All-optical switching of a signal by a pair of ... - Semantic Scholar

All-optical switching of a signal by a pair of interacting nematicons Ya. V. Izdebskaya,1,2∗ J. Rebling,3 A. S. Desyatnikov,1 G. Assanto,4 and Yu. S. Kivshar1 1 Nonlinear

Physics Center, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia 2 Department of Physics, Taurida National University, Simferopol 95007, Ukraine 3 University of Applied Sciences, Zwickau 08056, Germany 4 NooEL–Nonlinear Optics and OptoElectronics Lab, University “Roma Tre”, Rome, Italy ∗ [email protected]

Abstract: 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. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003). M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012). A. Piccardi, A. Alberucci, N. Tabiryan, and G. Assanto, “Dark nematicons,” Opt. Lett. 36, 1456–1458 (2011). 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). M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001). 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). Ya. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Yu. S. Kivshar, “Multimode nematicon waveguides,” Opt. Lett. 36, 184–186 (2011). M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in bulk nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002). 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). 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). 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). M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006). 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). R. Barboza, A. Alberucci, and G. Assanto, “Large electro-optic beam steering with nematicons,” Opt. Lett. 36, 2611–2613 (2011). 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). 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).

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Received 6 Jun 2012; revised 31 Aug 2012; accepted 30 Sep 2012; published 15 Oct 2012 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).

1.

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 reorientational nematic liquid crystals (NLC) spatial solitons are known as nematicons, [2] and the confinement (i.e. routing) of a weak signal by nematicon-induced waveguides has been demonstrated or bright solitons [4–7] in self-defocusing or self-focusing media, respectively. Particularly interesting are soliton-based guided-wave circuits and switches, such as junctions [8] and logic gates [9–11]. Additional degrees of control over soliton dynamics are provided by electric (voltage) tuning of nematic liquid crystals [2]. Voltage-controlled soliton refraction and reflection were reported [12–14] together with the trapping of weak signals in these bent waveguides. Soliton deviation was also demonstrated by interactions with other solitons [8, 9], including counter-propagating configurations [15, 16]. Noteworthy, the inherent high nonlocality [17] produces broad refractive potentials supporting longer wavelength and higher-order guided modes [4, 5, 7]. 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. 2.

Individual nematicon waveguides

We use an unbiased cell with an NLC layer sandwiched between two parallel polycarbonate slides separated by 110 μ m. 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#169842 - $15.00 USD (C) 2012 OSA


tons in the plane (xz) by injecting Gaussian beams with the waist of about 3μ m from a cw laser of wavelength λ1 =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 μ W) Gaussian beam from a cw laser of wavelength λ2 =671nm through the opposite side of the cell, using a 10X microscope objective, resulting in an input waist w ≈ 3μ m. 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 μ m, 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. 3.

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 Forward soliton 1

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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).

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CCD 2

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Fig. 2. Setup: L1, L2 - cw lasers; λ /2 - half-wavelength plates; BS - beam splitters; M1 mirror; M2 - mirror on a piezo-transducer; STM - dichroic mirror; MO1 and MO2 - 10 X microscope objectives; MO3 - 5X microscope objective; NLC - sample; RF - red band-pass filters; D - diaphragm; PM - power meter; CCD1 and CCD2 - cameras.

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Fig. 3. Evolution of two CO green nematicons for various excitations P (a-d), with the corresponding output transverse (x, y) profiles (e-h) and backward propagation (i-l) of the CP red signal.

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Fig. 4. (a) Probe power Ps (s = 1, 2, 3) in each of the three output spots versus excitation P of each nematicon. (b) Transverse profiles of the probe output for various soliton powers P.

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 μ m [(x, z) propagation, (a-d)] and the corresponding evolution of the weak signal (147μ W 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 P1 and P2 to the mid spot P3 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. 4.

Discussion

In order to explain the unexpected splitting of the CP signal, we recall the theory of higherorder nonlocal solitons [19–21]. 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 Schr¨odinger 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 cor rection to the refractive index, N(I) = K(|r − ρ |)I(ρ )dρ = 0, describes nematicon-induced

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Fig. 5. Nonlocal dipole soliton with a = 1. Graphs of Intensity profiles I(x, y = 0) (solid line) and refractive index N(x, y = 0) (dashed line) for (a) σ = 0.3 and P = 38.6, (b) σ = 1 and P = 84.8, (c) σ = 1.5 and P = 133.3. Note that the different vertical scales in (a)-(c).

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 −r2 /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) ∼ −Pr2 (see Ref. [23]). For two interacting beams we use a dipole ansatz, E(x, y, z) = Ax exp −r2 /2a2 + 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 = A1 /σ 2 , a = a1 σ , and k = k1 /σ 2 can be expressed in terms of A1 , a1 , k1 obtained for σ = 1. The scale invariant soliton power is P≡

|E|2 dr =

π 2 4 2π (2a2 + σ 2 )4 A a = 4 4 , 2 a 3a + a2 σ 2 + 2σ 4

(1)

and can be used as a universal parameter. The corresponding refractive index N (I(x, y)) is x2 + y2 σ2 σ2 A2 a6 2 1 + x exp − . (2) + N(x, y) = 2 (a + σ 2 )3 2 a2 a2 + σ 2 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 , Elinear = U(x, y) exp(iβ z), can be found as the stationary solutions to NNLSE, −β U + ∇2U + 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). 5.

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. #169842 - $15.00 USD (C) 2012 OSA


Acknowledgments We acknowledge support from the Australian Research Council.

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