December 1, 2002 / Vol. 27, No. 23 / OPTICS LETTERS
2097
Solitonic all-optical switch based on the fractional Talbot effect Stefano Minardi, Gianluca Arrighi, and Paolo Di Trapani Instituto Nazionale di Fisica Nucleare and Dipartimento di Scienze, Chimiche, Fisiche, Matematiche, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy
Arunas Varanaviˇcius and Algis Piskarskas Department of Quantum Electronics, Vilnius University, Sauletekio, 9, Building III, LT 2040 Vilnius, Lithuania Received June 6, 2002 A periodic pattern of hundreds of beams is shifted by half its transverse period as the result of excitation of parametric spatial solitons and the fractional Talbot effect. The all-optical switch that is obtained operates with 1-ps pulses. © 2002 Optical Society of America OCIS codes: 230.1150, 190.5530, 190.4410, 350.3950.
Optical control of transverse light patterns in nonlinear optics has always attracted much interest because of its potential for all-optical logical and computational tasks.1,2 Large-aperture lasers were operated as optical associative3 and rewritable digital memories.4 Similar results were obtained in single-feedback nonlinear systems.5 However, because of the feedback process, the switching speed of cavity-based devices is rather poor compared with that of traveling-wave schemes. Among the various types of traveling-wave transverse pattern sustained by quadratic nonlinear materials, spatial solitons proved to be good key elements for ultrafast (1– 20-ps) all-optical switching and addressing.6 In fact, solitons were used to build polarization-, phase-, and intensity-dependent optical switches,7 – 9 whereas the nonlinear mixing of focused vortex beams can excite regular sets of solitons whose number is given by simple algebraic rules.10,11 In this Letter we present an ultrafast, all-optical switch that is able to shift transversally an arbitrary large square-lattice pattern of narrow focused beams by half its period. The device exploits both the features of the seeded soliton excitation in a traveling-wave parametric amplif ication scheme12 and those of the Talbot effect13; The free propagation of an infinite, periodic transverse pattern leads to periodicity along the propagation coordinate, too, producing self-imaging of the prof ile of a given plane after each Talbot length ZT 苷 2p2 兾l. Note that ZT depends on only the transverse period of the pattern, p, and the light’s wavelength, l. Between two planes separated by a distance ZT , diffraction strongly modifies the appearance and the multiplicity of the pattern.14 However, the effect of diffraction on the field distribution of a pattern propagating for a distance ZT 兾2 is merely that of shifting transversely the pattern by half its period (fractional Talbot effect). The results of a numerical simulation 共2D 1 1 coupled-wave equations model, integrated with a split-step scheme) shown in Fig. 1 explain how our switch works. A matrix of narrow pump beams 0146-9592/02/232097-03$15.00/0
[Fig. 1(a)] at frequency vp impinges upon the input face of a quadratic nonlinear crystal operated to allow the parametric amplif ication of the degenerate subharmonic 共vp 兾2兲 in noncritical, type I phase matching. The crystal length is exactly ZT 兾2, so the output pattern [Fig. 1(b), array 1], of the pump f ield is a shifted copy of the input pattern, even in the case of spontaneous parametric generation that is not negligible. If a sufficiently intense subharmonic seed is launched in the crystal (spatially and temporally overlapping the pump), an array of spatial solitons is excited in the first few millimeters of propagation. The array of solitons at the crystal output [Fig. 1(c), array 2], is therefore aligned with the array of the input pump beams.15,16 That this is so proves that an optical signal can be used to switch from one array of light beams (array 1) to the other (array 2). For the experimental implementation of the optical switch we used 1-ps pulses from a Nd:glass laser system (TWINKLE, Light Conversion). The fundamental seed (1055-nm wavelength) and the second-harmonic pump (527.5 nm) are regulated in energy separately, in two different channels. A dichroic mirror is used to recombine the two channels, whose relative path length can be adjusted by means of a delay line. A two-dimensional array of microlenses (108-mm pitch, 4.6-mm focal length) was used to eff iciently transform the 3.5-mm-wide (FWHM) pump and seed beams into a pattern made up of 艐1100 beams arranged on a square lattice. By means of a telescope, the first focal plane of the array is imaged near the input face of a 22-mm-long LiB3 O5 crystal, cut, and operated for noncritical type I phase matching between the pump and seed wavelengths 共Dk 苷 0兲. We set the magnification of the telescope to 0.78 to match the ZT 兾2 length of the multibeam pattern with the crystal length. Finally, a CCD-based imaging system allows us to record the output face of the LiB3 O5 crystal in either wavelength. The experimental output pump cross sections along the line corresponding to the diagonal of two unit cells of the output beam arrays is depicted in Fig. 2(a). The © 2002 Optical Society of America
2098
OPTICS LETTERS / Vol. 27, No. 23 / December 1, 2002
ence fringes.17 With reference to Fig. 2(a), this quantity reads as 共Von/off 兲j 苷
FHj 2 FLj , FHj 1 FLj
j 苷 1, 2 ,
(1)
which could be interpreted as the visibility of a single beam in one of the arrays calculated between its on and off states (on– off visibility). The higher the visibility, the more distinguishable are the on and off states gauged by a hypothetical detector centered at the nodes of the array of beams. In Fig. 3, the average on–off visibilities of the pixels of both arrays are plotted as a function of the pump and the seed energies. Figure 3(a) shows that to operate the switch efficiently a minimum pump energy should be provided, as expected from the f inite soliton excitation threshold. From a comparison of Figs. 3(a) and 3(b) it is apparent that the best operating conditions of the switch are found in the strong seeding limit 共Eseed . 100 mJ兲 with the pump in the range 300 400 mJ. Visibility ratios larger than 0.75 and 0.4 are observed for arrays 2 and 1, respectively. We can explain the lower
Fig. 1. Results of a numerical simulation: Four unit cells of the (inf inite) lattice are shown. (a) Input pump prof ile. (b) Output pump prof ile in the unseeded configuration (array 1). Only a white seed at the quantum noise level is present. (c) Output pump prof ile when a seed is launched simultaneously (array 2). The seed prof ile is as in (a), but the peaks are twice as wide to ensure the same diffraction length for both the pump and the seed. Peak intensity of the pump, 40 GW兾cm2 ; crystal length, 22 mm. The side of each frame is 170 mm long.
peak-shifting effect of the pump beam is evident when the unseeded (dashed curve, array 1) and seeded (solid curve, array 2) cases are compared. The infrared radiation trapped under the peaks of array 2 (not shown) is consistent with the claim that the seed-excited array consists of spatial solitons. Figures 2(b) and 2(c) show the corresponding bidimensional pump f luence output profiles. Compared with Figs. 1(b) and 1(c), the experimental output in Figs. 2(b) and 2(c) shows a higher level of background with respect to the numerical results, but the qualitative features of the switch are essentially the same (see below for a more detailed discussion). To evaluate the eff iciency of the switch, for each of the two arrays (1 and 2) we def ined a quantity that recalls the well-known visibility of the interfer-
Fig. 2. (a) Experimental output f luence prof iles along the diagonal of two unit cells of the multibeam array. Dashed curve, unseeded conf iguration (array 1); solid curve, seeded conf iguration (array 2). (b), (c) Corresponding bidimensional f luence maps, in unseeded and seeded conf igurations, respectively. The diagonal lines in the contour maps represent the sampling line we used to get the f luence prof iles depicted in (a). The overall energy of the pump was f ixed to 330 mJ, and the seeding beam carried ⬃125 mJ, both distributed over an area of 3 mm 3 3 mm (crystal area corresponding to approximately 33 3 33 beams; maximum energy content of the unit cell, 艐0.5 mJ). The dimensions of the frames are 150 mm 3 180 mm; the beam diameter (FWHM) of the solitons is estimated in 17 mm.
December 1, 2002 / Vol. 27, No. 23 / OPTICS LETTERS
2099
different length. Finally, we point out that from Fig. 3(b) it is evident that a seed level as low at 10 mJ (3% of the pump energy) is enough to ensure a visibility better than 0.33 for both arrays (f luence ratio better than 2), thus showing the possibility of switching between the two states with a weak signal. In summary, we have shown how to combine the linear characteristics of a periodic light pattern with the features of a multisoliton array to arrange an ultrafast all-optical switch. This work was partially supported by the European Commission CEBIOLA project (contract ICAI-CT-2000-70027), a Young Researchers Grant of the University of Insubria, and the Information Society Technologies Future and Emerging Technologies project QUANTIM. S. Minardi’s e-mail address is
[email protected]. References
Fig. 3. On – off visibility of arrays 1 and 2 as a function of the overall (a) pump and (b) seed energies.
visibility ratio of the pixels in array 1 than array 2 by pointing out that, because of its Gaussian temporal shape, part of the pump pulse is below the threshold for the soliton formation. This part diffracts almost linearly, thus contributing to the observed residual peak, FL1 . Besides the temporal pulse-shape effects, another deviation from optimal exciting conditions could explain why our simulations give much better output visibilities than the experiment [compare Figs. 1(b) and 1(c) with 2(b) and 2(c)]. In fact, to operate the switch at its best, we had to focus the pump array not at the input face of the LiB3 O5 crystal but ⬃3 mm before it. This explains the poor contrast of the unseeded lattice 1 in Fig. 2(b). This limitation, which could be related to the chromatic aberration of the array of microlenses, the temporal group-velocity mismatch, or other effects not accounted for in the simulation, might be resolved by using a crystal of
1. L. Lugiato, Phys. Rep. 219, 293 (1992). 2. C. O. Weiss, Phys. Rep. 219, 311 (1992). 3. M. Brambilla, L. Lugiato, M. V. Pinna, F. Prati, P. Pagani, P. Vanotti, M. Y. Li, and C. O. Weiss, Opt. Commun. 92, 145 (1992). 4. V. B. Taranenko, C. O. Weiss, and W. Stoltz, Opt. Lett. 26, 1574 (2001). 5. B. Schäpers, M. Feldmann, T. Akemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000). 6. See special issue on optical solitons, Opt. Photon. News 13(2), 20–76 (2002). 7. W. E. Toruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996). 8. Y. Baek, R. Schiek, G. I. Stegeman, I. Bauman, and W. Sohler, Opt. Lett. 22, 1550 (1997). 9. H. Lopez-Lago, C. Simos, V. Couderc, and A. Barthelemy, Opt. Lett. 26, 905 (2001). 10. L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997). 11. S. Minardi, G. Molina-Terriza, P. Di Trapani, J. P. Torres, and L. Torner, Opt. Lett. 26, 1004 (2001). 12. M. T. G. Canva, R. A. Fuerst, S. Baboiu, G. I. Stegeman, and G. Assanto, Opt. Lett. 22, 1683 (1997). 13. M. Mansuripur, Opt. Photon. News 8(4), 42, (1997). 14. J. T. Wintrop and C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965). 15. S. Mindardi, S. Sapone, W. Chinaglia, P. Di Trapani, and A. Beržanskis, Opt. Lett. 25, 326 (2000). 16. A. Bramati, W. Chinaglia, S. Minardi, and P. Di Trapani, Opt. Lett. 26, 1409 (2001). 17. D. H. Kelley, Appl. Opt. 4, 435 (1965).
