Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Journal of Quantum Electronics

Stark-induced three-wave mixing in molecular gases - Part I: Theory

R. Abrams, Avigail Yariv, P. Yeh

Published Mar 1, 1977• 20 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1977.1069283

Related papers

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

Pochi Yeh

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.

•Jan 1, 1978•0 citations

AC Stark-effect-enhanced near-resonant wave mixing in a four-level system. 1: Experiment

Chen-Yu Tai, Charles C. Kim

Two laser beams at frequencies v(1) and v(2) are used to produce nonlinear scattering (wave mixing) in I2 vapor at frequency 2v(1) + v(2). The scattering results from near resonance allowed transitions in I2 molecules and is observed to be resonantly enhanced when neither the one-, two-, nor three-quantum transitions are in resonance.

•Jun 9, 1986•0 citations

DC-field-induced resonance and polarization effects in two-colour frequency mixing in atoms

Nikolai L. Manakov, Vitalii D Ovsiannikov, Nikolai L. Manakov

In a gas of free atoms interacting with a two-colour laser radiation, a DC electric field provides the necessary conditions for generation of sum-frequency radiation, together with a resonance enhancement of the frequency conversion process. The interference between the DC-field-induced and the dipole-forbidden three-photon amplitudes causes circular dichroism effects in the scattering of the sum-frequency photons at right angles to the incident laser beams. The DC-field-induced resonance effect is strongly dependent on the frequency detuning and the width of the resonant levels.

Journal of Physics B Atomic Molecular and Optical Physics•May 16, 2000•4 citations

ac-Stark-effect-enhanced four-wave mixing in a near-resonant four-level system

Chen-Yu Tai, Robert T. Deck, Charles Kim

We report on an ac-Stark-effect-enhanced wave-mixing experiment in ${\mathrm{I}}_{2}$ vapor in which an output uv signal at frequency 2${\ensuremath{\omega}}_{1}$+${\ensuremath{\omega}}_{2}$ is maximized when the input frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are both detuned in the same direction from the resonance frequencies of the free molecule. A theory based on a configuration interaction between the ``dressed molecular levels'' is presented to explain the strong enhancement of the uv signal under these conditions. The data presented demonstrate that tunable coherent radiation at ultraviolet and vacuum-ultraviolet frequencies can be generated by the wave-mixing process we describe.

Physical Review A•Jan 1, 1988•7 citations

Propagation of optically tunable coherent radiation in a gas of polar molecules

Piotr Gładysz, Piotr Wcisło, Karolina Słowik

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.

arXiv:2002.05469•Scientific Reports•Oct 19, 2020•7 citations

Observation of ac Stark-effect-enhanced four-wave mixing in a near-resonant four-level system

Chen-Yu Tai, Charles C. Kim, Robert T. Deck +1 more

Two laser beams at frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ are used to produce nonlinear scattering (wave mixing) in ${\mathrm{I}}_{2}$ vapor at frequency 2${\ensuremath{\nu}}_{1}$+${\ensuremath{\nu}}_{2}$. The scattering results from near-resonant allowed transitions in ${\mathrm{I}}_{2}$ molecules and is observed to be anomalously strong when both laser beam frequencies are detuned in the same direction from frequencies corresponding to resonance in the free molecule. The strong scattering is interpreted in terms of a resonantly enhanced ac Stark shift caused by a configuration interaction between the ``dressed molecular levels.'' By tuning the two pulses simultaneously, a tuning range of approximately 2 A\r{} (50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) is achieved in the mixed wave. The scattering process should therefore have practical application in the efficient generation of tunable coherent radiation in the ultraviolet and vacuum-ultraviolet range of the spectrum. Some of the spectroscopic properties of the three-quantum state at E\ensuremath{\sim}53 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are studied.

Physical Review A•Jun 1, 1986•6 citations
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.
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.
In a gas of free atoms interacting with a two-colour laser radiation, a DC electric field provides the necessary conditions for generation of sum-frequency radiation, together with a resonance enhancement of the frequency conversion process. The interference between the DC-field-induced and the dipole-forbidden three-photon amplitudes causes circular dichroism effects in the scattering of the sum-frequency photons at right angles to the incident laser beams. The DC-field-induced resonance effect is strongly dependent on the frequency detuning and the width of the resonant levels.
We report on an ac-Stark-effect-enhanced wave-mixing experiment in I2{\mathrm{I}}_{2}I2​ vapor in which an output uv signal at frequency 2${\ensuremath{\omega}}_{1}$+${\ensuremath{\omega}}_{2}$ is maximized when the input frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are both detuned in the same direction from the resonance frequencies of the free molecule. A theory based on a configuration interaction between the ``dressed molecular levels'' is presented to explain the strong enhancement of the uv signal under these conditions. The data presented demonstrate that tunable coherent radiation at ultraviolet and vacuum-ultraviolet frequencies can be generated by the wave-mixing process we describe.
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.
Two laser beams at frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ are used to produce nonlinear scattering (wave mixing) in I2{\mathrm{I}}_{2}I2​ vapor at frequency 2${\ensuremath{\nu}}_{1}$+${\ensuremath{\nu}}_{2}$. The scattering results from near-resonant allowed transitions in I2{\mathrm{I}}_{2}I2​ molecules and is observed to be anomalously strong when both laser beam frequencies are detuned in the same direction from frequencies corresponding to resonance in the free molecule. The strong scattering is interpreted in terms of a resonantly enhanced ac Stark shift caused by a configuration interaction between the ``dressed molecular levels.'' By tuning the two pulses simultaneously, a tuning range of approximately 2 A\r{} (50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) is achieved in the mixed wave. The scattering process should therefore have practical application in the efficient generation of tunable coherent radiation in the ultraviolet and vacuum-ultraviolet range of the spectrum. Some of the spectroscopic properties of the three-quantum state at E\ensuremath{\sim}53 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are studied.