Femtosecond Degenerate Four-wave Mixing Research Articles

The formic acid dimer (HCOOH)2 probed by time-resolved structure selective spectroscopy

Rotationally resolved spectra of the formic acid dimer (HCOOH)2 have been recorded by femtosecond degenerate four-wave mixing (fs DFWM) in the gas cell at room temperature (≈10 mbar, 298 K) and under supersonic jet conditions (≈60 K). Rotational recurrences of both, the monomeric and the dimeric species have been identified and assigned by fitted simulations of the fs DFWM spectra. For the first time the study of molecular clusters by fs DFWM is reported. From the fitted simulation based on a general nonrigid asymmetric rotor model the rotational and centrifugal distortion constants, and parametrized polarizability were derived for the dimeric structure of type O–H⋯O/O⋯H–O as well as for the formic acid monomer. With the assumption of unperturbed monomers a center-of-mass distance of R=2.990±0.001 Å for the monomers within the dimer is calculated from the spectroscopic results. The structure of the formic acid dimer and a possible isomer of the type C–H⋯O/O⋯H–O is discussed and compared to recent ab initio calculations.

Investigations of Nonlinear Optical Chromophores with Femtosecond Degenerate Four-Wave Mixing in Solutions

Time-resolved DFWM experiments were performed with 150 fs pulses at 800 nm in chloroform solutions of π-conjugated molecules: p-bis(o-methylstyryl)-benzene (Bis-MSB) and a newly synthesized derivative of distyrylbenzene: an oligomer of p-phenylenevinylene substituted in the para position with electron donating alkyleneoxy group bearing the methacrylic group and an electron accepting 2-ethylhexylsulfonyl group (MTPV-SOHE monomer). The asymmetric substitution causes a red shift (24 nm) of the absorption maximum and enhancement of third-order optical susceptibility. The second hyperpolarizability derived from a quadratic dependence of the phase matched DFWM signal on concentration of MTPV-SOHE was about 6 times bigger than that in Bis-MSB.

Rotational coherence spectroscopy of jet-cooled molecules by femtosecond degenerate four-wave mixing: non-rigid symmetric and asymmetric tops

Femtosecond degenerate four-wave mixing (fs DFWM) experiments are applied to study the rotational coherences of perdeutero-benzene (C 6D 6) and pyridine (C 5H 5N). These systems are investigated at 20–40 K in a collision-free seeded supersonic jet and the spectra are compared to those obtained in a gas cell (298 K). The differences between the non-rigid, symmetric oblate C 6D 6 and the slightly asymmetric oblate C 5H 5N are discussed. From the simulation and fitting, rotational constants are obtained in good agreement with literature data. For the first time, a fs DFWM spectrum (including asymmetry transients) of a non-rigid, asymmetric rotor molecule (C 5H 5N) was successfully fitted.

Large electronic third-order optical nonlinearities of cyanine dyes measured by resonant femtosecond degenerate four-wave mixing

Third-order optical nonlinearities of several cyanine dyes were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of at least two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several hundred picoseconds. The latter can be attributed to molecular rotational relaxation of these dyes. The values of electronic component of the optical nonlinear susceptibility, χ e xxxx (3) , for these dyes were ≈2×10 −12 esu at the very low concentration of 1×10 −5 mol dm −3 . The electronic component of molecular hyperpolarizability, γ e , was calculated to be ≈1×10 −28 esu for each dye.

Rotational coherence spectroscopy of benzene by femtosecond degenerate four-wave mixing

Femtosecond time-resolved non-resonant degenerate four-wave mixing (fs-DFWM) experiments were applied to study the rotational coherences in benzene molecules in the gas phase at room temperature. The experiments were performed in a cell filled with benzene vapour at reduced pressure (0.01 bar). The technique gives an excellent signal-to-noise ratio for the observed transients. For the first time transients up to a maximum time delay of 1.4 ns, mainly limited by collisional dephasing, have been obtained for a molecule of this size by fs-DFWM. From this data the rotational constant B = 0.18972 ± 0.00010 cm−1 for benzene at room temperature is obtained by a fitted simulation. The application of fs-DFWM to large molecules seems to be possible and might produce some interesting results in the future.

Phase relaxation dynamics of excitons and biexcitons in CuCl studied by femtosecond and picosecond degenerate four-wave mixing

The dephasing time ${T}_{2}$ of excitons and biexcitons is measured by femtosecond and picosecond four-wave mixing as function of frequency for different excitation intensities and temperatures. Their behavior is discussed in the frame of different scattering mechanisms. From this, the biexciton acoustic- and optical-phonon scattering cross sections are determined.

Femtosecond frequency mixing in thick bulk GaAs

Femtosecond degenerate four-wave mixing (FWM) experiments have been performed on bulk GaAs as a continuous function of the sample thickness. The FWM signals exhibit the transition from a real, excitonic regime to the virtual regime as the thickness increases from 3 to $17.5\ensuremath{\mu}\mathrm{m}.$ The results at the negative time delay show an extraordinary signal: even when the thickness is an order of magnitude larger than the penetration depth, there still exists a signal well above the band gap. These above-the-band-gap signals are mostly confined to the negative time delay region and shift further into the negative time delay as the detection energy increases. These unusual phenomena can be understood by the third-order frequency mixing $(2{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1};{\ensuremath{\omega}}_{2}>{\ensuremath{\omega}}_{1})$ between positively chirped spectral components.

Unequal dependence of the dephasing rates for inhomogeneously broadened excitons on the intensities of the exciting beams in four-wave-mixing measurements

We study exciton dephasing in 8 nm GaAs quantum wells (QW) at 8 K by resonantly exciting the excitons at low densities. For this, we perform femtosecond degenerate four-wave mixing (DFWM) measurements using two laser beams. The excitons in the QWs are inhomogeneously broadened, with a photoluminescence linewidth of 1.8 meV. We investigate how the time integrated DFWM signal and its decay rate $\ensuremath{\eta}$ change as the average intensity of either of the two exciting beams is varied separately. We find that the dependence of $\ensuremath{\eta}$ on the intensity of the first pulse is about twice as that for the delayed pulse. We compare the results with a theory based on optical Bloch equations and relaxation rate approximation, accounting phenomenologically for dephasing due to exciton-exciton scattering.

Numerical Analysis of Femtosecond Time-Resolved Degenerate Four-Wave Mixing Signal including Group-Velocity Dispersion Effect

We numerically analyze the group-velocity dispersion (GVD) effect of the nonlinear medium on the femtosecond time-resolved degenerate four-wave mixing (DFWM) signal with the third-order nonlinear delayed response. As a result, we find that material GVD greatly influences not only the magnitude but also the temporal profile of the DFWM signal.

Quantum beats of confined exciton-LO phonon complexes in CuCl nanocrystals

We have investigated coherent transient phenomena of confined excitons in CuCl nanocrystals with mean radii R in the range 3.4--23 nm, embedded in glass by means of femtosecond degenerate four-wave mixing (DFWM). Oscillating behaviors have been observed in the spectrally resolved DFWM signals. In large nano- crystals with $R>6.5$ nm, quantum beats between the confined exciton sublevels have been observed, while for $R<6.5$ nm we have observed quantum beats between the confined exciton and LO-phonon-assisted transitions. The LO-phonon energy extracted from the oscillation period is reduced with decreasing crystallite size, which is interpreted in terms of LO-phonon renormalization in the presence of an exciton.

Femtosecond Z-scan and degenerate four-wave mixing measurements of real and imaginary parts of the third-order nonlinearity of soluble conjugated polymers

We investigated the third-order nonlinear optical properties of several soluble π-conjugated polymers with a goal of reliable determination of the parameters that characterize the nonlinearity, such as the real and imaginary parts of the nonlinear refractive index n2 and the one-photon loss and two-photon loss merit factors W and T, respectively. The measurements were performed at 800 nm with 100-fs pulses from an amplified Ti:sapphire system. We present results of investigations of several 2,5-substituted poly(p-phenylene vinylenes), including poly[2-methoxy-5-(2′-ethyl-hexyloxy)-p-phenylenevinylene] and a soluble ladder poly (p-phenylene) polymer. In particular, Z-scan measurements of polymer solutions were found to be useful for the determination of the complex nonlinear refractive index. The results could be verified by time-dependent degenerate four-wave mixing studies performed on thin films of the polymers. We found generally good agreement between the values of n2 determined from Z scan and those from degenerate four-wave mixing. The results indicate that the nonlinear refractive index of the order of 10-12 cm2/W can be readily obtained for various conjugated polymers. However, the two-photon merit factors T larger than unity are commonly encountered within the two-photon absorption ranges of these compounds.

Femtosecond degenerate four-wave mixing of GaN on sapphire: Measurement of intrinsic exciton dephasing time

We describe time-integrated and spectrally resolved degenerate four-wave mixing (DFWM) on hexagonal GaN on sapphire for different laser energies and intensities. Our measured DFWM signal decays exhibit no contributions originating from polariton propagation effects in the 1- to 3-$\ensuremath{\mu}$m-thick bulk samples or from exciton/free-carrier scattering. At low temperatures and low excitation intensities the dephasing time of the $A$ exciton is as long as 3 ps and is most likely due to scattering by defects. At excitation densities above ${N}_{\mathrm{ex}}=5\ifmmode\times\else\texttimes\fi{}{10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ exciton-exciton scattering becomes the dominant dephasing mechanism and a fifth-order diffraction signal is observed above ${N}_{\mathrm{ex}}=3\ifmmode\times\else\texttimes\fi{}{10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.

Temperature dependence of a femtosecond degenerate four-wave mixing signal from 350-μm-thick undoped InP far below the band gap

We experimentally investigated the temporal and spectral profiles of the four-wave mixing (FWM) signals from 350-µm-thick undoped InP at various temperatures when the laser was tuned from the exciton resonance to 100 meV below the band gap. The temporal and spectral shapes of the observed FWM signals well below the band gap were nearly consistent with those of the excitation laser pulse and exhibited significantly different behavior from the excitonic properties in thin samples. Furthermore, we observed temperature-independent large blue shifts of the spectrally resolved FWM signals far below the band gap with respect to the excitation laser spectrum when the time delay moved from positive to negative. Based on our experimental observations, we conclude that this behavior can be explained not simply by the excitonic effects but by the instantaneously created virtual states and the frequency-broadening effect.

Femtosecond degenerate four-wave mixing in 500 μm undoped GaAs and 350 μm undoped InP far below band gap

Rather strong third- and fifth-order four-wave mixing (FWM) signals from a 500 μm thick undoped GaAs and a 350 μm thick undoped InP in detuning ranges of 80–170 meV below the band gap are observed. The spectrally resolved (SR) FWM signals for both samples far below the band gap are blue-shifted significantly with respect to the spectrum of the excitation laser pulse for negative time delays, whereas they are red-shifted for positive time delays. The temporal and spectral shapes of the FWM signals for both samples far below the band gap are nearly consistent with those of the excitation laser pulse but are remarkably different from the excitonic properties. The shifts of SR-FWM signals far below the band gap are interpreted as due to the instantaneously created virtual states by the temporal overlap of the excitation laser pulses.

Linear and nonlinear optical properties of a ladder poly( p-phenylene) polymer

Linear and nonlinear optical properties of a ladder polymer based on the poly( p-phenylene) backbone (LPPP) have been investigated. Femtosecond degenerate four-wave mixing (DFWM) was used for the determination of the nonlinear refractive index n 2 at 800 nm. Values of ‖ n 2‖ = (3–7) × 10 −13 cm 2/W were obtained from DFWM measurements on thin films and solutions of the polymer. The two-photon absorption coefficient of LPPP is estimated to be β=5×10 −9 cm/W at 800 nm.

Four-wave mixing in bulk GaAs microcavities at room temperature

We studied pico- and femtosecond degenerate four-wave mixing in bulk GaAs Fabry–Pérot microcavities at room temperature. For wavelengths below the GaAs band edge, a cavity with a finesse of approximately 20 yields an enhancement of the diffracted signal by more than two orders of magnitude as compared to a cavityless GaAs layer of the same thickness (685 nm). The cavity-enhanced nonlinearity of the interband transition results in a diffraction efficiency η≊0.5% for 150 pJ pulses with a duration of 900 fs at 878 nm, being 400 times larger than that for the bare GaAs reference sample.

Strong instantaneous contribution in femtosecond degenerate four-wave mixing from 350 μm InP due to virtual excitation

We have observed strong four-wave mixing (FWM) signals from the third up to the seventh order for a 350 μm undoped InP at 10 K with an excitation at far below the band gap. The third order spectrally resolved FWM signal shifts continuously to blue as time delay moves away from positive to negative. The peak intensities of the third and fifth order time-integrated FWM signals decrease rapidly as the detuning increases, as (detuning)−2 and (detuning)−6, respectively. The FWM signal at far below the band gap is attributable to the strong instantaneous contribution of the excitation pulse.

Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures.

Femtosecond degenerate four-wave mixing is used to investigate collective excitonic effects in radiatively coupled semiconductor multiple-quantum-well Bragg and anti-Bragg structures. The experimental and theoretical analysis of Bragg structures shows that the light-induced coupling causes a faster signal decay for increasing quantum-well numbers. For anti-Bragg structures, the predicted splitting of the excitonic resonances is observed in the four-wave-mixing spectrum causing quantum beats in the time-integrated signal.

Coherent exciton-exciton interaction in wide-gap II–VI quantum wells. The role of alloy disorder

This paper studies coherent exciton-exciton interaction in ternary ZnCdSeZnSe quantum wells by femtosecond degenerate four-wave mixing. Distinct two-exciton features are observed the appearance of which depends on the polarization of the excitation pulses. A signal for negative pulse delays disappears for larger Cd concentration.

Femtosecond Dynamics of Frenkel Excitons in Pseudoisocyanine J Aggregates

We report results of femtosecond pump-probe and degenerate four-wave mixing (DFWM) experiments in pseudoisocyanine J aggregates at 77 K. In the pump-probe experiments, the spectral oscillatory structure has been observed when the probe pulse precedes the pump pulse. This spectral oscillation is ascribed to the perturbed free induction decay of the J band. From the rise-up of the oscillation and results of DFWM experiments, the relaxation time is estimated from 300 to 600 fs. The time-resolved degenerate four-wave mixing spectroscopy is adopted to measure the coherent polarization decay in the J aggregates. The results clearly shows that the coherent polarization decay of the J band is ascribed to the free induction decay.