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We report the formation of surface self-written waveguides by means of surface pyrolitons in lithium niobate. By a specific orientation of the crystal axis the quasi-local slow photorefractive response of lithium niobate was used to induce a self-confined beam exactly at the crystal-air interface. The mode profile of the photo-induced waveguide is strongly asymmetric due to the interface presence.
© 2013 Optical Society of America
1. Introduction
With the expression “self-written” waveguides we intend a guiding refractive pattern for light written inside a photosensitive material by light itself. The mechanism is based on the condition that the material refractive index increases after exposition to light. In this way a guiding channel is assembled by the light that propagates inside it. Due to the temporal and spatial evolution of the photo-induced refractive index modification, the writing beam experiences a self-confinement that is usually known as “spatial soliton” [1-3].
Self-induced waveguides are usually generated in photosensitive media like polymers [4–7] or photorefractive media [8], just to cite the most used ones.
Photorefractivity was reported for the first time as a dielectric damage of the material in 1966 by Ashkin et al. [9] and only latter spatial solitons based on this nonlinear phenomenon were observed [10]. Photorefractive solitons got a very important role in the soliton waveguiding due to the ferroelectric domain inversion of the illuminated volume [11] which allows either permanent or erasable or transitory waveguiding.
In 2003 spatial solitons were observed in lithium niobate [12]. In such work the authors showed that soliton channels remain active for very long time after their creation, realising almost permanent waveguides. Since then, a large literature was published on solitons and solitonic waveguides in lithium niobate due to the enormous amount of nonlinear properties this material possesses [13], that make it very interesting for signal processing inside low-losses integrated circuits [14–18].
The observation of bright spatial solitons supported by the pyroelectric effect [19], the so-called pyrolitons, opened the possibility to realise photorefractive solitonic beams at the surface of lithium niobate crystals [20]. In fact, using the pyroelectric effect no electric contacts are needed to bias the medium, getting access to the material interface.
Surface solitons were already predicted [21–26] and observed in other materials like SBN [21,27,28] and BaTiO3 [29].
The photorefractive nonlinearity has indeed a nonlocal response, being mainly related to photoinduced electric current [21,22,30,31]. Alfassi et al. [32] demonstrated that nonlocal response of the optical nonlinearity cannot give rise to spatial solitons exactly at the interface linear-nonlinear media, but it lays few microns below it. You can imagine that charges need space to accumulate, forcing the light to be confined below. This was also confirmed in lithium niobate where surface solitons lay just below the (001) and (001) interfaces [20].
In the present paper we show that the photorefractive nonlinearity can act as local along the ordinary crystallographic directions while remaining non-local along the extraordinary direction (optical axis) where the charge movement occurs. Thus, playing with the crystallographic orientations it is possible to force the self-confined beam to be localized exactly at the interface between linear and nonlinear media, thanks to the quasi-local response orthogonally to the optical axis.
Such technological innovation is fundamental for applications, allowing to use soliton waveguides as evanescent wave sensors [18].
2. Surface pyroliton and associated waveguide
In the first experiment on photorefractive surface solitons in lithium niobate [20] the (001) surfaces was adopted to drive the beams. The natural bending [33] of solitons bows the light path towards the direction, bringing it to knock the lower interface that traps the beam [21]. Such dynamics is indeed governed by the photo-excited electric-charge movement which is defined by the equation of the [30, 31]:
where is the mobility inside the photorefractive medium of the electron spatial density ne, is the Boltzmann constant, is the local electric field, the photovoltaic cross section, I the light intensity while and are the intrinsic and photo-excited donor densities.The equilibrium between fixed and moving charges is indeed governed by the charge continuity equation:
The diffusion term in Eq. (1) is usually neglected with respect to because is lithium niobate an intense electric bias is needed to reach a positive variation of the refractive index inside the illuminated region. Among all, diffusion is the most isotropic of the current terms. Free and photo-voltaic conductions occur along the direction which consequently acts as nonlocal direction. No significant charge movement occurs along the and directions corresponding to quasi-local directions. Such phenomenon was also observed during the soliton formation transient, where the nonlocal direction experiences much faster selfocusing than the quasi-local directions [12, 34].In order to exploit the quasi-local nature of the photorefractivity along the [100] and [010] directions, we have generated Surface pyrolitons in the scheme shown in Fig. 1.
A z-cut lithium niobate crystal from a commercial wafer was used, whose dimensions were 5 mm along [100] and 1 mm thick along the optical axis [001] (i.e. ). The sample was mounted over a Peltier heater which created a nominal temperature gradient along the optical axis of about 11°C. Following the protocol defined by S.T. Popescu et alii [35], the input laser @405nm was focused onto the input YZ face down to a spot with an elliptical shape of 8x14 μm2 [FWHM]. The effective input power was set at about 10 μW. The soliton was formed over the (010) interface.
An optical system (magnification 21) images the output (100) plane over a CCD camera. The experimental pictures of the output beam profile are reported in Fig. 2.
At the beginning (0 sec) diffraction was slightly collected by the crystal surface (0-100 sec) at the (100)-(010) edge. As time passes, the photorefractive nonlinearity becomes more and more active letting light to be selfocused along the diffraction pattern. Between 130 and 180 sec mainly two selfocused channels emerge from diffraction, one exactly at the surface and very similar to a (1D + 1) soliton and one slightly inside the substrate, very similar to a (2D + 1) self-confined structure.
Such behaviour is very similar to previous observations in SBN [21,28]. As time passes, the 2D structure is attracted by the 1D one, which is more stable due to the presence of a strong refractive contrast induced by the interface. Consequently, the 2D beam collapses into the superficial one around 180-200 sec after the starting.
After collapse, a single 2D self-confined channel stabilises at the surface, getting almost the whole energy trapped with a triangular shape: in fact the transverse mode is somehow elongated along the crystal surface (i.e. along the [001] direction) with a beam waist (FWHM) as large as 18 μm, while orthogonally to it (i.e. along the [010] direction) the beam core is 12 μm (FWHM).
A long tail is also present in the [010] direction (i.e. inside the crystal) that penetrates for about 25-30 μm within the substrate (Fig. 2 – image at 240 sec). Such tail is given by the untrapped diffraction orthogonally to the interface and it is few microns above the self-trapped beam. Actually we should say the contrary, i.e. the self-trapped beam is few microns below the untrapped tail, being this displacement originated by the usual bending of the trapped light along the (001) direction.
An enlargement of the output beam profile at 240sec from the starting time (Fig. 3) shows clearly the asymmetric triangular shape of the self-confined beam. Outside the crystal surface a diffraction pattern is still visible, sign that the (100)-(010) edge is indeed hit by light.
The self-confined beam has indeed written a superficial waveguide. It was checked by switching off the heater and letting the crystal cool down in the dark in order to make the material thermalize and consequently eliminate any residual pyro-electric field. Consequently, all transient effects are cut away even if the refractive index modification remains active.
The 405 nm light is still guided after long time (Fig. 4), with a triangular mode very similar to the writing self-confined beam. At longer wavelengths the guided mode tends to ovalize itself, even if the interface presence gives an asymmetric shape to the transmitted beam.
Fig. 4 Propagation mode of the superficial soliton waveguide at different wavelengths. Spatial dimensions are in microns.
3. Numerical simulation
Numerical simulations has been performed using the dynamic three-dimensional photorefractive model introduced by Devaux et al. [36]. It is based on the temporal and spatial analysis of the photoexcited charges responsible of a local electric field which modifies the material refractive index by means of the electro-optic effect. This model considers that all spatial derivative operators are applied along the three dimensions of space, thus including possible influence of the three components of the space charge electric field on an anisotropic dielectrics. As a consequence, the local electric field induced by the photoexcited charges is calculated by solving the expression:
Such field is responsible for the refractive index modification by means the electro-optic effect:having called z the optical-axis direction.In the simulation we have considered for the material a refractive index ne = 2.33, the electro-optic coefficient r33 = 32 pm/V and a donor concentration as high as 2.02⋅1015 cm−3. About the electro-magnetic field, we have considered a dark illumination as low as 1 μW/cm2, with an input power at 405 nm as high as 10 μW focused on a 16μm x16μm (FWHM). The input beam was set 20 μm below the surface, with a slight angle toward it. The photovoltaic field was ranging between −3 and −5⋅104 V/cm.
In regime of pure linear propagation of the injected light beam, the outgoing beam shapes as diffracted pattern consequence of the interference between the straight and the internally reflected light from the interface. (Fig. 5 – diffraction).
As soon as the nonlinearity grows up, the most intense interference fringe selfocuses, attracting the whole light beam inside the self-generated refractive channel. Such dynamics becomes bistable, evolving towards a final self-confined beam laying exactly at the air-dielectric interface. The beam gets a triangular shape, elongated along the interface, as experimentally observed (Fig. 3).
The refractive index modification is shown in Fig. 6. The whole photoinduced waveguide is indeed asymmetric with respect to the interface. The index profile shapes as hyperbolic secant in the direction orthogonal to the interface (i.e. along the [010] crystallographic direction), well approximated by the following formula:
with fitting parameters δn = 6.7⋅10−4, z0 = 6 μm and σ = 9 μm. As a consequence, the profile gets the largest contrast at about 6 μm below the interface, decreasing towards the linear value of the refractive index in the bulk. In the transverse direction (i.e. along the [001] crystallographic direction) the central lobe gets almost a cosine shape, as shown in Fig. 6(b) with the back dotted lines. The effective waist (FWHM) is about 12 μm deep and 18 μm wide.Fig. 6 (a) Simulation of photoinduced refractive waveguide. (b) Fitting (with dotted back lines) of the numerical profiles: in red along the [010] direction and in blue along the [001] one.
4. Conclusion
We report the formation of a solitonic waveguide exactly at the interface between the air and the dielectric lithium niobate. Such result was reached taking advantage of the quasi-local nature of the photorefractive nonlinearity moving in a direction orthogonal to the optical axis.
The associated superficial waveguide is very attractive for sensing applications, due to the low losses of soliton waveguides and due to their self-aligning nature.
Acknowledgments
The present work was partially supported by the Italian MIUR contract PRIN2008 N° 20088ZA8H9 AMDG.
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