1. Coherently Coupled Optical Waveguide 報 告 者 ：陳 嘉 怜 指導教授：王 維 新 博 士

2. 2  Introduction  Paper Review  Principle of Operation  Experiences and Results  Summery  References Outline

3. 3 Introduction Motivation: Optical bending waveguide are used to change the direction of light propagation in many integrated optical devices such as MZ and directional couplers. In order to reduce the device area and increase the packing density, we must to find bend structures with large bend angles and low loss. Structure: Curved optical waveguide; Conventional bend waveguide; Etched-wall bend waveguide; Coupler bend waveguide; Prism waveguide. Principle of coupler bend waveguide: Coupled-bend transmission can be an oscillatory function of the interconnection length L due to interference between the guided and radiation modes. Material: Ti ; Ni ; Zn and Ni

4. 4  Introduction  Paper Review  Principle of Operation  Experiences and Results  Summery  References

5. 5 Conventional Bend Waveguide P 0 : output power P i : input power  0 : radiation and absorb parameter L o : distance of optical beam propagating in waveguide T: power combine parameter( )  < 2º z x n2n2 n1n1 n1n1 PiPi P0P0

6. 6 Etched-wall Bend Waveguide Advantage: power loss is lower than convention bend waveguide. Disadvantage: As  larger than 2 0, power loss will be higher and make this bending waveguide not to have the ability of light propagation.  z x n2n2 n1n1 n1n1 P0P0 PiPi  /2 Wave front in the part is speeded up to make bending easier and reduce the power loss.

7. 7 Coupler Bend Waveguide Advantage: power loss is lower with suitable coherent length.  z x n2n2 n1n1 n1n1 P0P0 PiPi  /2 d Wave front in the part is speeded down to make bending easier and reduce the power loss. Wave front in the part is speeded up to make bending easier and reduce the power loss.

8. 8  Introduction  Paper Review  Principle of Operation  Experiences and Results  Summery  References

9. 9 Principle of Coherent Coupler I L   X2X2 Z2Z2 X3X3 Z3Z3 W Electric field: Propagation constant: 1 2 3 Guided modeRadiation mode

10. 10 Principle of Coherent Coupler II Electric Field parameter: Waveguide 1: Waveguide 2: Waveguide 3: Electric field: L 1 2 3

11. 11 Principle of Coherent Coupler III Guided-mode transmission equation: The equation shows that the coupled-bend transmission can be an oscillatory function of the interconnection length L due to interference between the guided and radiation modes. Electric field: Guided modeRadiation mode L 1 2 3

12. 12 Principle of Coherent Coupler V Interconnection Length L: N eff : guided-mode effective index N effR :weighted-average effective index of the radiation modes excited after the first bend. If the phase difference between the modes shifts is: light coupled from the guided mode into an unguided mode at a bend can be completely coupled back into the guided mode at a succeeding bend. L 1 2 3

13. 13 Principle of Coherent Coupler VI INTERCONNECTING-SEGMENT LENGTH. L(um) GUIDE-MODE TRANSMISSION PHASE FRONTS L=180  m L=380  m L 1 2 3

14. 14  Introduction  Paper Review  Principle of Operation  Experiences and Results  Summery  References

15. 15 Coherently Coupler Bend Θ 2Θ L 4mm L SECTION LENGTH, L(  m ) ( Relative Transmission) 1/2

16. 16 Coherently Coupler Bend Θ L 4mm 2Θ 3Θ L NUMBER OF SECTIONS ( N ) ( Relative Transmission) 1/2 N = 2

17. 17 Coherently Coupler Bend Θ 2Θ 3Θ 4Θ Phase rocking region Θ 3Θ 4Θ Phase rocking region (a)standard structure (b)new structure

18. 18 Transmitted Power with Total Bending Angle

19. 19 Transmitted Power with Launching Wavelength

20. 20 Summery The transmission function of the coupler bend waveguide depends on the interference of guided mode and radiation mode in the interconnection length L. We study the principle of coupler bend waveguide which is better than conventional bend and etched-wall bend waveguide in being a suitable bending structure with large bend angles and low loss. Other new structures include prism and new structure couple bend waveguide.

21. 21 References L. M. Johnson and F. J. Leonberger, “Low-loss LiNbO3 waveguide bends with coherent coupling,” Optics Letters, Vol. 8, No. 2, Feb. 1983.” L. M. Johnson and D. Yap, “Theoretical analysis of coherently coupled optical waveguide bends,” Applied Optics, Vol. 23, No.17, 1 Sep.1984. 張文清, “An Investigation of integrated optical waveguide bends, ” 蘇振嘉, “Coherent-coupling-based wide-angle bending optical waveguide design and fabrication, ”