Download Light Propagation in Gain Media: Optical Amplifiers PDF

TitleLight Propagation in Gain Media: Optical Amplifiers
File Size2.8 MB
Total Pages286
Table of Contents
1 Introduction
	1.1 Maxwell's equations
		1.1.1 Maxwell's equations in the time domain
		1.1.2 Maxwell's equations in the frequency domain
		1.1.3 Maxwell's equations in the momentum domain
		1.1.4 Constitutive relations for different optical media
	1.2 Permittivity of isotropic materials
		1.2.1 Debye-type permittivity and its extensions
		1.2.2 Lorentz dielectric function
		1.2.3 Drude dielectric function
	1.3 Dispersion relations
		1.3.1 Dispersion relation in free space
		1.3.2 Dispersion relation in isotropic materials
		1.3.3 Refractive index and phase velocity
		1.3.4 Instabilities associated with a gain medium
	1.4 Causality and its implications
		1.4.1 Hilbert transform
		1.4.2 Kramers--Kronig relations
	1.5 Simple solutions of Maxwell's equations
		1.5.1 Continuous-wave plane waves
		1.5.2 Pulsed plane waves
2 Light propagation through dispersive dielectric slabs
	2.1 State of polarization of optical waves
	2.2 Impedance and refractive index
	2.3 Fresnel equations
		2.3.1 Case of plane s-waves
		2.3.2 Case of plane p-waves
		2.3.3 Fresnel equations in lossy dielectrics
	2.4 Propagation of optical pulses
		2.4.1 One-dimensional propagation model
		2.4.2 Case of a Gaussian pulse
		2.4.3 Numerical approach
	2.5 Finite-difference time-domain (FDTD) method
		2.5.1 FDTD algorithm in one spatial dimension
		2.5.2 Total and scattered electromagnetic fields
		2.5.3 Inclusion of material dispersion
		2.5.4 Perfectly matched layer for dispersive optical media
	2.6 Phase and group velocities
	2.7 Pulse propagation through a dielectric slab
		2.7.1 Fabry--Perot resonators
		2.7.2 Transfer function of a dielectric slab
3 Interaction of light with generic active media
	3.1 Reflection of light from a gain medium
		3.1.1 Total internal reflection and the Goos--Hänchen effect
		3.1.2 Total internal reflection from an active cladding
	3.2 Surface-plasmon polaritons
		3.2.1 SPP dispersion relation and other properties
		3.2.2 Propagation loss and its control
		3.2.3 Gain-assisted propagation of SPPs
	3.3 Gain-assisted management of group velocity
		3.3.1 Dispersion and group velocity
		3.3.2 Gain-assisted superluminal propagation of light
	3.4 Gain-assisted dispersion control
		3.4.1 Group velocity of a multilayer cylindrical nanowaveguide
		3.4.2 Silver nanorod immersed in an active medium
4 Optical Bloch equations
	4.1 The bra and ket vectors
	4.2 Density operator
	4.3 Density-matrix equations for two-level atoms
		4.3.1 Atomic states with even or odd parity
		4.3.2 Interaction of a two-level atom with an electromagnetic field
		4.3.3 Feynman--Bloch vector
		4.3.4 Rotating-wave approximation
	4.4 Optical Bloch equations
	4.5 Maxwell--Bloch equations
	4.6 Numerical integration of Maxwell--Bloch equations
5 Fiber amplifiers
	5.1 Erbium-doped fiber amplifiers
	5.2 Amplifier gain and its bandwidth
	5.3 Rate equations for EDFAs
	5.4 Amplification under CW conditions
	5.5 Amplification of picosecond pulses
		5.5.1 Inclusion of dopant's susceptibility
		5.5.2 Derivation of the Ginzburg--Landau equation
		5.5.3 Numerical solution of Ginzburg--Landau equation
	5.6 Autosolitons and similaritons
		5.6.1 Autosolitons
		5.6.2 Similaritons
	5.7 Amplification of femtosecond pulses
6 Semiconductor optical amplifiers
	6.1 Material aspects of SOAs
	6.2 Carrier density and optical gain
		6.2.1 Rate equation for carrier density
		6.2.2 Gain characteristics of SOAs
	6.3 Picosecond pulse amplification
		6.3.1 General theory of pulse amplification
		6.3.2 Method of multiple scales
		6.3.3 Pulse distortion and spectral broadening
		6.3.4 Impact of waveguide losses
	6.4 Femtosecond pulse amplification
7 Raman amplifiers
	7.1 Raman effect
		7.1.1 Spontaneous Raman scattering
		7.1.2 Stimulated Raman scattering
	7.2 Raman gain spectrum of optical fibers
	7.3 Fiber Raman amplifiers
		7.3.1 CW operation of a Raman amplifier
		7.3.2 Amplification of ultrashort pulses
	7.4 Silicon Raman amplifiers
		7.4.1 Coupled pump and signal equations
		7.4.2 CW operation of silicon Raman amplifiers
		7.4.3 Amplification of picosecond pulses
8 Optical parametric amplifiers
	8.1 Physics behind parametric amplification
	8.2 Phase-matching condition
	8.3 Four-wave mixing in optical fibers
		8.3.1 Coupled amplitude equations
		8.3.2 Impact of nonlinear effects on phase matching
		8.3.3 Parametric gain
		8.3.4 Signal gain in parametric amplifiers
		8.3.5 Amplifier bandwidth
		8.3.6 Dual-pump parametric amplifiers
	8.4 Three-wave mixing in birefringent crystals
		8.4.1 Uniaxial nonlinear crystals
		8.4.2 Ordinary and extraordinary waves
		8.4.3 Phase-matching condition
	8.5 Phase matching in birefringent fibers
		8.5.1 Polarization-maintaining fibers
9 Gain in optical metamaterials
	9.1 Classification of metamaterials
	9.2 Schemes for loss compensation in metamaterials
		9.2.1 Review of loss-compensation schemes
		9.2.2 Modeling of spaser-based amplifiers
	9.3 Amplification through three-wave mixing
		9.3.1 Configuration and basic equations for three-wave mixing
		9.3.2 Solution with undepleted-pump approximation
	9.4 Resonant four-wave mixing using dopants
		9.4.1 Density-matrix equations for the dopants
		9.4.2 Iterative solution for the induced polarization
		9.4.3 Coupled signal and idler equations
	9.5 Backward self-induced transparency
		9.5.1 Mathematical approach
		9.5.2 Bloch equations and Rabi frequencies
		9.5.3 Solution in the form of a solitary wave

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