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May 25, 2007Bilkent University, Physics Department1 Optical Design of Waveguides for Operation in the Visible and Infrared Mustafa Yorulmaz Bilkent University, Physics Department

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May 25, 2007 Bilkent University, Physics Department 2 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

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May 25, 2007 Bilkent University, Physics Department 3 Planar mirror waveguides 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: The angle of inclination is discrete, only a limited number of angles are permitted for constructive interference. Wave-fronts and raypaths

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May 25, 2007 Bilkent University, Physics Department 4 The number of modes of a waveguide is limited It is derived that the angle of inclination is discrete: since 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 λ max =2d or f min =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 single- mode for wavelengths down to 0.5μ, and multi-mode for lower wavelength operations.

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May 25, 2007 Bilkent University, Physics Department 5 Planar Dielectric Waveguides The condition for total internal reflection: The condition for constructive interference: Field distributions for TE guided modes in a dielectric waveguide.

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May 25, 2007 Bilkent University, Physics Department 6 Optical coupling 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. Light propagates in a waveguide in the form of modes, the complex amplitude of the Electric field is the superposition of these modes: α m is amplitude, u m (y) is transverse distribution The amplitude of the l th mode is found by the overlap integral of the l th mode and the light distributions s(y)

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May 25, 2007 Bilkent University, Physics Department 7 Simulation methodology Rib waveguide 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. 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:

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May 25, 2007 Bilkent University, Physics Department 8 Simulation program Waveguide Mode Solver by Hilmi Volkan Demir and Vijit Sabnis Finite difference method (FDM) Solving the polarised solutions of the wave equation. Cell structure of finite difference schemeGeometry of rib-waveguide structure Inputs and outputs of the simulation program

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May 25, 2007 Bilkent University, Physics Department 9 Structure of their design and our simulation results to their structure LayerThickness (nm) Air3000 Gan3000 Al0.088Ga0.912N4000 Sapphire6000 Rib-Width3000 Side-Width5000 Rib-Height2800 -Single mode -Power coupling efficiency is 0.81 -Active region overlap integral is 0.99 -It lacks of MQWs Rib-waveguide structure presented in * Parameters of rib-waveguide structure presented in * 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).

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May 25, 2007 Bilkent University, Physics Department 10 Structure of their design and our simulation results to their structure LayerThickness (nm)Loop Air1000 Al20Ga80N20 Al20Ga80N5 GaN2.430 Al20Ga80N2030 GaN1000 GaN30 Sapphire1000 Rib-Width500 Side-Width5000 Rib-Height750 -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 Rib-waveguide structure presented in ** Parameters of rib-waveguide structure presented in ** Our simulation result to the 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).

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May 25, 2007 Bilkent University, Physics Department 11 Challenges for Design Rib-width > 1 m for fabrication Single mode Having MQWs Circular mode profile Material overlap integral Coupling Efficiency

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May 25, 2007 Bilkent University, Physics Department 12 Our design @1550nm LayerThickness (nm)Loop Air1000 GaN1200 AlN (barrier)1.21 GaN (well)1.410 AlN (barrier)1.210 GaN50 AlN (barrier)1.21 GaN (well)1.410 AlN (barrier)1.210 GaN50 AlN (barrier)1.21 GaN (well)1.410 AlN (barrier)1.210 GaN300 GaN760 Sapphire1000 Rib-Width2500 Side-Width5000 Rib-Height1531.6 -MQWs are designed as ten periods of AlN(1.2nm)/GaN(1.4nm) layers. -The rib has a width of 2.5µm -Rib-width is 2.5 um > 1um -Single mode operation -Made of MWQs -Circular mode profile -Power coupling efficiency is 0.078 -Active region overlap integral is 0.05 Parameters of our rib-waveguide structure for IR region Our rib-waveguide design structure for IR region,E-field distribution of this structure

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May 25, 2007 Bilkent University, Physics Department 13 Our design @440nm LayerThickness (nm) Loop Air1000 GaN1240 Al10Ga90N10 GaN (barrier)4 1 In35Ga65N (well)4 5 GaN (barrier)4 5 In35Ga65N50 GaN (barrier)4 1 In35Ga65N (well)4 5 GaN (barrier)4 5 In35Ga65N50 GaN (barrier)4 1 In35Ga65N (well)4 5 GaN (barrier)4 5 GaN300 GaN560 Sapphire1000 Rib-Width1500 Side-Width5000 Rib-Height1632 -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 Our rib-waveguide design structure for IR region,E-field distribution of this structure Parameters of our rib-waveguide structure for IR region

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May 25, 2007 Bilkent University, Physics Department 14 Achievements with our rib-waveguide designs Having MQWs Satisfying single mode operation Rib width > 1 m (@440nm and @1550nm) Power coupling ~ 0.7-0.8 (@440nm and @1550nm) Material Overlap > 0.1 (@440nm)

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May 25, 2007 Bilkent University, Physics Department 15 New type of waveguide design: Slot-waveguide Different way for confining and enhancing light: Guiding light in low- index 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].

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May 25, 2007 Bilkent University, Physics Department 16 Verification of paper for slot-waveguide design nc1.44 ns1.44 nh3.48 wh180nm ws50nm h300nm Parameters and geometry of slot-waveguide structure presented in *** The contours of E-field amplitude and E- field lines that are shown in***. 3D surface plot of E-field amplitudes presented in *** *** V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209 (2004). [ISI]. Our simulation results to the 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.

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May 25, 2007 Bilkent University, Physics Department 17 Our-slot waveguide design for operation @ 1550nm nc1 ns1 nh2.031 wh400nm ws50nm h400nm -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 slot- waveguide

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May 25, 2007 Bilkent University, Physics Department 18 Thanks.. Questions?

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