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Proton exchanged channel waveguides in x-cut single-crystal lithium niobate thin film could avoid optical leakage loss which existed in the z-cut case. Indicated by simulations, the mechanism and condition of the optical leakage loss were studied. The light energy in the exchanged layer and the mode sizes were calculated to optimize the parameters for fabrication. By a very short time (3 minutes) proton exchange process without anneal, the channel waveguide with 2 μm width and 0.16 μm exchanged depth in the x-cut lithium niobate thin film had a propagation loss as low as 0.2 dB/cm at 1.55 μm. Furthermore, the Y-junctions based on the low-loss waveguide were designed and fabricated. For a Y-junction based on the 3 μm wide channel waveguide with 8000 μm bending radius, the total transmission could reach 85% ~90% and the splitting ratio maintained at a stable level around 1:1. The total length was smaller than 1 mm, much shorter than the conventional Ti-diffused and proton exchanged Y-junctions in bulk lithium niobate.
© 2015 Optical Society of America
1. Introduction
Single-crystal lithium niobate (LN) thin films on insulator (LNOI) fabricated by crystal ion slicing method have attracted much attention in recent years due to the high optical confinement and the optical properties as good as bulk LN [1]. Some excellent studies, including photonic crystal cavities [2,3], low-voltage tunable periodically poled LN [4], nanoscale waveguides [5], high-Q microresonators [6–8], and hybrid Ta2O5 or Si-LN modulators [9,10] have been reported, indicating that LNOI is an ideal platform for integrated optics. The thickness of the LN layer is generally below 1 μm for compact photonic devices. A low-loss optical waveguide with small size in LNOI is essential for photonic integrated circuits with low power consumption and high integration density. Dry etched photonic wires can confine the mode to a submicron size but high propagation loss arises from the rough etched walls [11]. In a recent work, the simple and low-cost annealed proton exchange (APE) method allowed us to produce the waveguides in z-cut LNOI with a low propagation loss of 0.6 dB/cm and a mode size as small as 4.6 μm2, because the APE process can effectively avoid the rough etched walls [12]. More efforts should be made to make the waveguide loss decrease further to facilitate high-efficiency waveguide devices.
The Y-junction, which has the ability to divide or combine the optical power, is a basic building block in photonic integrated circuits and is widely used in the photonic devices like Mach-Zehnder modulators or optical switches [13,14]. For quantum cryptography and quantum teleportation, Y-junction can be used to separate the correlated photon-pairs to realize mode de-multiplexing [15]. For the conventional Ti-diffused or proton exchange (PE) Y-junction in bulk LN, the half branching angle is usually very small to achieve sufficient high transmission, leading to the length of the whole Y-junction part at least several millimeters long [16]. To decrease the length of the Y-junction, larger branching angle is needed. Higher index contrast can improve the transmission at relatively large branching angle [17]. Waveguides in LNOI, which have higher index contrast and thus higher optical confinement compared with the conventional Ti-diffused waveguide in bulk LN [18], have a chance to reduce the length. So the more efficient wavelength conversion and optical modulation with higher level integration in LNOI based photonic integrated circuits and quantum network are expected.
In this report, the optical leakage due to the mode coupling [19] was theoretically analyzed by the full-vectorial finite difference simulations [20,21] in both z-cut and x-cut LNOI. For the z-cut LNOI, such coupling always happened and induced optical leakage loss in the PE waveguide. But in an x-cut LNOI, when the LN thickness was below 0.72 μm, there would be no optical leakage loss in the channel waveguide, because the effective refractive index (Neff) of the TE-like channel waveguide mode was larger than that of the modes in the planar LN waveguide. A method with short time PE without anneal process was introduced to form a very shallow exchanged layer to allow only a small fraction of light to be guided in the PE region and leave most of the LN film untouched. In experiment, by using this method, the channel waveguides in an x-cut LNOI exhibited a propagation loss as low as 0.2 dB/cm and the Y-junction had a transmission ranging from 85% to 90%.
2. No leakage channel waveguides
2.1 Simulation
Figures 1(a) and 1(c) show the schematic cross-sections of the channel waveguides structure fabricated using PE method in z-cut and x-cut LNOI, respectively. Since the lateral diffusioncould be ignored when the exchanged depth was much smaller than the mask width and the exchange process resulted in step-like index profiles, the designed PE region was a rectangle with W = the width of the PE region and D = exchanged depth [22]. The PE region formed the stripe-loaded channel waveguide, and the LN thin films on both side of the PE regions formed the planar waveguides. The anisotropy properties of the refractive index and the PE diffusion coefficient were considered in the simulation. Firstly, the leakage loss arising from the mode coupling was studied. All the parameters in the PE process, such as the diffusion coefficients, were determined according to Ref [22]. PE only increased the extraordinary refractive index (ne) of the crystal, and so only one type of mode was supported in the channel waveguides (TM-like mode in z-cut LNOI and TE-like mode in x-cut LNOI). To determine the refractive index change in the PE region in simulations, prism coupling was performed on the z-cut and x-cut PE planar waveguides under the same PE conditions as the channel ones (see section 2.2). Although the index profile of the channel waveguide at the borders of the mask was somewhat different from that of the planar waveguide, the index change in most part of the PE region in channel waveguide was the same as the planar one [22]. Then the measured index changes from the prism coupling method, Δne = 0.04 /Δno = −0.03 for z-cut and Δne = 0.08 /Δno = −0.05 for x-cut, were input into our simulations (see Figs. 1(a) and 1(c)). Figure 1(b) shows the Neff of the fundamental TE and TM modes of the planar waveguide (TE-P and TM-P) and the fundamental TM-like mode of the PE channel waveguide (TM-C-like) in the z-cut LNOI as a function of the thickness of the LN film (T). W and D were fixed at 2 μm and 0.16 μm, respectively. The Neff of all the modes increased with T, and the Neff of the TM-C-like mode was always a little larger than that of TM-P mode, fulfilling the wave guiding condition. However, the Neff of the TM-C-like mode was smaller than that of the TE-P mode, making the minor electric field component of TM-C-like mode (Ex) leak to the planar waveguide and caused leakage loss [19]. As illustrated in the inset, the Ex became propagating outside the PE region (the green line corresponded to the green star on the blue dashed line). For the x-cut LNOI with the same PE region as z-cut LNOI, the result is shown in Fig. 1(d). Below T = 0.72 μm, the Neff of TE-C-like mode was larger than that of TM-P mode. Hence the minor electric field component (Ex) was exponentially decayed and no leakage of electromagnetic field happened. The inset in Fig. 1(d) gives two different situations. When T = 0.7 μm, the Neff of TE-C-like mode was larger than that of TM-P mode. The Ex component was evanescent (the pink line corresponded to the pink star), and the channel waveguide had no optical leakage loss. When T = 0.85 um, the Neff of TE-C-like mode was smaller than that of TM-P mode, making the Ex component propagate in the planar waveguide (the green line corresponded to the green star), and so the channel waveguide had optical leakage loss. In summary, the conditions under which the mode coupling induced leakage loss in PE channel waveguides were as follows: For z-cut, Neff of TE-P ≥ Neff of TM-C-like; For x-cut, Neff of TM-P ≥ Neff of TE-C-like.
Fig. 1 (a) and (c): schematic image of the cross-section of the PE channel waveguides in z-cut and x-cut LNOI. Directions “x” and “z” corresponded to the crystal x-axis and z-axis, respectively. (b) and (d): Neff of the fundamental modes of the planar (red and black lines) and channel (blue dashed lines) waveguides at 1.55 μm in z-cut and x-cut LNOI as a function of T. W and D were fixed at 2 μm and 0.16 μm, respectively. Inset in (b): the Ex distribution of the channel waveguide modes along the x direction in (a). Inset in (d): the Ex distribution of the channel waveguide modes along the z direction in (c). The green and pink lines corresponded to the green and pink stars on the blue dashed lines, respectively.
The calculated propagation losses of the channel waveguides in Figs. 1 (a) and 1(c) are given in Fig. 2. In the simulations, the boundary condition was set to be perfectly matched layer (PML) to absorb the incident electromagnetic field. For the z-cut LNOI, since the Neff of TM-C-like mode was smaller than that of TE-P mode (see Fig. 1(b)), the leakage loss always existed although it was low in some value range of T (For example, when T > 0.5 μm, the loss was very small). In the x-cut LNOI, when T was smaller than 0.72 μm, no leakage loss was found because Neff of TE-C-like mode was larger than that of TM-P mode (see Fig. 1(d)). Above T = 0.72 μm, the leakage loss could reach as high as 2.4 dB/cm around T = 0.8 μm, and then reduced gradually. The shape of the curves, having the maximal values, was a consequence of the cancellation effect of the leakage [19,23].
Fig. 2 Calculated leakage losses of the z-cut (black curve, TM-like mode) and x-cut (red curve, TE-like mode) PE channel waveguides in Fig. 1 as a function of T at a wavelength of 1.55 μm. Below T = 0.72 μm, the leakage loss of the x-cut channel waveguide was zero.
The PE process could be performed in a very short time without the following anneal in LNOI, leaving most part of the LN layer untouched. This method could not be used to make channel waveguides in bulk LN because the waveguide core in bulk LN should be large enough to confine the light. In LNOI, however, any high refractive index region with arbitrary dimension could act as a loaded strip to guide light [24]. The relations between the light energy in the PE region and D for several values of W are shown in Fig. 3(a). T was fixed at 0.6 μm. Since the PE region without anneal induced high propagation loss and had almost vanished nonlinear and electro-optical coefficients [25–27], the light energy in the PE region should be kept as low as possible. The optical energy in the PE region increased with D or W. Since the mode size was important to the interaction between light and LN, the dependence of the mode sizes (product of 1/e intensity in the horizontal and vertical directions) on D and W are shown in Fig. 3(b). For instance, when W was fixed at 5 μm, the mode size decreased with the increasing D and reached a minimal value around D = 0.45 μm. Then it slightly increased. If D was fixed at 0.15 μm, the mode size did not change monotonously with W and reached a minimal value around W = 2 μm. These phenomena could be explained as follows. The mode size would increase with the expansion of the PE region. On the other hand, the increased Neff of the mode resulting from the enlarged PE region led to a stronger confinement of light. So the relation between the mode size and the dimension of the PE region was a competitiveresult of these two factors. It was interesting to make a comparison between PE and APE waveguides. The APE waveguide had a Gaussian index profile while the PE waveguide had a step-like index profile. In the APE technology, the fabrication parameters, such as the PE time and the anneal temperature, should be carefully adjusted to get a single phase (the low-loss α phase) [12]. In a PE waveguide, the PE time and temperature could be tuned to allow only a small fraction of light to be guided in the PE region, producing a low-loss waveguide.
Fig. 3 Dependence of the (a) light energy in the PE region and (b) mode sizes on D for various W (1 ~5 μm) when T was fixed at 0.6 μm for the TE-like guided mode at 1.55 μm. Dependence of the (c) light energy in the PE region and (d) mode sizes on T for various W (1 ~5 μm) when D was fixed at 0.16 μm for the TE-like mode at 1.55 μm.
The dependences of the light energy in the PE region on T is shown in Fig. 3(c) with D = 0.16 μm and W = 1 ~5 μm. The light energy decreased with the increasing T, because the increased T led to a smaller ratio of the PE region to the whole waveguide. The relation between the mode size and T is shown in Fig. 3(d) with D = 0.16 μm and W = 1 ~5 μm. The increased T resulted in the expansion of the waveguide, and so the mode sizes would increase.
2.2 Experiment
In experiment, a chromium (Cr) film was deposited on the LNOI which was prepared by the crystal ion slicing and wafer bonding method [1]. The LN thin film thickness was chosen to be 0.6 μm to avoid the optical leakage loss (see Fig. 1(d)). The 2 μm wide open channels along the y-axis of the LN crystal were defined on the Cr film by photolithography. After wet etching the exposed Cr and removing the photoresist, the sample was immersed in the benzoic acid to perform PE. From Fig. 3(a), D should be as small as possible to make low energy in the PE region and thus low loss. On the other hand, from Fig. 3(b), small D led to large mode size, which was detrimental to the efficient interaction between light and LN. So the condition of 200°C PE for 3 minutes (D = 0.16 μm), which led to only 12% energy in the PE region and a relatively small mode size = 1.4 μm2, was chosen as a tradeoff. Actually, one could decrease D to get a lower loss waveguide or increase D to get a stronger optical guiding waveguide. After removing the remaining benzoic acid and the Cr mask, the two end-faces were polished to facilitate end-face coupling.
The scanning electron microscope (SEM) image of the sample surface is shown in Fig. 4(a). The dark channel was the PE waveguide with a width of about 2 μm. Figure 4(b) shows the simulated fundamental mode profile (W = 2 μm, D = 0.16 μm and T = 0.6 μm). To evaluate the propagation loss of the channel waveguides, a linear polarized light at 1.55 μm from a tunable laser was coupled into the waveguide by a polarization maintaining fiber with a lensed tip, and then it was tuned to TE polarization by a rotator. Transmitted light from the waveguides was collected by a 40 × / 0.65 objective and detected by a germanium photodiode. The total insertion loss was about 10 dB. Since the vertical dimension of the waveguide (0.6 μm) was smaller than the resolution of the objective (~1.5 μm), the mode could not be precisely measured [18]. Only the simulated fundamental mode profile was given in Fig. 4(b). Figure 4(c) shows the transmission of the channel waveguide. Based on the Fabry-Perot method, the propagation loss α was evaluated by the following equation [28]:
Fig. 4 (a) SEM image of the channel waveguide surface. (b) Simulated fundamental mode profile with W = 2 μm, D = 0.16 μm and T = 0.6 μm for the TE-like guided mode at 1.55 μm. The PE region was indicated by the red dashed line. The mode size was 1.4 μm2. (c) Measured transmission (normalized) of the TE-like guided mode in the fabricated channel waveguide. The propagation loss was 0.2 dB/cm at 1.55 μm. (d) Black stars: propagation losses of the channel waveguides with 3 minutes, 5 minutes and 15 minutes PE, corresponding to D = 0.16 μm, 0.21 μm and 0.37 μm, respectively. Red line: fitting curve of the three points.
Imax and Imin were the maximum and minimum intensity of the transmitted light in Fig. 4(c). The end-face reflectivity was defined as the fraction of the reflected field that was returned in the fundamental mode after reflection at the end-face. A finite difference time domain (FDTD) solver was used to calculate it [12]. In the calculation, the fundamental mode of the waveguide was injected as the source field and then a monitor which was placed in front of the end-face collected the field information on the reflected field. The overlap between the source and reflected field was calculated to determine what fraction of the reflected field was returned in the fundamental mode. The calculated end-face reflectivity was 0.186. The propagation loss of the fabricated waveguide was 0.2 dB/cm at 1.55 μm, which was smaller than the previous one of 0.6 dB/cm in z-cut LNOI [12]. The decreased loss could be probably attributed to the different fabrication processes. PE process without anneal left most part of the LN film untouched, avoiding the influence of the diffused H+. Another possible reason was the elimination of the leakage loss in the x-cut PE waveguide. Lithium niobate suffered from optical damage when high power light transmitted through it. To evaluate the laser damage threshold of PE LNOI channel waveguide at fiber communication wavelength, a laser at 1.55 μm was launched into the 2 μm wide channel waveguide and the output power was detected [29]. The measured output power was approximately linearly proportional to the launched power, and the maximum output was 0.5 mW at the maximal launched power from the laser. This output power was stable, indicating there was no obvious optical damage in the waveguide at 1.55 μm. Considering the cross-section areas (1 μm2, calculated from full width at half maximum of the mode profiles) and the transmission of the objective (~90%) and the waveguide end-face (~74%), the 0.5 mW output power indicated about 74000 W/cm2 power intensity in the channel waveguide.
The PE region usually led to high propagation loss in waveguides due to the optical scattering in the mixed phase regions [27], and the more light guided in the PE region the higher loss would be. To test this point, two identical LNOI samples were prepared to fabricate the channel waveguides under the similar condition except longer PE times (5 and 15 minutes) that led to more light energy guiding in the PE region. The 5 minutes and 15 minutes PE resulted in a D of 0.21 μm and 0.36 μm, respectively. As shown in Fig. 4(d), the corresponding propagation losses were increased to 2 dB/cm and 9 dB/cm, respectively. The exchange time could be critical to the loss of the channel waveguide. The additional 2 minutes exchange (from 3 to 5 minutes) induced an extra loss of 1.8 dB/cm (from 0.2 to 2 dB/cm). To improve the exchange time tolerance, low PE temperature should be adopted because lower temperature led to a slower diffusion rate of H+ and gave more tolerance on the exchange time. For example, according to the calculation, for a D of 0.16 μm, an increased 1 minutes would result in a 0.03 μm increase in D for 200°C PE, while for 180°C PE, the increase in D was less than 0.01 μm.
3. Y-junction
3.1 Design and simulation
Figure 5 shows the schematic diagram of the Y-junction. It consisted of two symmetrical arms between one input and two output straight waveguides (waveguide width = W). Each arm was made of two identical circular arcs with radius = R smoothly connected by a straight waveguide which had the same width as the input and output waveguides. The light injected from the input waveguide was separated into the two arms by the Y-junction and finally transmitted in the two output waveguides separated by a distance of S. The transmission of the Y-junction was defined as the sum of the optical power in output 1 (P1) and output 2 (P2) divided by the output optical power in a reference straight waveguide (Pstraight): (P1 + P2)/Pstraight. The splitting ratio was defined as P1/P2. In general, the Y-junction should meet the following requirement: 1. high transmission; 2. Stable splitting ratio (1:1); 3. Small value of L at a given S.
Fig. 5 Schematic diagram of the symmetrical Y-junction. Between two red dashed lines: the Y-junction section consisting of two arms. On the left and right of the red dashed lines: input and output straight waveguides. Between the green dashed lines: a straight waveguide connecting two identical arcs.
Since the structure involved bend waveguide (the circular arcs in each arms), the relation between the bend loss and the bend radius is given in Fig. 6. The simulation method was the same as that used in Fig. 2 and the cross-section of the bend was the same as that shown in Fig. 1 (c) except W was 3 μm (the width we used in experiment in the following section). The bend loss decreased exponentially with the increasing R and for large R (> 3000 μm) the bend loss was negligible. This trend was consistent with the theory [30].
Fig. 6 Dependence of the bend loss on the radius of the bend waveguide. An exponential relationship between them was obvious. Inset: schematic diagram of the cross-section of the bend waveguide in simulation.
3.2 Experiment
The Y-junctions were fabricated on the 0.6 μm thick x-cut LN film by a similar procedure as in section 2.2 except a different mask pattern. W and S were designed to be 2 μm and 50 μm, respectively. Due to the fabrication errors in photolithography and wet etching of Cr (longer etching time leading to more serious lateral erosion), W expanded to about 3 μm. Different values of R were selected to study their influence on the performance of the Y-junction. As indicated in Fig. 6, the bend waveguides in all the three Y-junction (R = 4000, 6000, 8000 μm) have negligible bend loss. Since some previous research adopted the abrupt Y-branching structure [31], the effective branching angle α (as shown in Fig. 5) was given for reference. The parameters were summarized in Table 1.
Table 1. Parameters related to Y-junctions
Figure 7(a) shows the microscope image of the fabricated Y-junctions (#1, #2, and #3) and a reference channel waveguide. We used the Transmission-Mode (light was injected from the back of the sample and then collected by the objective) of the microscope to show the structure of the fabricated Y-junction. Then the microscope switched to the Reflection-Mode (light reflected from the surface of the sample and then collected by the objective) to capture the polished end-face, and the picture was shown in Fig. 7(b). A good polished end-face would facilitate the end-face coupling in the measurement.
Fig. 7 Optical microscope image (top view) of the (a) Y-junctions captured in the Transmission-mode and (b) polished end-face captured in the Reflection-mode.
Figure 8 shows the measured transmissions of the Y-junction at 1.55 μm. The transmission increased with R. Smaller branching angle α led to lower transmission loss [17]. #3 Y-junction with the largest R had the smallest α, and thus had the highest transmission (85% ~90%). The whole length of the #3 Y-junction was 922 μm, which was much shorter than the conventional Ti-diffused and PE Y-junctions in bulk LN with the similar transmission [31,32]. The high transmission and short device length in LNOI could probably attribute to the higher optical confinement. The Neff difference between the PE channel waveguide and the planar waveguide was 0.009, while the the Neff difference between the Ti-diffused channel waveguide and bulk LN was only 0.003. Transmission decreased with the increase of α. For a larger index difference, the rate of the transmission change with α was slower [17]. Therefore, at a large α, the transmission of the PE Y-branch in LNOI would be higher than that of the conventional waveguide with small index difference.
Fig. 8 Measured transmissions of #1 (black), #2 (blue), and #3 (red) Y-junction around the wavelength of 1.55 μm. All the transmissions have been normalized by a reference channel waveguide. #3 Y-junction (R = 8000 μm) had the highest transmission approximately ranging from 85% to 90%.
To test the coupling stability of the Y-junction, the splitting ratio under different input coupling conditions was measured. The waveguide was moved laterally relative to the tip of the optical fiber, as shown in the inset of Fig. 9. The measurement was performed under two random lateral positions. As shown in Fig. 9, the #3 Y-junction with a input waveguide of W = 3 μm exhibited stable splitting ratio around 1:1 (red and black curves) under the two coupling conditions. The small deviation from 1:1 ratio could be probably attributed to the little asymmetric structure resulting from the fabrication errors. The splitting ratio of another Y-junction with an input waveguide of W = 5 μm was also measured under two random lateral positions for comparison, and a big discrepancy was observed. The reason was that, for a straight input waveguide with T = 0.6 μm and D = 0.16 μm, the higher order mode, TE10-like mode (two peak of the electric field at the lateral direction and one peak at the vertical direction), was supported when W > 3.4 μm, which would make the mode profiles in the following taper section highly sensitive to input coupling conditions [33]. The instable mode profile in the taper section resulted in the deviation from the 1:1 splitting ratio in the two arms.
Fig. 9 Splitting ratio of the Y-junctions with W = 3 μm (red and black curves) and W = 5 μm (green and blue curves) in different input coupling conditions around the wavelength of 1.55 μm. The input coupling condition was changed by moving the input waveguide end-face laterally relative to the fiber tip. The splitting ratio of the Y-junction with the input waveguide of W = 3 μm stabilized at about 1:1.
4. Conclusions
In conclusion, a method using very short PE time (3 minutes) to form channel waveguide in x-cut LNOI was introduced. The shallow PE region could leave most part of the LN film untouched. By simulations, in the x-cut LNOI, the channel waveguides could avoid optical leakage loss when LN layer thickness was smaller than 0.72 μm, while in z-cut LNOI case, the optical leakage loss existed. The light energy in the PE region increased with D, and the mode size decreased in general with the increase of D. The fabricated channel waveguide had a propagation loss of 0.2 dB/cm. The optical loss was believed to relate to the PE region, verified by comparing with the longer time exchanged samples. The Y-junctions based on the low-loss channel waveguides were designed and fabricated. With a 3 μm wide input waveguide and 8000 μm radius, the Y-junction exhibited stable splitting ratio of 1:1 under different input coupling conditions, and the transmission could reach 85% ~90% around 1.55 μm. The whole length of the Y-junction was less than 1 mm. These results would benefit the development of high efficiency and low power consumption photonic devices like Mach-Zehnder modulators with high integration density in LNOI.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (NSFC) (Grants No. 11275116, No. 11375105 and No. 51272135).
References and links
1. G. Poberaj, H. Hu, W. Sohler, and P. Günter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photonics Rev. 6(4), 488–503 (2012). [CrossRef]
2. Y. Li, C. Wang, and M. Loncar, “Design of nano-groove photonic crystal cavities in lithium niobate,” Opt. Lett. 40(12), 2902–2905 (2015). [CrossRef] [PubMed]
3. H. Lu, B. Sadani, N. Courjal, G. Ulliac, N. Smith, V. Stenger, M. Collet, F. I. Baida, and M.-P. Bernal, “Enhanced electro-optical lithium niobate photonic crystal wire waveguide on a smart-cut thin film,” Opt. Express 20(3), 2974–2981 (2012). [CrossRef] [PubMed]
4. D. Djukic, G. Cerda-Pons, R. M. Roth, R. M. Osgood, S. Bakhru, and H. Bakhru, “Electro-optically tunable second-harmonic-generation gratings in ion-exfoliated thin films of periodically poled lithium niobate,” Appl. Phys. Lett. 90(17), 171116 (2007). [CrossRef]
5. R. Geiss, S. Saravi, A. Sergeyev, S. Diziain, F. Setzpfandt, F. Schrempel, R. Grange, E. B. Kley, A. Tünnermann, and T. Pertsch, “Fabrication of nanoscale lithium niobate waveguides for second-harmonic generation,” Opt. Lett. 40(12), 2715–2718 (2015). [CrossRef] [PubMed]
6. R. Wang and S. A. Bhave, “Free-standing high quality factor thin-film lithium niobate micro-photonic disk resonators,” arXiv:1409.6351v1 (2014).
7. J. Wang, F. Bo, S. Wan, W. Li, F. Gao, J. Li, G. Zhang, and J. Xu, “High-Q lithium niobate microdisk resonators on a chip for efficient electro-optic modulation,” Opt. Express 23(18), 23072–23078 (2015). [CrossRef] [PubMed]
8. J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5, 8072 (2015). [CrossRef] [PubMed]
9. P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21(21), 25573–25581 (2013). [CrossRef] [PubMed]
10. L. Chen, M. G. Wood, and R. M. Reano, “12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes,” Opt. Express 21(22), 27003–27010 (2013). [CrossRef] [PubMed]
11. H. Hu, R. Ricken, and W. Sohler, “Lithium niobate photonic wires,” Opt. Express 17(26), 24261–24268 (2009). [CrossRef] [PubMed]
12. L. Cai, Y. Wang, and H. Hu, “Low-loss waveguides in a single-crystal lithium niobate thin film,” Opt. Lett. 40(13), 3013–3016 (2015). [CrossRef] [PubMed]
13. W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007). [CrossRef] [PubMed]
14. H. Sasaki and I. Anderson, “Theoretical and experimental studies on active Y-junctions in optical waveguides,” IEEE J. Quantum Electron. 14(11), 883–892 (1978). [CrossRef]
15. Q. Zhang, X. Xie, H. Takesue, S. W. Nam, C. Langrock, M. M. Fejer, and Y. Yamamoto, “Correlated photon-pair generation in reverse-proton-exchange PPLN waveguides with integrated mode demultiplexer at 10 GHz clock,” Opt. Express 15(16), 10288–10293 (2007). [CrossRef] [PubMed]
16. W. K. Burns, R. P. Moeller, C. H. Bulmer, and H. Yajima, “Optical waveguide channel branches in Ti-diffused LiNbO(3).,” Appl. Opt. 19(17), 2890–2896 (1980). [CrossRef] [PubMed]
17. I. Anderson, “Transmission performance of Y-junctions in planar dielectric waveguide,” IEEE J. Micro. Opt. Acoust. 2(1), 7–12 (1978). [CrossRef]
18. L. Cai, S. L. Han, and H. Hu, “Waveguides in single-crystal lithium niobate thin film by proton exchange,” Opt. Express 23(2), 1240–1248 (2015). [CrossRef] [PubMed]
19. K. Ogusu and I. Tanaka, “Optical strip waveguide: an experiment,” Appl. Opt. 19(19), 3322–3325 (1980). [CrossRef] [PubMed]
20. Z. Zhu and T. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002). [CrossRef] [PubMed]
21. Lumerical Solutions, http://www.lumerical.com/
22. J. M. M. M. de Almeida, “Design methodology of annealed H+ waveguides in ferroelectric LiNbO3,” Opt. Eng. 46(6), 064601 (2007). [CrossRef]
23. S. T. Peng and A. A. Oliner, “Leakage and resonance effects on strip waveguides for integrated optics,” Trans. IECE Jpn. E-61(3), 151–154 (1978).
24. N. Uchida, “Optical waveguide loaded with high refractive-index strip film,” Appl. Opt. 15(1), 179–182 (1976). [CrossRef] [PubMed]
25. A. Méndez, G. De la Paliza, A. Garcia-Cabanes, and J. M. Cabrera, “Comparison of the electro-optic coefficient r33 in well-defined phases of proton exchanged LiNbO3 waveguides,” Appl. Phys. B 73(5-6), 485–488 (2001). [CrossRef]
26. M. L. Bortz, L. A. Eyres, and M. M. Fejer, “Depth profiling of the d33 nonlinear coefficient in annealed proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62(17), 2012–2014 (1993). [CrossRef]
27. M. M. Howerton, W. K. Burns, P. R. Skeath, and A. S. Greenblatt, “Dependence of refractive index on hydrogen concentration in proton exchanged LiNbO3,” IEEE J. Quantum Electron. 27(3), 593–601 (1991). [CrossRef]
28. R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985). [CrossRef]
29. O. Eknoyan, H. F. Taylor, W. Matous, T. Ottinger, and R. R. Neurgaonkar, “Comparison of photorefractive damage effects in LiNbO3, LiTaO3, and Ba1-xSrxTiyNb2-yO6 optical waveguides at 488 nm wavelength,” Appl. Phys. Lett. 71, 3051–3053 (1997). [CrossRef]
30. F. J. Mustieles, E. Ballesteros, and P. Baquero, “Theoretical S-bend profile for optimization of optical waveguide radiation losses,” IEEE Photonics Technol. Lett. 5(5), 551–553 (1993). [CrossRef]
31. N. Grossard, J. Hauden, and H. Porte, “Low-loss and stable integrated optical Y-junction on lithium niobate modulators,” in Proceedings of European Conference on Integrated Optics (ECIO, 2007), paper ThG08.
32. P. G. Suchoski, T. K. Findakly, and F. J. Leonberger, “Stable low-loss proton-exchanged LiNbO3 waveguide devices with no electro-optic degradation,” Opt. Lett. 13(11), 1050–1052 (1988). [CrossRef] [PubMed]
33. M. H. Chou, M. A. Arbore, and M. M. Fejer, “Adiabatically tapered periodic segmentation of channel waveguides for mode-size transformation and fundamental mode excitation,” Opt. Lett. 21(11), 794–796 (1996). [CrossRef] [PubMed]
