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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28974–28979
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Radially realigning nematic liquid crystal for efficient tuning of microring resonators

Tzyy-Jiann Wang, Wan-Jing Li, and Tien-Jung Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28974-28979 (2013)
http://dx.doi.org/10.1364/OE.21.028974


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Abstract

The efficient tuning of microring resonator with the radially realigning nematic liquid crystal (NLC) cladding is presented. By applying the voltage on the in-plane annular electrodes, the produced electric field realigns the homeotropically-aligned NLC in the radial direction. Under the voltage sufficient for 90° NLC reorientation, the guided mode senses the consistent cladding index distribution along the microring waveguide with the maximal index change equal to the optical anisotropy of NLC. The resultant tuning of the resonant wavelength has a blue shift of 23.1nm for the TM mode and a red shift of 10.1nm for the TE mode. The tuning rates for the TM and TE modes are −1.95nm/V and 0.90nm/V. The proposed microring resonator owns the excellent features of wide tuning ranges and high tuning rates for the TM and TE modes.

© 2013 Optical Society of America

1. Introduction

Microring resonators with wide tuning range and low operation voltage are desirable for various photonic applications, such as wavelength add-drop [1

1. K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express 16(19), 14421–14428 (2008). [CrossRef] [PubMed]

] and dispersion compensation [2

2. G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17(7), 1248–1254 (1999). [CrossRef]

]. In order to tune the resonant wavelength of the microring resonator, the effective index of the guided mode in the microring waveguide is varied by changing the index of the waveguide core or cladding. The variation of the waveguide index can be produced by using various physical effects, including thermo-optic effect [3

3. M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89(7), 071110 (2006). [CrossRef]

], electro-optic effect [4

4. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’innocenti, and P. Günter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics 1(7), 407–410 (2007). [CrossRef]

], free-carrier plasma dispersion effect [5

5. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

], and nematic liquid crystal (NLC) reorientation [6

6. B. Maune, R. Lawson, G. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003). [CrossRef]

10

10. W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011). [CrossRef] [PubMed]

]. Thermo-optic effect occurs in all materials and has an index increase of 1.1 × 10−3 for every 6°C rise for Si [11

11. G. T. Reed, Silicon Photonics: The State of the Art (Wiley, 2008).

]. The maximal index change produced by electro-optic effect is 1.6 × 10−3 for LiNbO3 [12

12. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuit (McGraw-Hill, 1985).

] and those for free carrier plasma dispersion effect are 2.1 × 10−3 for Si [13

13. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

] and ~10−2 for GaAs and InP [14

14. B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990). [CrossRef]

]. Although the first three effects act on the waveguide core, their tuning ranges are small due to the tiny index change. The maximal index change produced by NLC reorientation equals its optical anisotropy with the value of >0.1 [15

15. J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005). [CrossRef]

]. It has the potential to achieve the widest tuning of the resonant wavelength. In order to achieve this goal, the guided mode is required to experience the maximal index change produced by NLC reorientation along the whole microring path. Several kinds of microring resonators are proposed to reorient NLC molecules in the cladding, including the spin-coated NLC film with the hemi-circular-ended strip electrodes [6

6. B. Maune, R. Lawson, G. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003). [CrossRef]

], the NLC reorientation using the longitudinal field component [7

7. W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett. 34(13), 2054–2056 (2009). [CrossRef] [PubMed]

], the in-plane switching using interdigital electrodes on the circular microring [8

8. T. Cai, Q. Liu, Y. Shi, P. Chen, and S. He, “An efficiently tunable microring resonator using a liquid crystal-cladded polymer waveguide,” Appl. Phys. Lett. 97(12), 121109 (2010). [CrossRef]

] and the square microring [9

9. W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011). [CrossRef]

], and the silicon square microring with the input/output grating couplers [10

10. W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011). [CrossRef] [PubMed]

]. For these microring resonators, the optical field propagating at different positions along the microring waveguide senses a varying cladding index. It senses the maximal index change produced by NLC reorientation only in a small part of the microring. Even in some cases, the propagating optical field senses a cladding index increase in the partial path but a cladding index decrease in the other path. These situations result in the tuning range of <1nm for most of the microring resonators [16

16. T.-J. Wang, S.-C. Yang, T.-J. Chen, and B.-Y. Chen, “Wide tuning of SiN microring resonators by auto-realigning nematic liquid crystal,” Opt. Express 20(14), 15853–15858 (2012). [CrossRef] [PubMed]

].

Previously, we proposed a microring resonator with auto-realigned NLC cladding [16

16. T.-J. Wang, S.-C. Yang, T.-J. Chen, and B.-Y. Chen, “Wide tuning of SiN microring resonators by auto-realigning nematic liquid crystal,” Opt. Express 20(14), 15853–15858 (2012). [CrossRef] [PubMed]

]. Under the action of electric field, the uses of the ridge waveguide and the homeotropically aligned negative Δε NLC produce the auto-realignment of NLC along the microring waveguide. The measured tuning ranges are 13nm for the TM mode and 2.1 nm for the TE mode. Though the optical field senses the consistent index distribution along the microring waveguide, it does not sense the maximal index change provided by NLC reorientation. In this work, a novel microring resonator using the in-plane annular electrodes is proposed. The electric field in the radial direction reorients the NLC molecules such that the optical field propagating at any position of the microring waveguide always senses the maximal index change provided by NLC. The simulation results manifest the NLC orientation distribution at different voltages and the dependence of the resonant wavelength on the voltage. The experimental results confirm the device features, such as wide tuning range and small operation voltage.

2. Device design and fabrication

Figures 1(a)
Fig. 1 (a) Cross-sectional view of the microring ridge waveguide under no applied voltage; (b)(c) top view of the proposed microring resonator (b) under no applied voltage; (c) with the applied voltage sufficient for 90° NLC reorientation.
and 1(b) show the cross-sectional view of the microring ridge waveguide and the top view of the proposed microring resonator. The microring resonators with radius R = 25μm are produced over a 4μm-thick SiO2 (n = 1.45) film on the Si substrate. The thicknesses of the central and side SiN films (n = 1.98) are 0.48μm and 0.06μm. The widths of the input/output waveguides and the microring waveguide are 1.5μm and 2.5μm, respectively. The input optical field is coupled to the microring resonator through a 5μm-long zero-gap coupler. The microring resonators are produced by using the fabrication process in [17

17. T.-J. Wang, Y.-H. Huang, and H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” IEEE Photonics Technol. Lett. 17(3), 582–584 (2005). [CrossRef]

]. The ITO in-plane electrodes on the B270 glass substrate consist of a round electrode and a 30μm-wide annular electrode with the conductor lines connecting to the contact pads, as shown in Fig. 1(b). The annular electrode has the shape of 3/4 ring and the electrode gap is 10μm. The ITO electrodes are produced by optical lithography, ITO deposition by RF magnetron sputtering, and lift-off process. The polyimide films (AL60101L from JSR) used as homeotropic alignment layers are spin-coated on the top of the glass substrate and the Si substrate. These two substrates are aligned such that the microring waveguide is located under the center of the electrode gap. After aligning, they are glued together using UV adhesive with 3μm-diameter spacers. The positive Δε NLC (MDA-00-3461 from Merck, ne = 1.7718 and no = 1.5140 at λ = 589.3nm) is infiltrated into the gap between these two substrates by capillary force. Under no applied voltage, the NLC molecules are perpendicular to the substrate surface due to the action of the homeotropic alignment layer. Applying the voltage on the in-plane electrodes produces the electric field in the radial direction. When a voltage sufficient for 90° NLC reorientation is applied, the electric field makes the positive Δε NLC molecules tilt toward the substrate surface in the radial direction, as shown in Fig. 1(c). Thus the optical field propagating at any position of the microring waveguide experiences the same cladding index distribution produced by NLC reorientation. The variation of the effective index of the guided mode is mainly contributed by the cladding index change on the top of the microring ridge waveguide. During the electrical tuning process, the main electric field of the TM mode senses the index decrease from ne to no. As to the TE mode, the sensed index is varied from no to ne. Therefore, the guided modes for both polarizations sense the maximal index change (ne-no) produced by NLC reorientation along the microring path.

3. Simulation results

When the voltage is applied on the in-plane electrodes, the cladding index variation produced by NLC reorientation results in the effective index change of the guided mode and thus produces the tuning of the resonant wavelength. In order to obtain the dielectric tensor of the reoriented NLC, the orientation distributions of the NLC molecules at different voltages are calculated by the program using the finite element method to minimize the Oseen-Frank energy under the appropriate boundary condition [18

18. Z. Ge, T. X. Wu, R. Lu, X. Zhu, Q. Hong, and S.-T. Wu, “Comprehensive three-dimensional dynamic modeling of liquid crystal devices using finite element method,” J. Disp. Technol. 1(2), 194–206 (2005). [CrossRef]

]. Because the microring waveguide is located under the center of the gap between the inner round electrode and the outer annular electrode, the action of the electric field makes the NLC molecules around the electrode gap have a tilt angle θ with respect to the normal vector of the substrate surface. The tilt angle distributions of NLC molecules for the voltage V = 0V, 7V, 20V, and 100V are shown in Fig. 2
Fig. 2 Tilt angle distribution of NLC molecules for the applied voltage: (a) V = 0; (b) V = 7V, (c) V = 20V; (d) V = 100V.
. Because of the action of the homeotropic alignment layer, the NLC molecules under no applied voltage have a tilt angle θ = 0° except those around the sidewalls of the upper ITO electrodes and the lower ridge waveguide. When V = 7V, the NLC orientation has a symmetric distribution. The maximal tilt angle of 72.14° occurs at the vertical coordinate y = 1.74. When the voltage increases to 20V, the maximal tilt angle achieves 90°. The range with the tilt angle of 90° not only extends close to the top surface of the ridge waveguide but also extends toward its two sides. Due to the surface anchoring effect, the tilt angles of the NLC molecules near the top surface of the ridge waveguide are 0° and are hard to be changed. They are not reoriented to 90° until the voltage is 100V, as shown in Fig. 2(d).

In the simulation, the effective index of the guided mode is calculated by the full-vectorial mode solver considering the full anisotropy of NLC [19

19. M.-Y. Chen, S.-M. Hsu, and H.-C. Chang, “A finite-difference frequency-domain method for full-vectorial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor,” Opt. Express 17(8), 5965–5979 (2009). [CrossRef] [PubMed]

]. The NLC to be used is MDA-00-3461 from Merck. Merck intends to replace the widely-used E7 by the new MDA-00-3461. Because of the lack of its optical parameters around the wavelength 1550nm, the optical anisotropy of 0.22 in the simulation is inferred from the dispersion relation for the E7. In order to connect the central round electrode to the contact pad, the outer annular electrode has the opening to allow the pass of the conductor line. Because the NLC reorientation mainly occurs at the region near the electrode gap, the ratio of the central angle for the annual electrode to that for the whole ring (a) affects the tuning range of the resonant wavelength. For the electrode structure in Fig. 1(b), the resonant wavelength of the microring resonator with radius R is expressed as λm = {(2πR·a + Lneff + [2πR·(1-a) + Lneff, 0}/m, where neff,0 and neff are the effective indices of the guided mode without and with electrical tuning, L is the length of the zero-gap coupler, and m is the order number.

The dependences of the simulated resonant wavelength on the voltage for the TM and TE modes are shown in Fig. 3
Fig. 3 Dependence of the simulated resonant wavelength on the voltage for the annular electrode with the shape of 3/4 ring, 7/8 ring, and the whole ring, for (a) the TM mode; (b) the TE mode.
. For both polarizations, the threshold voltage for NLC reorientation is 6V. Because the main electric field of the TM mode senses an index decrease (neno), the resultant reduction of the effective index causes the decrease of the resonant wavelength with the voltage. The resonant wavelength shifts for a = 3/4, 7/8, and 1, are −30.13nm, −34.94nm, and −40.99nm. As to the TE mode, an index increase (none) experienced by the main electric field produces a red shift of the resonant wavelength. The wavelength shifts for a = 3/4, 7/8, and 1 are 10.92nm, 12.67nm, and 14.86nm. The TM mode has a larger tuning range than the TE mode because it has more evanescent field extending to the NLC cladding [16

16. T.-J. Wang, S.-C. Yang, T.-J. Chen, and B.-Y. Chen, “Wide tuning of SiN microring resonators by auto-realigning nematic liquid crystal,” Opt. Express 20(14), 15853–15858 (2012). [CrossRef] [PubMed]

]. The stronger evanescent field for the TM mode is due to the discontinuity of the vertical electric field on the top surface of the ridge waveguide. It leads the mode field to be easily disturbed by NLC reorientation and result in the slight twists of the resonant wavelength curve at the voltage 10V and 26V, as shown in Fig. 3(a). Because the TE mode has better optical confinement than the TM mode, the effect of the NLC reorientation on the mode field is smaller and the variation of its resonant wavelength with the voltage is smooth.

4. Experimental results and discussions

The NLC orientation distributions in the device are observed by polarized optical microscope (POM). Figure 4
Fig. 4 Photographs of polarized optical microscope for the NLC-cladded microring resonator with the applied voltage of 0V, 4.5V, 16V, and 20V.
shows the POM photographs of the microring resonator for V = 0V, 4.5V, 16V, and 20V. Because the directions of the polarizer and the analyzer are both along the vertical direction, the variation of the polarization state of the reflected light results in the appearance of the dark region. When V = 0V, the bright image is observed due to an isotropic medium with index no sensed by the incident light. The images of the ITO in-plane electrodes on the upper glass substrate and the microring waveguide on the lower Si substrate are clearly observed. When the voltage increases, the electric field produced around the electrode gap causes the consistent NLC reorientation in the radial direction and produces the dark region in the photograph. The enlargement of the dark region represents the enlarged region of NLC reorientation. Because the NLC molecules in the electrode gap at the 3 o’clock, 9 o’clock, and 12 o’clock positions of the central round electrode have the orientation in the parallel or the vertical direction, the polarization state of the input light after reflection is not changed and thus the bright region is observed. As to the region farther from the electrodes, because the action of electric field is weak, the reorientation of NLC molecules is small. The POM photographs confirm that the voltage applied on the in-plane annular electrodes produces the consistent distribution of the NLC orientation in the radial direction along the microring path on the top of the microring waveguide.

The characteristics measurement of microring resonator uses the setup in [16

16. T.-J. Wang, S.-C. Yang, T.-J. Chen, and B.-Y. Chen, “Wide tuning of SiN microring resonators by auto-realigning nematic liquid crystal,” Opt. Express 20(14), 15853–15858 (2012). [CrossRef] [PubMed]

]. The dependences of the measured resonant wavelength on the voltage for the TM and TE modes are shown in Fig. 5
Fig. 5 Dependence of the measured resonant wavelength on the voltage for (a) the TM mode; (b) the TE mode. (Inset: the transmission spectrums for the voltages of 0V and 16V.)
with the transmission spectrums as inset. The tuning of the resonant wavelength starts at the voltage 4.5V. As the voltage increases, the resonant wavelength has a blue shift for the TM mode and a red shift for the TE mode. These are consistent with the simulation results. When the voltage increases beyond 16V, the resonant wavelength approaches a constant. The free spectral ranges (FSR) for the TM and TE modes are 7.5nm and 7.6nm. The tuning ranges for the TM and TE modes are as large as 23.1nm and 10.1nm, which are 3.08 times and 1.33 times their FSR. To the best of our knowledge, the measured tuning range for the TE mode is the largest value up to now. The simulated tuning ranges for the TM and TE modes are 30.13nm and 10.92nm. The simulated result for the TE mode is close to the measured one. The larger operation voltage in the simulation than the measured one is inferred due to the discrepancy in the NLC parameters. After the NLC injection over the microring resonator, the Q-factor of the TE mode is degraded from 1043 to 421 due to the scattering loss induced by the NLC cladding. When the voltage increases to 16V, the Q-factor is gradually enhanced to 665. In the range of 4.5V~16V, the tuning rates are −1.95nm/V for the TM mode and 0.90nm/V for the TE mode, which are the largest values up to now.

The features of the proposed microring resonator include wide tuning range for both polarizations and small operation voltage. The obvious enhancement of the tuning range is attributed to the consistent cladding index distribution along the microring waveguide and the use of the maximal index change provided by NLC. The small operation voltage is due to the elimination of intermediate dielectric between the electrode and the NLC. The tuning performance can be further enhanced by using the annular electrode with the whole ring. It can be produced by using the two-step ITO electrode fabrication with the insulating layer between the annular electrode and the conductor line connecting to the central electrode. The proposed technique is rather universal and can be applied in the NLC tunable waveguide and the microring waveguide with the circular or square shape. Simultaneous efficient tuning of the TM and TE modes offers additional flexibility in the photonic applications.

5. Conclusion

We present a novel microring resonator with wide tuning range and low operation voltage by radially realigning NLC. By applying the voltage on the in-plane annular electrodes, the homeotropically aligned positive Δε NLC is realigned in the radial direction. When the voltage sufficient for 90° NLC reorientation is applied, the optical field propagating at any position of the microring waveguide always senses the consistent cladding index distribution with the maximal index change provided by NLC. It achieves the tuning range as large as 23.1nm and 10.1nm for the TM and TE modes, which are 3.08 times and 1.33 times their FSR. The tuning range larger than the FSR is important such that the microring resonator can be effectively utilized. The tuning rates for the TM and TE modes are −1.95nm/V and 0.90nm/V. The proposed microring resonator has the best tuning performance up to now, including the tuning range for the TE mode and the tuning rates for both polarizations. Further enhancement of the tuning performance can be made by designing the electrode structure.

Acknowledgments

This work was supported by National Science Council of the Republic of China under grants NSC 101-2221-E-027-096 and NSC 102-2221-E-027-101.

References and links

1.

K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express 16(19), 14421–14428 (2008). [CrossRef] [PubMed]

2.

G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17(7), 1248–1254 (1999). [CrossRef]

3.

M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89(7), 071110 (2006). [CrossRef]

4.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’innocenti, and P. Günter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics 1(7), 407–410 (2007). [CrossRef]

5.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

6.

B. Maune, R. Lawson, G. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003). [CrossRef]

7.

W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett. 34(13), 2054–2056 (2009). [CrossRef] [PubMed]

8.

T. Cai, Q. Liu, Y. Shi, P. Chen, and S. He, “An efficiently tunable microring resonator using a liquid crystal-cladded polymer waveguide,” Appl. Phys. Lett. 97(12), 121109 (2010). [CrossRef]

9.

W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011). [CrossRef]

10.

W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011). [CrossRef] [PubMed]

11.

G. T. Reed, Silicon Photonics: The State of the Art (Wiley, 2008).

12.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuit (McGraw-Hill, 1985).

13.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

14.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990). [CrossRef]

15.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005). [CrossRef]

16.

T.-J. Wang, S.-C. Yang, T.-J. Chen, and B.-Y. Chen, “Wide tuning of SiN microring resonators by auto-realigning nematic liquid crystal,” Opt. Express 20(14), 15853–15858 (2012). [CrossRef] [PubMed]

17.

T.-J. Wang, Y.-H. Huang, and H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” IEEE Photonics Technol. Lett. 17(3), 582–584 (2005). [CrossRef]

18.

Z. Ge, T. X. Wu, R. Lu, X. Zhu, Q. Hong, and S.-T. Wu, “Comprehensive three-dimensional dynamic modeling of liquid crystal devices using finite element method,” J. Disp. Technol. 1(2), 194–206 (2005). [CrossRef]

19.

M.-Y. Chen, S.-M. Hsu, and H.-C. Chang, “A finite-difference frequency-domain method for full-vectorial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor,” Opt. Express 17(8), 5965–5979 (2009). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(160.3710) Materials : Liquid crystals
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: October 10, 2013
Revised Manuscript: November 11, 2013
Manuscript Accepted: November 12, 2013
Published: November 15, 2013

Citation
Tzyy-Jiann Wang, Wan-Jing Li, and Tien-Jung Chen, "Radially realigning nematic liquid crystal for efficient tuning of microring resonators," Opt. Express 21, 28974-28979 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28974


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References

  1. K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express16(19), 14421–14428 (2008). [CrossRef] [PubMed]
  2. G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol.17(7), 1248–1254 (1999). [CrossRef]
  3. M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett.89(7), 071110 (2006). [CrossRef]
  4. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’innocenti, and P. Günter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics1(7), 407–410 (2007). [CrossRef]
  5. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
  6. B. Maune, R. Lawson, G. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett.83(23), 4689–4691 (2003). [CrossRef]
  7. W. De Cort, J. Beeckman, R. James, F. A. Fernández, R. Baets, and K. Neyts, “Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component,” Opt. Lett.34(13), 2054–2056 (2009). [CrossRef] [PubMed]
  8. T. Cai, Q. Liu, Y. Shi, P. Chen, and S. He, “An efficiently tunable microring resonator using a liquid crystal-cladded polymer waveguide,” Appl. Phys. Lett.97(12), 121109 (2010). [CrossRef]
  9. W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B28(1), 79–85 (2011). [CrossRef]
  10. W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett.36(19), 3876–3878 (2011). [CrossRef] [PubMed]
  11. G. T. Reed, Silicon Photonics: The State of the Art (Wiley, 2008).
  12. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuit (McGraw-Hill, 1985).
  13. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
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