An electrooptical channel waveguide array was constructed in potassium lithium tantalate niobate substrate by the implantation of He+ ions at high energies. The array was fabricated by two successive implantation sessions at 1.6 MeV and 1.2 MeV through a comb-like stopping mask that limited the implanted ions to penetrate the substrate in 1 μm wide stripes periodically distributed at 3.5 μm intervals. This generated a grating of amorphized stripes with reduced refractive index. This was followed by a uniform implantation of He+ ions at 1.8 MeV which created a bottom cladding layer below the array. Wave propagation in the array was studied by focusing a light beam at 636 nm into the central channel, and observing the wavefront it created at the output plane of the array. It was found that applying an electric field across the array strongly affects the coupling between adjacent channels, and governs the width of the wavefront at the output plane.
© 2009 Optical Society of America
Refractive Index Engineering (RI-Eng) by the implantations of fast ions has recently been proposed as a generic method for constructing integrated photonic circuits in electrooptical substrates. In this paper we describe the construction of an electrooptical waveguide (WG) array by RI-Eng, and its operation under an electric field.
The implantation of light ions in solid crystalline material is governed by two mechanisms, electronic stopping and nuclear stopping . Upon penetrating the material the ions are dominated by the electronic stopping mechanism: due to their high initial velocity the ions do not interact with the lattice atoms, and continue to travel in their initial direction almost without affecting the medium in which they propagate. However, they do interact with the electronic clouds that surround the lattice ions which cause them to slow down gradually while they travel deeper into the substrate. As they slow down the nuclear stopping mechanism becomes dominant, i. e. their cross section for interaction with the lattice atoms increases steeply. These interactions generate Frenkel defects which form a narrow layer of amorphized material well within the volume of the crystalline substrate. In this layer the refractive index (RI) differs significantly from that of the surrounding crystalline material. The depth of this layer, its width, the spatial distribution of the amorphization in the layer and change generated in the RI, depend on the nature of the implanted ions, their initial energy and dosage, and on the nature of the substrate .
In particular, it has recently been shown  that the implantations of He+ ions at 2.3 MeV in potassium lithium tantalate niobate (KLTN) crystalline substrate result in the formation of an amorphous layer of Frenkel defects several microns below the surface of the substrate. It was found that the RI in this layer is substantially lower than that of the surrounding crystalline material. It was also demonstrated that this layer can serve as a cladding to a slab waveguide in which the core is the crystalline material underneath the surface of the crystal. The propagation loss in this waveguide was measured to be 0.1–0.2 dB/cm. Furthermore, it was shown that following an annealing period at elevated temperatures the amorphized layer became thermally stable and remained unchanged after being heated to 150 °C for a week.
These phenomena brought forward the possibility to harness the implantation process as the basis of a generic method for constructing 3D structures with low RI and complex geometries within the depth of the KLTN substrate. In order to do so it was required to provide the technique for controlling the implantation process in the lateral dimension. This was accomplished by introducing the concept of the stopping mask. The stopping mask is a metallic film with varying thickness that determines the penetration depth of the implanted ions into the electrooptic substrate. Thus, the distribution of the Frenkel defects which are created during the implantation replicates the contour of the topography or the spatial density distribution of the stopping mask. The average depth of the implanted layer is set by adjusting the initial energy of the implanted ions. Hence the combination of a series of implantation sessions at different initial energies through a respective set of stopping masks can be used to form complex multi level 3D structures with submicron features within the depth of the substrate. RI-Eng was first demonstrated in KLTN by constructing a 1D channel waveguide. The waveguide was constructed by a single-shot implantation of He+ ions through a stopping mask in which a groove with slanted sides was opened in a 3 μm thick layer of gold. This resulted in the creation of 1D channel waveguide with trapezoidal profile. The construction of this waveguide and its operation are described in reference .
An extensive research of the waveguide fabrication by the ion implantation in optical materials was done in the last years . In particular, waveguides assembled in both ensembles of separated channels and in arrayed configurations for non-linear applications were fabricated in KNbO3  and KTP . This was done by single-shot implantations through photoresist masks. The electrooptical behavior of these structures was not studied.
In this paper we describe the application of the technique of RI-Eng by ions implantations to the construction of a 2D confined structure consisting of an array of coupled linear channel waveguides in an electrooptical substrate.
In general, WG arrays can be used for optical switching, power management and wavelength demultiplexing in optical fiber communication networks. The device reported here is the basic WG array structure consisting of an array of identical channel waveguides. It was constructed primarily to demonstrate that the coupling between adjacent channels can be controlled by an electric field. That is, as the construction of the array is done by partial amorphization of the regions between and below the cores of the channels, it was necessary to verify that the array remains electrooptically active. If so the method of RI-Eng by ion implantations can indeed become a generic method for constructing electrooptical integrated circuits.
2. Design of the WG array
Consider Fig. 1 depicting a schematic illustration of the WG array. The WG array was constructed in a KLTN crystalline substrate. The array is cladded from the top by the air above the surface of the KLTN substrate, and from the bottom by a layer of partially amorphized material with reduced RI. The core of each channel WG in the array is the crystalline KLTN material of the substrate. The sidewall claddings between the waveguides are constructed of partially amorphized material with reduced RI.
The WG array was fabricated by performing a series of implantations of He+ ions at different energies and dosages through a comb-like stopping mask. The stopping mask used was a square grating constructed of alternating stripes of gold and SU8 polymer. The mask was 2.9 μm thick. The grating period was 3.5 μm. The gold/SU8 widths ratio in each period was ≈5/2. The process flow for constructing the mask is presented in Fig. (2a) to (2e). First, a 20 nm Cr layer and a 200 nm Au layer were evaporated onto the KLTN substrate (Fig. 2b). Then a 2.7 μm thick layer of SU8 was spin coated on top of the gold layer (Fig. 2c). Using conventional optical lithography methods, a periodic grating of stripes that were 2.5 μm wide were opened in the SU8 layer exposing the 200 nm gold layer, and leaving 1 μm wide SU8 stripes between them (Fig. 2d). Finally, using electroplating techniques for which the thin gold layer served as seed electrode, the empty stripes between the SU8 stripes were filled with gold (Fig. 2e).
Detailed planning of the implantations was done by combining two computational tools: (i) TRIM simulations which provide the spatial distribution of the amorphization level generated during an implantation session in a given substrate, and manifested by the “Energy to Recoils” curve ; and (ii) the semi-empirical formula developed in Ref.  for computing the change in RI created in the substrate during an implantation session. For both tools, the implantation session is defined by the type of the implanted ion, its initial energy, the dosage of the implantation session, the topography and the morphology of the target.
The implantation sessions protocol for constructing the WG array derived from these computations consisted of a series of three implantation sessions: (i) a dosage of 3.0×1015 He+ ions/cm2 at the energy of 1.6 MeV implanted through the mask; (ii) a dosage of 3.2×1015 He+ ions/cm2 at 1.2 MeV implanted through the mask; and (iii) a dosage of 11.1×1015 He+ ions/cm2 at energy of 1.8MeV implanted directly into the KLTN substrate after the mask was removed. The sequence of the implantations is described schematically in Fig. 2f, 2g, and 2h.
The thickness of the gold layer was designed to prevent the implanted ions in implantations sessions (i) and (ii) from penetrating the KLTN substrate. Hence, the material beneath the gold covered sections of the grating was not exposed to the implantations, and remained crystalline KLTN. The stopping power of the 2.7 μm thick SU8 + 0.2 μm thick Au sections is significantly smaller than that of the Au sections of the thickness of 2.9 μm, since the specific density of SU8 is lower than that of the Au. (The specific densities fed into TRIM were ρSU8=1.15 g/cm3, ρAu=19.31 g/cm3, ρKLTN=6.12 g/cm3). Hence, implantations sessions (i) and (ii) of the implantations protocol created in the areas beneath the SU-8 covered sections of the grating an amorphized layer with reduced RI. The implantation session (iii) that was performed after the stopping mask was removed created a uniform amorphized layer beneath the grating that will act as the bottom cladding for the entire WG array.
The core-cladding RI distribution in the WG array along the x axis was computed by the following procedure:
- The index spatial profiles in the core section and the sidewall cladding section were computed by TRIM  and the semi empirical formula mentioned above , using the implantations protocols data for the respective sections. These yielded the index profiles presented in Fig. 3 for the core and cladding sections.
- Initial values for the effective RI of the transverse electrical (TE) mode at λ=633 nm in the core and cladding sections, ((nTE)core and (nTE)cladding respectively), are computed using the Chandler and Lama  method. Each section is treated as an infinite slab WG with a RI profile computed in phase (i).
- Refined values of (nTE)core and (nTE)cladding are obtained by treating the slab WG in each section as a multi-sliced structure which approximates the RI distribution derived in (i), while in every slice the RI is assumed to be constant. The electric field in each section is then obtained by solving the Maxwell equations in the multi-sliced structure under the conditions of continuity of the parallel components of the fields at the boundary between each two slices and under the constraint that the energy that leaks beyond the RI barrier to the substrate is minimal.
The final values that were obtained by this process are: (nTE)cladding=2.2305 and (nTE)core =2.2517 for the core regions and sidewall cladding regions respectively. Thus, the expected core-cladding contrast for the fundamental TE mode propagating in each channel of the WG array is 1.0 %.
3. Theoretical treatment of the device operation
Consider a light beam that is focused into the core of the central (m=0) channel waveguide. As it propagates, the light is leaking into the neighboring channels. The field in the m-th channel can be calculated by solving the equation 
where m is the channel number (m=0,±1,±2,…), α is the attenuation in the channel, and κ is the coupling coefficient between two adjacent channels (The coupling coefficient between the non-adjacent guides is negligibly small). The boundary conditions are E m≠0(0) = 0 and E 0(0) = 1. The solution of equation (1) above is given by
where Jm is the Bessel function of the m-th order. The coupling constant κ can be expressed as
where a here is a channel width, d is the pitch between adjacent channels, kx and kz are the propagation constants along the transversal x and propagation z axes respectively, and qx is the exponential falloff in the x direction outside the channel. kx, kz and qx are calculated using the Marcatili method .
Consider a channel WG array with a set of parameters given by: RI of the channel core (nTE)core=2.2517; the core width a= 2.5 μm; RI of the side cladding in the transversal direction x: (nTE)cladding =2.2305; and the pitch between the waveguides d=3.5 μm. For the Marcatili approximations the barrier in the implantation-longitudinal y-th direction was taken to be a step function with the RI of the bottom cladding n1=2.0855 at a depth of 4.1 μm, which coincides with the minimum of the RI in the simulated bottom cladding of the structure as appears in Fig. 3. The simulations were carried out for a 5.3 mm long sample in the propagation direction z. Assuming the propagation mode is the basic (Ex)11 mode, the intensity in the channel array waveguide at λ=633 nm is presented in Fig. 4. It should be noted that the choice of the wavelength (λ=633 nm) was not accidental. This was done to ensure that the coupling between the channels will be limited to a few neighboring channels only, so that the coupling constants can be reliably reconstructed. As can be seen in Fig. 4 the choice of λ=633 nm for the given set of parameters indeed fulfills this requirement.
4. Experimental part
The WG array was fabricated in a KLTN substrate with a phase transition at Tc=15.5 °C, RI at room temperature no=2.2677, and dimensions of 10×10×1.5 mm3. One of the substrate xz 10×10 mm2 faces was polished to the optical grade and subjected to the implantations protocol given above. After completing the implantations, the crystal was cut to a 5.3 mm long sample along the z axis. The xy faces of the crystal were polished to optical grade, and the yz faces were deposited with gold electrodes.
A preliminary study of the device was done by direct observation through an optical microscope. Silica spacers were attached on top of the array at both the front and back ends. The spacers were a 150 μm thick and 1.5 mm wide and were attached to the array by a ~10 μm thick transparent epoxy layer (Fig. 5). This was done in order to facilitate the polishing of the end edges of the array to optical quality. The WG array was illuminated by focusing a white light source at a wide angle onto approximately two channels at center of the input plane through an inverse microscope. The image of the intensity at the output plane is shown in Fig. 5(a) and 5(b). The intensity in Fig. 5(b) was inverse log scaled by the picture processing software in order to enhance the contrast between the intensity at the channel cores and the intensity at the inter-channel claddings. As can be seen the light that enters the WG array couples through the side claddings into the neighboring channels as it propagates along the channels, yet staying confined to a small number (~20) of channels in the output.
A detailed study of light propagation in the WG array was done by measurements of the near field at the output plane that was generated by a monochromatic beam focused into the central channel in the input plane. The light source was a diode laser operating at λ=636±2 nm polarized at both the TE and TM directions. The laser was focused onto the central channel at the input plane of the array using a ×50 microscope objective. The light emanating from the output plane was collected by a microscope with a ×100 objective, and was imaged onto the detector array of a CCD camera.
The coupling between the channels was modulated by applying an electric field along the x-axis. The device temperature during the experiment was maintained at T=19 °C (3.5 °C above Tc). The intensity of the near field distribution at the output plane taken at different levels of the applied field in the range between zero and 4 kV/cm are shown in Fig. 6. It can be seen that the coupling is enhanced strongly as the applied electric field is increased.
A qualitative analysis of the results requires estimating the effect of the applied field on the coupling. In KLTN at the paraelectric phase, the electric field induced change in the RI manifested by the quadratic electrooptical effect is given by 
where Δn is the induced birefringence, no is RI, geff is the relevant quadratic electrooptic coefficient, ε=ε0εr is the static (low frequency) dielectric constant (assuming εr>>1), and E is the applied field. Note, that if the electric field is applied across the width of the crystal then for the TE modes geff=g11=0.16 m4/C2, whereas for the TM mode geff=g12=-0.02 m4/C2. Note also that by nature of the fact that g11>0 whereas g12<0, the effect of applying the field will increase the coupling for the TE mode, and decrease the coupling for the TM mode. Thus, applying the field is expected to cause the TE component of the light at the output plane to be more widely distributed across the array, whereas it is expected to cause the TM component to become more confined to the central channels.
5. Results’ discussion and analysis
In a preliminary examination of the output intensity it can be seen that the core-cladding relative contrast between neighboring channels decreases as the applied field increases. Namely, the coupling between neighboring channels increases as the field increases. Considering equation (4), this implies that the light propagating in the array is dominated by TE modes for which geff=g11 so that Δn<0 in the electrooptic core region.
As the inter-channel cladding is constructed by partial amorphization, it is expected to be less electrooptical than the crystalline material of the core. Thus, for the TE modes, applying the electric field pushes the RI of the core towards the value of the RI in the inter-channel cladding.
Let us assume therefore that the light propagating in the WG array is a superposition of only TE modes (Ex)μv, each with its own set of parameters kx, kz, and qx. Each mode is coupled differently to the neighboring channels, with a distinct coupling constant κμv. For a given mode, the effective RI in the channel is uniquely related to the respective mode-dependent inter-channel coupling constant κμv in the following way. In general, the effective RI is lower for the higher modes. Hence, the effective core-cladding RI contrast is lower for the higher modes, and consequently they experience stronger inter-channel coupling. Thus, if one is interested to obtain the inter-channel coupling constants without going into the details of the intensity distribution in the cross section of each channel, there if a full analogy between the treatment, which takes into account a constant core-cladding RI contrast and a varying mode number and the treatment in which the mode number is constant and the core-cladding RI contrast is varying. In these terms, the multimodal intensity distribution between the channels at the output of the array can be treated as the superposition of the single-mode intensities at the output of a series of WG arrays with identical geometries that differ by the core-cladding RI contrasts, and thus by the coupling coefficients between neighboring channels. Assuming that in each of the arrays, the propagating mode is the (Ex)11 mode, limiting ourselves to two arrays (modes), the output intensity is given by
Here, l is the index of the array in which the inter-channel coupling constant κl of the basic (Ex)11 mode is equal to the inter-channel coupling constant of true respective mode in the actual WG array, Al is the relative amplitude of the mode propagating in the l’th array, and σ=2.04 μm is the width along the x direction of the (Ex)11 mode, propagating in a single channel. The width of the mode σ was estimated in a slab waveguide approximation for which (nTE)core=2.2517 and (nTE)cladding =2.2305 as computed above. α is the attenuation constant originating from the absorption and scattering for a mode propagating in the z direction. The calculation in (5) is restricted to the 10 channels on both sides of the central channel, because for the relevant wavelength the intensity is assumed to be confined mostly to ~20 central channels, as we observed on Fig. 5(a) and further approved by the simulation on Fig. 4. Note that it is assumed in (5) that inter-modal coupling does not occur, so that the overall power of each of the two propagating modes remains constant as they propagate through the channel.
Curves of the intensity across the array for the set of images of the output plane are shown in Fig. 6. Also shown in Fig. 6 is the intensity across the x axis sampled from the images. The intensity was sampled from the original snapshots taken by a CCD camera by averaging the measured images over the y axis and smoothing along the x axis until the intensity along x confined to each channel could be approximated by a Gaussian. This yields a curve for (I(x))E that was fitted by theoretical approximation expressed in (5). Note that the theoretical expression for the intensity distribution in (5) is a function of the coupling constants of each of the modes, which depend on the spatial distribution of the RI in the structure. Coupling constants resulting from the RI structure, which provide the best fit of (5) to the experimental data were obtained by scanning the value of RI of the core, which is expected to be changed by the application of the electric field E. The RIs of the core-surrounding claddings along the fitting procedure remained constant with values relying on the prediction given in Section 3 above. In such a way we obtain the effective RI contrast between the core and the inter-channel cladding for each level of the applied electric field as the product of the fitting procedure of (5) to the experimental intensity distribution in which the modal coupling constants are the free parameters.
It can be seen that (5) provides very good fitting to the experimental data. It should be noted that indeed the output intensity can be approximated by the superposition of two TE modes with constant ratio between their amplitudes (i.e. independent of the applied field). This substantiates the assumptions adopted in (5) for approximating the output intensity by superimposing a set of two arrays.
The effective RI contrast between the core and the side cladding of the channels in the array for different levels of the applied field for the basic (Ex)11 modes in the two superimposed waveguide arrays which constitute the device are presented in Fig. 7.
We assume that the mode for which the contrast is higher is the true basic (Ex)11 mode in WG array. Note in particular that the effective RI contrast between the channel core and side cladding for the basic mode was changed by 0.4 % when the applied field was varied from 0 to 4 kV/cm. In bulk KLTN the maximal electrooptically induced change in the birefringence is 0.5 %. This indicates that the electrooptic effect is not inhibited by the implantations, contrary to what was reported for waveguide devices fabricated in other oxygen perovskites such as LiNbO3 . It should also be noted however that the effective RI contrast between core and side cladding that was measured for the basic mode (2.0 %) is significantly larger than the value evaluated in the simulation (1.0 %). This can be attributed to two facts:
- After the implantation the SU8 layer blackens and seems to be partially “burned” (carbonized) as a consequence of the interaction with the ion beam. We have made the AFM measurement of the burning rate and it seems that SU8 became thinner by 0.5 μm after the grating implantation. This could affect the implanted regions, making the defect concentration peaks slightly diffused. Since the defect concentration develops according to exponential fill model , the overall number of defects in such a diffused peak will be higher than in a sharp peak for the same implantation dosage. Since the RI change is proportional to the defect concentration, the effective RI of the diffused peak is lower than that of the concentrated one.
- The semi empirical formula was initially developed based on data measured at λ=1.55 μm . The RI contrasts in the channel array were calculated here for λ=633 nm to fit the experimental data. Hence it is expected that the contrast would deviate from the experimental values if there is a non-zero differential dispersion between the crystalline and the amorphous KLTN composing the device.
In conclusion, the technique presented here for constructing a channel WG array demonstrate the potential of RI-Eng by ion implantations as a generic methodology for constructing structures with complex geometry in a KLTN substrates. Together with the fact that the electrooptical properties of the substrate were not inhibited by the implantation process, this implies that this method can become a generic method for constructing integrated electrooptical circuits in which multitude of different devices are interconnected by a mesh of waveguides and operate in unison.
This research was supported in part by THE ISRAEL SCIENCE FOUNDATION (grant No. 1519/08); The “Eshkol Scholarship” of Israel Ministry of Science, Culture and Sport (grant No. 3-4341); The Center for Characterization and Study of Electromagnetic Properties of Materials and the Application in Nanotechnology, Chemistry, Biology, Microelectronics and Optoelectronics of Israel Ministry of Science, Culture and Sport (grant No. 3-4602).
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