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Applied Physics Letters

Focusing and phase conjugation of photon echoes in Na vapor

N. C. Griffen, C. V. Heer

Published Nov 15, 1978• 23 citations
Publisher

Abstract

The focusing and phase conjugation of photon echoes was observed in Na vapor. If the radius of curvature of the first pulse was R1 and the second pulse R2, the radius of curvature of the echo was given by 1/RE=2/R2−1/R1 and the echo center of curvature or focus followed from the phase φE(r) =2φ2(r)−φ1(r) in the Na cell.
DOI
10.1063/1.90193

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It is shown that the radius of curvature ${R}^{\ensuremath{'}\ensuremath{'}}$ of the photon echo is related to the radius of curvature RRR of the first pulse and ${R}^{\ensuremath{'}}$ of the second pulse by $\frac{1}{{R}^{\ensuremath{'}\ensuremath{'}}}=\frac{2}{{R}^{\ensuremath{'}}}\ensuremath{-}\frac{1}{R}$ and yields a focusing effect for the photon echo.
Since for echo formation the off-diagonal density matrix element ${\ensuremath{\sigma}}_{\mathrm{ab}}$ evolves from ${\ensuremath{\sigma}}_{\mathrm{ba}}={\ensuremath{\sigma}}_{\mathrm{ab}}^{*}$ of the previous pulse, the eikonal $\ensuremath{\phi}\ensuremath{-}\ensuremath{\omega}t$ reverses sign with each pulse. If the radius of curvature of the first $\frac{\ensuremath{\pi}}{2}$ pulse is R1{R}_{1}R1​, the radius of curvature of the subsequent $\ensuremath{\pi}$ pulses R2{R}_{2}R2​, R3{R}_{3}R3​, etc., the radius of curvature of the photon echo which follows the second pulse is $\frac{1}{{R}_{E1}}=\frac{2}{{R}_{2}}\ensuremath{-}\frac{1}{{R}_{1}}$, the radius of curvature of the Carr-Purcell echo following the third pulse is given by $\frac{1}{{R}_{E2}}=\frac{2}{{R}_{3}}\ensuremath{-}\frac{2}{{R}_{2}}+\frac{1}{{R}_{1}}$, and for subsequent Carr-Purcell echoes by $\frac{1}{{R}_{E3}}=\frac{2}{{R}_{4}}\ensuremath{-}\frac{2}{{R}_{3}}+\frac{2}{{R}_{2}}\ensuremath{-}\frac{1}{{R}_{1}}$, etc. The influence of motion, adiabatic collisions, and velocity-changing collisions on the decay of echo amplitude is considered for curved wave fronts. Since the change in position from the constant-velocity position is important in the decay, a statistical theory for small displacement and its relationship to the forward scattering cross section is given. These results with ${r}^{\ensuremath{-}3}$ and ${r}^{\ensuremath{-}6}$ interactions between colliding molecules are compared with the experimental data for CH3{\mathrm{CH}}_{3}CH3​F and with an ${r}^{\ensuremath{-}6}$ potential with the data for SF6{\mathrm{SF}}_{6}SF6​ and SiF4{\mathrm{SiF}}_{4}SiF4​.
During the study of focusing and phase conjugation of photon echoes it became apparent that similar effects occur for either simultaneous pulses or continuous laser radiation. These effects are apparent in the simple two level atom theory in which the stimulated electric dipole is proportional for steady state to [EQUATION] where the electric field amplitude E = A eiφ + B . A(x,z) and φ(x,z) are the amplitude and phase of the signal wave and B is the amplitude of a plane carrier wave. The phase conjugate wave A e-1φ is generated by the A2 + B2 + 2 AB cosφ term in the denominator. Phase conjugation is limited to physically thin cells and a 1 mm Na cell limits the angular spread to ± 20 milliradians. Current experiments with a 2 mm thick Na cell will be discussed. For two laser beams at angle θ, radiation at the phase conjugate -θ, and at higher angles ± 2θ, ±3θ, etc. are observed. Limited phase conjugation such as focusing of a curved wavefront has been observed. More extensive phase conjugation results will be reported.