Orbital Angular Momentum States of Light provides an in-depth introduction to modelling of long-range propagation of orbital angular momentum (OAM) modes as well as more general structured light beams through atmospheric turbulence. Starting with angular spectrum method for diffraction and description of structured light states, the book discusses the technical details related to wave propagation through atmospheric turbulence. The review of historical as well as more recent ideas in this topical area, along with computer simulation codes, makes this book a useful reference to researchers and optical engineers interested in developing and testing of free-space applications of OAM states of light.
Key Features
- Includes modelling of long-range propagation using the angular spectrum approach
- Presents basic description of turbulence propagation using single or multi-phase screen models
- Provides information on advanced topics such as propagation polarization of singularities through turbulence
- Provides discussion on the spiral phase quadrature transform and its application for robust beam engineering
- Includes accompanying open-source software code snippets for modelling the propagation of scalar and vector beams through turbulence
Author(s): Kedar Khare, Priyanka Lochab, Paramasivam Senthilkumaran
Series: IOP Series in Advances in Optics, Photonics and Optoelectronics
Publisher: IOP Publishing
Year: 2021
Language: English
Pages: 190
City: Bristol
PRELIMS.pdf
Preface
Author biographies
Kedar Khare
Priyanka Lochab
Paramasivam Senthilkumaran
CH001.pdf
Chapter 1 Introduction
CH002.pdf
Chapter 2 Mathematical preliminaries
2.1 Fourier transform basics
2.2 Review of random processes theory
2.3 Simulating a random process with known spectral density
2.4 Complex signal representation
2.5 Spiral phase quadrature transform
References
CH003.pdf
Chapter 3 The angular spectrum method
3.1 Wave equation
3.2 The angular spectrum formalism
3.3 Sampling considerations and usage of fast Fourier transform routines
3.4 Numerical propagation of fields in free space
References
CH004.pdf
Chapter 4 Near-core structure of a propagating optical vortex
4.1 Vortex propagation using the angular spectrum method
4.2 Phase dip near the vortex core
References
CH005.pdf
Chapter 5 Orbital angular momentum states of light
5.1 Solutions of paraxial wave equation with phase singularities
5.2 Orbital angular momentum of LG modes
5.3 Topological charge of OAM carrying beams
5.4 Generation of OAM beams
5.4.1 Spiral phase plate
5.4.2 Diffractive optics
5.4.3 Spatial light modulators
5.4.4 Mode converters
5.4.5 Other methods
5.5 Detection of phase singularities
5.5.1 Interference based methods
5.5.2 Diffraction based methods
5.5.3 OAM detection using lens aberrations
5.5.4 Shack–Hartmann Wavefront Sensor
5.6 Propagation dynamics of beams embedded with vortices
5.7 OAM modes as a communication basis
References
CH006.pdf
Chapter 6 Introduction to polarization singularities
6.1 Polarization state of light beams
6.1.1 Stokes parameters
6.1.2 Azimuth and ellipticity
6.1.3 Poincaré sphere
6.2 Decomposition of a general state of polarization
6.2.1 Helicity and spin
6.2.2 Homogeneous and inhomogeneous polarization distributions
6.3 Singularities in optical fields
6.3.1 Phase singularities
6.3.2 Polarization singularities
6.3.3 Polarization singularities as vector superposition of OAM states
6.4 Stokes phase distribution and azimuth distribution
6.5 Generation and detection of polarization singularities
6.6 Applications of polarization singular beams
References
CH007.pdf
Chapter 7 Theory of wave propagation in a turbulent medium
7.1 Electromagnetic wave equation in random medium
7.2 Description of the refractive index fluctuations in atmosphere
7.2.1 Origin of fluctuations in the index of refraction
7.2.2 Spatial statistics of refractive index fluctuations
7.2.3 Temporal evolution of the fluctuations
7.2.4 Different models for power-spectral density of the refractive index fluctuations
7.2.5 Behavior of turbulence strength: Cn2 models
7.3 Classical perturbation methods
7.3.1 Born approximation
7.3.2 Rytov approximation
7.4 Extended Huygens–Fresnel integral approach
References
CH008.pdf
Chapter 8 Numerical simulation of laser beam propagation through turbulence
8.1 Split-step propagation method
8.1.1 Split-step formulation from the parabolic equation
8.1.2 Implementation of the split-step propagation method
8.1.3 Sampling requirements
8.2 Phase screen generation
8.2.1 Phase spectrum from the refractive index spectrum
8.2.2 FFT method for phase screen generation
8.2.3 Sub-harmonic correction to the phase screen
8.2.4 Some drawbacks of the FFT method
8.3 Other methods for generating random phase screens
8.3.1 Randomized spectral sampling method
8.3.2 Sparse spectrum method
8.4 Illustration of propagation of OAM states through turbulence
8.5 Beam quality parameters
8.5.1 Scintillation index
8.5.2 Signal-to-noise ratio for instantaneous beam profile
References
CH009.pdf
Chapter 9 Robust laser beam engineering using complementary diffraction
9.1 Complementary diffraction due to (0,1) OAM states
9.2 Beam quality assessment using instantaneous SNR
9.3 Speckle diversity
9.4 Long range propagation of converging polarization singularities through atmospheric turbulence
9.4.1 Evolution of intensity and polarization structure of the beams
9.4.2 Quantitative assessment of beam quality
References
APP1.pdf
Chapter
A.1 Initialization of parameters
A.1.1 Turbulence parameters (scales and strength)
A.1.2 Sampling grid parameters
A.1.3 Optical beam parameters
A.1.4 Number of phase screens
A.1.5 Generation of phase screen using FFT method
A.1.6 Generation of sub-harmonic phase screen
A.1.7 Free space propagation between two random phase screens
A.1.8 Simulation of propagation of vector beams through turbulence
