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Physical Review Letters

Time-Delayed Second Harmonic Generation

J. H. Brownell, Xilin Lu, Sven R. Hartmann

Published Nov 13, 1995• 6 citations
Publisher

Abstract

Second harmonic generation in Cs vapor is produced by the combined action of a polarized laser pulse and a magnetic field. It is delayed from the 10 ps excitation pulse by several hundred ps. The laser is two-photon resonant with the $6{S}_{\frac{1}{2}}\ensuremath{-}6{D}_{\frac{3}{2}}$ transition and initially induces a macroscopic quadrupole moment whose radiation pattern has a null in the forward direction. The magnetic field reshapes this pattern to produce second harmonic light, which is simply a free polarization decay signal evolving in a manner akin to the free induction decay following an adiabatic demagnetization.

DOI
10.1103/physrevlett.75.3657

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Journal of the Physical Society of Japan•Sep 1, 1983•6 citations
Second harmonic generation in Cs vapor is produced by the combined action of a polarized laser pulse and a magnetic field. It is delayed from the 10 ps excitation pulse by several hundred ps. The laser is two-photon resonant with the 6S12\ensuremath−6D326{S}_{\frac{1}{2}}\ensuremath{-}6{D}_{\frac{3}{2}}6S21​​\ensuremath−6D23​​ transition and initially induces a macroscopic quadrupole moment whose radiation pattern has a null in the forward direction. The magnetic field reshapes this pattern to produce second harmonic light, which is simply a free polarization decay signal evolving in a manner akin to the free induction decay following an adiabatic demagnetization.
Time-delayed second harmonic generation has recently been reported in an atomic vapor of Cs at a temperature near 180 degrees Celsius and situated in a magnetic field of the order of a killogauss. Short 10 ps excitation laser pulses at 885 nm were used to excite a macroscopic electric quadrupole density which was then observed to radiate at 442 nm after a delay of a few hundred picoseconds. The experiment is complicated by the presence of several superfluorescence transitions some of which radiate close to the 442 nm wavelength. These emissions are also delayed and our strategy is to set the experimental conditions so that they only become appreciable after the second harmonic emission is complete. In this paper we show how the second harmonic develops by considering the evolution of the radiation pattern of an isolated atomic radiator (not forbidden to radiate at the second harmonic even in the absence of a magnetic field). We estimate the intensity of the superradiant second harmonic emission and obtain agreement with experiment. Excellent agreement is also obtained between measured and calculated delay.
Second harmonic generation has hitherto been thought of as simultaneous with the excitation pulse which generates it. Recent experiments in Cs vapor demonstrate otherwise. A short two-photon 6D - 6S resonant excitation pulse in Cs vapor generates a superposition state which would radiate immediately were it not for destructive interference arising from the sample being large compared to the radiation wavelength. The radiation pattern of an isolated radiator (atom) starts out with a null in the plane transverse to the polarization (linear) direction but then rotates about the applied transverse magnetic field developing a radiation component along the phase matched direction which we detect. Experimental results are presented in excellent agreement with theory. Previous delay discrepancies have been resolved by using a nonmetallic sample cell. Cascade and yoked superfluorescence take place but not significantly until after the second harmonic emissions. Quantitative measurements of signal intensity are also presented.
A 10 ps transform limited optical pump pulse two-photon-resonant with the 6 S1/2-6 D32 442 nm transition in Cs vapor generates a coherent state superposition which, after a delay exceeding the pulse width, gives rise to second harmonic emission (when a transverse magnetic field is present) and superfluorescence (SF) directed against the pump on the upper 6 D3/2-6 P1/2 transition, followed by cooperative SF along the pump simultaneously on both the upper and lower 6 P3/2 − 6 P1/2 transitions, followed in turn by SF against the pump on the lower transition. Phase locked quantum beats associated with the 1.17 GHz hyperfine splitting of the 6 P1/2 appear on all SF emissions.
We investigated the process of magnetic field- induced optical second harmonic generation (SHG) in sodium vapor with a cw single-frequency dye laser tuned in the vicinity of the resonantly enhancing 3S-4D two-photon transition at 578.7 nm.1 All previous investigators have used pulsed dye lasers with relatively large linewidths.2 By exploiting the narrow linewidth capability of the cw dye laser (0.5 MHz) we have been able to investigate in detail for the first time properties of the SHG process which change across the line profile. We modeled the process on a theory developed from that reported by Uchlki et al.2 The two-photon absorption creates coherent quadrupole moments which rotate in the magnetic field due to Zeeman splitting to allow generation of the second harmonic.
A high-resolution study of magnetic-field-induced second-harmonic generation in sodium vapor has been carried out with use of a single-frequency continuous-wave dye laser. Resonant enhancement was obtained by tuning the laser to the frequency of the 3S\ensuremath{\rightarrow}4D two-photon transition of the sodium atom. Experimental and theoretical results are presented showing the variation of the power and polarization properties of the second-harmonic radiation as the laser is tuned across the two-photon resonance, and as the transverse magnetic field is varied.
We analyze second harmonic generation in sodium vapor in a transverse magnetic field induced by the two-photon resonant excitation of the 3S-3D transition. The phenomenon is explained by the rotation of the two-photon induced quadrupole moment in the magnetic field. The analysis explains well the saturation of the intensity and rotation of the polarization of the second harmonic radiation in the higher magnetic field ≳0.5{\gtrsim}0.5≳0.5 kG. The collisional decay rate of the coherence of the E1 forbidden transition has been measured as an application of this SHG.