1. Introduction

Microring resonators possess excellent wavelength-selective characteristics in a compact structure. They have been widely applied in many advanced applications, including high-speed intensity modulation [1], wavelength add-drop [2], dispersion compensation [3], biochemical sensing [4], laser resonator [5], and wavelength conversion [6]. The resonant wavelength of the microring resonator can be dynamically tuned by varying the index of waveguide core or cladding through physical effects, such as electro-optic effect [7, 8], thermo-optic effect [9], free-carrier plasma dispersion effect [10], and nematic liquid crystal (NLC) reorientation [11–15]. Among them, NLC reorientation produces the largest index change and has the potential to achieve the widest tuning of resonant wavelength. NLC has been used in various photonic applications [16, 17]. Several device structures are proposed to reorient NLC molecules in the cladding for effectively tuning the resonant wavelength. The spin-coated NLC film is realigned azimuthally by using two hemi-circular-ended strip electrodes. It produces a resonant wavelength shift of 0.22nm for TE mode in the Si microring resonator [11]. The reorientation of a NLC layer sandwiched between a SOI chip and an ITO glass plate achieves a tuning range of 0.6nm for TE mode in the Si microring resonator [12]. The NLC in-plane switching has been used to tune the polymer [13] and Si [14] microring resonators. Their tuning ranges for TE mode are 0.73nm and 1nm, respectively. The Si ring resonator using four straight sections and input/output grating couplers produces the resonant wavelength shifts of 31nm for TM mode and 4.5nm for TE mode [15].

In the previous works, the NLC molecules at different positions along the microring waveguide have individual orientation distribution relative to the microring waveguide. Thus the optical field propagating in the microring waveguide senses a varying cladding index at different positions. The propagating optical field senses the maximal cladding index variation before and after applying electric field only in some part of the microring. Besides, the sensed maximal cladding index variation is mostly smaller than the optical anisotropy of liquid crystal. Even in some cases, the propagating optical field senses a cladding index increase in one path but a cladding index decrease in the other path. The difference in their path lengths results in the resonant wavelength shift. These situations limit the available tuning range of the resonant wavelength of the microring resonators with NLC cladding. In this work, a widely tunable SiN microring resonator is designed deliberately such that the optical field propagating at any position of the microring waveguide senses the same cladding index distribution, no matter whether applying electric field or not. In order to understand the anisotropic index distribution in the NLC cladding, the distributions of electric field and the corresponding NLC orientation are simulated. By calculating the variation of the effective index of the guided mode with the applied voltage, the theoretical tuning characteristics of the microring resonators are derived and in comparison with the experimental results.

2. Device design

In order to have the same anisotropic cladding index distribution along the microring waveguide, the proposed microring resonator is designed as follows. The microring has the silicon nitride (SiN) ridge waveguide structure and the NLC cladding is formed by using negative Δε NLC combined with non-rubbed homeotropic alignment layers. As the applied voltage is zero, negative Δε NLC molecules are perpendicular to the substrate surface due to the action of homeotropic alignment layer. As a voltage sufficient for NLC reorientation is applied, negative Δε NLC molecules tilt toward the substrate surface. Because of using non-rubbed alignment layers, the NLC molecules tilt freely with arbitrary azimuth angles except those near the SiN waveguides. They are affected by the protruding of the ridge structure from the substrate surface and auto-reorient themselves such that their azimuth angle distribution follows the circular path turning of the microring waveguide. Therefore, the same cladding index distribution is sensed by the optical field propagating at any position of the microring waveguide, no matter whether applying electric field or not.

Figure 1(a) and 1(b) shows the designed device structure of the SiN (n = 1.98) microring resonator with NLC cladding. The microring resonator consists of 1μm-wide input/output waveguides and a 2.5μm-wide microring waveguide with radius R = 25μm. The input optical field is coupled to the microring resonator through a 5μm-long zero-gap coupler. The SiN ridge waveguides are produced over a 4μm-thick SiO₂ (n = 1.45) film on the Si substrate. The thicknesses of central and side SiN films are 0.48μm and 0.06μm. The fabrication process of SiN microring resonators is the same as that in our previous work [18]. The 70nm-thick polyimide films (AL60101L from JSR) used as homeotropic alignment layers are spin-coated on the top of the Si substrate and the ITO glass substrate. It is noted that the alignment layers are not rubbed such that the azimuth angles of the NLC molecules near the SiN waveguides can be affected by the protruding of the ridge structure from the substrate surface. The ITO glass substrate is glued on the Si substrate using UV adhesive with 5μm-diameter spacers. The ITO film and the Si substrate are used as the top and bottom electrodes. Finally, negative Δε NLC (MJ031801 from Merck, n_e = 1.6066 and n_o = 1.49) is infiltrated into the gap between the Si substrate and the ITO glass substrate by capillary force. Figure 1(c) shows the schematic illustration of the tilt NLC molecule with the tilt angle θ and the azimuth angle ϕ.

 

Fig. 1 (a) Top view; and (b) cross-sectional view of the proposed microring resonator; (c) schematic illustration of tilt NLC molecule (or director$\widehat{n}$).

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3. Simulation results

The reorientation of NLC molecules in Fig. 1(b) under various voltages has been calculated based on the minimization of Oseen-Frank energy [19]. Figure 2 shows the tilt angle distribution of NLC molecules for the voltage V = 0V, 5V, 10V, and 100V. When V = 0V, the tilt angles of the NLC molecules are 90° except those near the sidewalls of the ridge waveguides. Their orientations are perpendicular to the sidewall surface and have the tilt angles around 0°. As the voltage increases to 5V, the NLC molecules in the middle of the gap rotate to the tilt angles of ~30°. The orientation of the NLC molecules near the substrate surface is fixed due to the surface anchoring effect. When the voltage increases from 10V to 100V, most of the NLC molecules orient parallel to the substrate surface (θ = 0°). It is found that the orientations of the NLC molecules near the waveguide sidewalls are less affected by the applied voltage. During the electrical tuning process, the variation of the effective index of the guided mode is mainly contributed by the cladding index change induced by the NLC reorientation on the top of the SiN ridge waveguide.

 

Fig. 2 Tilt angle distribution of NLC molecules for the applied voltage: (a) V = 0; (b) V = 5V, (c) V = 10V; (d) V = 100V.

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In order to understand the voltage effect on the resonant wavelength, the full-vectorial mode solver considering the full anisotropy of NLC is used to calculate the effective index of the guided mode. The anisotropic optical property of the NLC directors with the specified tilt angle and azimuth angle is represented by dielectric tensor. The resonant wavelength of the microring resonator is determined by the effective index n_eff through the equation λ_m = (2πR + 2L) n_eff /m, where L is the length of the zero-gap coupler and m is the order number. In the numerical calculation, the boundary condition needs to be specified for obtaining the solution. Because the homeotropic alignment layer anchors the NLC directors along the direction perpendicular to the surface, the simulation uses the boundary conditions of θ = 90° and a certain ϕ value on the horizontal surface of the homeotropic alignment layer. The preset ϕ value affects the calculated director orientation distribution and thus the effective index. In the following simulation, the preset ϕ values of 0°, 45°, and 90° are considered. When the voltage increases from 0 to 100V, the effective index changes of TM mode are −1.27 × 10⁻², −1.38 × 10⁻², and −1.52 × 10⁻² respectively for ϕ = 0°, 45°, and 90°. For TE mode, the effective index changes are 2.10 × 10⁻⁴, 3.11 × 10⁻³, and 6.40 × 10⁻³. Figure 3 shows the dependence of the resonant wavelength on the voltage for TM and TE modes. For both polarizations, the threshold voltage for NLC reorientation is 4V. As the voltage increases further, the resonant wavelength has a blue shift for TM mode and a red shift for TE mode. The resonant wavelength shifts for TM mode are −11.71nm, −12.73nm, and −14.03nm, for ϕ = 0°, 45°, and 90°. As to TE mode, the corresponding resonant wavelength shifts are 0.19nm, 2.78nm, and 5.72nm. Consider the cladding index variation Δn experienced by the main electric field on the top of the ridge waveguide for the tilt angles of 90° and 0°. The Δn value depends on the azimuth angle. For TM mode, the Δn experienced by E_y is always (n_o-n_e) in the range of ϕ = 0°~90°. The dependence of resonant wavelength shift on the azimuth angle is due to the index sensed by the longitudinal electric field E_z. For TE mode, the Δn experienced by E_x changes from 0 to (n_e-n_o) as ϕ varies from 0° to 90°. The resonant wavelength shift for ϕ = 0° is due to the index change sensed by the longitudinal electric field E_z. The difference in Δn causes the obvious variation of resonant wavelength shift with the azimuth angle. Because the main electric field of TM mode (or TE mode) feels the decreasing (or increasing) index change, the resonant wavelength has a blue (or red) shift. The resonant wavelength shift for TM mode is larger than that for TE mode due to the larger |Δn| and more evanescent field extending to the NLC cladding, as shown in the inset of Fig. 3.

 

Fig. 3 Dependence of the simulated resonant wavelength for (a) TM mode; (b) TE mode; on the voltage for the preset azimuth angle ϕ = 0°, 45°, and 90°. (Inset: the field distribution of guided mode).

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4. Experimental results and discussions

Figure 4 shows the photographs of polarized optical microscope (POM) of the microring resonator with the applied voltage of 0V and 50V. As the voltage is zero, the incident linearly polarized light regards the homeotropically aligned NLC molecules as an isotropic medium with index n_o. Because the polarizations of the incident and reflected light are identical, the complete dark image is observed. As the voltage of 50V is applied, the tilt NLC molecules make the NLC layer act as an anisotropic medium. The phase difference between ordinary and extraordinary rays alters the polarization state of the reflected light. A 180° phase difference rotates the input polarization by 90° such that the brightest line (or highest intensity) is observed. It is noted in Fig. 4(b) that two bright lines appear on two sides of the microring waveguide and the straight waveguides. The difference in the gradual variation of brightness levels observed on the inner and outer sides of the microring waveguide is inferred due to the symmetric distribution of azimuth angles, which are ϕ for the NLC molecules on the outer side and -ϕ for those on the inner side, referred to Fig. 1(a). The POM photographs confirm that the protruding of the ridge waveguide structure produce the consistent azimuth angle distribution along the microring waveguide.

 

Fig. 4 Photographs of polarized optical microscope for the NLC-cladded microring resonator with the applied voltage of (a) 0V; (b) 50V. The directions of polarizer (P) and analyzer (A) are indicated in the figure.

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The tuning characteristics of the microring resonator are measured with a tunable laser and a power meter. The input polarization is controlled by a fiber polarization controller. The laser light is coupled into the microring resonator using a focuser and the output light is collected by objective lens. The voltage for modulating NLC is a 1kHz square wave, which is produced by a signal generator and a voltage amplifier. The maximal modulating voltage of 100V is limited by the voltage amplifier. Figure 5 shows the dependence of the measured resonant wavelength on the voltage for TM and TE modes. The threshold voltage for both polarizations is 5V. The variation trends of the measured resonant wavelength for TM and TE modes are consistent with the simulation results. When the voltage varies from 5V to 100V, the tuning ranges for TM and TE modes can be as large as 13nm and 2.1nm. They are close to the simulation results for ϕ = 45° (12.73nm for TM mode and 2.78nm for TE mode). It is inferred that the NLC molecules near the microring waveguide have the effective azimuth angle ϕ~45° on the outer side and ϕ~-45° on the inner side. Because of the scattering loss induced by the NLC cladding, the Q-factor of the microring resonator for TM mode degrades from 820 for the microring without NLC cladding to 500 for that with NLC cladding. The somewhat large modulating voltage is due to using thick SiO₂ films (4μm) and large spacers (diameter 5μm). It can be improved by depositing metal film over SiO₂ film except the regions with SiN waveguides as bottom electrode.

 

Fig. 5 Dependence of the measured resonant wavelength for (a) TM mode; (b) TE mode; on the voltage. (Inset: the transmission spectrum for the voltages of 0V and 100V).

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The improvements over the previous works include large tuning range and bi-polarization wavelength tuning. The use of negative Δε NLC with non-rubbed homeotropic alignment layers produces the consistent azimuth angle distribution of NLC molecules along the microring waveguide. Therefore, the optical field propagating at any position of the microring waveguide always senses the same cladding index distribution, no matter whether applying electric field or not. It avoids the problem in using the rubbed alignment layer that the NLC molecules at any positions along the microring waveguide have different relative azimuth orientation such that the NLC tuning effect is degraded. Using non-rubbed alignment layers has an additional advantage of reducing the propagation loss, which can enhance the extinction ratio. From the transmission spectrums in the insets of Fig. 5, it is found that the tuning range of TM mode is larger than the free spectral range (~7.8nm) such that the microring resonator can be effectively utilized. Besides, simultaneous tuning of TM and TE modes in this work offers additional flexibility in applications.

5. Conclusion

We have presented the widely tunable SiN microring resonator by auto-realigning nematic liquid crystal. Under the action of electric field, the use of the SiN ridge waveguide and the homeotropically aligned negative Δε NLC cladding produce auto-realignment of nematic liquid crystal along the microring waveguide. No matter whether applying electric field or not, the propagating field at any position of the microring waveguide always senses the consistent cladding index distribution. The wide tuning ranges of 13nm for TM mode and 2.1 nm for TE mode are achieved due to the consistent NLC azimuth angle distribution along the microring waveguide and the strong interaction between NLC and guided mode. Further improvement in the tuning range can be made by designing the waveguide structure.