"Second harmonic generation (SHG) has a wide range of applications in today's technological era, including nonlinear optics, quantum optics, lasers, material science, medical science, biological imaging, and high-resolution optical microscopy. In the laser industry, for example, SHG is prudent to create wavelength-specific high-energy lasers. It is also used to measure ultra-short pulse width with autocorrelators. SHG is now indispensable as a spectroscopic imaging tool in applications, such as biophysical characterization of the plasma membrane, biological sensing, disease diagnostics, and investigations of biomolecular interactions at interfaces. Because of its non-destructive detection, ultrafast response, and polarization sensitivity, SHG is exploited to describe crystal structures and materials. The use of SHG to characterize two-dimensional (2D) material structures gives crucial insights into their physical properties, thereby promoting the development of the relevant basic research, leading to theinvestigation of the potential applications of those materials. Developments in SHG research hold promising potentials of a large class of materials, such as magnetic- and nonmagnetic layered materials, perovskites, antiferromagnetic oxides, II-VI and III-V semiconductors, and nanotubes, for a variety of technological applications. This book focuses on the process of modelling and simulations of the SHG phenomenon in the area of nonlinear and quantum optics. The first chapter provides a visualization of the scientific landscape of research in SHG using scientometric analysis from 1962 to 2020 based on Scopus database. This chapter gives new postgraduate students in the subject useful information on hot themes in SHG research and how they are related to one another. There is also a brief mention of multinational collaborative networks. The following four research chapters look at the SHG from a classical standpoint, using Maxwell's equations to describe the nonlinear optical interaction between the electromagnetic wave and the medium. Such interaction is treated quantum mechanically in the second section of the book, with the SHG process described using a propagating Hamiltonian. As such, the volume adequately describes the SHG from both the classical andquantum mechanical standpoints. This allows the postgraduate researchers, focusing on the nonlinear phenomena, resulting from light-matter interaction, to find the content useful. In the second part of this volume, readers are introduced to a full theoretical analysis of the quantum features generated in certain optical devices, such as a two-waveguide device working under the SHG and coupled waveguide arrays with the combined second- and third-order nonlinear effects. To be more specific, this part discusses how SHG-enabled devices might be a useful source of nonclassical light. This section remains relevant for postgraduate students commencing their studies in quantum optics, where the nonclassical phenomena, such as squeezing and entanglement, requirea solid understanding of the underlying techniques, namely the phase space and the analytical perturbative methods"--
Author(s): Abdel-baset M. A. Ibrahim, Pankaj Kumar Choudhury
Series: Physics Research and Technology
Publisher: Nova Science Publishers
Year: 2022
Language: English
Pages: 240
City: New York
Preface
Chapter 1
Visualizing the Scientific Landscape of Research in Second Harmonic Generation: A Scientometric Review
Abstract
1. Introduction
2. Methodology
3. Discussion
3.1. The Growth Rate of SHG Research Publications
3.2. The Most Refereed Articles in SHG Research
3.3. Hot Topics in SHG Research
3.4. International Collaboration Network
Conclusion
Acknowledgments
References
Chapter 2
Modeling Efficient Second Harmonic Generation in Microcrystalline KDP Fibers – Part I
Abstract
1. Introduction
2. Nonlinear Optics
2.1. Electron in an Asymmetric Potential Well
2.2. External Electric Field and Induced Polarization
2.3. Maxwell’s Equations and the Wave Equation
3. Second Harmonic Generation
3.1. SHG Coupled Amplitude Equations
3.2. Approximations and Implications
3.3. A Fully Generalized Solution
3.4. Harmonic Power and Energy Exchange
4. The KDP Crystal
4.1. Sellmeier Equations, Effective Index and Phase-Matching
4.2. Snell’s Law, Fresnel Coefficients and KDP Structure
Conclusion
References
Additional Resources
Chapter 3
Modeling Efficient Second Harmonic Generation in Microcrystalline KDP Fibers – Part II
Abstract
1. Introduction
2. Numerical Model
2.1. Hexagonal Cross-Section of the KDP Fiber
2.2. Ray Geometry and Processing Algorithms
2.3. Code Structure and Source
3. Model Validation
3.1. Hallmarks of the SHG Signal
3.1.1. Energy Exchange Between Fundamental and Harmonic
3.1.2. Sensitivity to Beam Angle
3.1.3. Demonstration of Maker Fringes
3.1.4. Harmonic Amplitude Variation with Phase Mismatch
4. Simulation Results
4.1. Radiation and Guided Modes Inside the Crystal
4.2. Uniform Guided Mode
4.3. Non-Uniform Guided Mode
4.4. Comparison of Modes
4.5. SHG and Dimensional Scaling
5. Extension to 3D and Multi-Fiber Bundles
5.1. Incorporating Input Angle with Phase Matching
5.2. Multi-Fiber Bundles and SHG
Conclusion
Acknowledgements
References
Additional Resources
Chapter 4
Design and Analysis of Photonic Crystal-Based Integrated Optical Devices Using the Finite Difference Method
Abstract
1. Introduction
2. Formulations of The Yee’s FDTD Algorithm
2.1. Maxwell’s Equations
3. Yee’s FDTD Scheme
3.1. The Yee Cell
3.2. The Leapfrog Processing Scheme
4. Absorbing Boundary Conditions
5. Numerical Dispersion and Stability of the FDTDMethod
6. Source Excitation
7. Reflection and Transmission Coefficients
8. Applications and Related Simulation Results
8.1. Analysis and Design of One-Dimensional Structures
8.1.1. FSS Structures Using Inhomogeneous and Stratified Dielectric Multilayer
9. EBG Structures Using Inhomogeneous and Stratified Dielectric Multilayer
10. Analysis and Design Two-Dimensional Structures
10.1. Optical Filter
10.1.1. Two-dimensional Demultiplexing Structure Based on Photonic Crystals
10.2. Analysis and Design of Two-Channel Wavelength Division Demultiplexer
Conclusion
References
Chapter 5
Nonlinear Optical Properties in Single and Coupled InAs/GaAs Quantum Dots
Abstract
1. Introduction
2. Theory
2.1. Schrödinger Equation
2.2. Nonlinear Optical Properties
2.2.1. Optical Absorption Coefficients
2.2.2. Nonlinear Optical Rectification
2.2.3. Second Harmonic Generation
3. Validation
4. Single Quantum Dot
5. Laterally Coupled Quantum Dots
6. Vertically Coupled Quantum Dots
7. Lens-Shaped Core/Shell Quantum Dots
Conclusion
References
Chapter 6
Quantum Properties of Light in Codirectional Coupler with Second Harmonic Generation
Abstract
1. Introduction
2. Mathematical Formulation
2.1. Phase Space Method for Codirectional System
2.2. Analytical Method for Codirectional System
2.3. Scaling of The System
2.4. Squeezing in Codirectional Two-Channel System
2.5. Squeezing Measurement
3. Results and Discussion
Conclusion
Acknowledgments
References
Chapter 7
Quantum Dynamics of Contradirectional Nonlinear Coupler
Abstract
1. Introduction
2. Mathematical Formulation
2.1. Phase Space Method for Contra-Directional Two-Channel System
2.2. Analytical Method for Contra-Directional Two-Channel System
2.3. Squeezing in Contra-Directional Two-Channel System
3. Results and Discussions
Conclusion
Acknowledgments
References
Chapter 8
Squeezed Light in Coupled Waveguide Networks Induced by the Nonlinear Kerr Effect and Second Harmonic Generation
Abstract
1. Introduction
2. The Model
3. Discussion
Conclusion
Acknowledgments
References
About the Editors
List of Contributors
Index
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