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

Journal of the Physical Society of Japan

Phase-Conjugation by Four-Wave Mixing in CuCl: Resonance Enhancement by Exciton and Excitonic Molecule and Its Polarization Dependence

Goro Mizutani, N. Nagasawa

Published Jun 1, 1983• 27 citations
Publisher

Abstract

The phase-conjugation in crystalline CuCl has been studied at 1.6 K. It has been found that the two-photon resonance of the \(\varGamma_{1}\)-excitonic molecule and the one-photon resonance of the \(\varGamma_{5}\)-exciton contribute to the generation of the phase-conjugated wave. Each contribution has been separated spectroscopically by adjusting the polarization configuration of the incident fields adequately and has been compared qualitatively with the theory. The efficiency of the phase-conjugated reflection has become maximum at around the two-photon resonance of the excitonic molecule, 3.186 eV and has been ∼1% at the maximum.

DOI
10.1143/jpsj.52.2251

Related papers

Optical phase conjugation via degenerate four-wave mixing in copper chloride

M. L. Claude, Lloyd L. Chase, Daniele Hulin +1 more

Abstract We present a study of optical phase conjugation through degenerate four-wave mixing in CuCl, as a function of light frequency, intensity, polarization and sample temperature. The phase-conjugate signal exhibits two maxima at the frequencies of the T5 exciton (one-photon resonance) and of the biexciton (two-photon resonance). By appropriate combinations of the input beam polarizations, it is possible to single out the various terms contributing to the signal (small-spaced, large-spaced population grating and two-photon coherent excitation). The absolute value of X(3) responsible for the two-photon resonance has been determined ( x(3) (-w,w,w, -w) = 3.10-7 e.s.u.). It leads to ‘mirror’ efficiencies of the order of 10% for input pump intensities I0 » 105 W cm -2 and sample thickness d» 10-4 cm. At higher I0, a saturation of the reflection takes place. The variation of the conjugate beam with temperature has been studied in the range 15 K < T <70 K. Finally, the phase-conjugate nature of the signal has been verified by inserting an aberrator in the path of the input probe beam, and by checking the reconstruction of the reflected beam.

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Dec 18, 1984•2 citations

Optical phase conjugation near resonance with biexciton two-photon absorption in CuCl (A)

Lloyd L. Chase, Marion Claude, Daniele Hulin +1 more

Measurements have been made of phas conjugation from degenerate four-wav mixing (DFWM) based on the large nonlinear susceptibility resulting from the two-photo absorption (TPA) resonance of the excitoni molecule state in CuCl. The excitonic molecule in CuCl is a bound state of two exciton that is responsible for a very strong two-photon absorption resonance at a photo energy of 3.186 eV at T ~ 4.2 K.1

Journal of the Optical Society of America B•Jan 1, 1984•0 citations

Optical phase conjugation based on the giant two-photon resonance of the excitonic molecule in CuCl

Lloyd L. Chase, M. L. Claude, Daniele Hulin +1 more

Optical phase conjugation resulting from the two-photon coherence due to the excitonic molecule resonance in CuCl has been observed and studied as a function of frequency, polarization, and pump intensity. Reconstruction of the polarization of an aberrated probe beam is demonstrated.

Physical Review A•Dec 1, 1983•25 citations

Optical nonlinearities due to excitonic molecules: Optical Stark effects and phase conjugation

Eiichi Hanamura

Large, nonlinear-optical phenomena are shown theoretically to be observable under nearly two-photon resonant pumping of the excitonic molecule (EM), e.g., in a CuCl crystal. When the exciton polariton (EP) is resonantly pumped into the EM, they are hybridized with each other and show optical Stark splitting. These splittings can be observed, respectively, as a sharp dip in the reflection spectrum and two-photon absorption spectrum due to the EM. We can also clarify how these splittings change into the blueshifts and redshifts of the EP and the EM as functions of the pump frequency and power. The generation of the phase-conjugated wave is shown also to be enhanced under two-photon resonant pumping of the EM. Some characteristics about pump-probe frequency and polarization dependences are also clarified. We have also derived the effective Hamiltonian of the exciton and the EM from the first-principles equation of motion for the exciton coupled with that of the EM. This Hamiltonian has made possible the theoretical analysis of these nonlinear-optical phenomena.

Physical review. B, Condensed matter•Oct 15, 1991•15 citations

Two-Photon Resonant, Coherent Raman Scattering via Excitonic Molecules in CuCl

Yasuaki Masumoto, Shigeo Shionoya

The three-wave mixing process has been studied as functions of incident photon energy and also of the geometrical configuration when incident photon energy lies around the two-photon resonance of excitonic molecule. Experiments indicate that the intensity of the third order nonlinear light beam is enhanced when the phase matching condition derived from the dispersion of excitonic polariton holds or when incident photon energy is equal to the two-photon resonance of excitonic molecule. The relation between this three-wave mixing process and two-photon resonant Raman scattering so far observed is discussed. It is shown that this three-wave mixing process is regarded as the two-photon resonant, coherent Raman scattering via excitonic molecules.

Journal of the Physical Society of Japan•Dec 1, 1980•23 citations

Four-wave-mixing theory for two-photon generation of excitons in Cu2O

Igor V. Beloussov, John B. Ketterson, Yinghui Sun

We propose and examine theoretically a four-wave-mixing experiment in which excitons in ${\text{Cu}}_{2}\text{O}$ are pumped directly into a state with wave vector $\mathbf{k}=\mathbf{0}$ by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. Approximate analytical solutions of the time evolution equations are found which describe the time dependence of the exciton and photon densities. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time ${t}_{d}$ between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time ${t}_{d}$ is the same as the exciton density dependence on the time $t$. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.

Physical Review B•Dec 23, 2009•1 citation
The phase-conjugation in crystalline CuCl has been studied at 1.6 K. It has been found that the two-photon resonance of the (\varGamma_{1})-excitonic molecule and the one-photon resonance of the (\varGamma_{5})-exciton contribute to the generation of the phase-conjugated wave. Each contribution has been separated spectroscopically by adjusting the polarization configuration of the incident fields adequately and has been compared qualitatively with the theory. The efficiency of the phase-conjugated reflection has become maximum at around the two-photon resonance of the excitonic molecule, 3.186 eV and has been ∼1% at the maximum.
Abstract We present a study of optical phase conjugation through degenerate four-wave mixing in CuCl, as a function of light frequency, intensity, polarization and sample temperature. The phase-conjugate signal exhibits two maxima at the frequencies of the T5 exciton (one-photon resonance) and of the biexciton (two-photon resonance). By appropriate combinations of the input beam polarizations, it is possible to single out the various terms contributing to the signal (small-spaced, large-spaced population grating and two-photon coherent excitation). The absolute value of X(3) responsible for the two-photon resonance has been determined ( x(3) (-w,w,w, -w) = 3.10-7 e.s.u.). It leads to ‘mirror’ efficiencies of the order of 10% for input pump intensities I0 » 105 W cm -2 and sample thickness d» 10-4 cm. At higher I0, a saturation of the reflection takes place. The variation of the conjugate beam with temperature has been studied in the range 15 K < T <70 K. Finally, the phase-conjugate nature of the signal has been verified by inserting an aberrator in the path of the input probe beam, and by checking the reconstruction of the reflected beam.
Large, nonlinear-optical phenomena are shown theoretically to be observable under nearly two-photon resonant pumping of the excitonic molecule (EM), e.g., in a CuCl crystal. When the exciton polariton (EP) is resonantly pumped into the EM, they are hybridized with each other and show optical Stark splitting. These splittings can be observed, respectively, as a sharp dip in the reflection spectrum and two-photon absorption spectrum due to the EM. We can also clarify how these splittings change into the blueshifts and redshifts of the EP and the EM as functions of the pump frequency and power. The generation of the phase-conjugated wave is shown also to be enhanced under two-photon resonant pumping of the EM. Some characteristics about pump-probe frequency and polarization dependences are also clarified. We have also derived the effective Hamiltonian of the exciton and the EM from the first-principles equation of motion for the exciton coupled with that of the EM. This Hamiltonian has made possible the theoretical analysis of these nonlinear-optical phenomena.
The three-wave mixing process has been studied as functions of incident photon energy and also of the geometrical configuration when incident photon energy lies around the two-photon resonance of excitonic molecule. Experiments indicate that the intensity of the third order nonlinear light beam is enhanced when the phase matching condition derived from the dispersion of excitonic polariton holds or when incident photon energy is equal to the two-photon resonance of excitonic molecule. The relation between this three-wave mixing process and two-photon resonant Raman scattering so far observed is discussed. It is shown that this three-wave mixing process is regarded as the two-photon resonant, coherent Raman scattering via excitonic molecules.
We propose and examine theoretically a four-wave-mixing experiment in which excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are pumped directly into a state with wave vector k=0\mathbf{k}=\mathbf{0}k=0 by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. Approximate analytical solutions of the time evolution equations are found which describe the time dependence of the exciton and photon densities. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time td{t}_{d}td​ between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time td{t}_{d}td​ is the same as the exciton density dependence on the time ttt. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.