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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 601–606
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Integrated-optic polarization rotator with obliquely deposited columnar thin film

Tzyy-Jiann Wang and Yu-Chen Cheng  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 601-606 (2012)
http://dx.doi.org/10.1364/OE.20.000601


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Abstract

A new integrated-optic polarization rotator with anisotropic cladding formed by oblique angle deposition is presented. Optical anisotropy with tilt principal axes in the obliquely deposited columnar thin film induces hybrid polarization modes in the waveguide and thus produces polarization rotation. The dependence of device characteristics on columnar film parameters, such as column angle, film thickness, extraordinary index, and optical anisotropy, is investigated by 3D full-vectorial finite difference beam propagation method. The polarization rotator with Ta2O5 columnar thin film has polarization conversion efficiency as high as 99% and extinction ratio of 25dB.

© 2011 OSA

1. Introduction

Polarization manipulation, such as polarization rotation and splitting, in optical integrated circuits is essential in the applications, such as signal coherent detection and elimination of polarization dependence of device performance. In order to rotate light polarization in the waveguide, material birefringence or structure asymmetry is applied to the waveguide for inducing the coupling of two orthogonal polarization modes. Different kinds of waveguides, which are composed of distinct materials or have dissimilar waveguide structures, require a specific device structure or operation manner in the design of polarization rotator. Semiconductor-based materials, such as InP, GaAs, and SiN, are used to form high index contrast waveguides. Geometrical asymmetry on two sides of waveguide, such as asymmetric-loaded waveguides [1

1. K. Merterns, B. Scholl, and H. J. Schmitt, “Strong polarization conversion in periodically loaded strip waveguides,” IEEE Photon. Technol. Lett. 10(8), 1133–1135 (1998). [CrossRef]

], angled-faced waveguides [2

2. Z. Huang, R. Scarmozzino, G. Nagy, J. Steel, and R. M. Osgood, “Realization of a compact and single-mode optical passive polarization converter,” IEEE Photon. Technol. Lett. 12(3), 317–319 (2000). [CrossRef]

], curved waveguide bends [3

3. C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8(10), 1346–1348 (1996). [CrossRef]

], width transition of upper waveguide core [4

4. J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

], and one-side shallow trench on waveguide core [5

5. D. M. H. Leung, B. M. A. Rahman, and K. T. V. Grattan, “Numerical analysis of asymmetric silicon nanowire waveguide as compact polarization rotator,” IEEE Photon. J. 3(3), 381–389 (2011). [CrossRef]

], induces hybrid polarization modes to cause polarization rotation. The waveguides made of other materials achieve polarization rotation by producing principal axes rotation of index ellipsoid or non-zero off-diagonal elements of the dielectric tensor, which is induced by fabrication process or physical interaction in material. Polymer waveguides utilize electric field poling along the tilt direction to produce polarization rotation [6

6. M. C. Oh, S. S. Lee, and S. Y. Shin, “Simulation of polarization converter formed by poling-induced polymer waveguides,” IEEE J. Quantum Electron. 31(9), 1698–1704 (1995). [CrossRef]

]. Substrate birefringence of LiNbO3 combined with near-z-axis propagation offers non-zero off-diagonal elements of the dielectric tensor for polarization rotation [7

7. A. V. Tsarev, “New compact polarization rotator in anisotropic LiNbO3 graded-index waveguide,” Opt. Express 16(3), 1653–1658 (2008). [CrossRef] [PubMed]

]. In ion-exchanged glass waveguides and LiNbO3 waveguides, strain-optic effect is utilized to rotate the principal axes of index ellipsoid [8

8. T. Lang, F. Bahnmüller, and P. Benech, “New passive polarization converter on glass substrate,” IEEE Photon. Technol. Lett. 10(9), 1295–1297 (1998). [CrossRef]

,9

9. T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B 80(2), 193–198 (2005). [CrossRef]

]. External signals induce polarization rotation in the waveguide through physical effects of materials, such as electro-optic effect [10

10. H. Porte, J. P. Goedgebuer, R. Ferriere, and N. Fort, “Integrated TE-TM mode converter on y-cut z-propagating LiNbO3 with an electro-optic phase matching for coherence multiplexing,” IEEE J. Quantum Electron. 25(8), 1760–1762 (1989). [CrossRef]

] and acousto-optic effect [11

11. L. N. Binh, J. Livingstone, and D. H. Steven, “Tunable acousto-optic TE-TM mode converter on a diffused optical waveguide,” Opt. Lett. 5(3), 83–84 (1980). [CrossRef] [PubMed]

] in LiNbO3, and magneto-optic effect in garnet [12

12. P. K. Tien, R. J. Martin, R. Wolfe, R. C. Le craw, and S. L. Blank, “Switching and modulation of light in magneto-optic waveguides of garnet films,” Appl. Phys. Lett. 21(8), 394–396 (1972). [CrossRef]

].

In this work, we present a new polarization rotator using anisotropic thin film formed by oblique angle deposition as cladding. It can be applied on various waveguide structures to achieve polarization rotation. Evanescent field extending to anisotropic cladding with tilt principal axes induces coupling of hybrid polarization modes and thus produces polarization rotation. The effects of column angle, film thickness, extraordinary index, and optical anisotropy on polarization conversion efficiency and device length are discussed.

2. Device design

Figure 1
Fig. 1 Device structure of the polarization rotator with obliquely deposited columnar thin film.
shows the device structure of the proposed polarization rotator on the B270 glass substrate (n = 1.521). It consists of an ion-exchanged waveguide covered with obliquely deposited columnar thin film [13

13. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37(13), 2653–2659 (1998). [CrossRef] [PubMed]

]. The waveguide is formed by K+/Na+ ion exchange for 200min with mask opening of 4μm. Its index distribution is obtained by solving a nonlinear inter-diffusion equation [14

14. M. A. Swillam, D. A. Khalil, and A. H. Morshed, “Effect of the fabrication and design parameters on the performance of multimode interference devices made by ion exchange: a detailed study,” J. Opt. A, Pure Appl. Opt. 10(12), 125301 (2008). [CrossRef]

]. The obliquely deposited film has a columnar structure due to the self-shadowing effect and the limited mobility of the deposited atoms. It can be produced by using an electron beam evaporator with an angle-tunable substrate holder. The columnar film is designed such that the columns are aligned in the x-y plane and has an included angle θ with the substrate surface. The columnar structure produces the optical anisotropy of cladding film. As the optical field propagates through the polarization rotator, it extends to the columnar thin film and experienced optical anisotropy with tilt principal axes, which induces the excitation of hybrid polarization modes. The coupling level and the properties of the excited hybrid polarization modes, such as effective index and field distribution, depends on the optical wavelength and columnar film parameters, including column angle (θ), film thickness (t), extraordinary and ordinary indices (ne and no). The dielectric tensor of columnar film in the coordinate (x,y,z) system can be expressed as:

ε=[no2+(ne2no2)cos2θ(ne2no2)sinθcosθ0(ne2no2)sinθcosθno2+(ne2no2)sin2θ000no2]
(1)

At the output end of the polarization rotator, the interference result of all the hybrid polarization modes determines the output field distribution and thus the polarization conversion efficiency. The characteristics of polarization rotator are investigated by 3D full-vectorial finite-difference beam propagation method (BPM) [15

15. Q. Wang, G. Farrell, and Y. Semenova, “Modeling liquid-crystal devices with the three-dimensional full-vector beam propagation method,” J. Opt. Soc. Am. A 23(8), 2014–2019 (2006). [CrossRef] [PubMed]

]. The normalized power for quasi-TM or quasi-TE mode is evaluated by calculating the overlap integral between the propagating field of the polarization rotator and the guided mode of the input/output waveguide without anisotropic cladding. The conversion efficiency is defined as the ratio of normalized power of converted polarization at the output end to that of input polarization at the input waveguide. The extinction ratio is defined as the ratio of normalized power of converted polarization at the output end to that of the opposite polarization at the output end. The device length (L) is chosen at the position with the maximal conversion efficiency.

The materials which have been obliquely deposited include Al2O3, SiO2, Ta2O5, Ti2O5, and ZrO2 [13

13. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37(13), 2653–2659 (1998). [CrossRef] [PubMed]

]. Thus the usable refractive index range is large. As cladding material is chosen, its optical properties, such as column angle, extraordinary index, and optical anisotropy, can be tuned by varying deposition angle and oxygen flow rate. The features, such as (1) tuning ability of anisotropic optical properties; (2) hybrid mode coupling by anisotropic cladding, make the proposed polarization rotator possess the potential to be extensively applied to various waveguide structures. Polarization rotator can be produced on any kind of waveguide simply by depositing columnar thin film as cladding.

3. Results and discussion

Optical properties of columnar film, such as column angle, extraordinary index, and optical anisotropy (Δn = ne-no), vary with deposition angle [13

13. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37(13), 2653–2659 (1998). [CrossRef] [PubMed]

]. In order to understand the independent effect of the three parameters on the device performance, the influence of the individual parameter is separately considered with the other two parameters’ values fixed. After understanding the influences of the individual parameters, the performance of the polarization rotator with Ta2O5 columnar thin film is investigated. It demonstrates the composite effects of the columnar film parameters on conversion efficiency and device length.

Firstly, the dependence of normalized power for quasi-TE and quasi-TM polarizations on the propagation distance is investigated. Figure 2
Fig. 2 Dependence of normalized power for quasi-TM and quasi-TE polarizations on the propagation distance.
shows the 3D BPM simulated result for the polarization rotator with the parameters t = 1μm, θ = 65°, ne = 1.44, and Δn = 0.04. The optical wavelength is 632.8nm and the incident field is TM-polarized. It is found that the incident optical field produces a complete 90°-polarization rotation from quasi-TM to quasi-TE polarization or from quasi-TE to quasi-TM polarization, at the propagation interval of 3763μm. The conversion efficiency is 99.4% and the extinction ratio is 27.9dB.

Figure 3(a)
Fig. 3 Dependence of conversion efficiency and device length on (a) film thickness; (b) extraordinary index.
shows the effect of film thickness (t) on device characteristics for Δn = 0.02, 0.04, and 0.06, with the parameters ne = 1.49 and θ = 45°. Because the ne is less than the waveguide index, the peak of the propagating field remains in the waveguide and only the evanescent field extends to columnar film. As the film thickness increases, more evanescent field interacts with the columnar film and thus the conversion efficiency increases. As the film thickness is larger than the range of the evanescent field, the conversion efficiency becomes saturated at the value of 95% for each Δn. The required device length initially decreases with the film thickness and approaches a constant as the film thickness becomes larger. The saturated device lengths are 1240μm, 873μm, and 735μm for Δn = 0.02, 0.04, and 0.06. It is noted that the larger the optical anisotropy, the shorter the required device length. Because the film thickness with saturated conversion efficiency is 1μm, the following simulation uses this thickness value. Figure 3(b) shows the effect of extraordinary index (ne) on the device characteristics for Δn = 0.02, 0.04, and 0.06 with the parameters t = 1μm and θ = 45°. It is found that there exists an optimal ne value, which is near the substrate index. For the ne smaller than the optimal one, the conversion efficiency decreases due to insufficient interaction with columnar film. Larger Δn is helpful to enhance the interaction and thus increase the conversion efficiency. As the ne is larger than the substrate index, the field peak moves upward and excites higher-order hybrid modes. This results in reduction and oscillation of conversion efficiency with the ne value. The required device length has the opposite trend to the conversion efficiency.

Figure 4
Fig. 4 Dependence of (a) conversion efficiency; (b) device length; on column angle.
shows the effect of column angle (θ) on conversion efficiency and device length for ne = 1.40~1.54 with the parameters t = 1μm and Δn = 0.04. For each ne, there exists an optimal column angle with maximal conversion efficiency. As the ne increases, the optimal column angle value is reduced. They are 65°, 58°, 53°, 48° for ne = 1.44, 1.46, 1.48, 1.50. Among them, the case with ne = 1.44 has the maximal conversion efficiency (99.4% at θ = 65° and L = 3763μm). It reveals that the appropriate ne value is required to avoid the upward movement of the field peak to the columnar film and to reduce the loss coupled to the output waveguide. Besides, the required device length increases with column angle and has less variation for the larger ne.

Extraordinary index and optical anisotropy of the obliquely deposited film are functions of column angle [13

13. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37(13), 2653–2659 (1998). [CrossRef] [PubMed]

]. Thus the design parameters of polarization rotator are material type, column angle, and film thickness of columnar film. Figure 5
Fig. 5 Dependence of extraordinary index and optical anisotropy on column angle for Ta2O5 columnar film.
shows these properties for Ta2O5 columnar film. As column angle increases, extraordinary index grows and optical anisotropy decreases. It leads to composite behavior in the dependence of conversion efficiency on column angle. Figure 6(a)
Fig. 6 Dependence of conversion efficiency and device length on (a) film thickness; (b) column angle; in the polarization rotator using the Ta2O5 columnar thin film.
shows the effect of film thickness on conversion efficiency and device length in the polarization rotator using the Ta2O5 column film with θ = 45°. It is found that there exist an optimal film thicknesses (t = 0.4μm), which has conversion efficiency of 95.5%. Figure 6(b) shows the effect of column angle on device characteristics for t = 0.3μm and 0.4μm. Since extraordinary index and optical anisotropy vary with column angle, two optimal column angles appear at θ = 45° and 60° with polarization efficiency of 95.5% and 99.0% for t = 0.4μm. The corresponding device lengths are 235μm and 773μm. Variation of film thickness affects the optimal column angle and the corresponding maximal conversion efficiency.

In order to understand the causes which affect conversion efficiency, we compare the evolution of the normalized power and the propagating fields in two polarization rotators using the Ta2O5 columnar film with (θ, t) = (60°, 0.4μm) and (45°, 0.7μm), as shown in Fig. 7
Fig. 7 The evolution of (a) the normalized power; (b) the propagating field at the specified positions; in the polarization rotator with t = 0.4μm, θ = 60°, ne = 1.7423, and Δn = 0.0913.
and Fig. 8
Fig. 8 The evolution of (a) the normalized power; (b) the propagating field at the specified positions; in the polarization rotator with t = 0.7μm, θ = 45°, ne = 1.6458, and Δn = 0.1234.
. For the former, because the addition of columnar film over the waveguide still keeps the waveguide in single mode, no field distortion during the propagation process is observed. Each propagation interval of 773μm produces a complete 90°-polarization rotation, from quasi-TM to quasi-TE polarization or from quasi-TE to quasi-TM polarization. Its conversion efficiency is as high as 99% and the extinction ratio is 25dB. In the second device, because the columnar film is thicker and has a ne value larger than substrate index, several higher-order hybrid modes are excited during the propagation process. It not only affects the effective excitation of fundamental hybrid mode but also reduces the overlap integral due to the upward movement of field peak and the interference of several higher-order hybrid modes.

5. Conclusion

We present a new polarization rotator with obliquely deposited Ta2O5 columnar thin film as cladding. Optical anisotropy with tilt principal axes in the columnar film induces hybrid polarization modes and produces polarization rotation in the waveguide. The effects of column angle, film thickness, extraordinary index, and optical anisotropy, on the device performance are discussed. For effective polarization rotation, film thickness needs to be sufficient to cover most of the evanescent field and at the same time to avoid excitation of higher-order hybrid modes. The required film thickness decreases with the extraordinary index. Besides, column angle is an effective parameter to optimize conversion efficiency. The polarization rotator with the Ta2O5 oblique columnar film of thickness 0.4μm and column angle 60° has a conversion efficiency of 99% and extinction ratio of 25dB. More delicate parameter optimization can further enhance the device performance. The proposed polarization rotator has the features of high conversion efficiency, high extinction ratio, and easy application on various waveguide structures.

Acknowledgments

This work was supported by National Science Council of the Republic of China under grants NSC 97-2221-E-027-009-MY3 and NSC100-2221-E-027-060.

References and links

1.

K. Merterns, B. Scholl, and H. J. Schmitt, “Strong polarization conversion in periodically loaded strip waveguides,” IEEE Photon. Technol. Lett. 10(8), 1133–1135 (1998). [CrossRef]

2.

Z. Huang, R. Scarmozzino, G. Nagy, J. Steel, and R. M. Osgood, “Realization of a compact and single-mode optical passive polarization converter,” IEEE Photon. Technol. Lett. 12(3), 317–319 (2000). [CrossRef]

3.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8(10), 1346–1348 (1996). [CrossRef]

4.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

5.

D. M. H. Leung, B. M. A. Rahman, and K. T. V. Grattan, “Numerical analysis of asymmetric silicon nanowire waveguide as compact polarization rotator,” IEEE Photon. J. 3(3), 381–389 (2011). [CrossRef]

6.

M. C. Oh, S. S. Lee, and S. Y. Shin, “Simulation of polarization converter formed by poling-induced polymer waveguides,” IEEE J. Quantum Electron. 31(9), 1698–1704 (1995). [CrossRef]

7.

A. V. Tsarev, “New compact polarization rotator in anisotropic LiNbO3 graded-index waveguide,” Opt. Express 16(3), 1653–1658 (2008). [CrossRef] [PubMed]

8.

T. Lang, F. Bahnmüller, and P. Benech, “New passive polarization converter on glass substrate,” IEEE Photon. Technol. Lett. 10(9), 1295–1297 (1998). [CrossRef]

9.

T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B 80(2), 193–198 (2005). [CrossRef]

10.

H. Porte, J. P. Goedgebuer, R. Ferriere, and N. Fort, “Integrated TE-TM mode converter on y-cut z-propagating LiNbO3 with an electro-optic phase matching for coherence multiplexing,” IEEE J. Quantum Electron. 25(8), 1760–1762 (1989). [CrossRef]

11.

L. N. Binh, J. Livingstone, and D. H. Steven, “Tunable acousto-optic TE-TM mode converter on a diffused optical waveguide,” Opt. Lett. 5(3), 83–84 (1980). [CrossRef] [PubMed]

12.

P. K. Tien, R. J. Martin, R. Wolfe, R. C. Le craw, and S. L. Blank, “Switching and modulation of light in magneto-optic waveguides of garnet films,” Appl. Phys. Lett. 21(8), 394–396 (1972). [CrossRef]

13.

I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37(13), 2653–2659 (1998). [CrossRef] [PubMed]

14.

M. A. Swillam, D. A. Khalil, and A. H. Morshed, “Effect of the fabrication and design parameters on the performance of multimode interference devices made by ion exchange: a detailed study,” J. Opt. A, Pure Appl. Opt. 10(12), 125301 (2008). [CrossRef]

15.

Q. Wang, G. Farrell, and Y. Semenova, “Modeling liquid-crystal devices with the three-dimensional full-vector beam propagation method,” J. Opt. Soc. Am. A 23(8), 2014–2019 (2006). [CrossRef] [PubMed]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(130.3120) Integrated optics : Integrated optics devices

ToC Category:
Integrated Optics

History
Original Manuscript: November 14, 2011
Revised Manuscript: December 12, 2011
Manuscript Accepted: December 14, 2011
Published: December 22, 2011

Citation
Tzyy-Jiann Wang and Yu-Chen Cheng, "Integrated-optic polarization rotator with obliquely deposited columnar thin film," Opt. Express 20, 601-606 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-601


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References

  1. K. Merterns, B. Scholl, and H. J. Schmitt, “Strong polarization conversion in periodically loaded strip waveguides,” IEEE Photon. Technol. Lett.10(8), 1133–1135 (1998). [CrossRef]
  2. Z. Huang, R. Scarmozzino, G. Nagy, J. Steel, and R. M. Osgood, “Realization of a compact and single-mode optical passive polarization converter,” IEEE Photon. Technol. Lett.12(3), 317–319 (2000). [CrossRef]
  3. C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett.8(10), 1346–1348 (1996). [CrossRef]
  4. J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010). [CrossRef]
  5. D. M. H. Leung, B. M. A. Rahman, and K. T. V. Grattan, “Numerical analysis of asymmetric silicon nanowire waveguide as compact polarization rotator,” IEEE Photon. J.3(3), 381–389 (2011). [CrossRef]
  6. M. C. Oh, S. S. Lee, and S. Y. Shin, “Simulation of polarization converter formed by poling-induced polymer waveguides,” IEEE J. Quantum Electron.31(9), 1698–1704 (1995). [CrossRef]
  7. A. V. Tsarev, “New compact polarization rotator in anisotropic LiNbO3 graded-index waveguide,” Opt. Express16(3), 1653–1658 (2008). [CrossRef] [PubMed]
  8. T. Lang, F. Bahnmüller, and P. Benech, “New passive polarization converter on glass substrate,” IEEE Photon. Technol. Lett.10(9), 1295–1297 (1998). [CrossRef]
  9. T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B80(2), 193–198 (2005). [CrossRef]
  10. H. Porte, J. P. Goedgebuer, R. Ferriere, and N. Fort, “Integrated TE-TM mode converter on y-cut z-propagating LiNbO3 with an electro-optic phase matching for coherence multiplexing,” IEEE J. Quantum Electron.25(8), 1760–1762 (1989). [CrossRef]
  11. L. N. Binh, J. Livingstone, and D. H. Steven, “Tunable acousto-optic TE-TM mode converter on a diffused optical waveguide,” Opt. Lett.5(3), 83–84 (1980). [CrossRef] [PubMed]
  12. P. K. Tien, R. J. Martin, R. Wolfe, R. C. Le craw, and S. L. Blank, “Switching and modulation of light in magneto-optic waveguides of garnet films,” Appl. Phys. Lett.21(8), 394–396 (1972). [CrossRef]
  13. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt.37(13), 2653–2659 (1998). [CrossRef] [PubMed]
  14. M. A. Swillam, D. A. Khalil, and A. H. Morshed, “Effect of the fabrication and design parameters on the performance of multimode interference devices made by ion exchange: a detailed study,” J. Opt. A, Pure Appl. Opt.10(12), 125301 (2008). [CrossRef]
  15. Q. Wang, G. Farrell, and Y. Semenova, “Modeling liquid-crystal devices with the three-dimensional full-vector beam propagation method,” J. Opt. Soc. Am. A23(8), 2014–2019 (2006). [CrossRef] [PubMed]

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