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Physical Review A

Extra resonances in four-wave mixing triggered by radiative relaxation

Harry Friedmann, A. D. Wilson‐Gordon

Published Nov 1, 1982• 25 citations
Publisher

Abstract

It is predicted that, at sufficiently high laser intensity, the recently observed Raman-type extra-resonant enhancement of four-wave mixing [Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981)] should not vanish in the absence of collisions. The collisionless contribution to the extra resonance is associated with a three-photon scattering process which produces an extra-resonant signal intensity which is fourth order in the laser intensity.

DOI
10.1103/physreva.26.2768

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Europhysics Letters (EPL)•Feb 1, 1986•14 citations
It is predicted that, at sufficiently high laser intensity, the recently observed Raman-type extra-resonant enhancement of four-wave mixing [Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981)] should not vanish in the absence of collisions. The collisionless contribution to the extra resonance is associated with a three-photon scattering process which produces an extra-resonant signal intensity which is fourth order in the laser intensity.
Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state \ensuremath{\Vert}b〉 of the \ensuremath{\Vert}a〉\ensuremath{\rightarrow}\ensuremath{\Vert}b〉 transition, excited by near-resonant incident laser beams, decays to the lower state \ensuremath{\Vert}a〉 both directly (\ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉) and via one or two intermediate states: \ensuremath{\Vert}b〉\ensuremath{\rightleftarrows}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}c〉\ensuremath{\rightarrow}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.
It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\ensuremath{\rightarrow}| b 〉$ transition which produces the DFWM signal is coupled to another transition ($ | a 〉\ensuremath{\rightarrow}| d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state ∣b〉| b 〉∣b〉 and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth (1T1)ba{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}(T1​1​)ba​, the inverse lifetime of the state ∣b〉| b 〉∣b〉. The second effect derives from the effective lifetime acquired by the ground state ∣a〉| a 〉∣a〉 due to its strong coupling to state ∣d〉| d 〉∣d〉. This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth 12(1T1)da\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}21​(T1​1​)da​, which is half the inverse lifetime of the state ∣d〉| d 〉∣d〉. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.