Degenerate Four-wave Mixing Spectra Research Articles

Excitonic effects on the linear and nonlinear optical properties of solid C60 fullerene, insights from many-body first-principles calculations

We perform the many-body Bethe-Salpeter equation eigenstates based sum-over-states calculations for the linear and nonlinear optical properties of solid C60 fullerene. Excitonic and local field effects are included in the calculations. We calculate the one-photon absorption (OPA), third harmonic generation (THG), degenerate four-wave mixing (DFWM), and electric-field-induced second harmonic generation (ESHG) spectra of solid C60 fullerene. The overall agreement between the theoretical and experimental results is good for all calculated spectra. The OPA spectrum shows that the solid C60 fullerene has a large excitonic binding energy of 0.35 eV. The position and intensity of spectral peaks are modified significantly. By tracing the sum-over-states progress, we determine the type of nonlinear polarization resonances for the characteristic peaks of the THG process, which may clear up a discrepancy in two experimental results. The calculated DFWM spectrum is in excellent agreement with the available experimental results in terms of line shape and peak positions, and thus the two-photon absorption peaks can be well understood on the basis of the excitonic states of solid C60 fullerene. The dynamic ESHG spectrum is given as a reference for the future experiment.

Excitonic Effects on the Linear and Nonlinear Optical Properties of Solid C60 Fullerene, Insights from Many-Body First-Principles Calculations

We perform the many-body Bethe-Salpeter equation eigenstates based sum-over-states calculations for the linear and nonlinear optical properties of solid C 60 fullerene. Excitonic and local field effects are included in the calculations. We calculate the one-photon absorption (OPA), third harmonic generation (THG), degenerate four-wave mixing (DFWM), and electric-field-induced second harmonic generation (ESHG) spectra of solid C 60 fullerene. The overall agreement between the theoretical and experimental results is good for all calculated spectra. The OPA spectrum shows that the solid C 60 fullerene has a large excitonic binding energy of 0.35 eV. The position and intensity of spectral peaks are modified significantly. By tracing the sum-over-states progress, we determine the type of nonlinear polarization resonances for the characteristic peaks of the THG process, which may clear up a discrepancy in two experimental results. The calculated DFWM spectrum is in excellent agreement with the available experimental results in terms of line shape and peak positions, and thus the two-photon absorption peaks can be well understood on the basis of the excitonic states of solid C 60 fullerene. The dynamic ESHG spectrum is given as a reference for the future experiment.

Polarization‐ and time‐resolved DFWM spectroscopy of the A 2Σ+− X 2Π (0,0) band transitions of nascent OH radicals generated by 266 nm laser photolysis of H2O2

The potential of a non‐linear spectroscopic technique – degenerate four‐wave mixing (DFWM) spectroscopy – for photo‐dissociation studies is investigated. By applying a carefully considered control of the input beam polarizations, the technique is used to measure the line shapes of specific rovibrational transitions in the A 2Σ+ − X 2Π (0,0) band of nascent OH radicals upon pulsed photo‐dissociation of H2O2. The photofragmentation is performed by linearly polarized radiation at 266 nm, and DFWM spectra are observed at various time delays. In contrast to linear spectroscopic methods, isotropic and anisotropic components of the non‐linear susceptibility tensor are separately accessible by using appropriate polarization geometries. In particular, four‐wave mixing signals can be generated that are exclusively due to the occurrence of the transient anisotropy of the recoil velocity and angular momentum vector distributions of the fragments emerging from the dissociation reaction. The observed line shapes in isotropic and anisotropic DFWM spectra are governed by the Doppler effect and vectorial correlations between the parent H2O2 molecule's transition dipole moment, the OH fragments’ recoil velocity and angular momentum, as well as by the processes of collision‐induced rotational and translational relaxation. Copyright © 2013 John Wiley & Sons, Ltd.

Growth of high-quality CuCl thin films by a technique involving electron-beam irradiation

We have developed the molecular-beam epitaxy (MBE) method for CuCl thin films. The crystalline quality has been improved by an electron beam irradiation before the MBE growth. The qualified films show an exceptionally high speed nonlinear response of excitons at room temperature, wherein the excitons decay radiatively before its coherence is destroyed by dephasing. The radiative decay time of the excitonic state in films with a thickness of hundred nanometers reaches the order of 100fs, which is much faster than the dephasing process. The shapes of the measured degenerate four-wave mixing spectrum and the radiative decay profile closely reflect those of the calculated induced-polarization spectrum and the radiative decay profile obtained by real-time analysis, respectively.

Room temperature superradiance due to coherent coupling between light and extended single quantum state

We have established the newly-developed growth method of high-quality CuCl thin film based on molecular-beam epitaxy. In qualified films, where harmonized coupling between an excitonic polarization wave and a resonant electromagnetic wave over a range of multiple wavelengths is achieved, we have observed an exceptionally high speed nonlinear response of excitons at room temperature, wherein the excitons decay radiatively before its coherence is destroyed by dephasing. A component with extremely large radiative width can be observed in the nonlinear optical spectrum only when the other components with smaller radiative widths disappear by the room-temperature dephasing. The radiative decay time of the excitonic state with the largest radiative width reaches the order of 100fs, which is much faster than the dephasing process. The mechanism demonstrated by our results contradicts the conventional physical description of light–matter interaction based on the long-wavelength approximation. The shapes of the measured degenerate four-wave mixing spectrum and the radiative decay profile closely reflect those of the calculated induced-polarization spectrum and the radiative decay profile obtained by real-time analysis, respectively.

Flame temperature diagnostics with water lines using mid‐infrared degenerate four‐wave mixing

AbstractThe feasibility of using degenerate four‐wave mixing (DFWM) for hot gas thermometry in the mid‐infrared spectral region is, for the first time, demonstrated by probing molecular ro‐vibrational transitions of water. DFWM spectra of hot water were recorded in specially designed flames, providing a series of temperatures varying from 1000 to 1900 K and, the dramatic spectral structure variations were used as temperature indicator. The intensity ratios between two hot water line groups at around 3231 cm−1 were especially studied and composed into a calibration table for flame temperature measurement using DFWM spectra. The saturation properties of different lines were also studied by recording the line intensity ratios as a function of laser power, and the results indicated that saturated excitation was in favor of reliable temperature measurements. As validation, infrared DFWM spectra in an φ = 1.52 flat premixed methane/air flame were recorded, and a good temperature value was obtained. Moreover, the recently released HITEMP2010 database as well as its previous version HITEMP2000 were adopted to simulate the hot water spectra and to analyze the line intensity ratios. Copyright © 2011 John Wiley & Sons, Ltd.

Efficient radiative recombination of multinode-type excitons up to room temperature in CuCl thin films

We report the observation of anomalous temperature dependences of degenerate four-wave mixing spectra in CuCl thin films with high crystalline quality. The observed temperature dependence is in good agreement with the phase-decay-constant dependence of calculated induced-polarization spectrum. An excitonic state with large radiative width can be observed at high temperatures as superradiance is faster than the dephasing process. We succeeded in observing the DFWM signal up to room temperature based on the extremely large radiative width peculiar to the thickness region beyond the long-wavelength approximation regime.

Ultrafast Response Induced by Interference Effects between Weakly Confined Exciton States

We report an ultrafast response of weakly confined excitons in GaAs thin films observed by a degenerate four-wave-mixing (DFWM) technique. The time-domain signals excited by broadband pulses show an oscillatory structure with a period that varies according to the pulse spectral width and an ultrafast response comparable to the pulse width; on the other hand, the exciton dephasing time is hardly changed by the excitation spectral width. This ultrafast response is much faster than the radiative lifetime expected on the basis of the nonlocal response theory. The DFWM spectra measured at various time delays clearly indicate the contribution of weakly confined excitons to the ultrafast response. Moreover, in the measurement of excitation-energy dependence, the time-domain signals excited by a controlled spectral width exhibit the variation of the oscillation period and response time. These characteristics are similar to those of the excitation spectral width dependence. From the analysis of oscillatory structu...

Ultrafast nonlinear optical response of weakly confined excitons in GaAs thin films

We report on an ultrafast nonlinear optical response of weakly confined excitons in GaAs thin films observed by a two-beam degenerate four-wave-mixing (DFWM) technique. An ultrafast optical response comparable to the pulse width appears under ultrashort-pulse-laser excitation condition. We clarified from the DFWM spectra that the plural exciton states contribute to the ultrafast response. The results imply a possibility of ultrafast switching devices using weakly confined excitons. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Degenerate four-wave mixing spectra in a two-level atomic system with phase-modulated time-delayed coherent fields

We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the $3s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}$, $F=2$, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, $F=3$, ${m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.

Missing levels lead to additional lines: the influence of nuclear spin statistics on femtosecond degenerate four wave mixing spectroscopy of polyatomic systems

We present the results of comprehensive experimental and theoretical studies of the effect of nuclear spin statistics on the structure of rotational recurrences in femtosecond degenerate four-wave mixing (fs DFWM) spectra of asymmetric top molecules. New recurrences of J-type with a period of 1/[4(B + C)] are identified in fs DFWM spectra of near-prolate tops SO2 [H. M. Frey, P. Beaud, T. Gerber, B. Mischler, P. P. Radi and A. P. Tzannis, J. Raman Spectrosc., 2000, 31, 71] and NO2 [I. Pastirk, M. Comstock and M. Dantus, Chem. Phys. Lett., 2001, 349, 71]. Our measurements of the asymmetric oblate-like top CH3NO2 revealed new recurrences of A-type with a period of 1/(8A), A, B and C being the rotational constants.The incorporation of nuclear spin statistics into the fs DFWM simulation-fitting code allowed us to successfully reproduce all these new features and the subsequent theoretical analyses uncovered mechanisms of their appearance. The nuclear spin statistics is shown to have a profound effect on fs DFWM spectra of asymmetric top species, notably with several zero spin nuclei.

Highly predissociative levels of CH3S (A 2A1) detected with degenerate four-wave mixing

Following photodissociation of dimethyl disulfide (CH3SSCH3) in a supersonic jet with a KrF excimer laser at 248 nm, degenerate four-wave mixing spectra of the A 2A1←X 2E3/2 transition of CH3S in a spectral region 317–377 nm are recorded using a dye laser. Observed features extend to 5020 cm−1 above the origin, much greater than 1490 cm−1 for fluorescence spectra and 2979 cm−1 for fluorescence depletion spectra. In addition to extension to higher members of the known progressions 3v and 213v associated with C–S stretching (ν3) and CH3 umbrella (ν2) modes, three new progressions 113v, 3v41, and 213v41 (or 11213v) involving the symmetric CH3 stretching (ν1) and asymmetric CH3 (ν4) stretching modes of the A 2A1 state of CH3S are tentatively assigned, yielding values of ν1=2966 cm−1 and ν4=3006 cm−1 that are consistent with theoretical predictions. Vibrational spectral parameters for ν1, ν2, ν3, and ν4 modes of the A 2A1 state of CH3S are derived.

Propagation effects in spectrally resolved transient four wave mixing measurements on excitons in GaAs multiple quantum wells

We perform spectrally resolved degenerate four wave mixing (DFWM) measurements by resonantly exciting 1s heavy hole excitons in 8 and 17.5 nm wide GaAs multiple quantum wells (MQW) with subpicosecond laser pulses. The signal is detected in a self-diffraction mode in backward geometry. The DFWM spectra reveal a multiple peak structure, evolving into a double peak for positive delays. This may be related to the propagation effects in MQWs due to strong photon–exciton coupling. The different peaks in the DFWM spectra show a dissimilar dependence on pulse excitation intensity, delay and polarization.

Detailed velocity-dependent line shapes for degenerate four-wave mixing spectra in a two-level atomic system

We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the ${3s}^{2}{S}_{1/2},$ $F=2,$ ${m}_{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2},$ $F=3,$ ${m}_{\mathrm{F}}=3$ transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.

Photoinduced High-Density Phase of Exciton-Polariton Masses and their Coherent Propagation at Stacking Fault Interface in BiI 3

Photoinduced high-density phase of exciton-polariton masses excited at a two-dimensional stacking fault interface in BiI 3 has been studied by observing the degenerate four-wave-mixing (DFWM) signals. It was found that the increase in the dephasing rate due to exciton-exciton collisions is suppressed above a threshold excitation density. Above such density, a coherently propagating component of the exciton masses was detected on the space-resolved DFWM signals obtained by applying the spatially isolated two-spot excitation with a picosecond laser. In this scheme the off-diagonal element of the density matrix of the excitons at the one exciting laser spot propagates to the other, bringing about nonlinear polarization to yield the DFWM light. Time evolution of the space-resolved DFWM signals reveals evidently the macroscopic expansion of the exciton-polariton masses in a photoinduced condensed phase. Energy splitting of the DFWM spectra obtained with a narrow-band laser shows a repulsive interaction between the excitons.

Coherent motion of high-density exciton masses at a quasi-two-dimensional interface in BiI 3

Spatial correlation of a quantum coherence of weakly interacting stacking fault excitons (SFEs) excited heavily at a two-dimensional stacking fault interface in BiI 3 has been studied by performing the degenerate four-wave-mixing (DFWM) measurements. It was found that the increase in the dephasing rate due to exciton–exciton scattering is suppressed above a threshold excitation density. Above such density, a propagating component of the SFE was detected on the space-resolved DFWM signals as a coherent mass of the excitons with nearly the same velocity as the group velocity of the SFE-polaritons by applying the spatially isolated two-spot excitation. In this scheme the off-diagonal element of the density matrix of the excitons induced by the exciting laser field at the one spot propagates to the other laser spot, bringing about nonlinear polarization to yield the DFWM signals. The time evolution of the space-resolved DFWM spectra evidently shows a manifestation of the macroscopic spatial expansion of a condensed quantum state of the excitons.

Influence of the transverse velocity on TC-RFWM spectra of jet-cooled CH

A saturation dip has been observed recently by A. Kumar et al. [Chem. Phys. Lett. 297 (1998) 300] in degenerate four-wave mixing (DFWM) and two-color resonant four-wave mixing (TC-RFWM) spectra of jet-cooled CH. This observation suggests that expressions of the signal intensity established for double-resonance molecular spectroscopy in the weak field limit are no longer valid. While the line splitting has been explained, this is not the case for the asymmetry observed on this spectrum. Here, we clearly establish the origin of this asymmetry as resulting from the transverse molecular velocity which acts even for a small velocity component. The model conveniently reproduces line splitting and asymmetry.

Degenerate Four Wave Mixing of C2 in Forward Geometry: Spectral Lineshape Analysis and Temperature Determination

Forward phase-matched degenerate four-wave mixing (DFWM) spectrum of C2 molecules is studied to determine the temperature of a premixed oxyacetylene flame. Both theoretical calculation and experimental measurement of the d3Πg↔d3Πu swan band of C2 are performed at weak field intensity. The measured spectra excited with a narrow band optical parametric oscillator (OPO) showed good matches with the results of calculations. When a DFWM spectrum corresponding to the molecular transitions of both high (J=36–42) and low (J=8–15) rotational levels is used for a Boltzmann plot, we can determine the flame temperature of 3143 K with a very small temperature uncertainty of 1.6%. In addition, the uncertainty in temperature measurement caused by the line interference of the DFWM spectrum in the forward geometry is estimated to be only 0.5%, which is negligible for practical applications.

Space-resolved luminescence and degenerate four-wave-mixing spectra of heavily photo-created exciton states in a layered crystal GaSe

High-density effects on the exciton states in a layered GaSe single crystal have been studied by observing photoluminescence and degenerate four-wave-mixing (DFWM) signals. The luminescence peak of the lowest exciton states shifts from lower energy to the higher lying absorption peak of the exciton owing to the site-filling effects of the weakly bound exciton states under heavy excitation. For heavier excitation, the recoil (red-shifted) luminescence due to exciton–exciton and exciton–carrier scattering becomes dominant. The free exciton shows remarkable spatial propagation under the heavy excitation on the space- and time-resolved luminescence spectra, giving a group velocity ∼3×10 8 cm/s. The time correlated DFWM signals having a single exponential decay for lower excitation densities come to have multiple components due to many-body effects under higher excitation densities. In the negative time domain, the DFWM signals reveal the response from the excitonic molecule states. From the DFWM spectra in the negative time domain, the binding energy of the excitonic molecule is estimated to be ∼8 meV.

Analysis of degenerate four-wave mixing spectra of NO in a CH 4 /N 2 /O 2 flame

/N2/O2 flame to spectral simulations based on a two-level theory for stationary, saturable absorbers by Abrams et al. Temperatures determined from least-squares fits of simulations to experimental spectra in the A2Σ+?X2Π+(0,0) band are compared to temperatures obtained from OH absorption spectroscopy and a radiation-corrected thermocouple. We find that DFWM rotational temperatures derived from Q-branch spectra agree with thermocouple and are independent of pump laser intensity for low to moderate saturation (I≈Isat). However, the temperatures are systematically low and depend on pump intensity if the analysis neglects saturation effects. We demonstrate a method for obtaining an effective pump saturation intensity for use with the two-level model. This approach for analyzing saturated DFWM line intensities differs from previous work in that the use of the theory of Abrams et al. rather than a transition-dipole-moment power law allows treatment of a much wider range of saturation. Based on the observed signal-to-noise ratio an NO detection sensitivity of 25 ppm is projected, limited by a DFWM background interference specific to hydrocarbon flames.