We demonstrate the electro-activation of funnel waveguides through the quadratic electro-optic effect in paraelectric potassium-lithium-tantalate-niobate. This allows us to achieve electro-optic intensity modulation in a single optical beam, a 1×2 switch, and finally the electrically controlled morphing of a single waveguide into a 1×2 and a 1×4 divider.
© 2009 Optical Society of America
1. Introduction and motivation
In distinction to electric signals, optical signals can be used to handle links and information channels in massively parallel full three-dimensional geometries. A step towards the harnessing of this enormous potential is the identification and demonstration of a viable means to create compact and miniaturized optical circuits and devices that can be integrated together into functional assemblies. Ideally, this should be achieved directly inside a single three-dimensional solid-state support. Applications range from miniaturizing optical technology for telecommunications or data processing, or for more pioneering enterprizes, such as building dense three-dimensional circuits for the study of neural networks. The challenge in standard geometries is that working in the solid volume excludes conventional fabrication techniques, such as lithography. One solution is to use light to write the required structure in the solid in a single-step, through an appropriate photosensitive process, such as occurs in UV-cured epoxy , photopolymerization [2, 3, 4], photorefraction , combinations of these , or amorphization . Optical writing faces two general issues: (I) as the writing light enters into the volume it is distorted by diffraction; and (II) conventional photosensitive techniques do not support the integration of devices, such as electro-optic modulators, switches and filters. Both issues can be, in principle, overcome in photorefractive media. Diffraction can be overcome when the writing light is itself sensitive to the changes it produces in the material and guides itself through it, a process termed self-writing  supported by the formation of a photorefractive spatial soliton [9, 5], whereas active devices can be supported by soliton electro-activation, a versatile technique to produce a wide family of fast electro-optic functions using the self-written waveguides [10, 11, 12, 13]. The solution requires a quadratic electro-optic response, such as observed in room-temperature potassium-lithium-tantalate-niobate (KLTN) , in nano-poled strontium-barium-niobate (SBN)  and in organic photorefractive glass . Self-writing, however, becomes impractical when multiple-waveguide structures are involved, since the underlying solitons interact nonlinearly, a feature that influences even the writing of a simple two-soliton-based directional coupler .
In a recent set of experiments we successfully addressed the first issue (I) developing a non-solitonic method to write waveguides in the volume using the index pattern generated by a linear diffracting beam termed funnel waveguides [17, 18]. Since no solitons are involved, no nonlinear beam interaction intervenes and the waveforms need not coincide with those leading to self-trapping (soliton existence conditions). To achieve a funnel waveguide, the optical response is deactivated during the writing phase (WP) but activated during the reading phase (RP). It is saturation that distorts the index pattern written by the diffracting beam (the ”funnel”) into a tubular-like waveguide pattern during readout . The idea of funnel waveguides is general, can be directly extended to noncentrosymmetric crystals , such as lithium-niobate (LiNbO3) and SBN, but has yet to be demonstrated in these and in other photosensitive settings, such as glasses, polymers, and thermo-optic materials.
Here we demonstrate the electro-activation of funnel waveguides to achieve a single channel intensity modulator and a 1X2 switch in the RP, effectively addressing also the issue (II). To render explicit the vast possibilities of the technique, we also demonstrate the electro-optic morphing of a single waveguide into a 1×2 and a 1×4 splitter.
Novelty lies in waveguide electro-activation. The mechanism can be readily grasped considering the simplifying case in which all electric fields are parallel and the beam intensity changes only along their common direction (say the x axis). Appropriately illuminating the sample gives rise to the internal electric field E(x)=Ew+Esc(x), the superposition of the external homogeneous bias field Ew and the so-called space-charge field Esc(x) due to the semi-permanent rearrangement of light induced charges that typically screen Ew where the optical intensity is higher, i.e., at the beam center. For a quadratic electro-optic response, the index of refraction pattern Δnw=c(E)2=c(E 2 w+2EwEsc+E 2 sc) is focusing for c<0, simply because E is screened and hence lower at the center of the beam. Now, if the optical beam is attenuated or a non-absorbed (near-infrared) wavelength is used (in which case slight changes in the actual index values and electro-optic coefficients also intervene), the charges remain dislocated and Esc remains fixed, even though the external bias field can be set to an arbitrary Er, typically different from Ew. When Er≠Ew the resulting index pattern Δnr≠Δnw. For example, setting Er=0, Δnr=c(E 2 sc) which produces a defocusing effect (c<0) on the beam, since the originally screening Esc≠0 only in the beam path. The effect is clearly absent in linear electro-optic crystals, where Er≠Ew only changes an additive constant to the index pattern.
2. Electro-optic intensity modulation
Our experiments are carried out in a zero-cut and polished Lx=2.4 mm Ly=3mm Lz=1 mm sample of KLTN kept at T=19°C, above its ferroelectric Curie point at TC=14°C. The electro-optic response is quadratic, with background index of refraction n 0=2.35, static relative dielectric constant εr(T)=1.9×104, and the relevant components of the quadratic electro-optic tensor are g 12=-0.02m4C2 and g 11=0.16m4C2.
In the WP, the writing beam is a Gaussian TEM00 beam from a He-Ne laser operating at λ=543 nm, continuous wave, with average power Pw=800 nW, a minimum Full-Width-at-Half-Maximum (FWHM) Δx 0=Δy 0=7.5µm and linearly polarized in the y direction (p w‖yŷ). It is launched in the z direction and is focused either onto the input facet z 0=0 of the sample(”single funnel geometry”), or half-way through the sample at z 0=Lz/2 (”double funnel geometry”). The bias field is delivered in the x direction through two electrodes on the x facets Lx apart by appropriately applying the bias voltages Vw=V ±=±1.1kV, so that the field is prevalently in the x direction (E w=E ±‖x̂). Given the relative orientation of E w and p w, the maximum index of refraction modulation experienced during writing is Δnw=-(1/2)n 3 0 ε 2 0(εr-1)2 g 12 E 2 w~-3×10-5, a value insufficient to alter the beam diffraction. The duration of the WP for each beam Δt (the ”exposure”) determines the saturation of the observed response in the RP and hence the guiding properties of the waveguide.
In the RP, the same writing beam is used but with a reduced intensity Pr=10 nW, so that the resulting exposure (and nonlinearity) during the inspection is negligible, the polarization is rotated so that p r‖x̂, and z 0=0. The reading bias field is determined by the value of Vr which can vary and is in general Vr≠Vw. In particular, for E r≡E w (Vr=Vw), the fact that p r‖E r implies that the relevant maximum index of refraction change is Δnr~4×10-4, now capable of altering the diffracting beam propagation, i.e. the pattern is activated.
Beam propagation in both WP and RP is detected through the corresponding images of the output transmitted beam intensity distribution through a CCD camera and an appropriate imaging system.
In Fig. 1 we illustrate the demonstration of an intensity modulator based on the electro-activation of a single funnel waveguide. In the WP, a single beam is used with z 0=0 and Vw=V +, centered around the position (x 0,y 0). The output of the beam for different values of Δt is shown in the the top row of Fig. 1. The output FWHM of the beam remains approximately constant at Δx≃Δy≃15µm, as expected. In the RP, the reading beam is launched in (x 0,y 0) and the output distributions for the different values of Δt, for Vr=V + (second row of Fig. 1, and for Vr=V - (third row of Fig. 1), are shown. For Vr=V +, for Δt≃30 s, the beam is guided into a mode of Δx≃Δy≃8µm, and becomes elongated in the x direction for longer exposures, a process that does not lead to further changes for Δt>100 s. For Vr=V - (E r=-E w), only a weak defocusing effect is observed for low values of Δt=15, 30, 45 s). For longer values of Δt saturation spreads from the central region and antiguiding emerges. For Δt=120 s, light transmission can be efficiently switched on and off by changing the value of Vr: for Vr=+1.1kV, light is transmitted, for Vr=-1.1 kV, light transmission is blocked (second and third row of Fig. 1 for Δt=120 s).
3. Electro-optic 1x2 switching
To demonstrate 1x2 electro-optic switching, the WP involves two funnels written with opposite bias fields V w1=V + and V w2=V- (i.e., E w1=-E w2), with z 0=Lz/2. The two waveguides are formed shifted along the y direction, in the positions (x 0,y 0) and (x 0,y 0+30µm), each is written for an interval Δt=60 s, alternating the two writing processes at δt=3 s intervals. The shift is in the y direction so that the anisotropic components (along the x direction) do not intervene, and the double-funnel geometry is used to reduce the mutual tail overlap, simplifying and rendering practical the RP (see Fig. 2). In the RP, the same reasons that allow a single funnel waveguide to guide also allow a double-funnel to guide, so that when the beam is launched in (x 0,y 0), for Vr=V w1, it is guided (Fig. 2(a)). Analogously, when the beam is launched in (x 0,y 0+30µm), for Vr=V w2 it is guided (Fig. 2(b). When the read beam is launched in between the two patterns, in (x 0,y 0+15µm), it is routed on waveguide 1 when Vr=V w1 (E r=E w1) (Fig. 2(c)) and on waveguide 2 for Vr=V w2 (Fig. 2(d)), demonstrating the electro-optic 1x2 switch. For these two last conditions, the underlying pattern can be detected by launching a plane-wave as opposed to a focused down read beam for V=+1.1kV (V=-1.1 kV), as shown in Fig. 2(e), Fig. 2(f)).
4. Electrically controlled pattern morphing
We now demonstrate the electro-optic morphing of a waveguide into a y-junction, i.e. a static 1×2 splitter, as shown in Fig. 3. In the WP, two equally polarized double-funnel waveguides with V w1=V w2=V - (E w1=E w2) are stacked in the x direction, in the positions (x 0,y 0) and (x 0-40µm,y 0), as illustrated in Fig. 3(a),(b). In the RP, the read beam is launched in (x 0-20µm,y 0), in between the two, for Vr=V w1,2 the beam is split into two (Fig. 3(a),(c)), whereas it is guided in the center for Vr=-V w1,2 (Fig. 3(b),(d)). The reason for this can be appreciated observing the effect on a plane wave, as shown in Fig. 3(e): the anisotropic lobes of Fig. 1 third row now superimpose in the central region making it guiding. Analogous effects are observed for a lower read voltage. In particular, the case of Vr=±0.88 kV is shown in Fig. 3(f),(g),(h). The beam splitting is here more effective, as illustrated in Fig. 3(f), and the underlying pattern is evidence in the propagation of a plane wave, as shown in Fig. 3(h), where the defocusing effect of the two waveguides is weakened. So it is that the optimal morphing of a waveguide into a 1×2 y-junction is achieved for the cases Fig. 3(d) and (f), through the patterns of Fig. 3(e) and (h).
In the WP, three double-funnels can be written as illustrated in Fig. 4, two with V w1=V w2=V + (a,b) in positions (x 0,y 0) and (x 0,y 0+20µm), and a third with V w3=V- (c) in (x 0,y 0+10µm). In the RP, each guides a beam launched into it when Vr=Vwi (i=1,2,3), as shown in the output intensity distributions (Fig. 4(a–c)). However, when the read beam is launched in the (x 0,y 0+10µm) (central waveguide), as for Fig. 4(c), applying Vr=-V r3=V r1,2 gives rise to the electro-activation not of a 1×2, but a 1×4 divider, as shown in Fig. 4(d). This only apparently unexpected result is the product of the superposition of the three funnels, which provides the remarkable result of producing a whole set of guiding structures in and around the three funnel geometry, as illustrated in Fig. 5. When the same pattern is biased with Vr=+1.1 kV, four different and independent waveguides are formed along a diamond geometry, as illustrated in Fig. 5(a), where the output intensity distribution of a beam launched successively in the four waveguides is shown, and finally the pattern is inspected with a plane wave read-out. The activated waveguides, illustrated in dark grey, are superimposed with a different array of five waveguides, illustrated in light grey, that are in turn activated when Vr=-1.1kV, and (E r=E 3), as demonstrated in Fig. 5(b), where the guiding properties of each single member of the array is inspected launching in it the read beam. Again the pattern is detected through a plane-wave read out (bottom image), and the illustration indicates how the waveguide arrays have morphed from the original structure of a to b.
Concluding, we have demonstrated the electro-activation of funnel waveguides, a system in which saturation, spatial layout, anisotropy, polarization and applied electric fields allow the morphing of different and complex photonic devices through simple linear writing strategies.
Research was funded by the Italian Ministry for Research through the FIRB project RBIN04NYLH, and by the Regione Lazio through the FILAS 2008 initiative. A. P. is currently at the Laboratory of Physics of Interfaces and Thin Films (École Polytechnique - Paris). Support from F.Feliciangeli, F.Mancini, and S.Ricci is acknowledged. Address correspondence to Eugenio DelRe at firstname.lastname@example.org.
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