Phase-conjugate Geometry Research Articles

Mixed β-Pyrrole Substituted meso-Tetraphenylporphyrins and Their Metal Complexes: Optical Nonlinearity Using Degenerate Four Wave Mixing Technique

We have investigated the roles of structural modification and polar effects in the optical nonlinearities of a series of selectively mixed β-pyrrole functionalized tetraphenylporphyrin, MTPP(CHO)(R)2 (R = H, Br, 2-thienyl, phenyl (Ph), phenylethynyl (PE) compounds and their metal (Cu(II), Zn(II)) complexes in toluene. In the present study, we have used phase conjugation geometry of the four wave mixing process to measure the third order nonlinear susceptibility (χ(3)) and the second order hyperpolarizabilty ((γ)) with picosecond laser pulse excitation at 532 nm. An increase in the values of χ(3) and (γ) for electron-withdrawing groups was observed whereas an opposite trend was noticed for the electron-donating groups at the β-pyrrole positions. In the Cu(II) and Zn(II) complexes of substituted free base porphyrins, the distortion of the macrocyclic ring may be responsible for the reduction of the values of χ(3) and (γ). From fluorescence measurements, it has been found that the electron-donating and electron-withdrawing substituted groups at β-pyrrole positions and also the macrocyclic ring distortion of the porphyrin lead to increased radiationless transitions.

Wavelength dependent resonant nonlinearities in a standard saturable absorber IR26 on picosecond time scale

Nonlinear optical properties of a standard dye IR26 have been studied by using the Z-scan technique to decipher the difference in the mechanism of nonlinear absorption on picosecond time scale at two wavelengths i.e. at 1064 nm and 532 nm. A prominent contribution of nonlinear absorption is observed in the Z-scan profiles at 1064 nm. The dye exhibits the mechanism of self-defocusing at 1064 nm in contrast to that of self-focusing at 532 nm. While the two photon absorption has been found to be the dominant mechanism of reverse saturable absorption at 1064 nm, the mechanism of excited state absorption is operating at 532 nm. Additionally, the optical phase conjugate geometry of degenerate four wave mixing (DFWM) technique has been used to measure the third order nonlinear susceptibility values at 532 nm to compare with those obtained from the Z-scan profiles.

Kinetic temperature and electron density measurement in an inductively coupled plasma torch using degenerate four-wave mixing

Laser wave mixing is presented as an effective technique for spatially resolved kinetic temperature measurements in an atmospheric-pressure radio-frequency inductively coupled plasma. Measurements are performed in a 1 kW, 27 MHz radio-frequency plasma using a continuous-wave, tunable 811.5 nm diode laser to excite the 4s3P2→4p3D3 argon transition. Kinetic temperature measurements are made at five radial steps from the center of the torch and at four different torch heights. The kinetic temperature is determined by measuring simultaneously the line shape of the sub-Doppler backward phase-conjugate degenerate four-wave mixing and the Doppler broadened forward-scattering degenerate four-wave mixing. The temperature measurements result in a range of 3,500 to 14,000±150 K. Electron densities measured range from 6.1 (±0.3)×1015 cm−3 to 10.1 (±0.3)×1015 cm−3. The experimental spectra are analyzed using a perturbative treatment of the backward phase-conjugate and forward-geometry wave-mixing theory. The Stark width is determined from the collisional broadening measured in the phase-conjugate geometry. Electron density measurements are made based on the Stark width. The kinetic temperature of the plasma was found to be more than halved by adding deionized water through the nebulizer.

Study of optical nonlinearity of functionalized multi-wall carbon nanotubes by using degenerate four wave mixing and Z-scan techniques

The phase conjugation geometry of degenerate four wave mixing (DFWM) technique has been employed to study the third-order optical nonlinear susceptibility ( χ 3) and second-order hyperpolarizability of multi-wall carbon nanotubes (MWCNTs). MWCNTs were grown by thermal chemical vapor deposition method and, subsequently functionalized with carboxylic acid group to improve their solubility in an organic solvent, ethylene glycol. The average hyperpolarizability for each carbon atom has been found to be 4.74 × 10 −46 m 5/V 2 for the pump pulse of 8 ns at 532 nm. Decreasing the pulse width of the pump laser decreases the average value of hyperpolarizability. The absorption spectra show a monotonous increase from IR through visible and give an opportunity to estimate the imaginary part of the χ 3 by the open aperture Z-scan technique.

Doppler-free three-photon resonant six-wave mixing

We study the three-photon resonant six-wave mixing (SWM) with phase-conjugation geometry in Doppler system. The theoretical calculation indicates that the signal spectrum is Doppler-free when the laser line width is narrow. This technique provides a new spectroscopic tool for studying the highly excited atomic or molecular states with high resolution. It has advantages of uncritical phase matching condition, excellent spatial signal resolution and simple optical alignment.

Three-Photon Resonant Six-Wave Mixing with Phase-ConjugationGeometry in Na Atomic Vapour

We report a three-photon resonant six-wave mixing (SWM) with phase-conjugation geometry. It has advantages that phase matching condition isnot critical and the generation of SWM signal is efficient. Thistechnique provides a new spectroscopic tool for studying the highlyexcited atomic or molecular states with high resolution. The feasibilityof this technique is demonstrated in sodium vapour.

Spectral Zeeman hole burning in a quantum dot ensemble

Spectral hole burning experiments based on high-resolution magneto-CW four-wave mixing in the phase conjugate geometry show that both the spectral and spatial diffusion of excitons is negligible in the GaAs quantum dot system formed by interface disorder. Due to the strong Coulomb coupling, Zeeman spectral hole burning is observed when we resonantly excite one of the two orthogonally polarized excitons confined to each dot by two copolarized and frequency-degenerate fields and then probe the system by a third beam that is of opposite polarization and a Zeeman splitting away (in frequency). The experiments allow for a measure of the exciton decay rates and g factor.

Raman-enhanced polarization beats with phase-conjugation geometry

The Raman-enhanced polarization beats (REPB) with phase-conjugation geometry in carbon disulfide are investigated using chaotic and phase-diffusion models. The overall accuracy of using REPB to measure the resonant frequency of Raman-active vibrational mode is determined by the relaxation rates of the Raman mode and the molecular-reorientational grating. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence function. The difference between the REPB and the fourth-order coherence on ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.

Sixth-order correlation on Raman-enhanced polarization beats with phase-conjugation geometry

The correlation effects of sixth-order on the Raman-enhanced polarization beats (REPB) with phase-conjugation geometry in carbon disulfide are investigated using chaotic and phase-diffusion models. Based on two types of models, the cases that the pump beams have either narrow band or broadband linewidth are considered and it is found that the beat signal oscillates not only temporally with a 50.5 fs period but also spatially. The overall accuracy of using REPB to measure the resonant frequency of Raman-active vibrational mode is determined by the relaxation rates of the Raman mode and the molecular-reorientational grating. Moreover, the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the decay rates of the Raman mode and the molecular-reorientational grating. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence function. Furthermore, the different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The difference between the REPB and the fourth-order coherence on ultrafast modulation spectroscopy is discussed as well from a physical viewpoint. Therefore, the sixth-order coherence function theory of chaotic field is of vital importance in REPB.

Fourth-order interference on polarization beats in a four-level system

We have employed chaotic and phase-diffusion models to study the effects of laser fourth-order coherence on polarization beats with phase-conjugation geometry in a four-level system (PBFS). We found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Inasmuch as different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of phase fluctuation and amplitude fluctuation are pointed out. The cases that pump beams have either narrow-band or broadband linewidth are considered, and it is found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states that are dipolar forbidden from the ground state can be achieved. We also discuss the difference between the PBFS and ultrafast modulation spectroscopy from a physical viewpoint.

Fourth-Order Interference on Polarization Beats with Phase-Conjugation Geometry

The effect of fourth-order coherence on ultrafast modulation spectroscopy (UMS) with phase-conjugation geometry (PCUMS) in a cascade three-level system is investigated using chaotic and phase-diffusion models. It has been found that the modulation terms of the beat signal depend on the second-order coherence function, and different stochastic models of the laser field affect only the fourth-order coherence function. The difference between the PCUMS and UMS is discussed from a physical viewpoint.

Effects of fourth-order coherence on ultrafast modulation spectroscopy

The effect of fourth-order coherence on ultrafast modulation spectroscopy with phase-conjugation geometry (PCUMS) in a cascade three-level system is investigated using chaotic and phase-diffusion models. It has been found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation can be investigated in the time domain. The cases where the pump beams have either a narrow or broad band linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states can be achieved. The difference between the PCUMS and the DeBeer, UMS [D. DeBeer et al., Phys. Rev. Lett. 56, 1128 (1986)] is discussed as well from a physical viewpoint.

Phase matching and optical geometry considerations in ultrafast non-degenerate six-wave-mixing experiments

The generation in solution of optically induced second harmonics, through six-wave mixing, has been observed using three distinct optical geometries. The established phase-conjugate geometry is not useful for ultrafast time-resolved experiments. A grating scattering geometry, with the pump and probe pulses entering from the same side of the sample, provides the highest time resolution and signal strength although there is a strong interfering signal at time zero. A collinear geometry, which introduces a means for the coherent control of molecular orientation, is also discussed.

Experimental investigation of saturated degenerate four-wave mixing for quantitative concentration measurements

Degenerate four-wave mixing (DFWM) line shapes and signal intensities are measured experimentally in well-characterized hydrogen-air flames operated over a wide range of equivalence ratios. We use both low (perturbative) and high (saturating) beam intensities in the phase-conjugate geometry. Resonances in the A 2Sigma+ -X 2II (0,0) band of OH are probed with multiaxial-mode laser radiation. The effects of saturation on the line-center signal intensity and the resonance linewidth are investigated. The DFWM signal intensities are used to measure OH number densities in a series of near-adiabatic flames at equivalence ratios ranging from 0.5 to 1.5. Use of saturating pump intensities minimizes the effects of beam absorption, providing more-accurate number density measurements. The saturated DFWM results are in excellent agreement with OH absorption measurements and equilibrium calculations of OH number density. The polarization dependence of the P(1)(2) and R(2)(1) resonances is investigated in both laser intensity regimes. There is a significant change in relative reflectivities for different polarization configurations when saturated.

ENERGY-LEVEL DIFFERENCE AND LASER ABSOLUTE FREQUENCY MEASUREMENT BY POLARIZATION BEATS SPECTROSCOPY WITH PHASE-CONJUGATION GEOMETRY

We have studied the polarization beats spectroscopy with phase-conjugation geometry in a cascade three-level system.It was found that the accuracy for the energy-level difference measurement is determined by the homogeneous linewidths of the optical trans

Rhodium-doped barium titanate nonlinear mirror for high beam quality pulsed Nd:YAG lasers

We review the recent results obtained with Rh:BaTiO/sub 3/ as a phase conjugate mirror for a pulsed Nd:YAG laser operating in the near infrared (1.06 /spl mu/m). The phase conjugate reflectivity, the response time, and the fidelity obtained using an internal loop self-pumped phase conjugate geometry are presented. High beam quality master-oscillator power amplifier Nd:YAG lasers with an Rh:BaTiO/sub 3/ phase conjugate mirror are presented in both low-repetition rate flash-lamp pumped and high-repetition rate diode-pumped laser architectures. The performances of the Rh:BaTiO/sub 3/ crystal are compared with those obtained with a conventional Brillouin mirror.

High resolution spectroscopy and spectral simulation of C2 using degenerate four-wave mixing

Degenerate four-wave mixing in the sub-Doppler phase conjugate geometry was used to record high resolution spectra of the d 3Πg–a 3Πu (0–0) Swan band of C2 produced in an oxy-acetylene flame. The line positions of isolated transitions were measured to an accuracy of ∼3×10−3 cm−1 and calibrated using a Fizeau interferometer system. The data obtained from these spectra was used to calculate rotational constants and lambda doubling parameters for the 3Π states from which the line positions for the whole band were calculated. Noticeable improvements between experimental and calculated line positions are seen when compared to previously published values. The effect of inaccuracies in line positions on the simulation of degenerate four-wave mixing spectra is discussed and some examples of the improvement in simulation using the newly calculated line positions are presented.

Theoretical investigation of the forward phase-matched geometry for degenerate four-wave mixing spectroscopy

We examine theoretically the degenerate four-wave mixing (DFWM) signal intensities and line shapes obtained with the forward phase-matched geometry in which all beams propagate in the same direction and compare the results to those of the phase-conjugate geometry with counterpropagating pump beams. To examine the forward phase-matched geometry, we modify a theoretical approach used previously to calculate phase-conjugate DFWM signal intensities. This theoretical approach, which involves numerical integration of the time-dependent density-matrix equations, is validated for the forward phase-matched geometry by comparison of our calculated line shapes to both a perturbative solution and to experimental data. This methodology is then used to compare the signal intensities and line shapes obtained with the forward phase-matched geometry and the phase-conjugate geometry in the perturbative (low laser power) and saturated (high laser power) regimes. In the perturbative regime the forward phase-matched signal exhibits less sensitivity to the Doppler linewidth. At pump laser intensities approximately equal to the saturation intensity the signal for the forward phase-matched geometry is stronger than that for the phase-conjugate geometry for primarily Doppler-broadened resonances, assuming the same probe volume for both geometries. These advantages warrant further investigations employing the forward phase-matched configuration for DFWM measurements of gas-phase species.

One-photon resonant optical nonlinearity of soluble substituted group IV metallophthalocyanines

The synthesis and nonlinear optical characterization of highly soluble Ni-, Pd- and Pt-phthalocyanines is reported. When excited resonantly within the Q-band, the third-order nonlinearity is dominated by saturable absorption, observed using the z-scan technique. The imaginary part of the nonlinear susceptibility was observed at 665 nm. From a three-level model, ground-state recovery times in the picosecond regime were determined for all phthalocyanines studied. These fast recovery times were supported by time-resolved measurements using degenerate four-wave mixing in the phase-conjugate geometry.

Interaction of closely spaced resonances in degenerate four-wave-mixing spectroscopy

The interaction of two closely spaced resonances in degenerate four-wave-mixing spectra is investigated theoretically. Degenerate four-wave-mixing spectra for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integrating the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and summing the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision and Doppler broadened are considered. The homogeneously broadened results are found to agree with the results of the widely used Abrams–Lind expression for the case of stationary absorbers exposed to a steady-state excitation. We examine the effects of power broadening, pressure broadening, transition dipole moment, and population on the spectra of two neighboring homogeneously broadened resonances. As the laser power is increased, the real parts of the resonance susceptibilities destructively interfere with each other in the region between the lines, resulting in a significant and persistent dip in reflectivity. When Doppler broadening is included in the calculations, similar interference effects are observed, although at first the interference dip begins to disappear until the homogeneous part of the line shapes is broadened significantly by saturation. Using this numerical approach, we obtain good agreement with experimental results of primarily Doppler-broadened neighboring resonances.