the x axis maintains its linear polarization; then the problem can be adequately formulated as a scalar one.…”

Section: ؉ 1-dimensional Casementioning

confidence: 99%

“…ٌ ϭ ͑ ‫,ץ/ץ‬ ‫,ץ/ץ‬ ‫,͒ץ/ץ‬ ٌ Ќ ϭ ‫,ץ/ץ͑‬ ‫.͒ץ/ץ‬ (30) By assuming hereafter that the bias field is generated by voltage V applied to the crystal faces orthogonal to the x axis, we observe that in the trivial case in which the intensity is constant in the whole crystal, ͉u͉ 2 ϭ ͉u ϱ ͉ 2 , the basic Eqs. (27), (25), and (26), together with boundary condition (6) (and neglecting fringe effects at the crystal surface), have the simple solution…”

Section: ؉ 1-dimensional Casementioning

confidence: 99%

“…We can justify doing this by observing that the dark irradiance I d , which is associated with thermal charge-carrier generation, is artificially increased in screening-soliton experiments 29,30 by illumination of the whole crystal with a background uniform light . This is also true for ͉u͉ Ӷ 1, when the PR nonlinearity becomes of the Kerr type, whereas in a standard Kerr nonlinearity the soliton attenuates at twice the rate of a linear signal.…”

Section: Self-trapped Beam Propagationmentioning

confidence: 99%

“…In fact, PR solitons were the first optical solitons observed to be self-trapped in both transverse dimensions in a bulk material. [19][20][21][22][29][30][31][32] At present, three generic types of PR soliton are known: quasi-steadystate, [16][17][18][19][20][21][22][23] screening, [24][25][26][27][29][30][31][32][33][35][36][37][38][39][40][41][42][43] and photovoltaic 44,45 solitons. Quasi-steady-state solitons were discovered first.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Three-dimensional optical beam propagation and solitons in photorefractive crystals

et al. 1997

Self Cite

View full text Add to dashboard Cite

show abstract

Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media

et al. 2002

View full text Add to dashboard Cite

2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, lightinduced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can -in a broader sense -be interpreted as molecules of light.

show abstract

Two-dimensional steady-state photorefractive screening solitons

Cited by 179 publications

References 9 publications

Induced Coherence and Stable Soliton Spiraling

Induced Coherence and Stable Soliton Spiraling

Three-dimensional optical beam propagation and solitons in photorefractive crystals

Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media

Contact Info

Product

Resources

About