We report electro-optic (EO) long-period waveguide gratings (LPWGs) fabricated in a special lithium-niobate (LiNbO3) waveguide structure. The waveguide consists of a clad core formed with a two-step proton-exchange process and a thin cover layer created by an additional reverse proton-exchange process for the restoration of the EO strength of the waveguide. Using several LPWG samples, we demonstrate experimentally the effects of using different cladding modes and waveguide parameters on the grating performance. One of our 10-mm long samples shows a 27-dB rejection band at a driving voltage of 95 V with a center wavelength tunable thermally at a sensitivity of -0.4 nm/°C. Our analysis of the theoretical limit of the efficiency of such an EO grating suggests room for significant further improvement by optimizing the waveguide and electrode designs. The LiNbO3 LPWG provides an EO control of the grating strength and a thermo-optic control of the operating wavelength and thus opens up many new opportunities for high-speed applications, such as dynamic optical filtering and optical intensity modulation.
©2008 Optical Society of America
Since the idea of forming long-period gratings in planar waveguides, namely, long-period waveguide gratings (LPWGs), was proposed , there has been significant progress in the development of LPWG-based devices by taking advantage of the material and geometry flexibility offered by the optical waveguide technology. A number of LPWG devices, including, for example, variable attenuators , tunable optical filters , and add-drop multiplexers , have been demonstrated experimentally, which explore the large thermo-optic effect of polymer to achieve effective thermal tuning. However, the tuning speed of all these devices is intrinsically slow. To increase the tuning speed, it is necessary to employ a much faster effect, such as the electro-optic (EO) effect, to drive the LPWG. An EO long-period grating based on a slab waveguide model has been analyzed theoretically , which, however, is difficult to realize in practice. Recently, we have proposed a special waveguide structure suitable for the realization of LPWGs in the EO material lithium niobate (LiNbO3) , and reported briefly our first experimental attempt in demonstrating an EO LPWG in a LiNbO3 waveguide . This paper presents in detail our first batch of EO LPWG samples and demonstrates the effects of changing the grating and waveguide parameters on the performance of the grating. We also discuss the theoretical limit of the efficiency of an EO LPWG in a LiNbO3 waveguide, which serves as useful guidance for future studies.
LiNbO3 is a popular material for its excellent optical properties and large EO effect . The main challenge of using LiNbO3 for the realization of an LPWG rests on the formation of the waveguide structure required for the operation of the grating . The waveguide required must contain a cladding to support a discrete set of cladding modes, so that light can be coupled from the core mode to a cladding mode at a particular wavelength . To achieve that, we proposed a two-step proton-exchange (PE) process to fabricate a clad LiNbO3 waveguide . While the waveguide was good enough to demonstrate the grating effect by depositing a permanent grating on the waveguide surface , it could not be used without further processing for the implementation of an EO grating, because of the significant reduction of the EO effect in the PE process . To recover the EO effect, we applied a reverse proton-exchange (RPE) process to the clad LiNbO3 waveguide and produced a 10-mm long EO LPWG with a rejection band that could be varied by 25 dB with a driving voltage of 184 V . In this paper, we study the effects of the choice of the cladding mode and the waveguide parameters on the performance of the EO grating and demonstrate a 10-mm long sample with a rejection band of 27dB obtained at a driving voltage of 95 V, which is a significant improvement over the previous work. Our analysis on the theoretical limit of the efficiency of such an EO grating suggests room for further reduction of the driving voltage. In addition, we discuss thermal tuning of the operating wavelength of the EO grating. The center wavelength of the aforementioned sample can be tuned at a sensitivity of -0.4 nm/°C, which makes possible the application of the device over a wide range of wavelengths.
2. Device fabrication
We first applied a two-step PE process to fabricate a clad LiNbO3 waveguide . The substrate used was a polished z-cut, y-propagation LiNbO3 slide with a dimension of 10 × 15 × 0.5 mm (width × length × thickness). In the first step, we formed a slab waveguide on the substrate by the conventional PE and post-annealing processes. In the second step, we formed a core inside the slab waveguide by applying the PE process once more through a mask that defined the width of the core. The second PE process increased the H-ion concentration and thus raised the extraordinary index in the core area. As a result, a high-index core was created inside the slab waveguide and the remaining part of the slab waveguide had an index higher than the substrate and served as the cladding. The proton source used in both steps was stearic acid. However, the waveguide formed in this way had a high H-ion concentration, which led to a weak EO effect . To recover the EO effect, we applied an RPE process to the waveguide by submerging the sample into an RPE source, which was a mixture of lithium benzoate (30 mol%) and stearic acid [7, 9]. In the RPE process, the H-ions in HxLi1-xNbO3 were replaced by the Li-ions, so that a layer of HxLi1-xNbO3 was converted back into LiNbO3 on the surface [9–11]. Both the ordinary and extraordinary refractive indexes in that layer should recover their bulk values. The RPE process thus led to a thin outer layer of low extraordinary index on top of the core and the slab cladding and the EO coefficient of that layer should be almost the same as that of the bulk LiNbO3 . This outer layer helped to form a buried waveguide structure and thus reduce the coupling and scattering loss. At the same time, the EO coefficients in the core and the slab cladding were recovered partially during the RPE process because of the accompanied annealing effect caused by the relatively high processing temperature [9, 10]. The waveguide structure is shown schematically in Fig. 1(a), together with a sketch of the extraordinary refractive-index profile n e(z). To form an EO grating, we sputtered a 200-nm thick SiO2 buffer layer on the RPE layer and deposited a 10-mm long aluminum (Al) electrode with an interdigitated pattern with the desired pitch on the buffer layer. Because of the presence of the RPE layer, the SiO2 buffer needed was much thinner than those commonly used (600 – 850 nm) for other LiNbO3 devices . The interdigitated electrode pattern was 1 mm wide and 10 mm long. The electrode finger and the electrode gap had the same width, which was equal to a quarter of the grating pitch. The EO LPWG is shown schematically in Fig. 1(b).
For the present study, we fabricated two different waveguide structures, labeled as Waveguide A and Waveguide B, respectively. For Waveguide A, the substrate was first exchanged for 12 hours at 250 °C and annealed for 12 hours at 350 °C to form the slab waveguide. To form the core, the slab waveguide was covered by a chromium mask with a 4-µm wide opening and then exchanged the second time for 55 minutes at 250 °C. The waveguide then went through the RPE process for 17 hours at 320 °C. For Waveguide B, the substrate was first exchanged for 4 hours at 250 °C and annealed for 70 minutes at 400 °C to form the slab waveguide, which was then covered by the same mask as for Waveguide A and exchanged the second time for 55 minutes at 250 °C. The waveguide went through an additional annealing process for 50 minutes at 400 °C and then the RPE process for 3 hours at 320 °C. The Al electrode actually covered a large number of identical waveguides formed on the same substrate, as shown in Fig. 2.
The waveguides supported only the TM modes, whose effective indexes were measured with a commercial prism-coupler system (Metricon 2010). From the effective indexes measured for the slab waveguide, we were able to estimate the refractive-index profile of the slab waveguide with an inverse WKB algorithm . The availability of an array of identical cores formed on the same substrate also allowed us to measure the effective index of the core mode accurately . For Waveguide A, the waveguide supported one core mode and three cladding modes. The diffusion depth of the cladding layer was found to be ~5 µm from the index profile obtained before the RPE process. After the RPE process, the effective indexes were measured to be 2.1695 for the TM0 core mode and 2.1535, 2.1435, and 2.1380 for the TM1, TM2, and TM3 cladding modes, respectively. The thickness of the RPE layer was ~2 µm. On the other hand, Waveguide B supported one core mode and two cladding modes. The diffusion depth of the cladding layer, measured before the RPE process, was ~4 µm and the effective indexes, measured after the RPE process, were 2.1562 for the TM0 core mode and 2.1432, and 2.1385 for the TM1 and TM2 cladding modes, respectively. The thickness of the RPE layer was ~1 µm.
Figure 3 shows the near-field images of the output light patterns of Waveguide B captured by a charge-coupled device (CCD) camera at the wavelength 1550 nm with different launching conditions. The images confirm that the waveguide supports only one core mode and more than one cladding mode. The field intensity profile of the core mode is also shown in the image. The loss of the core mode was measured to be ~0.8 dB/cm by a transmission method at the wavelength 1550 nm .
3. Grating characterization and discussions
When we applied a DC voltage to the electrode, a periodic electric field was set up along the waveguide and produced an EO grating. We measured the transmission spectrum of the grating with a broadband light source and an optical spectrum analyzer. The pitch of the grating is determined by the phase-matching condition, Λ=λ 0/(N co-N cl), where λ 0 is the resonance wavelength and N co and N cl are the effective indexes of the core mode and the cladding mode, respectively. We used the measured effective indexes to determine the pitch.
To investigate the effect of the cladding mode on the grating characteristics, we employed different pitches for the two waveguide samples. For Waveguide A, we first used a 50-µm pitch. After characterizing the grating, we etched away the electrode and put on a new one with a 102-µm pitch. For Waveguide B, we used a 60-µm pitch and a 128-µm pitch, respectively. We compared the transmission spectra measured for different grating samples.
The transmission spectra measured for the two gratings fabricated in Waveguide A at a driving voltage of 184 V are presented in Fig. 4(a). The 50-µm pitch grating produces two rejection bands at ~1150 nm and ~1550 nm, which correspond to the couplings form the core mode (TM0) to the second (TM2) and third (TM3) cladding modes, respectively, while the 102-µm pitch grating produces only a single rejection band at ~1615 nm, which corresponds to the coupling to the first (TM1) cladding mode. The rejection band of the TM1 mode (25 dB) is much stronger than those of the TM2 and TM3 modes (much less than 10 dB), which indicates that the coupling efficiency of the TM1 mode is much higher. The transmission spectra measured for the two gratings fabricated in Waveguide B at a driving voltage of 95 V are shown in Fig. 4(b). Again, the coupling to the first (TM1) cladding mode is much stronger than that to the second (TM2) mode. These results show the significance of choosing the right cladding mode for maximizing the effectiveness of the grating. For our LiNbO3 waveguide structure shown in Fig. 1, it appears that the first cladding mode, which has the simplest mode-field pattern among all the cladding modes, is preferred.
Among the four grating samples, the one with the pitch 128 µm fabricated in Waveguide B is the most efficient one. Figure 5(a) shows the transmission spectra measured for this particular grating at different driving voltages and temperatures. The temperature of the grating was controlled by placing a hotplate under the device. The variation of the contrast (i.e., the attenuation at the center wavelength) of the grating with the driving voltage is shown in Fig. 5(b). It is seen from Fig. 5 that the contrast of the grating increases with the voltage up to a certain value. A further increase in the voltage results in over-coupling and hence reduces the contrast. We obtain a maximum contrast of 27 dB at a driving voltage of only 95 V (22 °C), which is about half of that (184 V) for the 102-µm pitch grating fabricated in Waveguide A. We attribute the significant improvement in the grating efficiency with Waveguide B to two major factors: (i) the duration of the first PE process for Waveguide B (4 hours) was much shorter than that for Waveguide A (12 hours), which led to a smaller amount of H-ions introduced and hence a stronger EO effect maintained in Waveguide B ; (ii) the thinner RPE layer in Waveguide B brought the core and cladding mode fields closer to the electrode, which resulted in a stronger EO effect. Our results show the possibility of increasing the efficiency of the grating significantly by changing the fabrication parameters (and hence the refractive-index profile) of the waveguide. As shown in Fig. 5(b), the efficiency of the grating drops at a higher temperature (130 V is needed to achieve a contrast of 24 dB at 59 °C, while less than 90 V is needed to achieve the same contrast at 22 °C), which is due to the fact that the field distributions of the core mode and the cladding mode (and hence the coupling coefficient of the grating) depend on the temperature.
The location of the rejection band can be tuned thermally, as shown in Fig. 5(a). The variation of the center wavelength with the temperature is shown in Fig. 6 for the 102-µm pitch grating (Waveguide A) and the 128-µm pitch grating (Waveguide B). The temperature sensitivities of the two gratings are -1.1 nm/°C and -0.4 nm/°C, respectively. The negative temperature sensitivity can be explained by the fact that the core and the cladding in our LiNbO3 waveguide structure are formed with different rhombohedral HxLi1-xNbO3 phases . We can categorize different phases of HxLi1-xNbO3 into two groups: one group has a higher refractive index but a smaller (positive) thermo-optic coefficient (like β1, κ2), and the other group has a lower refractive index but a higher (positive) thermo-optic coefficient (like α) . In our clad LiNbO3 waveguide, the core should be composed of more of the first group and less/none of the second group, while the cladding, on the contrary, should be composed of more of the second group and less/none of the first group, which leads to a negative thermo-optic index difference between the core and the cladding and hence a negative temperature sensitivity in the resonance wavelength according to the phase-matching condition. The difference in the magnitude of the temperature sensitivity between the two gratings is the result of the different phase compositions in the cores and the claddings of the two waveguides, which is caused by the use of different PE and PRE processes during the waveguide fabrication.
4. Theoretical limit of the efficiency of the EO grating
Our experimental results show that the efficiency of the EO grating depends significantly on the waveguide structure and the choice of the cladding mode. It is important to estimate the theoretical limit of the EO effect, so that we know to what extent the efficiency of the grating can be improved further.
The fraction of light coupled from the core mode to the cladding mode along an LPWG of length L is given by cos2 κL, where κ is the coupling coefficient, which is proportional to the amplitude of the index modulation and the spatial overlap between the fields of the core mode and the cladding mode in the region where the index modulation is introduced . Assuming a uniform index modulation in the mode-field overlap region, κ can be expressed as 
where λ is the free-space wavelength, Δn is the amplitude of the index modulation, and η is the normalized spatial overlap between the fields of the core mode and the cladding mode (0 ≤ η ≤ 1). The maximum possible mode-field overlap is 100% (i.e., when the index modulation is introduced across the waveguide with its sign following the sign of the cladding mode field). The maximum index modulation that can be produced in a waveguide by the EO effect is given by
where r 33 is the EO coefficient of LiNbO3 and V is the driving voltage, and d is the electrode gap across which the voltage is applied. To achieve maximum light coupling, the minimum value of κL required is π/2. The corresponding driving voltage, denoted as V π/2, the half-π voltage of the grating, can be found by putting Eq. (2) into Eq. (1) with η=1.0 and κ=π/(2L), i.e.,
At λ=1550 nm, with n ~2.15 and r 33~30.8×10-12 m/V, we have from Eq. (3)
For a 10-mm long grating with an electrode gap of 32 µm (the same values used in our 128-µm pitch sample), we obtain V π/2~16 V, which is about 6 times smaller than that (95 V) of our best sample. There exists much room for further improvement by optimizing the waveguide and electrode design. The theoretical limit given by Eq. (4) suggests the possibility of achieving a value of V π/2 much less than 10 V by increasing the grating length and reducing the electrode gap. For example, with L=30 mm and d=12 µm (a size comparable to the spot size of the core mode), we have V π/2~2 V. If the EO grating is used as an optical intensity modulation, it will be biased at a voltage equal to V π/2/2 to obtain the best linearity and the widest dynamic range, and the maximum amplitude of the modulation signal required to achieve a full modulation depth will also be equal to V π/2/2. While the theoretical limit is impossible to achieve in practice, a shortfall by a factor of 5 (V π/2~10 V), which calls for an improvement upon the efficiency of our best demonstrated sample by a factor of 3 (assuming a 30-mm grating), already puts the EO LPWG modulator on a par with the conventional LiNbO3 Mach-Zehnder intensity modulator. We should note that the theoretical limit is calculated for a sandwich electrode configuration, where the electric field is applied uniformly across the waveguide. Practical devices employ a coplanar electrode configuration, as shown in Fig. 1(b), where the electric field generated is non-uniform across the waveguide. Device optimization requires an accurate knowledge of both the mode-field distributions and the electric-field distribution, which is a subject for future investigation.
We fabricated several 10-mm long EO LPWGs on a special clad LiNbO3 waveguide structure. Through comparing the characteristics of these grating samples, we demonstrated the importance of using a low-order cladding mode and proper waveguide parameters for the achievement of good performance. Our best grating sample shows a 27-dB rejection band at a driving voltage of 95 V, i.e., V π/2~95 V. An evaluation of the theoretical limit suggests much room for further lowering of the value of V π/2 by optimizing the waveguide and electrode design, in addition to increasing the grating length. The challenge in the optimization of the grating performance rests mainly on an accurate modeling of the complicated graded-index profile of the clad LiNbO3 waveguide structure. In addition, we find that the operating wavelength of the EO grating can be tuned thermo-optically. For example, the operating wavelength of the aforementioned sample can be tuned by 15 nm with a temperature control of 40 °C, which allows the grating to operate over a wide range of wavelengths. The availability of EO LPWGs offers many opportunities for the development of new devices. By using an electrode design suitable for radio-frequency signal transmission, many high-speed applications could be developed, such as dynamic filters, dynamic power equalizers, variable attenuators, and intensity modulators. By employing EO gratings in the configuration of parallel LPWGs , it is possible to realize a new class of reconfigurable broadband add-drop multiplexers.
The authors thank C. K. Chow, K. P. Lor, and H. P. Chan for their technical assistance and many useful discussions. This research was supported by a research grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 111907].
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