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Abstract
The high performance of thin film lithium niobate on insulator (LNOI) platform shows potential for electro-optical signal processing and nonlinear optics systems. To realize precise polarization management for sub-wavelength devices, we theoretically and experimentally investigate fundamental transverse electric (TE) and transverse magnetic (TM) mode hybridization in an x-cut LNOI ridge waveguide. Sudden jumps in the free-spectrum-range (FSR) of these modes in a fabricated microring resonator demonstrate the mode hybridization. The measured Q-factor of the lithium niobate (LN) microring is 1.78 million near the critical coupling condition. The hybridization wavelength was designed at 1562 nm and observed at 1537 nm. Potential applications include fundamental mode conversion, polarization rotation, polarization splitter, and polarization insensitive waveguides in optical receiver module.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Lithium niobate (LN) has been an ideal candidate for high-speed electro-optic modulators and nonlinear wavelength conversion devices in communication systems for decades, as it has a wide transparency window (350-5000 nm), a high electro-optic coefficient (∼34 pm/V), a high intrinsic bandwidth and good temperature stability [1]. Traditional LN devices, however, are bulky and offer weak light confinement, thus are not suitable for high-speed integration in optical interconnection. Recently developed LNOI platform is attracting increasing attention, mainly because of its revolutionary performance in high-speed electro-optic modulators and wide band optical frequency combs [2,3]. The sandwich-like arrangement of LNOI, in which a thin film LN sits on top of a low-index layer (e.g., silica), can tremendously increase light confinement in waveguide and enhance the interaction between light and matter. LNOI has been demonstrated to have ultra-low light propagation loss (∼2.7dB/m) [4], and high-speed signal processing ability (over 100 GHz) [5,6]. A variety of functional devices have been investigated on LNOI, such as micro-cavity resonators [7–9], grating couplers [10,11], electro-optic modulators [12–14], and photonic crystal devices [15]. In other words, LNOI platform shows huge potential for functional photonic integration and could serve as a supplement towards silicon photonics.
Passive optical devices are an essential part of the optical interaction circuit. For instance, polarization-dependent devices based on waveguides are of great importance in polarization division multiplexing (PDM) and quadrature phase shift keying (QPSK) modulation systems. However, owing to the large structural birefringence, sub-micrometer photonic integrated devices suffer from severe polarization-dependent effects. The performance of the optical system could be greatly improved if the polarizations are precisely controlled. Mode hybridization is the phenomenon in the waveguide whereby two orthogonally polarized modes propagate with similar phase velocity and couple to each other. It occurs in both weakly coupled and strongly coupled modes. This feature could be utilized to realize waveguide-type mode conversion or polarization rotation [16–19]. Additionally, polarization insensitive devices could be fabricated for flexible signal processing based on mode hybridization [20,21]. Nevertheless, the silicon on insulator (SOI) platform which serves as the common signal processing substrate has no material birefringence, thus the effective refractive index for TE0 mode is always higher than that for the TM0 mode due to the significant structural birefringence. Therefore, mode hybridization on SOI always includes high-order modes. For the implementation of fundamental mode conversion (between TE0 and TM0) by means of mode hybridization, the TM0 mode is first converted into TE1 (a high-order TE mode) in a tapered waveguide which hybridizes these two modes, and TE1 is subsequently transformed into TE0 in a mode convertor. However, this process generally requires an unconventional and complicated design which introduces additional difficulty and tolerance requirements during fabrication [18,22].
Devices on LNOI has different mode characteristics compared with SOI and other isotropic platforms, because of the strong material birefringence. The difference in refractive indices between ordinary light and extraordinary light can be precisely managed to compensate for the structural birefringence in the waveguide. This allows TE0 and TM0 modes to possess almost the same effective refractive index, which serves as the basis for fundamental mode hybridization.
In this paper, we report the fundamental TE and TM mode hybridization in the LNOI platform for the first time to the best of our knowledge. It utilizes a simple method and has potential for use in polarization-dependent devices such as mode convertors and polarization rotators. There have been several investigations into polarization management in LNOI, while they are solely theoretical and don’t involve mode hybridization [23–25]. We analyze the conditions of fundamental mode hybridization in the ridge waveguide in chapter 2.1. Simultaneously we propose a novel way to observe the mode hybridization by fabricating a microring resonator and monitoring the jumps in the FSR of fundamental modes. The principles are discussed in detail in chapter 2.2, and the fabrication process and measurement results can be found in chapter 3. The waveguide which supports fundamental mode hybridization is simply ridge structural waveguide without any additional design, and our fabrication process is similar with silicon photonics including procedures such as lithography and plasma etching.
2. Design and analysis
2.1 Fundamental mode hybridization in LNOI ridge waveguide
According to the orientations of the LN crystal axis in relation to the wafer, the LNOI platform is classified into z-cut and x-cut (similarly, y-cut is also possible). X-cut LNOI is widely applied in electro-optic modulators because the electric field modulates TE polarizations with the maximum electro-optic coefficient: r33 ∼34 V/pm. In x-cut LNOI, the waveguide has two typical perpendicular orientations: along y-axis of LN and along z-axis of LN. Both waveguides have individual mode characteristics as a result of material birefringence. It should be noted that the refractive index of ordinary light (${\textrm{n}_\textrm{o}}$=2.21 at 1550 nm) is higher than that of extraordinary light (${\textrm{n}_\textrm{e}}$=2.14 at 1550nm) in LN (Fig. 1(c)). The TM polarizations have stronger evanescent field than TE polarizations, resulting in the lower structural effective refractive index. Thus, to compensate for the structural birefringence and realize fundamental mode hybridization, a higher material refractive index of TM polarizations is needed.
Fig. 1. (a) Schematic drawing of an x-cut lithium niobate on insulator (LNOI) ridge waveguide when the waveguide is oriented along the y-axis of the lithium niobate (LN). Blue arrows shows the optical axis of LN and red arrows shows the electric polarization direction of the transverse electric (TE) and transverse magnetic (TM) modes. (b) Cross-section drawing of LNOI waveguide. (c) Material refractive index of LN with different optical axes.
The best solution is to arrange the waveguide toward the y-axis in x-cut LNOI as shown in Fig. 1(a), so that the TE polarizations correspond with the extraordinary light of LN while TM polarizations correspond with the ordinary light of LN. We first analyze this “y-axis” waveguide to search for the mode hybridization region. The cross-sectional structure of the waveguide is shown in Fig. 1(b). The thickness of the LN thin film is investigated between 400-700 nm (commercially available), and the etching depth is about half of the film thickness (to prevent excess scattering loss with large depth, and mode cut-off with small depth). The angle of the sidewalls is set at 72° as a result of our fabrication process. The waveguide is air cladded and is set on top of a silicon dioxide layer. Here a finite-difference method (FDE) mode solver (LUMERICAL) is used to calculate the mode profiles and the effective refractive indices of all eigenmodes.
As shown in Figs. 2(a)-(c), TE0 and TM0 modes have far different effective refractive indices in the case of Hf = 400, 500, 600 nm (total thickness of LN), but as Hf and the etching depth, He, increase, the difference decreases. This behavior can be interpreted as follows: as the thickness of LN increases, the light confinement in the vertical direction of waveguide is weaker, therefore the contribution to the mode refractive indices induced by structural birefringence (nTE>nTM) is less significant compared to contribution of the material birefringence, where nTM>nTE. Notably, we observed strong mode hybridization between TM0 and TE1 modes when Hf = 400 nm and Wt (waveguide width) is set between 1.2-1.5 µm. This phenomenon could be used to achieve mode conversion between TE1 and TM0 by constructing a tapered waveguide, moreover, could possibly convert modes between TE0 and TM0 by using the TE1 as transition [22].
In Fig. 2(d), when Hf=700nm and He=400nm, the refractive indices of TE0 and TM0 cross over each other, additionally, both TE1 and TM1 modes have a similar effective refractive index. But the anti-crossing does not occur, which means the TE0 and TM0 modes are not hybrid. Because of the horizontal symmetry of ridge structure, the fundamental modes would not couple at the cross wavelength and they would expand in terms of the normal mode profile with a changed waveguide width. However, the horizontal symmetry of the ridge waveguide would be broken if there were a perturbation in the waveguide (e.g., bending in the horizontal orientation) [26,27]. As shown in Fig. 2(e), when the waveguide bends, the anti-crossing of the effective refractive indices of TE0 and TM0 occurs, indicating that these two modes are coupled with each other, and mode hybridization takes place. As for the ridge waveguide, the vertical symmetry is broken by the ridge structure itself and the angled sidewalls. It leads to the occurrence of the anti-crossing of TMi and TEi+2k-1, but the crossing of TMi and TEi+2k (where k is an integer, k ≥ 0). The bending feature additionally break the horizontal symmetry of the waveguide, which leads to the occurrence of the anti-crossing of TMi and TEi+2k, in particular, fundamental TE and TM modes. It can be seen in Fig. 2(f) that, mode 1 was in the form of a TM0-like mode with a small Wt, but as the waveguide width increases, it is gradually transformed into a TE0-like mode. The second picture in Fig. 2(f) shows the hybrid condition of mode 1 with Wt=1.4 µm. When carrying out simulations with different bending radii, we find that a smaller bending radius leads to stronger mode hybridization, and larger gap of anti-crossing between fundamental modes in the hybridization region.
Fig. 2. (a-e) Calculated mode effective refractive indices with different film thickness, Hf, and etching depth, He, varied by waveguide width, Wt; The wavelength of the light is 1565 nm. Orientation of waveguides are all in y-axis of LN. (a) Hf=400 nm, He=200 nm. (b) Hf=500 nm, He=250 nm. (c) Hf=600 nm, He=300 nm. (d) Hf=700 nm, He=400 nm (e) Hf=700nm, He=400 nm, and the waveguide has a bending radius of 100 µm. (f) Calculated Ex and EZ profiles of mode 1 (blue line in [e]). From top to bottom: Wt=0.6 µm, 1.4 µm, 2.1 µm. (g) Calculated gap of the anti-crossing for TE0 and TM0 modes (${\Delta }{\textrm{n}_{\textrm{eff}}} = {\textrm{n}_{\textrm{TE}}} - {\textrm{n}_{\textrm{TM}}}$) in Fig. 2(e) with changed bending radius.
In the lossy waveguide, the propagating loss has no effect on mode hybridization as it only changes the imaginary part of the propagation constant, while the mode hybridization is spatially-independent. When a silicon dioxide layer (nsio2=1.4) is cladded on top of the waveguide, the hybridization wavelength of fundamental modes is red-shifted to 1689nm.
2.2 Observation of fundamental mode hybridization in LNOI microring resonator
Mode hybridization has been demonstrated previously by its use in mode conversion. Here we demonstrate a method to directly observe the mode hybridization by using a microring resonator with a bending waveguide. Although there have been some reports on mode coupling in the microring [28,29], the principles and prospect of mode hybridization have not been investigated in detail. In the following manuscript, a specific analysis of this phenomenon is carried out.
The designed waveguide which enables fundamental mode hybridization has dimension as follows: Hf=700 nm, He=400 nm, Wt=1400 nm, sidewall angle ${\theta } = 72$°, and the bending radius is 100 µm. The waveguide is oriented along y-axis of LN, corresponding to location A and A’ in Fig. 3(a). The refractive index of LN is set as: ne=2.138 and no=2.211, in the simulation wavelength range. The calculated effective refractive indices and group indices of TE0 and TM0 modes for varying wavelengths are shown in Figs. 3(b) and(c). There is a sharp jump in the group indices of both modes in the hybridization region (see curves -A). Since the mode group index, ng, not only depends on the mode effective index but also the gradient, they are related as follows:
Where neff is the effective refractive index and λ is the wavelength. The sharp jumps in the group indices should result from the perturbation of the effective indices in the hybridization region, owing to strong coupling between these two modes. The FSR of an individual mode in a microring resonator has an inversely proportional relationship with its group index as follows: where c is the speed of light and L is length of the resonator. Therefore, the jumps on the curve of the group index should have a similar appearance to the FSR curve in the same wavelength region. In Figs. 3(b) and 3(c), we calculate the effective refractive indices and group indices of TE0 and TM0 modes both in location A and B, the illustration “TE0-A” means the TE0 mode in location A. Since the mode hybridization occurs in location A, the mode 1 and mode 2 are defined. The mode 1 is in state of TM0 in the short wavelength, and in state of TE0 in the long wavelength, and in state of the hybrid mode around 1562nm whose refractive index is higher than mode 2.Fig. 3. (a) Schematic drawing of the designed microring resonator and the eigenmodes in location A and B. (b) Effective refractive indices of fundamental modes in cross-section A and B. (c) Group refractive indices of fundamental modes in cross-section A and B. (d) Electric vectorial overlap coefficient of u and v. (e) Calculated FSR of fundamental modes in the microring. The cross wavelength is 1562 nm.
Notably, the material birefringence of LN makes it complicated to analysis the propagation characteristics of TE modes on the x-cut LNOI platform, because the orientations of TE polarizations and the optical axis of LN are constantly changing in the different locations of the microring. The angle between the TE-polarization direction and the z-axis of LN varies from 0° to 180° in the whole ring resonator, and the material refractive index of TE-polarized light is constantly changing between ordinary light and extraordinary light. Although the difference is small (${\Delta \textrm{n}} \approx 0.07$), the influence on TE-mode characteristics such as mode profile and the propagation constant in different locations within the microring cannot be ignored, making the calculation of the average effective refractive index and average group index of modes significantly more difficult. To accurately calculate these parameters, we may need to make a differential of the microring and separately calculate the various cross-sections or create a 3D finite-difference time-domain (3D-FDTD) simulation to indirectly obtain the propagation characteristics of different modes. Here we present a simplified analysis.
Considering of the structural symmetry of the microring, the average propagation constant, β, of each mode is approximately the arithmetic average of the propagation constant in two locations, A and B, inside the microring as shown in Fig. 3(a) (the waveguides in locations A and B are separately oriented along y-axis and z-axis of LN). This is expressed by
Because the refractive index construction in these two typical locations puts equivalent effect on the characteristics of light. Therefore, we get the average group index of the microring as the average of the group index calculated at A and B:
To analyze the precision of the empirical formula, a 3D-FDTD simulation of the microring is launched. The interval of adjacent pulses inside microring is exacted to calculate the group velocity of the propagating modes, and the group velocity calculated by FDTD is very similar with that calculated in the empirical formula.
When the wavelength is far from the hybridization region, we could use this equation to estimate the total group index of the microring and further calculate the FSRs of TE0 and TM0. But in the hybridization region, modes are strongly coupled, and hybridization modes cannot be simply regarded as either a TE mode or a TM mode. It is essential to say that the behavior in the bending waveguide A-to-B in Fig. 3(a) is similar to a tapered straight waveguide, and if it has a large length, hybrid mode 1 (which has a higher ${\textrm{n}_{\textrm{eff}}}$ than mode 2) would gradually transform into TE0 and mode 2 would transform into TM0 (see [16]). However, the hybridization of mode 1 and mode 2 is so strong (the gap of anti-crossing of the two hybridization modes is small with a bending radius of 100 µm) that a larger length is required for conversion, and the change in refractive index along a microring is more significant than in a tapered waveguide. Thus the mode conversion in such a microring is seriously insufficient, and the mode excitation principles dominate the mode behavior in the bending waveguide. That is, the type of propagating modes in location B mainly depends on the vectorial profile overlap between the hybridization modes in location A and the fundamental modes in location B (e.g., at the cross wavelength, mode 1 would excite 50%TE0 and 50%TM0 in location B). Then we correct the average group index of mode 1 and mode 2 so that it is given by:
To carry out the experiment, we utilize grating couplers for fiber-to-chip light coupling. The whole structure of the microring resonator can be found in Fig. 4(d). The design details of the grating couplers can be found in our previous works [30]. The grating coupler is designed for TE-polarizations, and the width of the waveguide which joins the grating coupler is set as 0.9 µm (not supporting high-order modes) to ensure that only the TE0 can enter. The bus waveguide width is tapered from 0.9 µm to 1.4 µm prior to the coupling area, thus the widths of the bus waveguide and the microring waveguide is the same which maximize TE0-TE0 coupling. Notably, it may also excite a bit power of TM0 mode in the microring because of the proximity of effective indices between TE0 and TM0, but the high-order modes are hardly motivated. We have investigated and applied the critical coupling conditions of the TE0 mode with a coupling gap of 570 nm.
Fig. 4. (a-c) Scanning Electron Microscope (SEM) images of the devices and waveguides of the microring resonator. (a) Grating coupler. (b) Coupling region of microring. (c) Cross-section of waveguide. (d) Schematic drawing of the structure of the designed microring resonator.
3. Device fabrication and measurement
Our devices were fabricated on a 700-nm-thick x-cut congruent single-crystalline LN thin film sitting on a 1.8-µm-thick buried silicon dioxide layer (produced commercially by NANOLN). The pattern was defined in ZEP-520A resist by e-beam lithography and transferred onto the LN layer by a RIE-ICP etching. We have optimized the etching conditions to produce smooth sidewalls. Figures 4(a)-(c) show the scanning electron microscope (SEM) images of the grating coupler, waveguide cross-section and the coupling area of the microring.
We performed the measurement of the microring resonator using a continuous tunable laser (Santec TLS-510) in the range of 1520-1580 nm. The light is emitted from the laser and TE polarized by a polarization controller. Each grating coupler has a coupling efficiency of 20% (−6.9 dB) for TE polarizations and the output light is collected by an optical power meter (YOKAGAWA AQ2211). The transmission spectrum of the microring resonator is obtained by continuous scanning the wavelength from 1520 nm to 1580 nm.
Figures 5(a)-(d) show the transmission spectra of the microring with different wavelength ranges. We could see two sets of modes in the spectra but only one of the modes exists in the entire range of 1520-1580 nm. We judge the red-line mode to be the TE0 mode for three reasons: (1) Owing to our design, the only mode in the bus waveguide is the TE0 mode, and the majority of the power is in the TE0 mode in the microring due to the same width of both waveguides in the coupling area. (2) The red-line mode has higher FSR, which corresponds to the TE0 mode in the simulation. (3) The TE0 mode should have a higher Q-factor since the TM0 mode has a stronger evanescent field, which may lead to greater scattering loss in the sidewalls of waveguide. Figure 5(e) shows that the Q-factor of a TE0 resonance peak at 1572.6 nm is 1.78 million, by Lorentz fitting of the measurement data with an extinction ratio of 7 dB. The Q-factor of the hybrid TE0-TM0 mode at 1538.0nm is 1.4 million. Only fundamental modes have been observed in the transmission spectrum because the 100-µm-radius of the microring is small enough to filter out higher-order modes due to the large bending losses. We calculated the FSR of each mode for different wavelengths and have plotted them together in Fig. 5(f). The figure shows a clear jump in the FSRs of the two modes around 1537 nm, which confirms that the mode hybridization between TE0 and TM0 is taking place. The TM0 mode (blue dots) appears only in the mode hybridization region, because it is only in this wavelength range that the TM0 has a similar effective refractive index with TE0, and thus could be exited from the coupling area. The extinction ratio of the TM0 mode is diminished when the wavelength is far from the hybridization range, which also confirms this conclusion.
Fig. 5. (a-d) Transmission spectrum of the microring resonator with different wavelength range. (e) Measured FSRs of TE0 and TM0 modes in the microring in 1520-1580 nm. (f) Lorentz fitting of the resonance peak at 1572.6 nm, the Q-factor is 1.78 million.
These results are in strong agreement with our simulation. Although the hybridization wavelength is designed at 1562 nm but observed at 1537 nm, the shift may result from the tolerance of the waveguide size in the fabrication. The FSRs of the TE0 and TM0 modes are 205/195GHz, respectively, when wavelengths are far from the hybridization region. These results are consistent with our calculation, which demonstrates the accuracy of our empirical formula in the analysis. The demonstration of fundamental mode hybridization provides us with the potential to build polarization-dependent devices in the LNOI platform. We could utilize continuously-bending waveguides (such as an S-shape) with variant width to achieve fundamental mode conversion. Furthermore, the fundamental modes have almost the same group velocity in the designed waveguide without polarization dispersion, and that may be useful in polarization insensitive systems.
4. Conclusion
In conclusion, by utilizing the material birefringence of LN, we have designed and experimentally demonstrated fundamental mode hybridization in the LNOI ridge waveguide. We proposed a detail analysis of the mode hybridization, and found that when light propagates along y-axis in x-cut LNOI, and the waveguide has a total thickness around 700 nm, TE0 and TM0 modes have a similar effective refractive index. By introducing a bending structure as perturbation, we theoretically predict the existence of the TE0 and TM0 mode hybridization. To disclose the phenomenon, we utilize a microring resonator and observed sudden jumps in the FSR of TE0 and TM0 modes. This is a simple and feasible method because the hybridization waveguide bends exactly like a microring and the changes in the FSR could be easily read from the spectrum. We also observed the mode hybridization between TM0 and TE1 in the simulation, when the LN thickness was 400 nm and the width of waveguide was around 1.2 µm.
The fundamental mode hybridization is potential for use in the fundamental mode conversion and polarization rotation in LNOI. Additionally, in the hybridization region, fundamental modes possess the same group velocity without polarization dispersion and there may be potential for building compact devices for polarization insensitive applications.
Funding
National Natural Science Foundation of China (11574102, 61835008, 61905079, 61905084); State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, China (2019GZKF03008).
Acknowledgements
We thank the Center of Micro-Fabrication and Characterization (CMFC) of WNLO of HUST for the facility support. Thanks for Dr. Jiagui Wu from University of California, Los Angeles for the quality improvement of the manuscript.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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