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Japanese Journal of Applied Physics

Self-Modulation and Picosecond-Pulse Generation by Stimulated Raman Scattering

Kōichi Shimoda

Published Dec 1, 1969• 6 citations
Publisher

Abstract

The regular structure in frequency broadening spectrum of the self-trapped laser and Raman radiations is produced by the phase-modulation of light waves propagating in the filament with intensity-dependent index of refraction. A quantum-mechanical calculation of double quantum transition in a three-level system is shown to explain the process of self-modulation and the production of picosecond pulses in the Raman process. Coherent coupling of the laser and the Stokes waves produces mutual modulation of large amplitude, if the optical field is strong and the vibrational relaxation time is long. Numerical evaluation for CS2 gives a modulation frequency of about 1011 Hz, when an optical power of 10 kW is trapped in a filament of 2 µm radius. Besides, the effect of self-modulation on the spatial distribution of anti-Stokes emission along the filament is discussed and shown to agree with the experimental results observed by Stoicheff and his co-workers.

DOI
10.1143/jjap.8.1499

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The regular structure in frequency broadening spectrum of the self-trapped laser and Raman radiations is produced by the phase-modulation of light waves propagating in the filament with intensity-dependent index of refraction. A quantum-mechanical calculation of double quantum transition in a three-level system is shown to explain the process of self-modulation and the production of picosecond pulses in the Raman process. Coherent coupling of the laser and the Stokes waves produces mutual modulation of large amplitude, if the optical field is strong and the vibrational relaxation time is long. Numerical evaluation for CS2 gives a modulation frequency of about 1011 Hz, when an optical power of 10 kW is trapped in a filament of 2 µm radius. Besides, the effect of self-modulation on the spatial distribution of anti-Stokes emission along the filament is discussed and shown to agree with the experimental results observed by Stoicheff and his co-workers.
A simple description of the stimulated Raman emission of Stokes radiation, and of the induced absorption found by Stoicheff at the anti-Stokes frequency, is based on the semiclassical theory of radiation. This theory gives the well-known formulas for absorption and stimulated emission when carried to the first order in the time-dependent perturbation due to the interaction of the light beam with the molecules. If there are two light beams of frequencies ωL and ω, the second-order perturbation may be associated with stimulated emission at the Stokes frequency ω=ω−1=ωL—ωR and with induced absorption at the anti-Stokes frequency ω=ω1=ωL+ωR, where ωL is the laser frequency and ωR a Raman-active vibrational frequency; in both cases, there is a molecular transition to the excited vibrational state. The highly directional and very sharp anti-Stokes emission at ω1 arises from the conversion by molecules in intense beams at ωL and ω−1 of two ωL photons into an ω−1, ω1 pair. Like spontaneous emission from excited states, the production of this anti-Stokes radiation requires the full quantum theory of radiation for an adequate description. The emission of ω1 and the observed directional absorption of ω−1 due to the reverse conversion ω−1+ω1→2ωL are explained. The anti-Stokes emission is proportional to the Stokes intensity and to the square of that of the laser, and to the square of the molecular number density; its sharpness is due to the absence of a molecular transition. The generation of photon pairs ω−n+ωn, where ωn=ωL+nωR, can occur for all values of n, but it is most efficient for n=1, due to resonance in the appropriate molecular hyperpolarizability and to the intensity of the Stokes beam at ω−1.
A calculation is made of the intensity of the Stokes radiation in the stimulated Raman scattering of ultrashort light pulses in a dispersive medium employing the asymptotic approximation for arbitrary modulation of the amplitude and phase of the pump pulse. Particular attention was paid to the effect of phase modulation on the stimulated Raman scattering. Calculations were also made of the intensity of the anti-Stokes component in the scattering of an ultrashort pulse in a dispersive medium and of the optimal angle for the observation of the anti-Stokes rings.
The results of numerical calculations of the transient stimulated Raman scattering reported previously have been verified experimentally under conditions where both linear dispersion and self-focusing effects were negligible. The existence of a delay between maxima of the laser and Stokes pulses is experimentally demonstrated for the first time, while the pulse shortening in time via Raman scattering is established more firmly than in previous work. The incident-laser-pulse duration, generated-Stokes-pulse duration, and delay between intensity maxima for the laser and Stokes pulses were measured with the two-photon absorption-fluorescence technique. The effective phonon-dephasing time is determined via spontaneous Raman scattering. By using these measured quantities, inferences are made as to the magnitude of the transient gain and the shape of the exciting picosecond laser pulse.
The self-induced suppression (SIS) of stimulated electronic Raman scattering (SERS) is discussed. The nature of SIS is that SERS induces in gaseous media the generation of new fields by a four-wave mixing (FWM) process which destructively interferes with SERS and results in its suppression. The behaviour of Stokes radiation is investigated under SIS of SERS, both in the steady-state case and in the non-stationary regime of interaction with an ultrashort pump pulse. The effect is shown to be absent in the non-stationary case. On the basis of this result the author is able to explain in a simple manner the 'strange' dependence of the Stokes wavelength on pump pulse duration observed experimentally in barium vapours. The author also discusses the possible application of SIS of SERS for Stokes frequency switching. This can be achieved by stimulation of destructive interference between SERS and FWM if, simultaneously with the pump pulse, a signal wave at a frequency of one of the parametrically generated fields is switched on. As a result the FWM is intensified leading to strong suppression of SERS on a given transition and the Stokes radiation is now generated on the other transition with a new frequency. The method can be used to convert the laser frequency into the far-IR region and for a new spectroscopic study of gaseous media.
We have observed self-modulation and self-compression of a femtosecond laser pulse after passing the beam through a Raman-active medium of hydrogen. Femtosecond pulses produce Stokes emissions of ortho-hydrogen and para-hydrogen, depending on the input beam conditions. The shape of the output pulses drastically changed as a function of the intensity of the Stokes emissions and the total width of the spectrum. This is attributed to nonlinear modulation of the wave form induced by coherent rotational motions of hydrogen molecules in the time domain.
Transient stimulated rotational Raman scattering induced by a polarization-modulated femtosecond pulse whose polarization varies with time is reported. The peak intensity of the polarization-modulated pulse produced in this study is low compared to that of a pulse without polarization variation, and this leads to the low efficiency of self-phase-modulation and thus the high efficiency of stimulated Raman scattering compared to the case of a pump pulse without polarization modulation. The scattering process is unique in terms of the high peak ratio of the anti-Stokes to Stokes emissions compared to the ratio in the case of the scattering induced by linearly, circularly, and elliptically polarized pump pulses. Under optimum conditions, the ratio approaches 1, which is not realized in the general case of stimulated rotational Raman scattering.