Electromagnetic resonances in nonlinear optics /

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Bibliographic Details
Author / Creator:	Nevière, M.
Imprint:	Amsterdam : Gordon & Breach Science Publishers, c2000.
Description:	viii, 389 p. : ill. ; 26 cm.
Language:	English
Series:	Advances in nonlinear optics ; v. 5.
Subject:	Nonlinear optics. Electromagnetic waves -- Diffraction. Electromagnetic waves -- Diffraction. Nonlinear optics.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/4403694

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ISBN:	9056993178

Table of Contents:

Introduction to the Series
Chapter I. Introduction
Chapter II. Introduction to Diffraction Grating Theory
II.1. Introduction
II.2. Grating fundamentals in linear optics
II.3. Grating resonances
II.4. Gratings in nonlinear optics
II.5. Review of the gratings problems in linear optics
II.6. Basic principles of rigorous electromagnetic theories in linear grating optics
II.6.1. The Rayleigh theory
II.6.2. Differential theory
II.6.3. The method of Moharam and Gaylord
II.6.4. The classical modal method
II.6.5. The integral theory
II.6.6. The method of coordinate transformation
II.6.7. Grating theory user guide
Chapter III. Electromagnetic Theory of Nonlinear Optics
III.1. Fundamental laws and constitutive relations
III.2. Nonlinear polarization in second harmonic generation
III.2.1. Dielectrics
III.2.2. Metals
III.2.3. Undepleted pump approximation
III.3. Nonlinear polarization for optical Kerr effect
III.4. Propagation equations
III.5. Boundary conditions
Chapter IV. Rigorous Nonlinear Electromagnetic Theory of Corrugated Dielectric Waveguides
IV.1. Theory of undepleted second harmonic generation in corrugated dielectric waveguides
IV.1.1. Curvilinear coordinate transformation
IV.1.2. The Rayleigh-Fourier method as applied to second harmonic generation
IV.1.3. Differential method
IV.1.3.1. Solution at the pump frequency [omega]
IV.1.3.2. Nonlinear polarization inside the homogeneous region
IV.1.3.3. Nonlinear polarization inside the modulated region
IV.1.3.4. The field inside the modulated region
IV.1.3.5. The field inside the homogeneous nonlinear region
IV.1.3.6. The boundary conditions
IV.2. Numerical methods for analysis of pump field depletion in second harmonic generation and optical Kerr effect
IV.2.1. General considerations
IV.2.2. Plane incident wave - the classical differential method
IV.2.2.1. Optical Kerr-effect
IV.2.2.2. Second-harmonic generation
IV.2.3. Waveguide mode propagation: beam-propagation finite-difference method
IV.2.4. Waveguide mode propagation: finite-elements method
IV.3. Multilayered grating - elimination of numerical instabilities
IV.3.1. Errors
IV.3.2. Growing exponents and numerical instabilities
IV.3.3. Exponential terms inside the corrugated region
IV.3.4. S-matrix algorithm
Chapter V. Theory of Undepleted Second Harmonic Generation in Relief Metallic Gratings
V.1. The surface term of P[superscript NL]
V.2. The problem of boundary conditions
V.3. The propagation equations
V.4. The polarization dependence
V.5. The integral method
V.6. The differential method
Chapter VI. Polology: Phenomenological Approach to (Quasi) Phase Matching
VI.1. Introduction
VI.2. An interesting example - resonantly enhanced or reduced second-harmonic absorption
VI.2.1. Pump wavelength 1.319 [mu]m.
VI.2.2. Pump wavelength 1.064 [mu]m.
VI.3. Phenomenological approach to electromagnetic resonance effects in linear optics
VI.3.1. Scattering matrix
VI.3.2. The electromagnetic resonance
VI.3.3. The zeros of b[subscript n]
VI.3.4. Loci of [delta superscript p](h) and [delta superscript z](h) in the complex [delta]-plane
VI.4. Polology in Nonlinear Optics
VI.4.1. Second Harmonic Generation
VI.4.2. Optical Kerr Effect
VI.5. Optimization algorithm for second harmonic generation
VI.5.1. An optimization algorithm
VI.5.2. Behavior of coupling coefficients
VI.5.3. Some limitations and precautions
VI.5.4. Numerical examples
Chapter VII. Leaky Modes in Nonlinear Optical Resonators
VII.1. General considerations
VII.2. Different representations of the electromagnetic field in linear planar structures
VII.2.1. The longitudinal representation
VII.2.2. The transverse representation: guided modes and radiation fields
VII.2.3. The transverse representation: orthogonality relations and the equation of evolution of a mode amplitude
VII.2.3.1. Demonstration of the Lorentz reciprocity theorem
VII.2.3.2. Orthogonality relations
VII.2.3.3. Determination of the amplitude of a mode: guided or radiated
VII.2.3.4. Equation of evolution of a mode amplitude
VII.2.4. The leaky mode representation
VII.2.4.1. The leaky modes
VII.2.4.2. The different types of modes
VII.2.5. Brief summary
VII.3. Equation of evolution of a leaky mode amplitude in planar resonators
VII.3.1. Evaluation of J[superscript in subscript Q]
VII.3.2. Evaluation of J[superscript NL subscript Q]
VII.3.2.1. Preliminary considerations
VII.3.2.2. Calculation of J[subscript II] and N[subscript II,rad]
VII.3.2.3. Calculation of N[subscript Q,rad] when two classes of radiation "modes" are resonantly excited
VII.3.3. General equation of evolution of a leaky mode amplitude
VII.3.4. The relation between the electromagnetic fields inside and outside the resonator
VII.4. Examples
VII.4.1. A prism coupler in linear optics
VII.4.1.1. Solution in the transverse representation for an incident plane wave
VII.4.1.2. Solution in the leaky mode representation
VII.4.2. A prism coupler in nonlinear optics
VII.4.2.1. Solution in the transverse representation
VII.4.2.2. Solution in the leaky mode representation
VII.5. Grating structures
VII.5.1. Homogeneous solution: general considerations
VII.5.2. Equation of evolution of a leaky mode amplitude
VII.5.2.1. The in-coupling process
VII.5.2.2. The influence of nonlinear polarization
VII.5.3. Amplitude of the diffracted orders in the outside media
VII.5.4. Extension to the time domain
VII.6. General summary
Chapter VIII. Linear Distributed Couplers
VIII.1. Radiation pattern of distributed couplers in the stationary regime: null points and m-lines
VIII.1.1. Near field-pattern and null points
VIII.1.2. Far-field pattern and m-line
VIII.1.3. Far-field criterium
VIII.1.4. Is there a link between the null point and the m-line?
VIII.2. Spatio-temporal linear analysis of distributed couplers
VIII.2.1. Prism couplers
VIII.2.2. Grating couplers
Chapter IX. Kerr-Type Leaky Resonators
IX.1. Optical bistability
IX.1.1. Stationary plane wave study of optical bistability
IX.1.1.1. The nonlinear transmission
IX.1.1.2. The nonlinear reflection
IX.1.2. Diffraction-induced transverse effects due to the finite width of the pump beam
IX.1.2.1. General considerations
IX.1.2.2. Some comments on the plane wave solution
IX.1.2.3. Transverse effects in Kerr-type leaky resonators
IX.2.. Spatio-temporal phenomena in Kerr-type leaky resonators
IX.2.1. Basic theoretical tools for stability analysis
IX.2.2. Plane wave solution in instantaneous Kerr media
IX.2.3. Plane wave solution in noninstantaneous Kerr media
IX.2.3.1. Linear stability analysis
IX.2.3.2. Nonlinear dynamics
IX.2.4. Spatio-temporal instabilities in Kerr-type resonators
IX.2.4.1. Static modulational instabilities in normal incidence
IX.2.4.2. Dynamic modulational instabilities in normal incidence
IX.2.4.3. Influence of the angle of incidence
Chapter X. Second Harmonic Generation in Leaky Resonators
X.1. Second harmonic generation at grating couplers: general results
X.1.1. The basic equations
X.1.2. Electromagnetic resonances and phase-matching
X.2. The undepleted pump plane wave solution
X.2.1. The same grating is used for the in-coupling and the resonant excitation of guided modes
X.2.1.1. Theoretical results
X.2.1.2. Numerical results
X.2.2. Nonlinear m-lines at the second harmonic frequency
X.2.3. Grating-assisted phase-matching: subwavelength grating
X.3. Cerenkov second harmonic generation
X.4. Optical bistability/instabilities in [chi superscript 2]-optical resonators
X.4.1. Stationary plane wave study of [chi superscript 2]-induced optical bistability
X.4.1.1. Second harmonic generation
X.4.1.2. Sub/second harmonic generation
X.4.2. Instabilities in [chi superscript 2]-optical resonators
Appendix A. Curvilinear transformation of coordinate system
Appendix B. Propagation equation in TM polarization
Appendix C. Propagation equation in TE polarization
Appendix D. The multiplicity of the poles
Appendix E. Radiation modes and related topics
Appendix F. Resonant excitation of two classes of radiation modes
Appendix G. Meaning of the spectral width of the resonance curve
Appendix H. Hopf bifurcation in leaky resonators described by eqs.IX.47
Appendix I. Numerical integration procedure of equations IX.55
Index

Electromagnetic resonances in nonlinear optics /

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