We report on low-loss vertical tapers for efficient coupling between confined LiNbO3 optical ridge waveguides and Single Mode Fibers. 3D-Pseudo-Spectral-Time-Domain calculations and Optical-Coherence-Tomography-based methods are advantageously used for the numerical and experimental study of the tapers. The tapered-section is done simultaneously with the ridge waveguide by means of a circular precision dicing saw, so that the fabrication procedure is achieved in only two steps. The total insertion losses through a 1.6 cm long ridge waveguide are measured to be improved by 3 dB in presence of the taper. These tapered-ridge waveguides open the way to the low-cost production of low-loss phase modulators or resonators.
© 2015 Optical Society of America
Tightly confined optical waveguides such as ridges or photonic wires are expected to become building blocks of miniature photonic integrated circuits. In this context, LiNbO3 appears as a very attractive substrate, due to its large electro-optic and nonlinear coefficients. The tight confinement of light reduces the LiNbO3-components’ footprint by enhancing the electro-optical  and nonlinear effect , or by allowing very small waveguides curvatures . Mature technologies such as ion-slicing  or polishing  are now available for the production of photonic wires in thin LiNbO3 films, and they have led to miniature electro-optical microrings , Mach-Zehnders , photonic crystals (PhCs)  or wavelength converters . On the other hand, a photonic wire with a 1 µm2 cross-section typically shows insertion losses larger than 10 dB when connected to SMF28 fibers, due to optical mode-mismatch. Tapers have been proposed to address this issue , but they require additional machining steps, making the fabrication process even harder to implement.
High-aspect-ratio-diced LiNbO3 ridges have emerged as an alternative to produce compact electro-optical , pyroelectric  or nonlinear LiNbO3 components . They are achieved by easy-to-implement techniques -namely proton exchange and/or Ti-indiffusion, followed by precise dicing. These waveguides provide a tight lateral light confinement, and they can guide both TE and TM polarizations with propagation losses lower than 1 dB/cm . Moreover, they offer opportunities to realize high aspect ratio or tridimensional LiNbO3 Photonic Crystals (PhCs) , so that the active length of the photonic components is reduced to a few micrometers. However, the tight lateral confinement of light also generates mode-mismatch with SMF28 fibers, resulting in high insertion losses. While tapers varying the size of the waveguide have shown their efficiency in many occasions , they cannot easily be implemented in high aspect ratio ridges.
In this paper we propose a new vertical taper produced simultaneously with the ridge waveguide by means of a circular precision saw. The taper is shorter than 1 mm and shows transition losses as low as 1 dB for both TE and TM polarizations. Additionally to its low insertion losses, the proposed configuration offers the advantage of being compatible with standard pigtailing techniques, and the process can easily be extrapolated to any material having a vertical index profile.
The tapers are modeled thanks to a three-dimensional pseudo-spectral time domain (PSTD) algorithm  in order to characterize the beam propagation and the influence of the taper’s curvature.
2. Description and numerical study
The proposed transition is schematically depicted in Fig. 1(a). The extremity of the waveguide in contact with the fiber is made of a gradient index waveguide that weakly confines the optical mode. Trenches are etched on both sides of the waveguide and their depth increases along the propagation direction. Hence the gradient index waveguide turns into a ridge waveguide. As the cross-section of the waveguide is progressively decreased along the propagation direction, this vertical transition can be denoted as a “taper”. This approach is particularly easy-to-implement in lithium niobate substrates. The first step is the production of a gradient-index waveguide by Ti-indiffusion or Annealed Proton Exchange, which vertically confine the light. Note that the waveguide can indifferently be a channel waveguide as represented in Fig. 1(a), or a planar waveguide. Then, trenches are designed in the substrate by optical-grade dicing , meaning that the substrate is diced and polished at the same time by means of a circular precision saw. The ridge waveguides result from the remaining matter between two trenches. The transition is done simply by lifting the saw blade before the end of the ridge waveguide. The circular shape of the blade is hence inscribed along the propagation direction of the ridge waveguide, allowing a progressive variation of the ridge's depth. The larger the radius of curvature of the blade is, the longer the taper. As an example, a radius of curvature of 5 mm will lead to a taper length of 316 µm, and this length will become 707 µm for a radius of 25 mm if the depth of the ridge is of 10µm. SEM views of lithium niobate transitions are seen in Figs. 1(b) and 1(c). Finally the optical waveguide is sliced and polished at its extremities. A distance can be left between the end of the taper and the output facet, so as to ease the pigtailing, as represented in Fig. 1(a). The tapered-ridge can also be sliced directly at the extremity of the taper (see the red line in Fig. 1(b)). This latter approach should be adopted if the vertical confinement is initially provided by a planar waveguide.
For the sake of illustration, we have studied and developed Ti-indiffused tapered-ridge waveguides. In a first step, both 6 µm wide channel waveguides and planar waveguides were fabricated in X-cut substrates. They were achieved by evaporating a 90 nm thick layer of Ti over the substrate, and by diffusion at 1030 °C for 10 hours. The resulting diffusion depth was d = 4 µm. Then, the tapered-ridge waveguides were produced by optical-grade dicing. The rotation speed and the moving speed of the dicing saw were, respectively, 10,000 rpm and 0.2 mm/s. Information about the index profile and about the optical confinement as a function of depth and width can be found in . Particularly, it was observed that the lateral confinement of light increases with the ridge’s depth δ until δ equals to δa = 1.25⋅d. In the presented process, δa = 5 µm. Beyond δ = δa, the lateral optical confinement is no more influenced by the ridge’s depth δ.
In order to evaluate the propagation of light in this tapered-ridge waveguide, we have implemented a 3D-PSTD algorithm (Pseudo-Spectral Time Domain) [17,18]. In PSTD algorithms, Maxwell’s curl equations are calculated with discrete Fourier transforms in order to solve the spatial derivatives on an unstaggered, collocated grid. This spatial differential process converges with infinite order of accuracy for grid-sampling densities of two or more points per wavelength, provided that the medium optical properties are sampled in accordance with the Nyquist theorem. In consequence, this numerical method allows the study of various problems on larger scales, more efficiently and with a better accuracy than finite-difference time-domain method (FDTD) methods. In our simulations, a 440 mW continuous light source emitting a gaussian beam (Full Width at Half Maximum of 5.5 µm) linearly polarized along the Z-axis was numerically injected inside 300 µm long lithium niobate waveguides at 1.55 µm wavelength. The light source was designed to mimic the output light coming from a SMF28 fiber. Three cases were successively simulated: firstly a standard 6 µm wide X-cut Ti-indiffused channel waveguide, then a Ti-indiffused ridge waveguide with a width of 6 µm and a depth of 10 µm, and finally a tapered-ridge with transitions resulting from a 5 mm radius of curvature of the saw blade. The index profile was chosen to be the same as reported in .
The light propagation inside the waveguides is depicted in Fig. 2. For each waveguide, top, lateral and output views of the light intensity are presented. The top and lateral views correspond to slices of the light distribution at X = 0 and Y = 0, respectively. For each view, the contours of the air-lithium niobate interfaces are represented by the solid lines. In each case, the numerical simulation is stopped when few tens of interference fringes, resulting from the interference between the incident light and the reflected light, are observed at the end of the waveguides.
We can see in Fig. 2(a) that the light experiences little diffraction at the input of the Ti-indiffused waveguide. Then it propagates inside the waveguide without being perturbed. On the other hand, strong intensity fluctuations can be observed in Fig. 2(c) when the light is directly connected to the ridge. This shows that the diffraction of light by the narrow input ridge aperture excites many spatial guided modes and they interfere with each other during the propagation. Only the fundamental mode is seen at the output of the ridge in Fig. 2(d). Indeed, the fundamental mode predominates over the higher order modes.
Finally it is seen in Fig. 2(e) that the intensity fluctuations of the guided light are significantly reduced when the fiber-to-the-ridge connection is done by means of a taper. In other words, only the fundamental mode is excited and guided in the tapered-ridge: the taper acts as a mode filter. Moreover, we can conclude from Figs. 2(b), 2(d) and 2(f) that the output light exiting from the tapered-ridge waveguide at Y = 140 µm is more confined than the light exiting from the other waveguides. This tapered-ridge’s mode is expected to converge to a pure ridge’s waveguide after 300 µm of propagation inside the ridge’s section of the waveguide.
From the numerical simulations, total guided powers Pg, and transmitted powers Pt are calculated for the different waveguides. Firstly, the optical power Pg,y is integrated at a given abscissa Y, over a cross section such that X∈[-5,11] µm and Z∈[-8,8] µm. Note that the optical power is measured to be negligible outside this cross section. Then, the total guided power Pg is calculated by averaging Pg,y over the interval Y∈[80, 100] µm. The transmitted power Pt is the optical power measured at Y = 141 µm after the interface waveguide/air. As for the tapered-ridge, calculations are also performed for different radii of curvature of the saw blade.
All these values are reported in Table 1. As we might expect, while the guided and the transmitted powers are optimized when light is injected in a standard channel Ti-indiffused waveguide, the optical power density is higher inside a ridge waveguide, which yields a lower driving power in electro-optical ridge-based components . Indeed, the high optical power density indicates that the light is tightly confined, which contributes to increase the electro-optic overlap coefficient, and to decrease the driving voltage in the ridge. A compromise between the strong light confinement of ridges and the low coupling losses of Ti-indiffused waveguides is accomplished with the “tapered-ridge” configuration interfacing the SMF fiber with a Ti-indiffused waveguide that gradually turns into a ridge waveguide.
The numerical results seen in Table 1 show that the guided and the transmitted powers increase when the radius of curvature of the saw blade increases. When the radius is greater than 1 mm, the tapered-ridge becomes more efficient than the ridge waveguide and we show that efficiency of the tapered-ridge tends towards that of the Ti-indiffused waveguide for large radii of curvature curvature (R>20 mm). Note that different taper’s profiles were successively studied. It was observed that a taper with a curvature radius R behaves similarly as a taper with a depth varying linearly along a length L = (2⋅R⋅δ-δ 2)1/2, where δ is the depth of the ridge. Consequently, the length L of the taper can be regarded as the main parameter governing the efficiency of the taper. In optimal conditions, δ>δa and R>20mm, so that the length of the taper has to be larger than 447 µmd if δa = 5 µm. It is also worth noting that there was no difference between the behavior of a planar-waveguide-based and a channel-waveguide-based tapered-ridge.
3. Experimental study
Several tapered-ridge waveguides were produced according to the previously-mentioned process. The radius of the blade was chosen to be of 25 mm so as to get very low coupling losses. The resulting length of the taper was L = 707 µm. A linearly polarized infrared laser light was injected at the input, and the output mode was visualized by means of a x20 microscope objective focusing the light on a Vidicon infrared camera.
The tapered-ridges were firstly sliced at the extremity of the taper represented by the dashed red line in Fig. 1(b). The corresponding optical modes of TE and TM polarized lights are seen in Figs. 3 (a) and 3(c) for a 6 µm wide and 10 µm deep tapered-ridge waveguide: the modes are weakly confined, which favors a strong overlap with the broadly distributed mode of the SMF28 fiber. Then the waveguides were sliced at the output of the ridge section (blue dashed line in Fig. 1(b)), so that the tapered section was removed. The output mode is confirmed to be tightly laterally confined (see Figs. 3(b) and 3(c)). These experimental results confirm that the tapered section acts as a Spot-Size-Converter.
The tapered-ridges were then analyzed by Optical Coherence Tomography as described in . A C-band infrared polarized beam was injected at the input of the tapered-ridge waveguides. The reflected power was collected by means of an optical circulator connected to the broadband laser source. Transmitted and reflected optical spectrum densities were finally measured using a high-resolution optical spectrum analyzer (AP2040A APEX). Oscillations were observed in the spectra, corresponding to a Fabry-Perot effect between the input and the output facets of the tapered-ridge waveguide. These oscillations were converted into peaks by calculating the Fourier Transform of the optical spectrum densities. Hence we get the auto-correlation of the impulse response: each peak seen in the response is the signature of an optical echo in the waveguide. The response seen in Fig. 4 was collected at the input of an X-cut Ti-indiffused tapered-ridge waveguide with a total length of Ltot = 1.6 cm, propagating in the Z-direction of the crystal. Hence, the two polarizations were oriented along the ordinary axes of the crystal. A main optical echo can be seen in the figure, at a time of t1 = 0.240 ns for whatever polarization, and a secondary peak is measured at a time of t2TE = 0.4814 ns and t2TM = 0.4815 ns for TE and TM polarizations respectively. The first peak coincides with a round-trip of the light between the two facets of the waveguide, and the secondary peaks are the signature of a second round trip. From this second peak, we can deduce the global effective group index of each polarization: ngeff = t2⋅c0/(4⋅Ltot), c0 being the speed of light. The resulting effective group indexes are neffTE = 2.255 ± 0.005 and neffTM = 2.256 ± 0.005 for TE and TM polarizations respectively. So a slight anisotropy is observed, but it is of the order of measurement uncertainty.
The global propagation losses were then assessed from the amplitude of the secondary peak and from the reflected and transmitted spectral densities, as described in : they were of αTE = 0.26 ± 0.05 dB/cm and αTM = 0.85 ± 0.05 dB/cm. It is worth noting that more than ten tapered-ridge waveguides were fabricated in similar conditions, but with varying widths and depths, and the measured global propagation losses fluctuated between 0.1 and 2 dB/cm. The minimal value was obtained for a 30 µm deep and 7 µm wide Ti-indiffused tapered-ridge, and the maximal value was measured for a 5 µm deep and 4 µm wide Ti-indiffused tapered-ridge. These values were measured to be unchanged after the removing of the tapered section of the waveguide. So the tapers do not induce enhanced propagation losses inside the waveguides. This is also confirmed by taking a closer look at Fig. 4: indeed, there is no significant trace of distributed echoes in the responses, meaning that the tapered section does not provoke parasitic echoes in the waveguide.
Finally, the total insertion losses were measured from a fiber-fiber test coupling. After a reference measurement, the tapered-ridge waveguide was introduced between two cleaved SMF-28 fibers. Light-coupling was achieved at the input and output facets by using a matching index liquid. The total insertion losses were measured to be of αTE = 2.4 ± 0.2 dB and αTM = 2.9 ± 0.2 dB at 1.55 µm wavelength for TE and TM polarizations respectively. The transition losses (including transmission losses, coupling losses and radiation losses in the transition) are deduced by subtracting the propagation losses in the 14.6 mm long ridge-section of the tapered-ridge waveguide: they are estimated to be of 1.0 ± 0.3 dB per transition for both TE and TM polarization. This can be advantageously compared with the measurements performed through the same ridge waveguide without taper: the measured insertion losses were respectively of αTE = 5.3 ± 0.4 dB and αTM = 5.9 ± 0.4 dB, meaning that the losses are of 2.5 ± 0.5 dB per facet if there is no taper between the SMF fiber and the ridge. It can thus be concluded that the taper enables a reduction of the losses of 1.5 dB per facet in comparison with a direct fiber-ridge connection, and consequently the total insertion losses are improved by 3 dB in presence of the tapered extremities. This 3 dB reduction of the insertion losses was verified on ten tapered-ridge waveguides with a width varying between 4 µm and 7 µm, and it is mainly attributed to a better mode-matching between the SMF28 fiber and the input of the tapered-ridge waveguide, as compared with a direct fiber-to-the-ridge connection.
In conclusion, we have proposed an easy-to-implement method for the production of tapered-ridge waveguides with a laterally confined optical mode and insertion losses lower than 3 dB for both polarizations. This represents a great improvement over standard ridge waveguides, which are affected by mode mismatch at the interface fiber-ridge. We have implemented a powerful 3D-PSTD algorithm that shows how the tapers enable an efficient gradual adaptation of the guided mode and the key role played by the blade’s radius and its length.
The tapered-ridge waveguides are made in only two steps –namely Ti-indiffusion and optical-grade dicing, and the transition losses are lower than 1 dB if the blade's curvature is larger than 20 mm, which corresponds to a length of 447 µm. With this approach, the ridge waveguide becomes a standard waveguide at its extremities, allowing the standard pigtailing techniques. Work is in progress to integrate electrodes on the edges of the ridge so as to get phase modulators with very low driving voltages.
The authors gratefully acknowledge Jean-Charles Beugnot and Thibaut Sylvestre for their help with optical characterization, and Vincent Biniguer for his developments on precise dicing with two blades working at the same time. This work was supported by the ANR Materiaux et Procedes pour les Produits Innovants 2012 under project CHARADES, by the FRI project MEP contract A1401001, by the Labex ACTION program (contract ANR-11-LABX-01-01). The work was partly supported by the French RENATECH network and its FEMTO-ST technological facility
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