book

Laser Beam Propagation in Nonlinear Optical Media

Name: Laser Beam Propagation in Nonlinear Optical Media
Author: Shekhar Guha
ISBN: 9781351832953

by Shekhar Guha

December 2017

Intermediate to advanced

334 pages

6h 50m

English

CRC Press

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Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
List of Tables
Preface
Author Biographies

Acknowledgements
1 Light Propagation in Anisotropic Crystals
1.1 Introduction1.2 Vectors Associated With Light Propagation1.2.1 Plane waves1.2.2 Non-plane waves1.3 Anisotropic Media1.3.1 The principal coordinate axes1.3.2 Three crystal classes1.3.3 The principal refractive indices1.4 Light Propagation In An Anisotropic Crystal1.4.1 Allowed directions of D and E in an anisotropic medium1.4.2 Values of n for a given propagation direction1.4.3 Directions of D and E for the slow and fast waves1.5 Characteristics Of The Slow And The Fast Waves In A Biaxial Crystal1.5.1 ns and nf1.5.2 ρs and ρf1.5.3 The components of ds and df1.5.4 The components of ês and êf1.6 Double Refraction And Optic Axes1.6.1 Expressions for components of d in terms of the angles θ, ϕ and Q1.6.2 Relating the angle δ to Ω, θ and ϕ1.6.3 Directions of E and S1.6.4 The walk-off angles ρs and ρf1.6.5 An interim summary1.7 Propagation Along The Principal Axes And Along The Principal Planes1.7.1 Introduction1.7.2 Propagation along the principal axes X, Y and Z
1.7.3 Propagation along the principal plane YZ
1.7.4 k along YZ plane, Case 1: nX < nY < nZ1.7.5 k along YZ plane, Case 2: nX > nY > nZ1.7.6 Propagation along the principal plane ZX1.7.7 k along ZX plane, Case 1a: nX < nY < nZ, θ < Ω1.7.8 k along ZX plane, Case 1b: nX < nY < nZ, θ > Ω1.7.9 k along ZX plane, Case 2a: nX > nY > nZ, θ < Ω1.7.10 k along ZX plane, Case 2b: nX > nY > nZ, θ > Ω1.7.11 Propagation along the principal plane XY1.7.12 k along XY plane, Case 1: nX < nY < nZ1.7.13 k along XY plane, Case 2: nX > nY > nZ1.7.14 Summary of the cases of propagation along principal planes1.8 Uniaxial Crystals1.8.1 Field directions of the D and E vectors for extraordinary and ordinary waves1.8.2 ρ ≠ 0 Case (extraordinary wave)1.8.3 Another expression relating ρ and θ1.8.4 ρ = 0 Case (ordinary wave)1.8.5 Two special cases: θ = 0 and θ = 90°1.9 Propagation Equation In Presence Of Walk-off1.9.1 Transformation between laboratory and crystal coordinate systems1.9.2 The propagation equation in presence of walk-offBibliography
2 Nonlinear Optical Processes
2.1 Introduction2.2 Second Order Susceptibility2.3 Properties of χ(2)2.3.1 Properties of χ(2) away from resonance2.3.2 Kleinman’s symmetry2.4 d coefficients and the contracted notation2.4.1 d coefficients under Kleinman symmetry2.5 The Non-Zero d Coefficients Of Biaxial Crystals2.6 The Non-Zero d Coefficients Of Uniaxial Crystals2.7 Nonlinear polarizations2.7.1 Nondegenerate sum frequency generation2.7.2 Difference frequency generation2.7.3 Second harmonic generation (SHG)2.7.4 Optical rectification2.7.5 Convention used for numbering the three interacting beams of light2.7.6 Summary of polarization components for non-degenerate three wave mixing2.7.7 Summary of polarization components for degenerate three wave mixing (SHG and degenerate parametric mixing)2.8 Frequency Conversion And Phase Matching2.8.1 Phase matching in birefringent crystals2.8.2 Calculation of phase matching angles2.9 Walk-Off Angles2.9.1 Calculation of walk-off angles in the phase matched case in KTPBibliography
3 Effective d coefficient for Three-Wave mixing Processes
3.1 Introduction3.1.1 Definition of deff3.1.2 Effective nonlinearity for nondegenerate three wave mixing processes3.1.3 Effective nonlinearity for the degenerate three wave mixing process3.1.4 Type I degenerate three wave mixing process3.1.5 Type II degenerate three wave mixing process3.2 Expressions for deff3.2.1 deff of biaxial crystals under Kleinman Symmetry Condition
3.2.2 Reduction of deff to expressions in the literature
3.3 deff Values for Some Biaxial and Uniaxial Crystals of Different Classes3.3.1 deff for KTP for propagation in a general direction3.3.1.1 deff for KTP for a Type I (ssf) mixing process3.3.1.2 deff for KTP for a Type II(sff) mixing process3.3.1.3 deff for KTP for a Type II(fsf) mixing process3.3.2 deff for KTP for propagation along principal planes3.4 deff for Uniaxial Crystals
3.5 deff for Isotropic Crystals
3.5.1 The direction of the nonlinear polarization3.5.2 Propagation along principal planes3.5.3 Propagation through orientation patterned materialBibliography
4 Nonlinear Propagation Equations and Solutions
4.1 Nonlinear Propagation Equations4.1.1 Normalized form of the three wave mixing equations4.2 Solutions To The Three Wave Mixing Equations In The Absence Of Diffraction, Beam Walk-off And Absorption4.2.1 An interlude - the Manley-Rowe relations4.2.2 Back to solutions of the three wave mixing equations4.2.3 Another interlude - Jacobian elliptic functions4.2.4 Return to the solution of the coupled three wave mixing equations4.3 Unseeded Sum Frequency Generation (ω1 + ω2 = ω3)4.3.1 SFG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion4.3.2 SFG irradiance for collimated beams with phase matching (σ = 0) and with pump depletion4.3.3 SFG power and energy conversion efficiency for collimated beams with arbitrary spatial and temporal shapes4.3.4 SFG power and energy conversion efficiency for collimated Gaussian beams
4.3.5 SFG power and energy conversion efficiency for collimated Gaussian beams with phase mismatch (σ ≠ 0) and no pump depletion
4.3.6 Some results of SFG power and energy conversion efficiency for collimated Gaussian beams4.3.7 SFG conversion efficiency for focused Gaussian beams4.3.8 Optimization of focusing parameters for SFG4.4 Unseeded Second Harmonic Generation (2ωp = ωs)4.4.1 Solution of SHG equations in the absence of diffraction, beam walk-off and absorption4.4.2 Another interlude - the Manley-Rowe relations for SHG4.4.3 Back to the solutions of SHG equations4.4.4 SHG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion4.4.5 SHG irradiance for collimated beams with phase matching (σ = 0) and with pump depletion4.4.6 SHG power and energy conversion efficiency for collimated beams4.4.7 SHG power and energy conversion efficiency for collimated Gaussian beams4.4.8 SHG power and energy conversion efficiency for collimated Gaussian beams with phase matching (σ = 0) in presence of pump depletion
4.4.9 SHG power and energy conversion efficiency for collimated Gaussian beams with no pump depletion
4.4.10 SHG conversion efficiency for focused Gaussian beams4.4.11 An interlude - Boyd and Kleinman theory for SHG4.4.12 Return to the case of SHG for focused Gaussian beams including pump depletion effects4.4.13 Optimum value of the focusing parameter4.4.14 Analytical (fitted) expressions for SHG conversion efficiency hsm, optimized with respect to σ4.4.15 Analytical expressions for SHG conversion efficiency hsmm, optimized with respect to σ and ξp4.5 Unseeded Difference Frequency Generation (ω1 = ω3 − ω2)4.5.1 DFG irradiance for collimated beams with no phase matching (σ ≠ 0) and with no pump depletion4.5.2 DFG irradiance for collimated beams with phase matching (σ = 0) in presence of pump depletion4.5.3 DFG conversion efficiency for focused Gaussian beamsBibliography
5 Quasi-Phase Matching
5.1 Quasi Phase Matching, QPM5.1.1 Plane wave analysis of quasi phase matching5.2 Effects Of Focusing And Pump Depletion On Quasi Phase Matched SHG5.2.1 Quasi phase matched SHG for collimated beams, with δ1 ≠ 0, and with no pump depletion5.2.2 Effects of focusing and pump depletion on quasi phase matched SHGBibliography
6 Optical Parametric Oscillation
6.1 Optical Parametric Oscillation6.1.1 Plane wave analysis of OPO (SRO) including phase mismatch and pump depletion6.1.2 SRO efficiency and threshold for collimated Gaussian beams6.1.3 Results for the case of collimated Gaussian beams including phase mismatch6.1.4 SRO with focused Gaussian beams6.1.5 Results of optimization of the focusing parameters in an SROBibliography
7 Numerical Beam Propagation Methods
7.1 Introduction7.2 Propagation in Linear Media7.2.1 Hankel Transform Method7.2.2 Fourier Transform Method7.3 Propagation in Nonlinear Media7.3.1 Split Step Method7.4 Application Examples7.4.1 Phase Retrieval7.4.2 Second Harmonic GenerationBibliography
A Computer Codes for SFG Efficiency
A.1 The MATLAB codes for the collimated Gaussian beam caseA.1.1 The file sfg_PE.mA.1.2 The file getysfg_p.m for the power conversion efficiencyA.1.3 The file getysfg_e.m for the energy conversion efficiencyA.2 The Fortran Code For The Focused Beam Case of SHGA.2.1 The file sfgJimm.fA.2.2 s fghmm_in.txtA.2.3 sfg_hmm_fileout.txt
B Computer Codes for SHG Efficiency
B.1 MATLAB code for SHG efficiency of collimated Gaussian beamsB.1.1 shg_IPE.mB.1.2 The file getyshg_I.m for the irradiance conversion efficiencyB.1.3 The file getyshg_P.m for the power conversion efficiencyB.1.4 The file getyshg_E.m for the energy conversion efficiencyB.2 The Fortran Code For The Focused Beam Case of SHGB.2.1 The file sfg_hmax.fB.2.2 shg_hmax_in.txtB.2.3 shg_hmax_fileout.txt
C The Fortran Source Code for QPM-SHG Efficiency
C.1 qpmshg.fC.2 qpmshg_in.txtC.3 qpmshg_fileout.txt
D The Fortran Source Code for OPO Threshold and Efficiency 295
D.1 OPO.f
Index

Content preview from Laser Beam Propagation in Nonlinear Optical Media

1.7.3 Propagation along the principal plane Y Z

Another special case of light propagation in an anisotropic crystal is that of propagation along a principal plane, such as the XY, YZ or ZX planes. We start with the propagation vector k lying in the YZ plane, so that m_X = 0 and $m_{Y}^{2} + m_{Z}^{2} = 1$ . With m_X = 0, Eqns. 1.55 give

$A = n_{Y}^{2} m_{Y}^{2} + n_{Z}^{2} n_{Z}^{2}, B = n_{Y}^{2} m_{Z}^{2} + n_{X}^{2} A, and C = n_{X}^{2} n_{Y}^{2} n_{Z}^{2} .$

(1.109)

The two cases of n_X < n_Y < n_Z and n_X > n_Y > n_Z are considered separately in the next two subsections.

1.7.4 k along YZ plane, Case 1: n_X < n_Y < n_Z

In this case, from 1.56 $D = n_{Y}^{2} n_{Z}^{2} - n_{X}^{2} A$ , since $D$ is defined to be positive and $A$ takes the values from $n_{Y}^{2}$ to $n_{Z}^{2}$ as m_Y goes from 1 to 0. Thus, the possible values of n (from Eqn. 1.57) are

$n$

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Laser Beam Propagation in Nonlinear Optical Media

by Shekhar Guha

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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