Laser Beam Propagation in Nonlinear Optical Media

Laser Beam Propagation in Nonlinear Optical Media

by Shekhar Guha
Released December 2017
Publisher(s): CRC Press
ISBN: 9781351832953

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Book description

"This is very unique and promises to be an extremely useful guide to a host of workers in the field. They have given a generalized presentation likely to cover most if not all situations to be encountered in the laboratory, yet also highlight several specific examples that clearly illustrate the methods. They have provided an admirable contribution to the community. If someone makes their living by designing lasers, optical parametric oscillators or other devices employing nonlinear crystals, or designing experiments incorporating laser beam propagation through linear or nonlinear media, then this book will be a welcome addition to their bookshelf."
—Richard Sutherland, Mount Vernon Nazarene University, Ohio, USA

Laser Beam Propagation in Nonlinear Optical Media provides a collection of expressions, equations, formulas, and derivations used in calculating laser beam propagation through linear and nonlinear media which are useful for predicting experimental results.

The authors address light propagation in anisotropic media, oscillation directions of the electric field and displacement vectors, the walk-off angles between the Poynting and propagation vectors, and effective values of the d coefficient for biaxial, uniaxial, and isotropic crystals.

They delve into solutions of the coupled three wave mixing equations for various nonlinear optical processes, including quasi-phase matching and optical parametric oscillation, and discuss focusing effects and numerical techniques used for beam propagation analysis in nonlinear media, and phase retrieval technique. The book also includes examples of MATLAB and FORTRAN computer programs for numerical evaluations.

An ideal resource for students taking graduate level courses in nonlinear optics, Laser Beam Propagation in Nonlinear Optical Media can also be used as a reference for practicing professionals.

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. List of Figures
  8. List of Tables
  9. Preface
  10. Author Biographies
  11. Acknowledgements
  12. 1 Light Propagation in Anisotropic Crystals
    1. 1.1 Introduction
    2. 1.2 Vectors Associated With Light Propagation
      1. 1.2.1 Plane waves
      2. 1.2.2 Non-plane waves
    3. 1.3 Anisotropic Media
      1. 1.3.1 The principal coordinate axes
      2. 1.3.2 Three crystal classes
      3. 1.3.3 The principal refractive indices
    4. 1.4 Light Propagation In An Anisotropic Crystal
      1. 1.4.1 Allowed directions of D and E in an anisotropic medium
      2. 1.4.2 Values of n for a given propagation direction
      3. 1.4.3 Directions of D and E for the slow and fast waves
    5. 1.5 Characteristics Of The Slow And The Fast Waves In A Biaxial Crystal
      1. 1.5.1 ns and nf
      2. 1.5.2 ρs and ρf
      3. 1.5.3 The components of ds and df
      4. 1.5.4 The components of ês and êf
    6. 1.6 Double Refraction And Optic Axes
      1. 1.6.1 Expressions for components of d in terms of the angles θ, ϕ and Q
      2. 1.6.2 Relating the angle δ to Ω, θ and ϕ
      3. 1.6.3 Directions of E and S
      4. 1.6.4 The walk-off angles ρs and ρf
      5. 1.6.5 An interim summary
    7. 1.7 Propagation Along The Principal Axes And Along The Principal Planes
      1. 1.7.1 Introduction
      2. 1.7.2 Propagation along the principal axes X, Y and Z
      3. 1.7.3 Propagation along the principal plane YZ
      4. 1.7.4 k along YZ plane, Case 1: nX < nY < nZ
      5. 1.7.5 k along YZ plane, Case 2: nX > nY > nZ
      6. 1.7.6 Propagation along the principal plane ZX
      7. 1.7.7 k along ZX plane, Case 1a: nX < nY < nZ, θ < Ω
      8. 1.7.8 k along ZX plane, Case 1b: nX < nY < nZ, θ > Ω
      9. 1.7.9 k along ZX plane, Case 2a: nX > nY > nZ, θ < Ω
      10. 1.7.10 k along ZX plane, Case 2b: nX > nY > nZ, θ > Ω
      11. 1.7.11 Propagation along the principal plane XY
      12. 1.7.12 k along XY plane, Case 1: nX < nY < nZ
      13. 1.7.13 k along XY plane, Case 2: nX > nY > nZ
      14. 1.7.14 Summary of the cases of propagation along principal planes
    8. 1.8 Uniaxial Crystals
      1. 1.8.1 Field directions of the D and E vectors for extraordinary and ordinary waves
      2. 1.8.2 ρ ≠ 0 Case (extraordinary wave)
      3. 1.8.3 Another expression relating ρ and θ
      4. 1.8.4 ρ = 0 Case (ordinary wave)
      5. 1.8.5 Two special cases: θ = 0 and θ = 90°
    9. 1.9 Propagation Equation In Presence Of Walk-off
      1. 1.9.1 Transformation between laboratory and crystal coordinate systems
      2. 1.9.2 The propagation equation in presence of walk-off
    10. Bibliography
  13. 2 Nonlinear Optical Processes
    1. 2.1 Introduction
    2. 2.2 Second Order Susceptibility
    3. 2.3 Properties of χ(2)
      1. 2.3.1 Properties of χ(2) away from resonance
      2. 2.3.2 Kleinman’s symmetry
    4. 2.4 d coefficients and the contracted notation
      1. 2.4.1 d coefficients under Kleinman symmetry
    5. 2.5 The Non-Zero d Coefficients Of Biaxial Crystals
    6. 2.6 The Non-Zero d Coefficients Of Uniaxial Crystals
    7. 2.7 Nonlinear polarizations
      1. 2.7.1 Nondegenerate sum frequency generation
      2. 2.7.2 Difference frequency generation
      3. 2.7.3 Second harmonic generation (SHG)
      4. 2.7.4 Optical rectification
      5. 2.7.5 Convention used for numbering the three interacting beams of light
      6. 2.7.6 Summary of polarization components for non-degenerate three wave mixing
      7. 2.7.7 Summary of polarization components for degenerate three wave mixing (SHG and degenerate parametric mixing)
    8. 2.8 Frequency Conversion And Phase Matching
      1. 2.8.1 Phase matching in birefringent crystals
      2. 2.8.2 Calculation of phase matching angles
    9. 2.9 Walk-Off Angles
      1. 2.9.1 Calculation of walk-off angles in the phase matched case in KTP
    10. Bibliography
  14. 3 Effective d coefficient for Three-Wave mixing Processes
    1. 3.1 Introduction
      1. 3.1.1 Definition of deff
      2. 3.1.2 Effective nonlinearity for nondegenerate three wave mixing processes
      3. 3.1.3 Effective nonlinearity for the degenerate three wave mixing process
      4. 3.1.4 Type I degenerate three wave mixing process
      5. 3.1.5 Type II degenerate three wave mixing process
    2. 3.2 Expressions for deff
      1. 3.2.1 deff of biaxial crystals under Kleinman Symmetry Condition
      2. 3.2.2 Reduction of deff to expressions in the literature
    3. 3.3 deff Values for Some Biaxial and Uniaxial Crystals of Different Classes
      1. 3.3.1 deff for KTP for propagation in a general direction
        1. 3.3.1.1 deff for KTP for a Type I (ssf) mixing process
        2. 3.3.1.2 deff for KTP for a Type II(sff) mixing process
        3. 3.3.1.3 deff for KTP for a Type II(fsf) mixing process
      2. 3.3.2 deff for KTP for propagation along principal planes
    4. 3.4 deff for Uniaxial Crystals
    5. 3.5 deff for Isotropic Crystals
      1. 3.5.1 The direction of the nonlinear polarization
      2. 3.5.2 Propagation along principal planes
      3. 3.5.3 Propagation through orientation patterned material
    6. Bibliography
  15. 4 Nonlinear Propagation Equations and Solutions
    1. 4.1 Nonlinear Propagation Equations
      1. 4.1.1 Normalized form of the three wave mixing equations
    2. 4.2 Solutions To The Three Wave Mixing Equations In The Absence Of Diffraction, Beam Walk-off And Absorption
      1. 4.2.1 An interlude - the Manley-Rowe relations
      2. 4.2.2 Back to solutions of the three wave mixing equations
      3. 4.2.3 Another interlude - Jacobian elliptic functions
      4. 4.2.4 Return to the solution of the coupled three wave mixing equations
    3. 4.3 Unseeded Sum Frequency Generation (ω1 + ω2 = ω3)
      1. 4.3.1 SFG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion
      2. 4.3.2 SFG irradiance for collimated beams with phase matching (σ = 0) and with pump depletion
      3. 4.3.3 SFG power and energy conversion efficiency for collimated beams with arbitrary spatial and temporal shapes
      4. 4.3.4 SFG power and energy conversion efficiency for collimated Gaussian beams
      5. 4.3.5 SFG power and energy conversion efficiency for collimated Gaussian beams with phase mismatch (σ ≠ 0) and no pump depletion
      6. 4.3.6 Some results of SFG power and energy conversion efficiency for collimated Gaussian beams
      7. 4.3.7 SFG conversion efficiency for focused Gaussian beams
      8. 4.3.8 Optimization of focusing parameters for SFG
    4. 4.4 Unseeded Second Harmonic Generation (2ωp = ωs)
      1. 4.4.1 Solution of SHG equations in the absence of diffraction, beam walk-off and absorption
      2. 4.4.2 Another interlude - the Manley-Rowe relations for SHG
      3. 4.4.3 Back to the solutions of SHG equations
      4. 4.4.4 SHG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion
      5. 4.4.5 SHG irradiance for collimated beams with phase matching (σ = 0) and with pump depletion
      6. 4.4.6 SHG power and energy conversion efficiency for collimated beams
      7. 4.4.7 SHG power and energy conversion efficiency for collimated Gaussian beams
      8. 4.4.8 SHG power and energy conversion efficiency for collimated Gaussian beams with phase matching (σ = 0) in presence of pump depletion
      9. 4.4.9 SHG power and energy conversion efficiency for collimated Gaussian beams with no pump depletion
      10. 4.4.10 SHG conversion efficiency for focused Gaussian beams
      11. 4.4.11 An interlude - Boyd and Kleinman theory for SHG
      12. 4.4.12 Return to the case of SHG for focused Gaussian beams including pump depletion effects
      13. 4.4.13 Optimum value of the focusing parameter
      14. 4.4.14 Analytical (fitted) expressions for SHG conversion efficiency hsm, optimized with respect to σ
      15. 4.4.15 Analytical expressions for SHG conversion efficiency hsmm, optimized with respect to σ and ξp
    5. 4.5 Unseeded Difference Frequency Generation (ω1 = ω3 − ω2)
      1. 4.5.1 DFG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion
      2. 4.5.2 DFG irradiance for collimated beams with phase matching (σ = 0) in presence of pump depletion
      3. 4.5.3 DFG conversion efficiency for focused Gaussian beams
    6. Bibliography
  16. 5 Quasi-Phase Matching
    1. 5.1 Quasi Phase Matching, QPM
      1. 5.1.1 Plane wave analysis of quasi phase matching
    2. 5.2 Effects Of Focusing And Pump Depletion On Quasi Phase Matched SHG
      1. 5.2.1 Quasi phase matched SHG for collimated beams, with δ1 ≠ 0, and with no pump depletion
      2. 5.2.2 Effects of focusing and pump depletion on quasi phase matched SHG
    3. Bibliography
  17. 6 Optical Parametric Oscillation
    1. 6.1 Optical Parametric Oscillation
      1. 6.1.1 Plane wave analysis of OPO (SRO) including phase mismatch and pump depletion
      2. 6.1.2 SRO efficiency and threshold for collimated Gaussian beams
      3. 6.1.3 Results for the case of collimated Gaussian beams including phase mismatch
      4. 6.1.4 SRO with focused Gaussian beams
      5. 6.1.5 Results of optimization of the focusing parameters in an SRO
    2. Bibliography
  18. 7 Numerical Beam Propagation Methods
    1. 7.1 Introduction
    2. 7.2 Propagation in Linear Media
      1. 7.2.1 Hankel Transform Method
      2. 7.2.2 Fourier Transform Method
    3. 7.3 Propagation in Nonlinear Media
      1. 7.3.1 Split Step Method
    4. 7.4 Application Examples
      1. 7.4.1 Phase Retrieval
      2. 7.4.2 Second Harmonic Generation
    5. Bibliography
  19. A Computer Codes for SFG Efficiency
    1. A.1 The MATLAB codes for the collimated Gaussian beam case
      1. A.1.1 The file sfg_PE.m
      2. A.1.2 The file getysfg_p.m for the power conversion efficiency
      3. A.1.3 The file getysfg_e.m for the energy conversion efficiency
    2. A.2 The Fortran Code For The Focused Beam Case of SHG
      1. A.2.1 The file sfgJimm.f
      2. A.2.2 s fghmm_in.txt
      3. A.2.3 sfg_hmm_fileout.txt
  20. B Computer Codes for SHG Efficiency
    1. B.1 MATLAB code for SHG efficiency of collimated Gaussian beams
      1. B.1.1 shg_IPE.m
      2. B.1.2 The file getyshg_I.m for the irradiance conversion efficiency
      3. B.1.3 The file getyshg_P.m for the power conversion efficiency
      4. B.1.4 The file getyshg_E.m for the energy conversion efficiency
    2. B.2 The Fortran Code For The Focused Beam Case of SHG
      1. B.2.1 The file sfg_hmax.f
      2. B.2.2 shg_hmax_in.txt
      3. B.2.3 shg_hmax_fileout.txt
  21. C The Fortran Source Code for QPM-SHG Efficiency
    1. C.1 qpmshg.f
    2. C.2 qpmshg_in.txt
    3. C.3 qpmshg_fileout.txt
  22. D The Fortran Source Code for OPO Threshold and Efficiency 295
    1. D.1 OPO.f
  23. Index

Product information

  • Title: Laser Beam Propagation in Nonlinear Optical Media
  • Author(s): Shekhar Guha
  • Release date: December 2017
  • Publisher(s): CRC Press
  • ISBN: 9781351832953