We experimentally demonstrate the possibility of photorefractive 2D self-focusing in bulk Cerium doped Strontium Barium Niobate (SBN:Ce) directly at telecommunications wavelengths (1.06 μm and 1.55 μm). Although the electro-optic coefficient of SBN is smaller at infrared wavelengths, 2D infrared self-trapping is observed and analyzed versus different parameters such as the laser beam intensity, the external applied electric field and time.
© 2011 Optical Society of America
The fundamental concept of light guiding light, based on the propagation of self-confined laser beams , gives a unique possibility of 3D photoinduced circuits created in nonlinear bulk media without any fabricated optical waveguide. Optical waveguides in cristalline materials are usually realized by physical or physico-chemical methods (ion implantation, proton exchange, ion diffusion), giving rise to static integrated optics structures. Furthermore, these techniques are typically invasive. Photoinscription using photorefractive (PR) self-focusing is a softer technique to induce 3D devices and low loss circular waveguide in a single step process. Such reconfigurable waveguides can find interest for various applications. Different photonic components such as waveguides , directional couplers , light-induced Y and X-couplers and beam-splitters , switches [5,6] have been demonstrated using photorefractive solitons formed at visible wavelengths and used for guiding infrared (IR) light. Only few researches deal with the build up of self-confined laser beams in PR materials at telecommunications wavelengths: PR self-focusing was reported both at steady state and transient state, in planar He-implanted Strontium Barium Niobate (SBN) waveguides [7–9], in bulk semiconductor InP:Fe [10–15], CdTe  and SPS [17,18]. Semiconductors exhibit several advantages due to their sensitivity to near-infrared wavelengths and to their shorter response time, but they do not allow to fix the waveguide and are more dedicated to reconfigurable components. However, SBN is a very good candidate for fixed photonic components [19, 20].
In this paper, we make use of bulk photorefractive insulators SBN at IR telecommunications wavelengths and we demonstrate that despite its low sensitivity to infrared wavelengths (the absorption is equal to 0.58 cm−1) and its smaller electro-optic coefficient (r33 = 215pm/V) , SBN allows 2D infrared self-focusing. We study experimentally the self-focusing behavior for two different wavelengths (1.06 μm and 1.55 μm); the influence of different parameters such as the laser beam intensity, the external applied electric field and time will be discussed.
2. Self-focusing at IR wavelengths
2.1. Experimental set-up
For the experimental observation of the self-focusing in SBN at IR wavelengths, we use a standard set-up: an IR laser beam coming from either a YAG-Nd laser (λ = 1.06 μm; maximum power 200 mW) or a laser diode operating at λ = 1.55 μm (maximum power 10 mW) is focused at the entrance face of a SBN sample with an input waist of 20 μm. The sample is a bulk SBN:61 material doped with cerium (0.02% per weight) with dimensions (5*5*10 mm). The light propagation direction is along the 10 mm axis. The electric field is applied along the crystallographic c axis, parallel to the beam polarization direction. The output face of the crystal is observed through a camera using a 2f-2f imaging system, allowing to analyze the beam behavior versus time, intensity and electric field applied.
2.2. Self-focusing at λ = 1.06 μm wavelength
First we investigate the self-focusing process with the λ = 1.06 μm laser. Measurements of the output beam profile evidencing self-focusing have been performed for intensities in the range 25 W/cm2 to 100 W/cm2. At these light powers in the range of tens of microwatts, it should be noted that steady-state solitons can only be achieved using a background illumination. In this experiment, we do not use a background illumination and we analyze the transient self-focusing state reached using these intensities in a shorter time than the steady-state. A typical self-focusing is presented in Fig. 1 for a maximum intensity equal to 68 W/cm2. Figure 1(a) illustrates the diffracted output beam when no electric field is applied. Figure 1(b) shows a strong self-focusing for an applied electric field equal to 4 kV/cm. Figure 1(c) illustrates the transverse spatial output profile of the laser beam in the direction parallel to the electric field applied. This image confirms the self-focusing of the 1.06 μm laser beam and shows that together with self-focusing, the laser beam is bended as observed previously in bulk crystals at visible wavelengths  or in planar SBN waveguides .
We also observe the temporal dependence of the self-trapping, by collecting a sequence of images after we launch the laser beam in the crystal with a 3 kV/cm external electric field. Figure 2 illustrates the temporal evolution of the self-focusing process versus time for an intensity I = 48 W/cm2. We define the self-focusing ratio as the ratio of the output beam waist with the electric field applied over the output beam waist without field; by this way, the self-focusing ratio allows to quantify the self-focusing process. Note that a self-focusing ratio equal to 1 corresponds to the natural diffraction: in our case, this corresponds to a waist of 80 μm at the output face of the crystal. When the laser is launched, the beam is transiently self-focused, reaching a minimum value corresponding to the saturation process and relaxing to a less focused state. The same behavior was previously observed experimentally and confirmed the predictions of numerical calculations based on the Kukhtarev band transport model , at visible wavelengths in insulators [22,23] as in planar SBN waveguides at IR wavelengths . Furthermore, for testing the influence of the intensity of the injected laser beam I and of the external applied electric field E, we measured the evolution of the self-focusing ratio for I in the range 25 W/cm2–100 W/cm2 and for E in the range 1 kV/cm–4 kV/cm.
Figure 3 summarizes the self-focusing behavior versus intensity for different electric field at steady state. We observe that, for an electric field of 4 kV/cm, for intensities I below 20 W/cm2 no change in the beam profile appears. For an intensity of 30 W/cm2, the laser beam begins to be slightly self-focused. Increasing the intensity, the process becomes more intense and reaches a maximum for an intensity equal to 60 W/cm2. For intensities larger than 60 W/cm2, the self-focusing state relaxes to a less focused state.
The above observations concern the steady-state regime. This behavior reproduces qualitatively the previously observed behavior in insulators at visible wavelengths excepted that self-focusing at IR wavelengths in SBN crystals needs a more intense laser beam. For smaller values of the applied electric field (1 kV/cm–3 kV/cm), we measure a weaker self-confinement. In Fig. 4 we illustrate the dependence of the beam width on the externally applied electric field. We observe a linear behavior of the self-focusing ratio versus the electric field as observed at visible wavelengths. Our investigations have demonstrated the possibility for a single 1.06 μm laser beam to be self-focused in bulk photorefractive SBN in the two transverse dimensions. The behavior versus time, intensity and electric field has been studied and shows a similar behavior to visible wavelengths. We propose now to analyze the self-focusing behavior at 1.55 μm.
2.3. Self-focusing at λ = 1.55 μm wavelength
In this section, we will show self-focusing experiments at 1.55 μm without background illumination, as previously explained for the 1.06 μm. To show self-focusing, we have performed measurements of the output beam profile for intensities in the range 8 W/cm2 and 185 W/cm2 for a waist w = 20 μm, corresponding to a diffracted waist equal to approximatly 100 μm at the output face of the crsytal.
Figure 5 illustrates typical beam profiles at the output face of the crystal for an input intensity equal to 185 W/cm2. This value corresponds to the maximal intensity we can reach at the crystal entrance face. Figure 5 shows a typical measurement of self-focusing of a 1.55 μm laser beam in SBN for an electric field equal to 4 kV/cm: Fig. 5(a) illustrates the diffracted output beam when no electric field is applied; Fig. 5(b) shows that the beam is self-focused in both transverse dimensions under a 4 kV/cm electric field. This result is promising for photoinducing directly a waveguide through photorefractive self-focusing at telecommunications wavelengths in SBN.
In the following, we analyze the role played by intensity on the self-trapping process using the self-focusing ratio as defined at 1.06 μm, choosing the most focused state corresponding to transient state. The diameters are calculated at FWHM (Full Width at Half Maximum). Figure 6 shows the self-focusing ratio as a function of the input beam intensity: the self-focusing becomes stronger for higher intensities, reaching a value equal to 0.65 for I = 185 W/cm2.
This observed behavior of self-focusing versus intensity is in qualitative agreement with previous experimental results in SBN samples at visible wavelengths.
In summary, we thus demonstrated that photorefractive self-focusing process is possible even at IR wavelengths (both at 1.06 and 1.55 μm) in bulk Ce:SBN. We tested the dependency of the self-focusing ratio as a function of different parameters such as the laser beam intensity, the applied electric field and time. Our work complements previous experiments of self-focusing but on planar SBN waveguides with wider input beams. We also demontrate that, in spite of a smaller electro-optic coefficient, the self-focusing behavior in SBN is similar at IR wavelengths than at visible wavelengths. This study initiates deeper investigations on the possibility to create 3D photoinduced circuits directly at telecommunications wavelengths, which are of interest for optical interconnects applications.
The authors acknowledge the support of the Conseil Regional de Lorraine and COST European Action MP0702.
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