Citation
Nilsen, Joseph Michael (1982) Phase Conjugation via FourWave Mixing in a Resonant Medium. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RV9BGV44. https://resolver.caltech.edu/CaltechTHESIS:02182014143316560
Abstract
This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate fourwave mixing in resonant media. The theoretical work models the resonant medium as a twolevel atomic system with the lower state of the system being the ground state of the atom. Working initially with an ensemble of stationary atoms, the density matrix equations are solved by thirdorder perturbation theory in the presence of the four applied electromagnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be nondepleted counterpropagating pump waves while the third wave is an incident signal wave. The fourth wave is the phase conjugate wave which is generated by the interaction of the three previous waves with the nonlinear medium. The solution of the density matrix equations gives the local polarization of the atom. The polarization is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Studying the dependence of the phase conjugate signal on the various parameters such as frequency, we show how an ultrahighQ isotropically sensitive optical filter can be constructed using the phase conjugation process.
In many cases the pump waves may saturate the resonant medium so we also present another solution to the density matrix equations which is correct to all orders in the amplitude of the pump waves since the thirdorder solution is correct only to firstorder in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate fourwave mixing and also describe the ac Stark effect and how it modifies the frequency response of the filtering process. We also show how a narrow bandwidth optical filter with an efficiency greater than unity can be constructed.
In many atomic systems the atoms are moving at significant velocities such that the Doppler linewidth of the system is larger than the homogeneous linewidth. The latter linewidth dominates the response of the ensemble of stationary atoms. To better understand this case the density matrix equations are solved to thirdorder by perturbation theory for an atom of velocity v. The solution for the polarization is then integrated over the velocity distribution of the macroscopic system which is assumed to be a gaussian distribution of velocities since that is an excellent model of many real systems. Using the Doppler broadened system, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile.
Since it is a resonant system, sodium vapor is used as the nonlinear medium in our experiments. The relevant properties of sodium are discussed in great detail. In particular, the wavefunctions of the 3S and 3P states are analyzed and a discussion of how the 3S3P transition models a twolevel system is given.
Using sodium as the nonlinear medium we demonstrate an ultrahighQ optical filter using phase conjugation via nondegenerate fourwave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10^{3}. However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  FourWave Mixing  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Physics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  7 April 1982  
NonCaltech Author Email:  nilsen1 (AT) llnl.gov  
Funders: 
 
Record Number:  CaltechTHESIS:02182014143316560  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:02182014143316560  
DOI:  10.7907/RV9BGV44  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  8081  
Collection:  CaltechTHESIS  
Deposited By:  Benjamin Perez  
Deposited On:  18 Feb 2014 22:55  
Last Modified:  18 Jun 2020 21:27 
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