All-optical switching of a signal by a pair of interacting nematicons

We investigate a power tunable junction formed by two interacting spatial solitons self-trapped in nematic liquid crystals. By launching a counter-propagating copolarized probe we assess the guided-wave behavior induced by the solitons and demonstrate a novel all-optical switch. Varying soliton power the probe gets trapped into one or two or three guided-waves by the soliton-induced index perturbation, an effect supported by the nonlocal nonlinearity. © 2012 Optical Society of America OCIS codes: (190.6135) Spatial solitons; (160.3710) Liquid crystals. References and links 1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003). 2. M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012). 3. A. Piccardi, A. Alberucci, N. Tabiryan, and G. Assanto, “Dark nematicons,” Opt. Lett. 36, 1456–1458 (2011). 4. M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells”, Appl. Phys. Lett. 77, 7–9 (2000). 5. M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001). 6. J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, M. Haelterman, “Simulations and experiments on selffocusing conditions in nematic liquid-crystal planar cells,” Opt. Express 12, 1011 (2004). 7. Ya. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Yu. S. Kivshar, “Multimode nematicon waveguides,” Opt. Lett. 36, 184–186 (2011). 8. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in bulk nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002). 9. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and G. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystal,” Appl. Phys. Lett. 81, 3335–3337 (2002). 10. S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial soliton all-optical logic gates,” IEEE Photon. Techn. Lett. 18, 1287–1289 (2006). 11. A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010). 12. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006). 13. Ya. V. Izdebskaya, V. G. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Soliton bending and routing induced by interaction with curved surfaces in nematic liquid crystals,” Opt. Lett. 35, 1692–1694 (2010). 14. R. Barboza, A. Alberucci, and G. Assanto, “Large electro-optic beam steering with nematicons,” Opt. Lett. 36, 2611–2613 (2011). 15. J.-F. Henninot, J.-F. Blach, and M. Warenghem, “Experimental study of nonlocality of spatial optical soliton excited in nematic liquid crystal,” J. Opt. A 9, 20–25 (2007). 16. Ya. V. Izdebskaya, V. G. Shvedov, A. S. Desyatnikov, W. Z. Krolikowski, M. Belic, G. Assanto, and Yu. S. Kivshar, “Counterpropagating nematicons in bias-free liquid crystals,” Opt. Express 18, 3258–3263 (2010). #169842 $15.00 USD Received 6 Jun 2012; revised 31 Aug 2012; accepted 30 Sep 2012; published 15 Oct 2012 (C) 2012 OSA 22 October 2012 / Vol. 20, No. 22 / OPTICS EXPRESS 24701 17. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media”, J. Opt. B 6, S288 (2004). 18. M. Szaleniec, R. Tokarz-Sobieraj, and W. Witko “Theoretical study of 1-(4-hexylcyclohexyl)-4isothiocyanatobenzene: molecular properties and spectral characteristics,” J. Mol. Model. 15, 935, (2009). 19. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media”, Phys. Rev. Lett. 98, 053901 (2007). 20. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang “Stable rotating dipole solitons in nonlocal optical media”, Opt. Lett. 6, 1100–1102 (2006). 21. Ya. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Yu. S. Kivshar, “Dipole azimuthons and vortex charge flipping in nematic liquid crystals,” Opt. Express 19, 21457–21562 (2011). 22. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003). 23. A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538 (1997). 24. M. Izutsu, Y. Nakai, and T. Suet, “Operation mechanism of the single-mode optical-waveguide Y junction,” Opt. Lett. 7, 136–138 (1982).


Introduction
The interaction of optical spatial solitons [1] has been studied extensively as a robust mechanism for all-optical, i.e. power-dependent, and reconfigurable spatial switching and routing of optical signals.
In this paper we experimentally investigate the all-optical confinement and switching of a weak probe counter-propagating (CP) with respect to two interacting nematicons (CO, forward) forming a power-dependent (Y or X) junction by way of their mutual attraction.In particular, we study the transverse output profile of the CP probe versus the launch power of the two CO nematicons.The probe signal tends to split in the two arms of a Y-junction for low nematicon powers, it gradually gives rise to three outputs (two guided signals and a beam) at intermediate soliton excitations and, eventually, forms a single output beam at powers large enough for the nematicons to interlace into an X-junction.This symmetric switching and redistribution of signal power stems from the nonlocal index distribution produced by the reorientationl solitons and can be illustrated by a simple analytical model.The phenomenon presented hereby could become the core of a novel all-optically reconfigurable interconnect and/or signal router.

Individual nematicon waveguides
We use an unbiased cell with an NLC layer sandwiched between two parallel polycarbonate slides separated by 110 μm.The NLC 4-(trans-4'-hexylcyclohexyl) isothiocyanatobenzoate (6CHBT [18], with birefringence Δn ≈ 0.16) was planarly oriented in (x, z), with its elongated organic molecules anchored with optic axis (molecular director) at 45 • with respect to z.The cell was sealed at input and output by extra glass interfaces with rubbing along x in order to prevent the formation of a meniscus and beam depolarization [4].We excited CO spatial soli-tons in the plane (xz) by injecting Gaussian beams with the waist of about 3μm from a cw laser of wavelength λ 1 =532 nm, with electric field extraordinarily polarized (E||x) in order to induce nonlinear reorientation even below the Freedericks threshold.Figure 1(a) displays the image of a forward propagating beam launched with an input power P=2 mW, forming a nematicon with xz trajectory along the Poynting vector at a walk-off of nearly 5 • with respect to the input wave-vector along z due to the birefringence of the NLC.
We launch a CP weak (147 μW) Gaussian beam from a cw laser of wavelength λ 2 =671nm through the opposite side of the cell, using a 10X microscope objective, resulting in an input waist w ≈ 3μm. Figure 1 (b,c) shows the evolution of the extraordinarily-polarized CP signal undergoing diffraction [Fig.1(b)] or guided-wave trapping [Fig.1(c)] in the absence or in the presence of a CO nematicon, respectively.In all the experiments we keep constant the CP launch power while varying the nematicon power P from 1 to 3 mW.Normalized intensity profiles of the CP signal, acquired in the plane (x, z) for various P, are shown in Fig. 1(d) after backward propagation over about 960 μm, as indicated by dashed lines in Fig. 1(b,c).It is apparent that, owing to the nonlocal character of the all-optical response, [4] the nematicon waveguide excited at 532nm effectively confines the backward propagating signal at the longer wavelength 671nm.

Nematicon Y-junction
Here we study the evolution of the CP signal interacting/guided by a symmetric Y-junction stemming from attraction and merging of two CO nematicons.Figure 2 is a sketch of the experimental setup.We employ a Mach-Zehnder arrangement (beam splitters BS1 and BS2, mirrors M1 and M2) to launch two closely-spaced CO nematicons.In order to guarantee mutual attraction and prevent interference, M2 was mounted on a piezoelectric transducer and rendered the two input beams mutually incoherent.Two equi-power extraordinarily-polarized beams at 532 nm are focused by a 10X lens and launched with parallel wave-vectors into the cell.The extraordinarily polarized probe beam is injected from the other end of the cell using the lens MO2.The beam dynamics along the cell is monitored by the camera CCD1 by collecting the light scattered through the top plate of the cell.The transverse dynamics (output images) of the signal is monitored by CCD2 with the aid of the semi-transparent mirror STM.The green light is blocked by band-pass filters (RF).Figure 3 shows some typical experimental results demonstrating the power-dependent dynamics of two interacting incoherent CO green nematicons initially separated by about 33 μm [(x, z) propagation, (a-d)] and the corresponding evolution of the weak signal (147μW constant power) backward propagating in the presence of the light-induced index perturbation [(x, y) transverse (e-h) and (x, z) longitudinal (i-l) views].For high enough green excitation, two spatial solitons are generated with trajectories depending on power: Fig. 3(a) shows two 0.6 mW solitons which travel in parallel while the CP red beam diffracts [Fig.3(e,i)]; as the power P increases up to 1.6 mW, the CO solitons attract and merge forming a Y-junction [Fig.3(b)], while the signal gets confined in a pair of soliton-induced waveguides and splits into two guided-wave outputs [Fig.3(f,j)]; for P >2 mW the two green solitons interlace [Fig.3(c)] and the signal propagates in the two arms of the Y as well as between them [Fig.3(g,k)], with more and more power in the middle spot at P increases, until eventually we observe just one centered output for P > 3.2 mW [Fig.3(h,l)].The signal mid-spot is substantially smaller than the diffracted spot [Fig.3(e,i)], suggesting that the probe is actually guided by the index perturbation induced by the soliton pair.Noticeably, the results are similar if the separation between nematicons increase up to 1.5 times.
Next we measure the signal powers in the three output spots versus input nematicon power P [Fig.4(a)], placing aperture and power meter 1.5 m away from the output.The inset in Fig. 4(a) identifies the various data sets: power transfer is apparent from outputs P 1 and P 2 to the mid spot P 3 versus soliton excitation P.This trend is better illustrated in Fig. 4(b), where we compare the intensity profiles of the three signal outputs versus P. Different input powers P correspond to the various profiles, as indicated in the legend: just two signal spots are visible for P = 1.3 mW, whereas the third output is observed for P > 2.2 mW.

Discussion
In order to explain the unexpected splitting of the CP signal, we recall the theory of higherorder nonlocal solitons [19][20][21].In fact, pairs of CO nematicons can form bound states, similar to dipole solitons [20] and belonging to the broader class of soliton clusters [19], including spiraling dipoles [21].Here we consider the propagation of a paraxial beam in a dielectric medium with a Kerr-type nonlinearity described by the nonlocal nonlinear Schrödinger equation (NNLSE), i∂ E/∂ z + ∇ 2 E + N(I)E = 0, where z and (x,y) stand for one propagation and two transverse coordinates, respectively, and ∇ = (∂ x , ∂ y ) [2,22].The nonlinear correction to the refractive index, N(I) = K(| r − ρ|)I( ρ)d ρ = 0, describes nematicon-induced waveguide potentials.The kernel K of the convolution integral is determined by the physical mechanism supporting the nonlinear response [17].Here we assume a Gaussian response K(r) = π −1 σ −2 exp −r 2 /σ 2 , with σ the nonlocality range.When σ → 0 we recover the (local) Kerr model with K(r) → δ (r) and N(I) ∝ I, whereas in the limit of a large nonlocality σ a (with a a characteristic transverse scale of the intensity localization), the waveguide effectively approaches a harmonic trap N(I) ∼ −Pr 2 (see Ref. [23]).For two interacting beams we use a dipole ansatz, E(x, y, z) = Ax exp −r 2 /2a 2 + ikz , with real amplitude A, half-width a, and propagation constant k.Variational solutions can then be derived [19] writing A and a as functions of soliton constant k and spatial scale σ .However, the NNLSE scaling property is such that the solution for any σ , A = A 1 /σ 2 , a = a 1 σ , and k = k 1 /σ 2 can be expressed in terms of A 1 , a 1 , k 1 obtained for σ = 1.The scale invariant soliton power is and can be used as a universal parameter.The corresponding refractive index N (I(x, y)) is Figure 5 graphs the changes in index profile (Eq.2) with soliton power P; we use a constant soliton width a = 1 and allow σ to vary.The power P clearly plays the role of scaling parameter for solitons, the shape of which in turn defines the profile of the induced waveguides.The guided modes with propagation constant β , E linear = U(x, y) exp(iβ z), can be found as the stationary solutions to NNLSE, −βU + ∇ 2 U + N(x, y)U = 0.The dipole soliton itself describes the antisymmetric mode with β = k.At low powers, a CP signal input in the Y-junction generates the symmetric mode [24] of the double-hump potential in Fig. 5(a), as observed in Fig. 3(f).As the soliton power increases, the index profile resembles a harmonic potential [23], as in Fig. 5(c); hence, the lowest order symmetric mode is bell-shaped, as in Fig. 3(h).

Conclusions
We demonstrated all-optical switching based on a signal confined by two interacting nematicons.At low powers the "nematicon beam-splitter" can guide the counter-propagating signal to the two outputs of a Y junction, at higher powers a third spot appears and progressively drags power from the guided modes of the junction, eventually carrying the whole signal excitation.The effect stems from the highly nonlocal nonlinearity, providing a wide guiding potential even when the nematicons do not overlap.The reported phenomenon is promising for the implementation of novel all-optically reconfigurable interconnects and signal processors.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .
Fig. 1.Individual nematicon waveguide and counter-propagating probe signal: (a) green forward nematicon excited at P=2 mW and propagating along the extraordinary walk-off angle with respect to the input wave-vector along z, (b) diffracting CP probe beam in the absence of nematicon; (c) nematicon-guided CP signal.(d) Intensity profiles of the CP probe for various nematicon excitations P; the transverse profiles are acquired from images of signal evolution in the plane (x, z) nearby z = 0, as marked by white dashed lines in (b,c).