Counterpropagating Pump Beams Research Articles

Collinear ultrasonic four‐wave mixing in suspensions of particles and bubbles.

The interaction of sound with sound in a suspension can be mediated by the suspension’s response to acoustic radiation pressure [H.J. Simpson and P.L. Marston, J. Acoust. Soc. Am. 98, 1731–1741 (1995)]. Four wave mixing mediated by a suspension with collinear pump and probe waves is investigated. Radiation pressure from counter propagating pump beams induces a periodic grating in the number density of hollow glass microspheres suspended in a water/sugar mixture designed to make the particles neutrally buoyant. The Bragg scattering amplitude was measured using a single PVDF transducer as both the probe source and receiver that is parallel with the standing pump wave nodal planes. Reflection coefficients are calculated by comparing the reflected and transmitted waves. By increasing the particle concentration, total Bragg reflectivities from the established grating reaching 20% have been seen, which is still in the region of agreement between the Born approximation and transfer matrix theory. The dynamics of both the grating formation and dissolution have been studied, leading to the conclusion that grating dissolution is not dominated by diffusion alone. Bragg scattering by gratings of gas bubbles caused by cavitation was detected. [Work supported by the Office of Naval Research.]

Detection of CN by degenerate four-wave mixing

The detection of CN, an important intermediate in the nitrogen oxidation chemistry of hydrocarbons, in the B2∑+ –X2∑+ electronic band by degenerate four-wave mixing is reported. The radical source consisted of a H2/O2/N2/C2H2/NO atmospheric-pressure premixed flame. We estimate a detection limit of 3 × 1013 CN molecules/cm3 and a rotational temperature of 920 K. A tilted backward pump beam degenerate four-wave mixing geometry is investigated, and results show an order-of-magnitude increase in the signal-to-noise ratio over the conventional counterpropagating pump beam geometry.

Spectral gain hole burning and modulation instability in a Brillouin fiber amplifier

We investigate theoretically the gain spectrum of a Brillouin fiber amplifier in the saturated region. When the amplifier is operated in the saturated region a hole is burned in the single-pass Brillouin gain spectrum, and peaks appear at frequencies determined mainly from the round-trip time of the amplifier, causing modulation instability in the amplified signal. This type of modulation instability originates intrinsically from signal amplification by the counterpropagating pump beam, which is depleted by the strong signal beam.

Probe transmission in a one-dimensional optical molasses: Theory for circularly-cross-polarized cooling beams.

We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.

Hexagonal pattern formation due to counterpropagation in KNbO_3

We report the transverse instability of laser beams due to counterpropagation in photorefractive KNbO3. Hexagonal unstable emission emerges around two counterpropagating pump beams. This emission is in the same linear polarization with the pump beams and is observed in configurations where reflection gratings are dominant.

Probe transmission in one-dimensional optical molasses: Theory for linearly cross-polarized cooling beams.

We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.

Nearly degenerate four-wave mixing using phase-conjugate pump beams

A novel configuration has been developed for performing degenerate four-wave mixing (DFWM) experiments using optical phase conjugation from stimulated Brillouin scattering in a cell. The typical geometry for DFWM requires that two pump beams counterpropagate through the measurement volume, which is accomplished either by splitting off a portion of the beam and directing it in from the opposite direction or reflecting the first pump beam back onto itself. In both approaches it can be difficult to maintain alignment between the counterpropagating pump beams, particularly in combustion systems that present thermal and density gradients. DFWM has been demonstrated for OH in a flame by using counterpropagating pump beams that are phase conjugate. The optical phase conjugation is achieved by focusing the first pump beam into a cell containing hexane, which produces a counterpropagating beam through stimulated Brillouin scattering. This approach greatly simplifies DFWM experiments by relaxing alignment constraints and sensitivities to index-of-refraction gradients in the flow.

Self-bending of light beams in photorefractive phase conjugators

Stimulated photorefractive phase conjugators often exhibit well-defined curved beam paths that cannot be explained by simple beam fanning. We propose a model of these apparently curved paths as a series of straight-line segments, with beams propagating in both directions along these segments. These line segments spring from the amplification of scattered light between regions of the crystal already containing counterpropagating pump beams. As these line segments form, they create new interaction regions that generate new segments, thereby making the final beam path appear to be curved. Application of our model to a single-interaction-region mutually pumped phase conjugator shows that the threshold coupling strength required for the appearance of these new segments is only slightly higher than the threshold for the phase conjugator itself.

Double phase-conjugate four-wave mixing of oh in flames

A novel configuration has been developed for performing degenerate four-wave mixing (DFWM) experiments using optical phase-conjugation from stimulated Brillouin scattering in a cell. The typical geometry for DFWM requires that two pump beams counter-propagate through the measurement volume, which is accomplished either by splitting off a portion of the beam and directing it in from the opposite direction or reflecting the first pump beam back on itself. In both approaches it can be difficult to maintain alignment between the counter-propagating, pump beams, particularly in combustion systems which present thermal and density gradients. DFWM has been demonstrated for OH in a flame using counter-propagating pump beams that are phase-conjugate. The optical phase-conjugation is achieved by focusing the first pump beam into a cell containing hexane which produces a counter-propagating beam via stimulated Brillouin scattering. This approach greatly simplifies DFWM experiments by relaxing alignment constraints and sensitivities to index of refraction gradients in the flow. The method has been applied to temperature measurements in flames and to the imaging of a turbulent diffusion flame simplifying, the spatial ambiguites which arise from signal beam steering. Additionally, it is, observed that at high laser intensities the spectral profiles display a dip at line center. The effect is attributed to saturation of the molecular transition.

Transient stimulated thermal scattering in a field of quasiplanar counterpropagating pump beams

Theoretical analyses and experimental studies are made of transient stimulated thermal scattering in a thermal nonlinear medium subjected to a field of counterpropagating quasiplane waves. The equations for the counterpropagating four-beam interaction are solved analytically for pairwise counterpropagating scattered waves using the constant pump wave intensity approximation. The conditions for the occurrence of an absolute instability of the scattered waves are determined and the angular dependence of their increment is obtained; these results are in good agreement with experimental data. An investigation is reported of the dynamics of spiky lasing in a laser with resonators coupled by a dynamic hologram in which stimulated thermal scattering is a source of radiation initiating lasing in the system as a whole.

A review of Brillouin-enhanced four-wave mixing

When a Brillouin-shifted signal interacts with a two strong counterpropagating pump beams in a Brillouin active medium, a conjugate field will grow exponentially in time until it depletes the power of the pump beams and hence produce very high reflectivities (>10/sup 6/). The technique can be used to conjugate very weak signals (<10/sup -13/ J), or alternatively a large fraction of the pump power can be transferred into the conjugate beam. A review of the technique is presented and aspects such as the exponential growth rate, the minimum signal requirement, the beam quality, and the threshold for parasitic oscillation between the four-wave mixing cell and a reflecting surface are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium

We report the observation of an instability when two counter-propagating pump beams interact with sodium atoms. The instability appears as a coherent emission around the pump beams axis. This oscillation has only been observed on the self-focusing side of the resonance in agreement with theory. The characteristics of the oscillation are very different from those of the usual conical emission.

GAIN/FEEDBACK APPROACH TO OPTICAL INSTABILITIES IN SODIUM VAPOR

We use the gain-feedback approach1 to explain a number of instabilities observed in sodium vapor with the laser frequency vL tuned to the defocusing side of line center at v0. The gain curve, which includes motion of the atoms, predicts two regions of possible gain: Rayleigh gain for frequencies v just above vL and Raman gain for v ≅ vL-vR, where vR is the on-resonance Rabi frequency; see Fig. 1.2 Lasings based on these two gain mechanisms have been seen in two different feedback configurations. The new observations are: Rayleigh-gain lasing with no external mirrors using the distributed feedback of counterpropagating pump beams, Rayleigh-gain lasing without a foreign gas, and Raman-gain lasing in a ring cavity. The gain curve for moving atoms2 is shown in Figure 1 and differs substantially from that for stationary atoms.3

Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers.

The effects of finite laser bandwidth on resonant degenerate four-wave mixing (DFWM) are calculated with use of a model in which the intense, counterpropagating pump beams are characterized by a chaotic field, the probe beam is weak and monochromatic, and the medium consists of a gas of two-level atoms. We present a steady-state solution in the limit where the pump-laser bandwidth exceeds all other atomic relaxation rates. Although the mean intensity due to the fluctuating fields is spatially independent (no steady-state standing-wave pattern is established), the analytic results indicate that, for intensities above the saturation intensity ${I}_{\mathrm{sat}}$, spatially periodic saturation effects are important. Increasing bandwidth is shown to lead to an increase in the effective saturation intensity resulting in lower phase-conjugate reflectivity for I${I}_{\mathrm{sat}}$ than for coherent pump fields, in contrast to the results for narrow-bandwidth chaotic fields. The resonant DFWM line shape is also calculated and compared to the coherent result. We comment on the application of the model to other four-wave-mixing processes employing broad-bandwidth lasers.

Optogalvanic detection of optical pumping

Reports the optogalvanic detection of observables induced by optical pumping in metastable states of neon. As with optical methods signals are obtained which are related to electronic and nuclear orientation or alignment. Many optical pumping experiments may thus be performed using optogalvanic techniques, including the Hanle effect and 'velocity selective optical pumping' described. Different mechanisms are discussed from which optogalvanic signals related to non-scalar observables may originate. Profiles obtained from frequency sweeps of two polarisation-modulated counterpropagating pump beams indicate the dominant mechanism is a second-order pumping effect which induces a modulated depletion of the metastable state. No effect has been observed arising from a variation of the Penning collision cross section when the two metastable colliding atoms are oriented. The analogy between signals produced by optogalvanic and optical methods are pointed out.

Coherence phenomena in phase-modulation laser spectroscopy

The technique of phase-modulation laser spectroscopy is used to detect a coherent four-wave interaction in ${\mathrm{I}}_{2}$ vapor. A phase-modulated probe beam induces in the sample an oscillating population which in turn modulates a counterpropagating pump beam that reveals a characteristic two-resonance spectrum. The observations fully confirm an earlier density-matrix calculation.

Bistability and hysteresis in phase-conjugated reflectivity

An externally driven nonlinear Fabry-Perot interferometer with bistable transmission characteristics is probed through a weak optical field. The nonlinear interaction among the counterpropagating pump beams and the probe beam generates the phase-conjugated beam through intracavity degenerate four-wave mixing. It is shown that the phase-conjugated reflectivity displays bistability and that hysteresis as the driving field is varied in a continuous manner. The analysis is carried out in the mean-field approximation and is valid for the case of low absorption and a high- Q cavity. Both the dispersive and the absorptive effects arising due to saturation of the one-photon resonance are included, and their effect on the phase-conjugated reflectivity is discussed. The results show that, when a bistable device switches on, the reflectivity decreases by a few orders of magnitude. We discuss possible applications and suggest materials where the proposed effects can be seen.