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Optical Design of Waveguides for Operation in the Visible and Infrared Mustafa Yorulmaz Bilkent University, Physics Department May 25, 2007 Bilkent University, Physics Department 1 Outline Waveguide theory Simulation Methodology State-of-the-art of rib-waveguides Our rib-waveguide designs State-of-the art of slot-waveguides Our slot-waveguide design Achievements May 25, 2007 Bilkent University, Physics Department 2 Planar mirror waveguides Wave-fronts and raypaths The picture shows the wave-fronts in addition to the ray model. In order to have constructive interference, the twice reflected wave must be in phase with the incident wave: 2AC / 2 2AB / 2q q 0,1,2,... The angle of inclination is discrete, only AC AB 2d sin sin m m May 25, 2007 2d m 1,2,.. a limited number of angles are permitted for constructive interference. Bilkent University, Physics Department 3 The number of modes of a waveguide is limited It is derived that the angle of inclination is discrete: sin m m 2d since sin m 1 M 2d / The total number of modes is M, which is a function of waveguide thickness and the wavelength. If 2d/λ<1 no modes available thus λmax=2d or fmin=c/2d (cut-off frequency). If M=1, i.e. 1<2d/λ<2 then the wave guide is called single-mode Example: If d=0.5μ, the cut-off wavelength is 1μ. The waveguide is singlemode for wavelengths down to 0.5μ, and multi-mode for lower wavelength operations. May 25, 2007 Bilkent University, Physics Department 4 Planar Dielectric Waveguides Field distributions for TE guided modes in a dielectric waveguide. The condition for total internal reflection: cos1 (n2 / n1 ) The condition for constructive interference: 2 2d sin 2 r 2m May 25, 2007 Bilkent University, Physics Department 5 Optical coupling Light propagates in a waveguide in the form of modes, the complex amplitude of the Electric field is the superposition of these modes: E( y, z) amum ( y) exp( j m z) m αm is amplitude, um(y) is transverse distribution The amplitude of different modes depend on the light source used to “excite” the waveguide. If the source has a distribution that matches perfectly that of a specific mode, only that mode is excited. A source of arbitrary distribution excites different modes by different amounts. l s( y)u ( y)dy l The amplitude of the lth mode is found by the overlap integral of the lth mode and the light distributions s(y) May 25, 2007 Bilkent University, Physics Department 6 Simulation methodology The geometrical structure and the piecewise constant n(x,y) profile, makes analytical solutions of field distributions very difficult. Numerical methods provide reliable approximate solutions. Rib waveguide Finite Difference Method: the structure is divided into cells so that inside the cell the refractive index is constant. The differential operator is replaced by: f ' ( x) May 25, 2007 Bilkent University, Physics Department f ( x x) f ( x) x 7 Simulation program Waveguide Mode Solver by Hilmi Volkan Demir and Vijit Sabnis Finite difference method (FDM) Solving the polarised solutions of the wave equation. Geometry of rib-waveguide structure Cell structure of finite difference scheme Inputs and outputs of the simulation program May 25, 2007 Bilkent University, Physics Department 8 Structure of their design and our simulation results to their structure Rib-waveguide structure presented in * Layer Thickness (nm) Air 3000 Gan 3000 Al0.088Ga0.912N 4000 Sapphire 6000 Rib-Width 3000 Side-Width 5000 Rib-Height 2800 -Single mode -Power coupling efficiency is 0.81 Parameters of rib-waveguide structure presented in * -Active region overlap integral is 0.99 -It lacks of MQWs Our simulation result to the structure presented in * * R. Hui, Y. Wan, J. Li, S. X. Jin, J. Y. Lin, and H. X. Jiang, “III-nitride-based planar lightwave circuits for long wavelength optical communications,” IEEE J. Quantum Electron. 41, 100-110 (2005). May 25, 2007 Bilkent University, Physics Department 9 Structure of their design and our simulation results to their structure Rib-waveguide structure presented in ** Our simulation result to the structure presented in ** Layer Thickness (nm) Loop Air 1000 Al20Ga80N 20 Al20Ga80N 5 GaN 2.4 30 Al20Ga80N 20 30 GaN 1000 GaN 30 Sapphire 1000 Rib-Width 500 Side-Width 5000 Rib-Height 750 -It has MQWs -E-field distribution doesn’t project on active layer -It has a rib-widht smaller than 1um -Power coupling efficiency is 0.6 -Active region overlap integral is 0.001 Parameters of rib-waveguide structure presented in ** ** T. N. Oder, J. Y. Lin and H. X. Jiang, “Propagation Properties of Light in AlGaN/GaN Quantum Well Waveguides.” Appl. Phy. Lett. 79, 2511 (2001). May 25, 2007 Bilkent University, Physics Department 10 Challenges for Design Rib-width > 1mm for fabrication Single mode Having MQWs Circular mode profile Material overlap integral Coupling Efficiency May 25, 2007 Bilkent University, Physics Department 11 Our design @1550nm Layer Thickness (nm) Loop Air 1000 GaN 1200 AlN (barrier) 1.2 1 GaN (well) 1.4 10 AlN (barrier) 1.2 10 GaN 50 AlN (barrier) 1.2 1 GaN (well) 1.4 10 AlN (barrier) 1.2 10 GaN 50 -MQWs are designed as ten periods of AlN(1.2nm)/GaN(1.4nm) layers. AlN (barrier) 1.2 1 -The rib has a width of 2.5µm GaN (well) 1.4 10 AlN (barrier) 1.2 10 GaN 300 GaN 760 Sapphire 1000 Rib-Width 2500 Side-Width 5000 Our rib-waveguide design structure for IR region, -Rib-width is 2.5 um > 1um -Single mode operation -Made of MWQs -Circular mode profile Rib-Height 1531.6 Parameters of our rib-waveguide structure for IR region May 25, 2007 E-field distribution of this structure -Power coupling efficiency is 0.078 -Active region overlap integral is 0.05 Bilkent University, Physics Department 12 Our design @440nm Layer Thickness (nm) Air 1000 GaN 1240 Al10Ga90N 10 GaN (barrier) 4 1 In35Ga65N (well) 4 5 GaN (barrier) 4 5 In35Ga65N 50 GaN (barrier) 4 1 In35Ga65N (well) 4 5 GaN (barrier) 4 5 In35Ga65N 50 GaN (barrier) 4 1 In35Ga65N (well) 4 5 GaN (barrier) 4 5 GaN 300 GaN 560 Sapphire 1000 Rib-Width 1500 Side-Width 5000 Rib-Height 1632 Loop Our rib-waveguide design structure for IR region, E-field distribution of this structure -MQWs are designed as five periods of In35Ga65N(4nm)/GaN(4nm) layers. -Rib-width is 1.5 um > 1um -Single mode operation -Made of MWQs -Circular mode profile -Power coupling efficiency is 0.074 -Active region overlap integral is 0.13 Parameters of our rib-waveguide structure for IR region May 25, 2007 Bilkent University, Physics Department 13 Achievements with our rib-waveguide designs Having MQWs Satisfying single mode operation Rib width > 1mm (@440nm and @1550nm) Power coupling ~ 0.7-0.8 (@440nm and @1550nm) Material Overlap > 0.1 (@440nm) May 25, 2007 Bilkent University, Physics Department 14 New type of waveguide design: Slot-waveguide Different way for confining and enhancing light: Guiding light in lowindex materials According to the Maxwell’s laws that the electric field must undergo a large discontinuity with much higher amplitude in the low index side to satisfy the continuity of the normal component of electric flux density for a high-index-contrast interface. So that, this discontinuity is used to strongly enhance and confine light in a nanometer-wide region of low index material Parameters •nc •ns •nh •wh •ws •h Geometry of slot-waveguide structure presented *** *** V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209 (2004) . [ISI] . May 25, 2007 Bilkent University, Physics Department 15 Verification of paper for slot-waveguide design nc 1.44 ns 1.44 nh 3.48 wh 180nm ws 50nm h 300nm The contours of E-field amplitude and Efield lines that are shown in***. 3D surface plot of E-field amplitudes presented in *** Our simulation results to the structure presented in *** Parameters and geometry of slot-waveguide structure presented in *** -In this study, we confirm the result of paper [***] and we also calculate power coupling efficiency and active region overlap integral of their structure. They are 0.63 and 0.65 respectively. *** V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209 (2004) . [ISI] . May 25, 2007 Bilkent University, Physics Department 16 Our-slot waveguide design for operation @ 1550nm nc 1 ns 1 nh 2.031 wh 400nm ws 50nm h 400nm -We obtained our slot-waveguide-design made of AlN -Single-mode operation -At nano-meter scale -Important for future integration of waveguides in optoelectronic and photonic devices -Power coupling efficiency is 0.8 and active region overlap integral is 0.48 of this slotwaveguide May 25, 2007 Bilkent University, Physics Department 17 Thanks.. Questions? May 25, 2007 Bilkent University, Physics Department 18