Two-photon Resonant Four-wave Mixing Research Articles

Two-photon resonant forward four-wave mixing in rubidium vapor involving Rydberg states

We report on observations of four-wave mixing in rubidium vapor via two-photon resonant excitation with nd and (n+2)s states, for n=14–20. The intensity of the generated beam is studied in a collinear configuration, and the results are consistent with the predictions of a theoretical model based on the semiclassical Maxwell–Bloch equations, considering interference effects associated with multiple excitation pathways and with internally generated fields. We have also observed spectral broadening of the two-photon resonant lines, which is well described by a linear dependence on atomic density, in accordance with collision-induced broadening.

Study of two-photon resonant four-wave sum mixing in xenon in the spectral region of 105–110 nm

The two-photon resonant four-wave sum and difference mixing in Xe gaseous medium was studied by subjecting a variety of molecular samples, including acetone, furan, thiophene, triethylamine, and dimethylsilacyclobutane, to the coherent radiation sources produced from the four-wave mixing processes for ionization. Ionization of all samples studied showed similar behavior and is due to the laser radiation from four-wave sum mixing. It is demonstrated that in a vacuum ultraviolet (VUV) spectral region of 105–110 nm four-wave sum mixing in Xe can only occur in five discontinued regions, all of which are to the blue of a Xe atomic transition. The peak positions and widths of the five spectral regions were characterized. Study of the triethylamine sample with its ionization energy lower than the photon energy of the VUV radiation from the difference mixing illustrated the competition between the sum and difference mixing occurring simultaneously in the Xe gas cell.

Probe of I( 2P j) atoms using two-photon resonant four-wave mixing spectroscopy following the 266-nm photodissociations of various alkyl and perfluoroalkyl iodides

Two-photon resonant four-wave mixing spectroscopy has been utilized successfully for probing I and I ∗ nascent from the 266 nm photodissociations of various alkyl and perfluoroalkyl iodides. The relative quantum yields for I ∗, as well as the recoil anisotropy parameters, were extracted. Recoil anisotropy parameters close to the limit value for parallel transition indicates that the ground-state I( 2P 3/2) originates from the curve crossing from the initially prepared 3Q 0 to 1Q 1 state. The curve-crossing probabilities for alkyl and perfluoroalkyl iodides were obtained and tried to explain using the well-known Landau–Zener model. In the cases of perfluoroalkyl iodides, it is necessary to consider the fluorination effect to describe the detailed dynamics observed in this study and has been revealed that the electronic effect due to fluorine atom substitution is dominant, leading to decrease in the curve-crossing probability.

Enhanced generation of vacuum-ultraviolet radiation by four-wave mixing in mercury using pulsed laser vaporization

The efficiency of a coherent vacuum ultraviolet (VUV) source at 125 nm, based on two-photon resonant four-wave mixing in mercury vapor, has been enhanced by up to two orders of magnitude. This enhancement was obtained by locally heating a liquid mercury surface with a pulsed excimer laser, resulting in a high-density vapor plume in which the nonlinear interaction occurred. Energies up to 5 μJ (1 kW peak power) have been achieved while keeping the overall mercury cell at room temperature, avoiding the use of a complex heat pipe. We have observed a strong saturation of the VUV yield when peak power densities of the fundamental beams exceeded the GW/cm2 range, as well as a large intensity-dependent broadening (up to ∼ 30 cm-1) of the two-photon resonance. The source has potential applications for high-resolution interference lithography and photochemistry.

Two-photon resonant four-wave mixing in a dressed atomic system: Polarization interference in a Doppler-broadened system

We study dressed-atom two-photon resonant nondegenerate four-wave mixing (NFWM) in a Doppler-broadened system. It is found that there exists interference between the macroscopic field polarizations from different ensembles of atoms within the atomic velocity distribution. This polarization interference can cause significant modification of the NFWM spectra. We also show that two-photon resonant NFWM in dressed atoms can be employed as a new type of Doppler-free high-resolution Autler-Townes spectroscopy for measuring transition dipole moments between two highly excited atomic states.

Two-photon resonant four-wave mixing in a dressed atomic system

We study two-photon resonant nondegenerate four-wave mixing (NFWM) in a dressed cascade four-level system. In the presence of a strong coupling field, the two-photon resonant NFWM spectrum exhibits Autler-Townes splitting, accompanied by either suppression or enhancement of the NFWM signal. Such phenomena are demonstrated in Ba through inducing of atomic coherence between the ground state $6{s}^{2}$ and the doubly excited autoionizing Rydberg state $6pnd$. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.

157-nm coherent light source as an inspection tool for F_2 laser lithography

We have developed a 157-nm coherent light source by two-photon resonant four-wave mixing in Xe, with two tunable single-mode 1-kHz Ti:sapphire laser systems at 768 and 681 nm. This light source has been developed to determine the instrumental function of a vacuum ultraviolet spectrometer and to evaluate optical designs for ultra-line-narrowed F(2) laser lithography. The spectral linewidth of the source was less than 0.008 pm (FWHM), with an average power of 0.6 mW.

Generation of milliwatt narrow-bandwidth vacuum ultraviolet radiation by an all-solid-state tunable high-average-power laser system

Generation of milliwatt narrow-bandwidth vacuum ultraviolet radiation by two-photon resonant four-wave mixing in Xe at 153 nm is demonstrated. The output of extreme ultraviolet radiation was at the microwatt level at 85 nm. For this demonstration, we developed an all-solid-state tunable 5-kHz Ti:sapphire laser system that produces 0.6-ns 0.7-GHz-bandwidth pulses at an average power of 32 W at the fundamental, 12 W at the second harmonic, and 6.3 W at the third harmonic.

Ultrafast modulation spectroscopy in cascading three-level and four-level systems

We study theoretically ultrafast modulation spectroscopy in Doppler-broadened cascading three-level and four-level systems. The pump beams consist of two frequency components that drive two-pathway excitation. The four-wave mixing (FWM) signal exhibits damping oscillation as the relative time delay τ between the two pump beams is varied, from which the resonant frequencies between energy levels can be deduced. Furthermore, Doppler-free precision in the measurement of the resonant frequencies can be achieved when the pump beams have either narrow-band or broadband linewidths. We study two-photon resonant FWM induced by time-delayed correlated fluctuating fields in a Doppler-broadened cascading three-level system. It is related intrinsically to the sum-frequency trilevel echo when the pump beams have broadband linewidths. However, unlike the corresponding incoherent-light stimulated photon echo, the maximum of the FWM signal is shifted from τ≃0. If we consider the fluctuations of the pump beams, the FWM signal exhibits damping oscillation when the laser frequency is off resonant from the two-photon transition.

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 x 10(9) atoms/cm(3). Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to seed the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.

Femtosecond-pulse two-photon resonant difference-frequency mixing in gases: A technique for tunable vacuum-ultraviolet femtosecond-pulse generation and a spectroscopic tool for studying atoms in strong laser fields

Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.

Detection of oxygen atoms in a high pressure surfatron microwave discharge via two-photon four-wave mixing

PJ) oxygen atoms are detected in a high pressure surface wave discharge driven at 2.45 GHz via two-photon resonant degenerate four-wave mixing spectroscopy (TP-DFWM) in the forward folded BOX configuration. The nonlinear optical signal provides a direct measure of the relative oxygen atom concentration with high spatial resolution inside the discharge up to pressures of 1 bar and without distortions due to linear absorption or saturation effects. The axial distribution of oxygen atom concentration is observed to depend sensitively on total pressure and gas flux. For total gas pressures up to 600 mbar both in case of a mixture of 10% O2/He and 10% O2/Ar the concentration of oxygen atoms increases linearly with pressure. At higher pressures an increase with larger slope is observed for 10% O2/Ar, while the concentration remains constant for 10% O2/He. This is interpreted by an increase of the three-body recombination rate in O2/He mixtures.

Two-photon four-wave mixing as a new probe for oxygen atoms

We report on the fine structure selective observation of 3P J oxygen atoms using two-photon resonant degenerate four-wave mixing spectroscopy (TP-DFWM) in the forward folded BOXCARS configuration. The oxygen atoms are generated in a microwave discharge from mixtures of molecular oxygen with helium and neon. The nonlinear optical character of the method allows to determine directly inside the discharge the relative oxygen atom yield while varying gas mixture or pressure. Absolute number densities are determined by calibration via NO 2 titration.

Observation of the two-photon resonant parametric four-wave mixing in the NO C 2Π ( ν = 0) state

When the laser frequency was tuned through the C 2Π (ν = 0) « X 2Π (ν″ = 0) two-photon transition of NO, near-IR as well as UV radiations were ejected along the laser propagation with a narrow solid angle. It was shown that the UV wave corresponds to the A 2 Σ + ( ν′ = 0) → X 2 Π ( ν″ = 0) transition. Temporal profiles and polarization properties of output waves indicate that the parametric four wave mixing (PFWM) process is mainly responsible for the simultaneous generation of near-IR and UV radiations. Excitation spectra corresponding to the C 2Π (ν = 0) « X 2Π (ν″ = 0) band exhibited an excellent S/N ratio, implying that the PFWM technique might be utilized as a novel spectroscopic method which can interrogate the two-photon resonant levels.

Generation of tunable coherent extreme-ultraviolet radiation at wavelengths as low as 66 nm by resonant four-wave mixing

Tunable coherent extreme-ultraviolet (XUV) radiation at wavelengths as low as 66.86 nm was generated by two-photon resonant four-wave mixing in a hydrogen molecular gas jet. In this investigation, an ArF excimer laser was tuned to the E,F(1)Sigma(+)(g)(upsilon' = 6)-X(1)Sigma(+)(g)(upsilon' = 0) Q(1) transition of H(2), and the second-harmonic radiation of a dye laser was mixed to obtain the resultant XUV radiation. To our knowledge, this tunable XUV radiation is the shortest wavelength obtained so far by two-photon resonant four-wave mixing.

Generation of coherent XUV radiation by two-photon resonant four-wave mixing combined with stimulated Raman scattering

A new scheme to develop a continuously tunable coherent XUV source shorter than 70 nm is proposed, in which two-photon resonant four-wave mixing is combined with stimulated Raman scattering. A preliminary experiment of this scheme has been conducted and XUV radiation at 66.2 and 68.1 nm has been generated simultaneously in a hydrogen gas jet by resonant four-wave mixing of an ArF excimer laser beam with its stimulated Raman scattering.

Absorption Coefficient and Sensitivity of Positive and Negative Resists in the Vacuum Ultraviolet Region

Absorption coefficients for the resist materials (polymethyl methacrylate (PMMA) and partially chloromethylated polystyrene (CMS-DU)) were obtained in the vacuum ultraviolet (VUV) region. Negative and positive resist characteristics were investigated using a coherent VUV radiation source (λ=110-150 nm) generated by two-photon resonant four-wave mixing in Cd vapor. A very low exposure energy of approximately 1 mJ/cm2 was realized by employing a very thin resist film and using VUV light from the high-absorption region of the resist materials.

Generation of tunable coherent XUV radiation in a hydrogen gas jet by two-photon resonant four-wave mixing

Tunable coherent XUV radiation down to 75 nm was generated by two-photon resonant four-wave mixing of a tunable ArF excimer laser with a dye laser in a molecular gas jet of hydrogen. The obtained XUV spectral profiles reflected the double resonance effect at Rydberg states in H 2 molecules. This scheme has a possibility to extend the shortest wavelength limit of the tunable radiation down to 66 nm by using a frequency-doubled dye laser.

Polarization properties of optical phase conjugation by two-photon resonant degenerate four-wave mixing.

We develop a semiclassical theory of the polarization properties of phase conjugation by two-photon resonant degenerate four-wave mixing. The theory includes the effects of saturation by the pump waves. We solve the density-matrix equations of motion in steady state for a nonlinear medium consisting of stationary atoms with a ground and excited state connected by two-photon transitions. As an illustration of the general results, we consider an ${S}_{0}$\ensuremath{\rightarrow}${S}_{0}$ two-photon transition, which is known to lead to perfect polarization conjugation in the limit of third-order theory. We show that the fidelity of the polarization-conjugation process is degraded for excessively large pump intensities. The degradation can occur both due to transfer of population to the excited state and due to nonresonant Stark shifts. Theoretical results are compared to those of a recent experiment [Malcuit, Gauthier, and Boyd, Opt. Lett. 13, 663 (1988)].

Rotational dependence of nonlinear parametric processes in diatomic molecules

Theoretical results on the rotational dependence of nonlinear parametric processes in diatomic molecules are generalized. Well-known results such as the parity of the nonvanishing nonlinear susceptibilities or the polarization effects are retrieved. Nonresonant susceptibility does not depend on the J rotational quantum number of the molecules involved in the process nor, consequently, on the temperature. It does depend on the J quantum numbers of both the ground and resonant state. The general rotational dependence of the resonant nth-order nonlinear susceptibility is derived in the general case of a single resonance. Three examples are given: /sup 1/ Sigma -/sup 1/ Pi three-photon resonant four-wave mixing, /sup 1/ Sigma -/sup 1/ Sigma two-photon resonant four-wave mixing, and /sup 2/ Pi -/sup 2/ Sigma two-photon resonant four-wave mixing. All the coefficients needed to compute the nonlinear susceptibility describing any four-wave mixing experiment are tabulated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>