2d photonic crystals based on vertical cavity surface emitting lasers vcsels arrays
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2D- Photonic Crystals based on Vertical Cavity Surface Emitting Lasers (VCSELs) arrays PowerPoint PPT Presentation


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2D- Photonic Crystals based on Vertical Cavity Surface Emitting Lasers (VCSELs) arrays. Presentation for the Photonic Crystal Course, June 2009. Elodie Lamothe Ing. Microtechn . Dipl. EPF PhD . Student in Photonic School LPN EPF Lausanne. Plan of the Presentation. Introduction

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2D- Photonic Crystals based on Vertical Cavity Surface Emitting Lasers (VCSELs) arrays

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2d photonic crystals based on vertical cavity surface emitting lasers vcsels arrays

2D-Photonic Crystals based on Vertical Cavity Surface Emitting Lasers (VCSELs) arrays

  • Presentation for the Photonic Crystal Course, June 2009

ElodieLamothe

Ing. Microtechn. Dipl. EPF

PhD. Student in Photonic School

LPN EPF Lausanne


Plan of the presentation

Plan of the Presentation

  • Introduction

    • Vertical Cavity Surface Emitting Laser (VCSEL)

    • Photonic crystal based on VCSEL

  • Modellisation of VCSELs-array

    • Formalism of coupled mode theory

    • Fabry-Perot cavity model

    • Equivalent 3D photonic crystal model

  • Optical Properties

    • Homogeneous structures

    • Heterostructure and mode confinement

    • Coupling between two confine modes

  • Conclusion

  • Plan of the Presentation


    Introduction

    Introduction

    Plan of the Presentation

    Introduction


    Vcsel description

    VCSEL Description

    p-contact

    hole

    p-DBR (AlGaAs/GaAs)

    active region(InGaAs)

    n-DBR(AlGaAs/GaAs)

    electron

    n-contact

    • Two Distributited Bragg Reflectors (DBR) define the cavity

    • Light is amplified by stimulated emission in the active region

    • Emission of the ligth through the lower DBR (n-DBR)

    Plan of the Presentation

    Introduction


    Photonic crystals based on vcsel

    Photonic Crystals based on VCSEL

    • Photonic crystals are obtained by modulatingthe reflectivity of the top DBR reflector: => RAu>RCr

    • p-contact

    • 2D-Photonic crystal

    • Active Photonic crystal

    • Au

    • Cr

    • Such structures incoporate gain and losses

    • Optical Bloch waves are stimulated at each lattice site

    • Optical coupling

    • n-contact

    • Optical coupling between adjacent microcavities via diffraction of the optical field at the edges of the pixels

    • Au

    • Cr

    • H. Pier and al., Nature (London), 407,880-883, 2000

    Plan of the Presentation

    Introduction


    Condition on the wavelength

    Condition on the wavelength

    • Usual photonic crystals

    • Photonic crystal based on VCSELs

    • Condition

    • Bragg condition

    • Photoniccrystalbased on VCSEL have lattice constants significantlyexceeding the opticalwavelength.

    • Only the transversal component of the wavevectorundergoes Bragg condition

    • |kp| << |kz|

    Plan of the Presentation

    Introduction


    Modellisation

    Modellisation

    Introduction

    Modellisation


    Couple mode theory cmt

    Couple Mode Theory (CMT)

    • 1) Consider an isolated waveguide (WG)

    • propagation constant

    • 2) Electric field distribution is obtained by solving Helmolz equation for each WG

    • => Set of orthogonal eigenmodes

    • 3) Each solitary WG is placed in a periodic lattice

    • => slight perturbation of the fields at the WG

    • => weak coupling between adjacent WGs

    • Total field :

    • SUPERMODE = superposition of the separated orthogonal WG modes

    Introduction

    Modellisation


    Cmt applied to 3x3 homogeneous array

    CMT applied to 3x3 homogeneousarray

    • Near fields Amplitude

    • Far fields Intensities

    • Out-of-phase mode

    • Limited far field

    • pattern

    • In-phase mode

    Introduction

    Modellisation


    Fabry perot cavity approach

    Fabry-Perot cavity approach

    • Replace the bottom DBR and the top DBR by mirrors with modulated reflection

    • 2)Consider the VCSELs-array as a Fabry-Perot cavity with an effective length Leff

    • Cavity description by Rayleight-Sommerfeld diffraction integral

    • Rayleight-Sommerfeld integral is solved iteratively by numerical computation.

    • A. E. Siegman, Lasers, University Science, Mil Valley, CA, 1986

    Introduction

    Modellisation


    Equivalent 3d photonic crystal 1

    Equivalent 3D-Photonic Crystal (1)

    • 1) VCSEL cavity is unfolded => an effective 2L-periodicity along z-axis is induced.

    • 2) The reflections at the DBR are replaced by thin equivalent layers

    • 3) The resulting 3D-PhC is analyzed using Orthogonal Plane Wave expansion method

    • G. Guerrero, PhD Thesis, Thèse N°2837, EPFL, Lausanne, Switzerland, 2003

    • D. L. Boiko and al., Opt. Express,12, 2597-2602, 2004

    Introduction

    Modellisation


    Equivalent 3d photonic crystal 2

    Equivalent 3D-Photonic Crystal (2)

    Brillouin zone of the

    equivalent 3D photonic crystal

    • Model of the VCSEL-based photonic crystal

    • T

    • Z

    • Master Equation

    • 2D-Hamiltonien eigenvalue problem in transversal plan

    • paraxial approximation

    • small reflectivity modulation

    • G. Guerrero, PhD Thesis, Thèse N°2837, EPFL, Lausanne, Switzerland, 2003

    • D. L. Boiko and al., Opt. Express,12, 2597-2602, 2004

    Introduction

    Modellisation


    Band diagram

    Band Diagram

    • Parameters

    • Photon energy

    • Mode Losses

    Imaginary part of the eigenvalue

    Real part of the eigenvalue

    => No Bandgap for photon energy

    => Bandgap in terms of losses

    Lowest loss mode T5

    • Bloch theorem

    Phase difference between complex reflection coeffecient Au and Cr

    out-of-phase relationshipbetween adjacent lattice site

    • L.D.A. Lundeberg and al., IEEE J. Top. Quant. Elec., 13,5, 2007

    Introduction

    Modellisation


    Lowest loss mode simulations of the optical field

    Lowest Loss Mode:Simulations of the Optical Field

    • Near Field

    • Geometrical Model

    • Numerical Solution of Master Equation

    • Amplitude

    • Phase

    • Far Field

    • pi phase shift between adjacent VCSELs

    • Frauhenofer

    • diffraction

    • out-of-phase coupling between VCSELs

    • L.D.A. Lundeberg, Thèse N°3911, EPFL, Lausanne, Switzerland

    Introduction

    Modellisation


    Optical properties

    Optical Properties

    Modellisation

    Optical Properties


    Homogeneous structures

    Homogeneous Structures

    • Near Field Patterns

    • Far Field Patterns

    • Stimulated

    • Emission

    • Stimulated

    • Emission

    • Spontaneous

    • Emission

    • 4 lobes

    • out-of-phase

    • lasing mode

    • H. Pier and al., Nature (London), 407,880-883, 2000

    Modellisation

    Optical Properties


    Modes confinement

    Modes Confinement

    • Confinement Structure

    • Mode confinement can be achieved by creating photonic crystal heterostructure

    • Domain with lower fill factor FF presents higher loss

    • Rectangular shape PhC island with higher FF in a sea of lower FF material confines supermodes

    • Numerical Calculation

    • Measurement

    • out-of-phase relationship between adjacent VCSEL elements is maintain

    • L.D.A. Lundeberg and al., App. Phys. Lett.,87, 241120, 2005

    • L.D.A. Lundeberg and al., IEEE J. Top. Quant. Elec., 13,5, 2007

    Modellisation

    Optical Properties


    Coupled islands

    CoupledIslands

    • Structure

    • Numerical Analysis

    • Near Field

    • Far Field

    • FFisland = 0.694

    • FFsea= 0.25

    • λ=960nm

    • Λ=6μm

    |B>

    |A>

    • Far field intensity distribution of one principal lobe along θx

    • Coupling between two islands

    • Bonding state |B>

    • Anti-bonding state |A>

    • L.D.A. Lundeberg and al., App. Phys. Lett.,87, 241120, 2005

    Modellisation

    Optical Properties


    Coupled islands1

    CoupledIslands

    • Measurement

    • Modal loss considerations

    • Bloch part of the wave function gives an out-of-phase relationship between adjacent pixels:

    Bright fringe in the centre of the lobes

    => Bonding state |B> is lasing

    • |B> : This phase relationship is maintained => lowest loss

    • |A>: This phase relationship is altered => higher loss

    • L.D.A. Lundeberg and al., App. Phys. Lett.,87, 241120, 2005

    Modellisation

    Optical Properties


    Conclusion

    Conclusion

    • 2D-Photonic Crystal can be realized using VCSEL-array

    • The lasing supermode predicted by simulation and experiments presents an out-of-phase relationship between each pixel

    • Well designed heterostructures can confine the supermode

    • A coupling between two confined supermodes can be achieved

    • => This coupling results in a bonding state.

    Optical Properties

    Conclusion


    Questions

    Questions

    Thankyou for your attention

    Questions

    Conclusion


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