Counterpropagating Pump Waves Research Articles

Observation of the Strong Magneto-Optical Rotation of the Polarization of Light in Rubidium Vapor for Applications in Atomic Magnetometry

Nonlinear resonances in alkali metal vapor, which are detected by the magneto-optical rotation of the linear polarization of light, are actively used in quantum magnetometry to fabricate atomic magnetometers. The magneto-optical rotation in most such sensors is due to magnetic birefringence, and rotation angles usually do not exceed tens of milliradians. In this work, an experiment where magneto-optical resonances of linear polarization rotation of a probe wave are due to strong dichroism induced in a medium by a counterpropagating pump wave has been proposed. Both waves are in resonance with the Fg = 2 → Fe = 1 optical transition in the 87Rb D1 line (λ ≈ 795 nm). Experiments have been carried out with a 2-cm-long cylindrical cell filled with a buffer gas, and the maximum rotation angle is ≈390 mrad (22°) at a width of resonance of about 300 nT. The results show that the configuration proposed for the observation of magneto-optical rotation is promising for the fabrication of compact high-sensitivity atomic magnetometers.

Observation of the Strong Magneto-Optical Rotation of the Polarization of Light in Rubidium Vapor for Applications in Atomic Magnetometry

Nonlinear resonances in alkali metal vapor, which are detected by the magneto-optical rotation of the linear polarization of light, are actively used in quantum magnetometry to fabricate atomic magnetometers. The magneto-optical rotation in most such sensors is due to magnetic birefringence, and rotation angles usually do not exceed tens of milliradians. In this work, an experiment where magneto-optical resonances of linear polarization rotation of a probe wave are due to strong dichroism induced in a medium by a counterpropagating pump wave has been proposed. Both waves are in resonance with the Fg = 2 → Fe = 1 optical transition in the 87Rb D1 line (λ ≈ 795 nm). Experiments have been carried out with a 2-cm-long cylindrical cell filled with a buffer gas, and the maximum rotation angle is ≈390 mrad (22°) at a width of resonance of about 300 nT. The results show that the configuration proposed for the observation of magneto-optical rotation is promising for the fabrication of compact high-sensitivity atomic magnetometers.

Spatial and temporal characteristics of a four-wave radiation converter with due regard for Earth's gravity field acting on nanoparticles dissolved in a transparent liquid

A theoretical analysis of the dynamics of the spatial spectrum of the object wave in a degenerate four-wave mixing in a transparent solution of nanoparticles in the classical scheme with counterpropagating pump waves is carried out. It is shown that when pump waves propagate orthogonally to the gravity force, a dip arises in the modulus of the spatial spectrum of the object wave, with its half-width nonmonotonically decreasing over time and increasing in the direction of gravity force with increasing radius of the nanoparticles. There is an optimal time over which the half-width of the dip in the direction of the gravity force reaches the lowest value. This time decreases monotonically with increasing nanoparticle radius, as well as with a decrease in the solution thickness.

New matrix solution of the phase-correlation technique in a Brillouin dynamic grating sensor

In the phase-correlation measurement technique of Brillouin dynamic grating sensors, two counterpropagating pump waves are modulated by a pseudo-random bit sequence (PRBS) that applies a random phase shift of either 0 or π with a specified period. In order to define the sensing length and spatial resolution, the shape of the correlation peak has to be found. So far, many methods have been used to demonstrate the phase correlation, but they often require several lengthy and sometimes complicated mathematical assumptions and equations. One of the techniques that has the best reported spatial resolution is called the time gated phase-correlation technique. We introduce a novel method based on a matrix solution to show the phase modulation in the phase-correlation technique. It is a straightforward and intuitive pattern to visualize the phase modulation of the pumps and to attain the shape of the phase-correlation peaks. Finally, the results of the matrix method are completely consistent with the previous results.

Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis

Correlation-domain analysis has enabled distributed measurements of Brillouin gain spectra along optical fibers with high spatial resolution, up to millimeter-scale. The method relies on the joint modulation of counter-propagating Brillouin pump and signal waves so that their complex envelopes are correlated in select positions only. Brillouin optical correlation-domain analysis was first proposed nearly 20 years ago based on frequency modulation of the two waves. This paper reviews two more recent variants of the concept. In the first, the Brillouin pump and signal waves are co-modulated by high-rate binary phase sequences. The scheme eliminates restricting trade-offs between the spatial resolution and the range of unambiguous measurements, and may also suppress noise due to residual Brillouin interactions outside the correlation peak. Sensor setups based on phase coding addressed 440,000 high-resolution points and showed potential for reaching over 2 million such points. The second approach relies on the amplified spontaneous emission of optical amplifiers, rather than the modulation of an optical carrier, as the source of Brillouin pump and signal waves. Noise-based correlation-domain analysis reaches sub-millimeter spatial resolution. The application of both techniques to tapered micro-fibers and planar waveguides is addressed as well.

Frequency up-shift in the stimulated thermal scattering under two-photon absorption in liquids and colloids of metal nanoparticles

We report the results of the experimental and theoretical study of stimulated temperature scattering in toluene and hexane solutions of Ag-nanoparticles, as well as in pure toluene in the two-photon absorption regime. A four-wave mixing scheme with two counter-propagating pump waves of the same frequency is utilised to demonstrate the lasing effect and the amplification of the backscattered anti-Stokes signal. For the first time, we have measured anti-Stokes spectral shifts which turn out to appreciably exceed the Rayleigh line widths in those liquids. It is shown that the amplification effect is provided predominantly by thermally induced coherent polarisation oscillations, while the dynamic interference temperature grating causes the formation of a self-induced optical cavity inside the interaction region.

Electromagnetically-induced-absorption resonance with high contrast and narrow width in the Hanle configuration

The method for observing the high-contrast and narrow-width resonances of electromagnetically induced absorption (EIA) in the Hanle configuration under counter-propagating pump and probe light waves is proposed. Here, as an example, we study a ‘dark’ type of atomic dipole transition in D1 line of 87Rb, where usually the electromagnetically induced transparency can be observed. To obtain the EIA signal one should properly choose the polarizations of light waves and intensities. In contrast to regular schemes for observing EIA signals (under a single traveling light wave in the Hanle configuration or under a bichromatic light field consisting of two traveling waves), the proposed scheme allows one to use buffer gas for significantly improving the properties of the resonance. Also the dramatic influence of atomic transition openness on the contrast of the resonance is revealed, which is advantageous in comparison with cyclic atomic transitions. The nonlinear resonances in a probe-wave transmitted signal with contrast close to 100% and sub-kHz widths can be obtained. The results are interesting in high-resolution spectroscopy, nonlinear and magneto-optics.

On temporal dynamics of Sn_2P_2S_6 oscillation in semi-linear cavity

Experimental measurements and calculations revealed an unusual type of oscillation dynamics of Sn(2)P(2)S(6) in the semi-linear cavity. It consists of a pronounced saw-tooth modulation of oscillation intensity--although it is not 100% in contrast--with the cw component being shifted in frequency with respect to the pump wave. This effect is attributed to the hybrid mode of two semi-linear oscillation geometries, one with a single pump wave and the other with two counterpropagating pump waves.

Quasi-normal-modes description of transmission properties for photonic bandgap structures

We use the quasi-normal-modes (QNM) approach for discussing the transmission properties of double-side opened optical cavities: in particular, this approach is specified for one-dimensional (1D) photonic bandgap (PBG) structures. Moreover, we conjecture that the density of the modes is a dynamical variable that has the flexibility of varying with respect to the boundary conditions as well as the initial conditions; in fact, the electromagnetic (e.m.) field generated by two monochromatic counterpropagating pump waves leads to interference effects inside a quarter-wave symmetric 1D-PBG structure. Finally, here, for the first time to the best of our knowledge, a large number of theoretical assumptions on QNM metrics for an open cavity, never discussed in literature, are proved, and a simple and direct method to calculate the QNM norm for a 1D-PBG structure is reported. (c) 2009 Optical Society of America

Spatially Resolved Measurement in Waveguides With Arbitrary Chromatic Dispersion

A high-resolution technique for dispersion measurement in waveguides with arbitrary chromatic dispersion is reported. The technique is based on localization of four-photon mixing achieved by abrupt increase in signal-probe interaction along the measured waveguide. Arbitrary increase in optical power is achieved by counter colliding power transfer between signal and counterpropagating pump wave. The new technique was used to demonstrate meter-scale dispersion retrieval from highly nonlinear fiber for the first time. The measurement sensitivity exceeds that of the existing methods by two orders of magnitude.

Optical hysteresis in a semilinear photorefractive coherent oscillator

High contrast optical bistability is found experimentally in the pump-ratio dependences of the output intensity of a semilinear photorefractive coherent oscillator with two counterpropagating pump waves. The data are in qualitative agreement with the results of calculation.

Cw hyper-Raman laser and four-wave mixing in atomic sodium

Continuous wave hyper-Raman (HR) generation in a ring cavity on the 6s→4p transition at 1640 nm in sodium is realized for the first time by two-photon excitation of atomic sodium on the 3s→6s transition with a continuous wave (cw) dye laser at 590 nm and a single frequency argon ion laser at 514 nm. It is shown, that the direction and efficiency of HR lasing depends on the propagation direction of the pump waves and their frequencies. More than 30% HR gain is measured at 250 mW of pump laser powers for counter-propagating pump waves and a medium length of 90 mm. For much shorter interaction lengths and corresponding focussing of the pump waves a dramatic increase of the gain is predicted. For co-propagating pump waves, in addition, generation of 330 nm radiation on the 4p→3s transition by a four-wave mixing (FWM) process is observed. Dependencies of HR and parametric four-wave generation have been investigated and will be discussed.

Semilinear coherent oscillator with reflection-type photorefractive gratings

The saturation intensity, oscillation spectrum, and temporal dynamics of oscillation are studied for a semilinear coherent oscillator with two counterpropagating pump waves and a photorefractive crystal with dominating reflection gratings. The instability of the single-frequency oscillation spectrum is revealed, similar to that known for an oscillator with dominating transmission gratings. The experimental manifestation of this transition in the output characteristics of the oscillator is favourably compared with numerical calculations.

High-efficiency optical phase conjugation by degenerate four-wave mixing in volume media of disperse red 1-doped poly(methyl methacrylate)

High-efficiency optical phase conjugation (PC) by degenerate four-wave mixing in stress-processed volume media of disperse red 1 (DR1)-doped poly(methyl methacrylate) in the transparent region (647 nm) is reported. With vertically polarized counterpropagating pump waves, PC reflectivities of 43% and 37% were achieved, respectively, for a horizontally and vertically polarized probe wave, which is 50 times higher than the value reported on resonance. Reflectivities over 30% were achieved over a wide range of intensity for both polarization configurations. Photoinduced reorientation of the DR1 chromophore through trans-cis-trans isomerization is the dominant mechanism for the PC wave generation. Other mechanisms involved in the configuration of all vertical polarization waves are also examined. The roles of the polymer matrix and azo-dye photoisomerization in this high-efficiency PC process are also discussed.

Second-order optical phase transition in a semilinear photorefractive oscillator with two counterpropagating pump waves

Soft-mode onset of coherent oscillation is revealed in a semilinear cavity with two counterpropagating pump waves. From the dynamics of the oscillation intensity and the dynamics of the grating decay with the feedback applied, critical behavior is detected: Both the characteristic time of oscillation onset and grating decay time go to infinity exactly at the threshold coupling strength. A conclusion is made about the similarity of this type of oscillator to the second-order phase transition.

Manifestation of Curie-Weiss law for optical phase transition

Considerable slowing down is observed for both the temporal development of the coherent oscillation slightly above the threshold and the refractive index grating decay slightly below the threshold for a semilinear photorefractive oscillator with two counter-propagating pump waves. It is shown that in the vicinity of the threshold the reciprocal characteristic time is a linear function of deviation from the threshold coupling strength. This behaviour is similar to an empirical Curie–Weiss law and points to the analogy of the oscillation threshold to a second-order phase transition.

Supplementary optical phase transition in photorefractive coherent oscillator

The semilinear photorefractive coherent oscillator with two counterpropagating pump waves may exhibit two optical phase transitions: one from a disordered state of wide-angle photorefractive scattering into a high-ordered state with the immobile photorefractive grating and the other one from the state with immobile grating into the state with two moving photorefractive gratings. We show, both experimentally and from calculations, that two these phase transitions are the second-order phase transitions.

Resonant continuous four-wave mixing and parametric amplification

Theoretical and experimental investigations of continuous four-wave mixing and parametric amplification in a resonantly driven double-Λ scheme of Na2 molecules are reported. Cases of copropagating and counterpropagating pump waves are analyzed. Macroscopic propagation of the generated fields and the interplay of absorption, Raman gain, four-wave mixing, and parametric amplification are studied.

Self-oscillation in a photorefractive phase-conjugate mirror with linear absorption I Isotropic four-wave mixing

The effects of linear absorption on the degenerate and nondegenerate self-oscillation conditions of a photorefractive phase-conjugate mirror are explored. In this study, phase-conjugation results from nonlinear mixing of two strong undepleted parallel-polarized counterpropagating pump waves with a probe wave. Numerical results are presented that illustrate that the linear absorption tends to increase the value of the coupling coefficient required for self-oscillation. It is also found that the pump intensity ratio r is almost independent of the linear absorption for positive normalized detuning Δωτ between the probe and the pump frequencies and of the zero phase shift, ϕ, between the gratings and the light interference patterns when the gratings are stationary. For ϕ = ±π/2, the variation of r with respect to absorption is symmetric for positive and negative detunings.

Self-oscillation in a photorefractive phase-conjugate mirror with linear absorption II Anisotropic four-wave mixing

The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.