Coherent Control of Four-Wave Mixing

by Zhang, Yanpeng; Nie, Zhiqiang; Xiao, Min

• ISBN13: 9783642191145
• ISBN10: 3642191142
• Format: Hardcover
• Copyright: 2011-08-02
• Publisher: Springer Verlag

Summary

"Coherent Control of Four-Wave Mixing" discusses the frequency, temporal and spatial domain interplays of four-wave mixing (FWM) processes induced by atomic coherence in multi-level atomic systems. It covers topics in five major areas: the ultrafast FWM polarization beats due to interactions between multi-color laser beams and multi-level media; coexisting Raman-Rayleigh-Brillouin-enhanced polarization beats due to color-locking noisy field correlations; FWM processes with different kinds of dual-dressed schemes in ultra-thin, micrometer and long atomic cells; temporal and spatial interference between FWM and six-wave mixing (SWM) signals in multi-level electromagnetically induced transparency (EIT) media; spatial displacements and splitting of the probe and generated FWM beams, as well as the observations of gap soliton trains, vortex solitons, and stable multicomponent vector solitons in the FWM signals.The book is intended for scientists, researchers, advanced undergraduate and graduate students in Nonlinear Optics.Dr. Yanpeng Zhang is a professor and Zhiqiang Nie is a Ph. D. student at the Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, China. Dr. Min Xiao is a professor of physics at the University of Arkansas, Fayetteville, U.S.A.

Author Biography

Dr. Yanpeng Zhang is a professor and Zhiqiang Nie is a Ph. D. student at the Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, China. Dr. Min Xiao is a professor of physics at the University of Arkansas, Fayetteville, U.S.A.

Table of Contents

Introduction	p. 1
Nonlinear Susceptibility	p. 2
Coherence Functions	p. 3
Suppression and Enhancement of FWM Processes	p. 6
Double Dressing Schemes of Probe and Four-Wave Mixing Fields	p. 8
Spatial Optical Modulation via Kerr Nonlinearities	p. 10
Formations and Dynamics of Novel Spatial Solitons	p. 15
References	p. 18
Ultrafast Polarization Beats of Four-Wave Mixing Processes	p. 23
Four-level Polarization Beats with Broadband Noisy Light	p. 23
Basic Theory	p. 25
FLPB in a Doppler-broadened System	p. 32
Photon-echo	p. 34
Experiment and Result	p. 39
Ultrafast Sum-frequency Polarization Beats in Twin Markovian Stochastic Correlation	p. 44
Basic Theory	p. 45
Second-order Stochastic Correlation of ASPB	p. 50
Fourth-order Stochastic Correlation of ASPB	p. 62
References	p. 76
Raman, Rayleigh and Brillouin-enhanced FWM Polarization Beats	p. 81
Attosecond Sum-frequency Raman-enhanced Polarization Beats Using Twin Phase-sensitive Color Locking Noisy Lights	p. 81
Basic Theory of Attosecond Sum-frequency REPB	p. 83
Homodyne Detection of Sum-frequency REPB	p. 89
Heterodyne Detection of Difference-frequency REPB	p. 104
Competition Between Raman and Rayleigh-enhanced Four- Wave Mixings in Attosecond Polarization Beats	p. 112
Basic Theory	p. 113
Stochastic Correlation Effects of Rayleigh and Raman-enhanced FWM	p. 116
The Raman and Rayleigh-enhanced Nonlinear Susceptibility in cw Limit	p. 124
Homodyne Detection of ASPB	p. 126
Heterodyne Detection of ASPB	p. 132
Discussion and Conclusion	p. 140
Coexisting Brillouin, Rayleigh and Raman-enhanced Four-Wave Mixings	p. 144
Basic Theory	p. 145
Homodyne Detection of ASPB	p. 148
Heterodyne Detection of ASPB	p. 152
Phase Angle	p. 162
Discussion and Conclusion	p. 164
References	p. 166
Multi-Dressing Four-Wave Mixing Processes in Confined and Non-confined Atomic System	p. 169
Temporal and Spatial Interference Between Four-Wave Mixing and Six-Wave Mixing Channels	p. 169
Intermixing Between Four-Wave Mixing and Six-Wave Mixing in a Four-level Atomic System	p. 176
Interplay Between FWM and SWM	p. 177
Discussion	p. 183
Coexistence of Four-Wave, Six-Wave and Eight-Wave Mixing Processes in Multi-dressed Atomic Systems	p. 183
Parallel and Nested Dressing Schemes	p. 185
Interplay Among Coexisting FWM, SWM and EWM Processes	p. 193
Controlled Multi-Wave Mixing via Interacting Dark States in a Five-level System	p. 198
Basic Theory	p. 199
Numerical Results	p. 208
Discussion	p. 221
Polarization Interference of Multi-Wave Mixing in a Confined Five-level System	p. 221
Basic Theory	p. 223
MWM in Long Cells	p. 232
MWM in Ultra-thin and Micrometer Cells	p. 238
Discussion	p. 246
References	p. 247
Enhancement and Suppression in Four-Wave Mixing Processes	p. 253
Interplay among Multi-dressed Four-Wave Mixing Processes	p. 253
Observation of Enhancement and Suppression of Four-Wave Mixing Processes	p. 260
Controlling Enhancement and Suppression of Four-Wave Mixing via Polarized Light	p. 266
Theoretical Model and Analysis	p. 266
Experimental Results	p. 269
Enhancing and Suppressing Four-Wave Mixing in Electroma-genetically Induce Transparency Window	p. 273
References	p. 280
Multi-Wave Mixing Processes in Multi-level Atomic System	p. 283
Modulating Multi-Wave Mixing Processes via Polarizable Dark States	p. 284
Polarization Spectroscopy of Dressed Four-Wave Mixing in a Three-level Atomic System	p. 298
Various Nonlinear Susceptibilities for Different Polarization Schemes	p. 300
Nonlinear Susceptibilities for Zeeman-degenerate System Interacting with Polarized Fields	p. 302
Third-order Density-matrix Elements in Presence of Dressing Fields	p. 306
Controlling FWM and SWM in Multi-Zeeman Atomic System with Electromagnetically Induced Transparency	p. 314
Basic Theory	p. 315
Dual-dressed EIT	p. 319
Four-Wave Mixing	p. 323
Six-Wave Mixing	p. 328
References	p. 330
Controlling Spatial Shift and Spltting of Four-Wave Mixing	p. 333
Basic Theory	p. 333
Electromagnetically-induced Spatial Nonlinear Dispersion of Four-Wave Mixing Beams	p. 337
Spatial Dispersion Induced by Cross-phase Modulation	p. 346
Experimental Demonstration of Optical Switching and Routing via Four-Wave Mixing Spatial Shift	p. 351
Theoretical Model and Experimental Scheme	p. 352
Optical Switching and Routing via Spatial Shift	p. 354
Controlled Spatial Beamsplitter Using Four-Wave Mixing Images	p. 358
Spatial Splitting and Intensity Suppression of Four-Wave Mixing in V-type Three-level Atomic System	p. 365
References	p. 370
Spatial Modulation of Four-Wave Mixing Solitons	p. 373
Basic Theory	p. 373
Calculation of Double Dressed Cross-Kerr Nonlinear Index of Refraction	p. 374
Calculation of Analytical Solution of One-dimensional Bright and Dark Spatial Solitons	p. 380
Novel Spatial Gap Solitons of Four-Wave Mixing	p. 384
Dipole-mode Spatial Solitons of Four-Wave Mixing	p. 391
Modulated Vortex Solitons of Four-Wave Mixing	p. 398
References	p. 408
Index	p. 411
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