1 Introduction 1.1 Nonlinear Susceptibility 1.2 Coherence Functions 1.3 Suppression and Enhancement of FWM Processes 1.4 Double Dressing Schemes of Probe and Four-Wave MixingFields 1.5 Spatial Optical Modulation via Kerr Nonlinearities 1.6 Formations and Dynamics of Novel Spatial Solitons References 2 Ultrafast Polarization Beats of Four-Wave Mixing Processes 2.1 Four-level Polarization Beats with Broadband Noisy Light 2.1.1 Basic Theory 2.1.2 FLPB in a Doppler-broadened System 2.1.3 Photon-echo 2.1.4 Experiment and Result 2.2 Ultrafast Sum-frequency Polarization Beats in Twin MarkovianStochastic Correlation 2.2.1 Basic Theory 2.2.2 Second-order Stochastic Correlation of ASPB 2.2.3 Fourth-order Stochastic Correlation of ASPB References 3 Raman, Rayleigh and Brillouin-enhanced FWM PolarizationBeats 3.1 Attosecond Sum-frequency Raman-enhanced Polarization BeatsUsing Twin Phase-sensitive Color Locking Noisy Lights 3.1.1 Basic Theory of Attosecond Sum-frequency REPB 3.1.2 Homodyne Detection of Sum-frequency REPB 3.1.3 Heterodyne Detection of Difference-frequency REPB 3.2 Competition Between Raman and Rayleigh-enhanced Four-WaveMixings in Attosecond Polarization Beats 3.2.1 Basic Theory 3.2.2 Stochastic Correlation Effects of Rayleigh andRaman-enhanced FWM 3.2.3 The Raman and Rayleigh-enhanced Nonlinear Susceptibility incw Limit 3.2.4 Homodyne Detection of ASPB 3.2.5 Heterodyne Detection of ASPB 3.2.6 Discussion and Conclusion 3.3 Coexisting Brillouin, Rayleigh and Raman-enhanced Four-WaveMixings 3.3.1 Basic Theory 3.3.2 Homodyne Detection of ASPB 3.3.3 Heterodyne Detection of ASPB 3.3.4 Phase Angle 3.3.5 Discussion and Conclusion References 4 Multi-Dressing Four-Wave Mixing Processes in Confined andNon-confined Atomic System 4.1 Temporal and Spatial Interference Between Four-Wave Mixing andSix-Wave Mixing Channels 4.2 Intermixing Between Four-Wave Mixing and Six-Wave Mixing in aFour-level Atomic System 4.2.1 Interplay Between FWM and SWM 4.2.2 Discussion 4.3 Coexistence of Four-Wave, Six-Wave and Eight-Wave MixingProcesses in Multi-dressed Atomic Systems 4.3.1 Parallel and Nested Dressing Schemes 4.3.2 Interplay Among Coexisting FWM, SWM and EWM Processes 4.4 Controlled Multi-Wave Mixing via Interacting Dark States in aFive-level System 4.4.1 Basic Theory 4.4.2 Numerical Results 4.4.3 Discussion 4.5 Polarization Interference of Multi-Wave Mixing in a ConfinedFive-level System 4.5.1 Basic Theory 4.5.2 MWM in Long Cells 4.5.3 MWM in Ultra-thin and Micrometer Cells 4.5.4 Discussion References 5 Enhancement and Suppression in Four-Wave Mixing Processes 5.1 Interplay among Multi-dressed Four-Wave Mixing Processes 5.2 Observation of Enhancement and Suppression of Four-Wave MixingProcesses 5.3 Controlling Enhancement and Suppression of Four-Wave Mixingvia Polarized Light 5.3.1 Theoretical Model and Analysis 5.3.2 Experimental Results 5.4 Enhancing and Suppressing Four-Wave Mixing inElectronm-genetically Induce Transparency Window References 6 Multi-Wave Mixing Processes in Multi-level Atomic System 6.1 Modulating Multi-Wave Mixing Processes via Polarizable DarkStates 6.2 Polarization Spectroscopy of Dressed Four-Wave Mixing in aThree-level Atomic System 6.2.1 Various Nonlinear Susceptibilities for DifferentPolarization Schemes 6.2.2 Nonlinear Susceptibilities for Zeeman-degenerate SystemInteracting with Polarized Fields 6.2.3 Third-order Density-matrix Elements in Presence of DressingFields 6.3 Controlling FWM and SWM in Multi-Zeeman Atomic System withElectromagnetically Induced Transparency 6.3.1 Basic Theory 6.3.2 Dual-dressed EIT 6.3.3 Four-Wave Mixing 6.3.4 Six-Wave Mixing References 7 Controlling Spatial Shift and Spltting of Four-Wave Mixing 7.1 Basic Theory 7.2 Electromagnetically-induced Spatial Nonlinear Dispersion ofFour-Wave Mixing Beams 7.3 Spatial Dispersion Induced by Cross-phase Modulation 7.4 Experimental Demonstration of Optical Switching and Routingvia Four-Wave Mixing Spatial Shift 7.4.1 Theoretical Model and Experimental Scheme 7.4.2 Optical Switching and Routing via Spatial Shift 7.5 Controlled Spatial Beamsplitter Using Four-Wave MixingImages 7.6 Spatial Splitting and Intensity Suppression of Four-WaveMixing in V-type Three-level Atomic System References 8 Spatial Modulation of Four-Wave Mixing Solitons 8.1 Basic Theory 8.1.1 Calculation of Double Dressed Cross-Kerr Nonlinear Index ofRefraction 8.1.2 Calculation of Analytical Solution of One-dimensionalBright and Dark Spatial Solitons 8.2 Novel Spatial Gap Solitons of Four-Wave Mixing 8.3 Dipole-mode Spatial Solitons of Four-Wave Mixing 8.4 Modulated Vortex Solitons of Four-Wave Mixing References Index
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