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Stark-Induced Optical Nonlinearity in Gaseous NH_2D and Optical Waves in Layered Media

Pochi Yeh

Published Jan 1, 1978• 0 citations
Publisher

Abstract

The first part of this work describes theoretical and experimental studies of Stark-induced three-wave mixing in gaseous NH2D. Application of a dc electric field to a gaseous system destroys the basic inversion symmetry and allows two-photon mixing processes to occur. A theoretical derivation of this effect under conditions of resonantly enhanced non-linearities is given for a three-level system. Calculations are presented for mixing of a CO2 laser with a 4 GHz microwaves in the molecule NH2D, producing single lower sideband radiation. Experimental observation of resonantly enhanced, dc-induced, three-wave mixing in gaseous NH2D is presented. The dependence of this effect on gas pressure, microwave frequency, applied dc field, and microwave power are presented and compared with theoretical predictions. The experiment was done at Hughes Research Laboratories by Abrams and his coworkers. The second part of this work describes the propagation of electromagnetic waves in periodic layered media. The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-finite and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. The theory of electromagnetic Bloch waves in periodic stratified media is then applied to the problems of birefringence, and group velocity in these media. The relevance of periodic media to phase matching in nonlinear mixing experiments-and to laser action in the x-ray region is discussed. New types of guided waves such as Bragg guided waves and optical surface waves are theoretically predicted and experimentally observed.

DOI
10.7907/mbfm-x335.

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Application of dc electric field to a gaseous system destroys the basic inversion symmetry and allows three-wave mixing processes to occur. A theoretical derivation of this effect under conditions of resonantly enhanced nonlinearities is given for a three-level system. Calculations are presented for mixing of a CO2laser with 4-GHz microwaves in the molecule NH2D, producing single lower sideband radiation.

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
The first part of this work describes theoretical and experimental
studies of Stark-induced three-wave mixing in gaseous NH2D. Application
of a dc electric field to a gaseous system destroys the basic inversion
symmetry and allows two-photon mixing processes to occur. A theoretical
derivation of this effect under conditions of resonantly enhanced
non-linearities is given for a three-level system. Calculations are presented
for mixing of a CO2 laser with a 4 GHz microwaves in the molecule NH2D,
producing single lower sideband radiation. Experimental observation of resonantly enhanced, dc-induced,
three-wave mixing in gaseous NH2D is presented. The dependence of this effect
on gas pressure, microwave frequency, applied dc field, and microwave
power are presented and compared with theoretical predictions. The
experiment was done at Hughes Research Laboratories by Abrams and his coworkers. The second part of this work describes the propagation of electromagnetic
waves in periodic layered media. The propagation of electromagnetic
radiation in periodically stratified media is considered. Media
of finite, semi-finite and infinite extent are treated. A diagonalization
of the unit cell translation operator is used to obtain exact
solutions for the Bloch waves, the dispersion relations, and the band
structure of the medium. The theory of electromagnetic Bloch waves in periodic stratified
media is then applied to the problems of birefringence, and group velocity
in these media. The relevance of periodic media to phase matching
in nonlinear mixing experiments-and to laser action in the x-ray region
is discussed. New types of guided waves such as Bragg guided waves and optical
surface waves are theoretically predicted and experimentally observed.
Coherent, optically dressed media composed of two-level molecular systems without inversion symmetry are considered as all-optically tunable sources of coherent radiation in the microwave domain. A theoretical model and a numerical toolbox are developed to confirm the main finding: the generation of low-frequency radiation, and the buildup and propagation dynamics of such low-frequency signals in a medium of polar molecules in a gas phase. The physical mechanism of the signal generation relies on the permanent dipole moment characterizing systems without inversion symmetry. The molecules are polarized with a DC electric field yielding a permanent electric dipole moment in the laboratory frame; the direction and magnitude of the moment depend on the molecular state. As the system is resonantly driven, the dipole moment oscillates at the Rabi frequency and, hence, generates microwave radiation. We demonstrate the tuning capability of the output signal frequency with the drive amplitude and detuning. We find that even though decoherence mechanisms such as spontaneous emission may damp the output field, a scenario based on pulsed illumination yields a coherent, pulsed output of tunable temporal width. Finally, we discuss experimental scenarios exploiting rotational levels of gaseous ensembles of heteronuclear diatomic molecules.
Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
Strong and short coherent pulses of electromagnetic radiation propagate through extended absorbing media with anomalously low absorption, they are delayed and reshaped. This article presents experimental results and calculations for propagation of 10.6-\ensuremath{\mu} wavelength pulses through gaseous SF6{\mathrm{F}}_{6}F6​. The degeneracy of overlapping levels of SF6{\mathrm{F}}_{6}F6​ in that spectral region is important, and enables us to use a simple model to describe observed phenomena. We assume a continuous distribution of dipole moments. Results are particularly interesting in two regimes of excitation. One corresponds to very strong excitation and \ensuremath{\sim}20 absorption lengths in the medium: Pulses sharpen at their leading edge, while their front part gets absorbed. The other pertains to much lower excitation and only 2 absorption lengths: Reradiation can be distinguished and long delays result which qualitatively resemble the behavior of a two-level system in self-induced transparency. Fairly conclusive agreement is obtained between a previous theoretical treatment of a homogeneously broadened multilevel medium and experiment. The agreement is substantiated by computer calculations. In three Appendixes we present the observation of focusing effects, the theory of an experiment related to transient nutation, and some remarks on photon-echo polarization experiments in optically thick media.
This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level 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 third-order perturbation theory in the presence of the four applied electro-magnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be non-depleted 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 ultrahigh-Q 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 third-order solution is correct only to first-order in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate four-wave 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 third-order 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 3S-3P transition models a two-level system is given. Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave 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.
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.