Guiding and dividing waves with photorefractive solitons
Introduction
Photorefractive spatial screening solitons are the topic of extensive research in the last decade (e.g. Refs. [1], [2], [3]). Their creation and their characteristics have been examined thoroughly and also their capability of guiding another light beam was reported [5]. Because of their robustness and the simplicity of their creation at low laser power, the idea of deploying them in waveguide applications is evident. Furthermore, the non-local character of their anisotropic potential, which makes them unique among other types of spatial solitons, gives reason for different interaction scenarios between two or more of them and therefore enables the realization of different waveguide coupling devices or waveguide switches.
Photorefractive spatial screening solitons form when the self-focusing of a light beam inside the material exactly balances the diffraction of the beam. The refractive index modulation created by this light beam can be used to guide a second beam and therefore acts as a waveguide [5]. When looking for the development of this waveguide more thoroughly it can be seen that the guided wave exactly follows the trajectory of the soliton and even copies its shape. Due to the anisotropy of the electrostatic potential in the two transverse dimensions, the refractive index is modulated in an anisotropic way which results in a rather elliptical than circular shape of the waveguide [6]. Additionally, the interaction of two solitons, which happens in photorefractive material due to the saturable character of the non-linearity, is strongly influenced by the anisotropy and causes two or more solitons to interact in a variety of different ways (e.g. attraction, fusion, repulsion, rotation, spiraling, see e.g. Refs. [7], [8], [9], [10]).
Aligning two solitons parallel in the plane of the applied electric field they interact in an attractive or repulsive manner depending on their mutual distance. When the plane in which the solitons propagate is tilted to the x- or y-direction, they will rotate around their common center of mass. Additionally introducing an initial mutual angle can cause them to spiral around each other while propagation [11]. Furthermore under certain geometrical conditions situations involving a mutual exchange of energy between the solitons can be found [12]. When applying these interacting solitons for waveguide purposes it is possible to steer a probe beam guided in one soliton by launching a second one or to divide a probe beam by guiding it in a soliton which exchanges energy with a second one. This will be shown in detail in this paper.
Section snippets
Experimental setup
The experimental investigations were realized in a standard configuration [3]. One or two beams are derived from a frequency-doubled Nd:YAG laser () and are focused to a size of nearly 10 μm (FWHM) each onto the front face of a photorefractive Sr0.60Ba0.40Nb2O6 (SBN:Ce) crystal. In our experiments two different samples of crystals of the same material and dopand (0.002 wt.% CeO2) but of different length were used. The dimensions of the crystals were 5×5×13.5 and 5×5×20 mm3 respectively.
Guidance of a single beam
In a first experiment, the principal guidance of a second beam in a (2+1)D-soliton is shown. One soliton is created using a low power beam of the Nd:YAG laser at 532 nm (intensity I≈30 mW/cm2) while one probe beam of nearly the same power derived from a HeNe laser is focused on the same spot at the front face of the crystal. Here the propagation length is 13.5 mm. To clearly separate the green writing beam from the red probe beam, a prism is induced in front of the CCD camera, which makes the
Waveguiding in interacting solitons
In a next experiment, the capability of guidance of two incoherent interacting solitons is examined. Here, two different cases of soliton interaction can be distinguished. Depending on the initial launching conditions (mutual distance in both transverse directions and tilt) the two solitons can propagate with or without a mutual exchange of energy [12]. To examine the waveguide capability of interacting solitons we extended the setup as shown in Fig. 2. To obtain a second soliton, the beam from
Independent guidance in two interacting solitons
In case of no mutual exchange of energy between the two interacting beams, a soliton which guides a signal wave can be moved to another position by launching the second soliton as a controlling beam. This builds the basis for a real all optical switch. The switching time is ruled to the response time of the material which is rather slow (in the range of seconds). Anyhow, in this experiment the effects can be examined thoroughly and demonstrated well and therefore it can serve as a model for
Waveguide division with interacting solitons
In the case of mutual energy-exchange between the two interacting solitons a division of the probe beam can be realized. The principle of waveguide division due to such interaction was previously shown in Ref. [19], even though only for the one-dimensional case. In our experiment we investigated the case for two-dimensional beams. The foci of the two writing beams of which each had an intensity of 76 and 68 mW/cm2 respectively, are adjusted on the front face of the crystal to a distance of
Conclusion
In this paper we showed the principal guidance of a single beam in a photorefractive (2+1)D-soliton in a time-resolved manner. The guided beam can be found to follow exactly the path of the writing beam and yet copies its shape while the soliton forms. Moreover we show the first time to our knowledge the guidance of a probe beam in interacting solitons. Here two situations of interacting solitons with and without a mutual exchange of energy have been realized. While in the case of no energy
Acknowledgements
This research was partially supported by the Deutsche Forschungsgemeinschaft under contract KA-708/1-1. The authors acknowledge kind support by Prof. Dr. T. Tschudi, Institute of Light- and Particle Optics, Darmstadt University of Technology.
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