Three-photon Resonance Research Articles

Third-order nonlinear optical spectroscopy in the two-dimensional cupratesNd2CuO4andLa2CuO4

We have measured third-order nonlinear susceptibility $({\ensuremath{\chi}}^{(3)})$ spectra of the two-dimensional (2D) cuprates ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ by third-harmonic generation. The $|{\ensuremath{\chi}}^{(3)}|$ spectra exhibit broad peaks with maximum values of $0.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\mathrm{esu}$ in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\mathrm{esu}$ in ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}.$ These peaks are attributable to three-photon resonance to the charge transfer (CT) excited state. The ${\ensuremath{\chi}}^{(3)}$ phase spectrum of ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ has revealed that the two-photon resonance to the even CT state are hidden on the high-energy side of the ${\ensuremath{\chi}}^{(3)}$ peak. The difference in ${\ensuremath{\chi}}^{(3)}$ values between the 2D and 1D cuprates is discussed by considering differences in spin-charge coupling and in charge configurations between the 2D and 1D cases.

Large Optical Nonlinearity in 1D and 2D Cuprates Investigated by Third Harmonic Generation Spectroscopy

Spectra of third-order nonlinear susceptibility |X (3) | have been investigated for 1D Mott insulators (Mls), Sr 2 CuO 3 and Ca 2 CuO 3 and 2D Mls, Nd 2 CuO 4 and La 2 CuO 4 , by using third-harmonic generation (THG) spectroscopy. The three-photon resonance to the odd-charge-transfer (CT) state enhances |X (3) |. The maximum values of |X (3) | in the 2D MIs (∼10 -10 esu) are one order smaller than those in the 1D Mls(∼10 -9 esu). The difference of the magnitudes and spectral shapes of |X (3) | between the 1D and 2D Mls can be explained by taking account of the concept of spin-charge separation.

Nonlinear optical response in two-dimensional Mott insulators

We theoretically examine the nonlinear optical responses in two-dimensional Mott insulators. The photoexcited states of the Mott insulators are described by an effective model in the strong-coupling limit of a half-filled Hubbard model. By comparing the linear optical absorption, nonlinear optical two-photon absorption and third harmonic generation (THG), we clarify the nature of photoexcited states such as the distribution of odd-parity and even-parity states. In the THG spectrum, main contribution is found to come from the process of three-photon resonance associated with the odd-parity states. As a result, the two-photon resonance process is less pronounced in the THG spectrum. The calculated THG spectrum is qualitatively consistent with recent experimental data.

Nonlinear optical response in two-dimensional Mott insulators

We study the third-order nonlinear optical susceptibility ${\ensuremath{\chi}}^{(3)}$ and photoexcited states of two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that the coupling of charge and spin degrees of freedom plays a crucial role in the distribution of the dipole-allowed states with odd parity and the dipole-forbidden states with even parity in the photoexcited states. This is in contrast with the photoexcited states in one dimension, where the charge and spin degrees of freedom are decoupled. In the third-harmonic generation (THG) spectrum, the main contribution is found to come from the process of three-photon resonance associated with the odd-parity states. As a result, the two-photon resonance process is less pronounced in the THG spectrum. The calculated THG spectrum is compared with recent experimental data. We also find that ${\ensuremath{\chi}}^{(3)}$ with a cross-polarized configuration of pump and probe photons shows spectral distributions similar to ${\ensuremath{\chi}}^{(3)}$ with a copolarized configuration, although the weight is small. These findings will help analyses of the experimental data of ${\ensuremath{\chi}}^{(3)}$ in 2D Mott insulators.

Three-photon resonances due to autoionizing states incalcium

In the present study we have investigated three-photon ionization inCa in which autoionizing states are engaged. The two-photon resonantprocess (from the Ca ground state 4s2 1S0) occurredthrough or at least in the vicinity of one of the following states:4s4d 1D2, 4p2 3P2, 4s6s 1S0, 4p2 1D2 and 4p2 1S0, with the third photon either reachingthe continuum directly or one of the autoionizing states. The three-photonresonant transitions to 3dmp, mf: 1P1, 3P1 and 3D1 autoionizing states for m up to 21 have beenobserved. Some of the autoionizing resonances which we have found hadnot been observed before in a high-resolution one-photon absorptionexperiment (for J = 1) and in multiphoton experiments (for J = 3). We have compared the ionization signal as a function of thelaser detuning and the laser intensity with theoretical curvesobtained within a simple model (three-level atom + one-mode laserfield). This gives information about the order of magnitude of thethree-photon ionization probability through autoionizing states.

Large third-order optical nonlinearity of Cu-O chains investigated by third-harmonic generation spectroscopy.

Spectra of the third-order nonlinear susceptibility chi((3)) have been investigated for one-dimensional Mott insulators, Sr(2)CuO(3) and Ca(2)CuO(3), by applying the third-harmonic generation (THG) spectroscopy on their single-crystalline thin films. The three-photon resonance to the lowest charge-transfer (CT) state with odd parity strongly enhances chi((3)), which is of the order of 10(-9) esu. The two-photon resonant structure unravels the even-CT state, located close to the odd-CT state. Two types of chi((3)) spectra obtained from THG and the electroreflectance measurements are explained based on the concept of spin-charge separation.

Abnormal behavior in the three-photon resonance enhanced multiphoton ionization spectroscopy of CO E 1Π←X 1Σ+(0,0)

The abnormal behavior of CO E 1Π(v=0)←X 1Σ+(v=0) three-photon resonance enhanced multiphoton ionization (REMPI) spectroscopy is studied, including the anomalous band structures and adverse pressure effects on the spectral intensity. One- and two-color experiments with laser beams in co- and counterpropagations have been performed to elucidate the mechanisms. It is demonstrated that the abnormalities originate from two mechanisms, i.e., the reabsorption of the resultant third harmonic generation (THG) in the one-color case or four wave mixing sum frequency generation (FWSFG) in the two-color case, and the interference cancellation between the one-photon excitation channel induced by THG/FWSFG reabsorption and the three-photon direct excitation channel. The former mechanism dominates in the wing region of a resonant transition profile, while the latter is restricted within the kernel portion of the transition.

Two-photon resonant third-harmonic generation in La2CuO4.

Combining linear absorption and nonlinear third harmonic generation (THG) experiments, we investigate details of the electronic structure of the highly correlated electronic system in La2CuO4. We demonstrate strong THG mainly due to the charge transfer excitation from O (2p(sigma)) to Cu (3d(x2-y2)). The THG spectrum shows pronounced features due to three-photon and two-photon resonance enhancement as well as quantum interference effects. We obtain excellent agreement with a THG spectrum calculated in terms of the excitonic cluster model and can identify both odd and even symmetry excitation modes.

Formation of nonclassical states of light in media with a three-photon resonance

The process of simultaneous absorption of three photons in a medium subjected to a three-photon parametric perturbation is considered. It is shown that in such a medium one can observe the formation of the radiation field states, which are the quantum superposition of three coherent components. One-photon and twophoton absorption processes in the medium also destroy the interference between the components of the superposition state. The states being formed are investigated in both the temporal development (numerically) and the stationary limit (numerically and analytically); the Wigner functions, as well as the quantum entropy, are calculated for a whole series of initial states. It is shown that depending on the initial state of the radiation field, the interference between the three-component superposition states being formed can lead, for example, to the almost total localization of the system in a two-component state or to the destruction of the interference between different coherent components.

Formation of Nonclassical States of Light in Media with a Three-Photon Resonance

Formation of Nonclassical States of Light in Media with a Three-Photon Resonance

Origin of the 0.89 eV peak inχ(3)(−3ω;ω,ω,ω)of polyacetylene: Electron correlation effects

The third-order optical susceptibility {chi}{sup (3)} of polyacetylene is calculated by the Lanczos-based density-matrix renormalization group. The theoretical results now remarkably agree with two different sets of experimental data: both the positions of two major peaks and their relative intensities. The 0.89 eV peak, originally assigned to a two-photon resonance, is actually a three-photon resonance due to the nB{sub u} state. This state lies above the band-edge state jB{sub u} which itself accounts for a hidden hump on the right shoulder of the 0.6 eV peak. The electron correlation effect is the main origin of these rich features. (c) 2000 The American Physical Society.

Nonlinear optical spectra of C 70

We employ a continuously tunable 100 fs pulse source to measure the time-resolved degenerate four-wave-mixing (DFWM) spectrum of an amorphous C 70 film. The observed nonlinear optical response is essentially instantaneous and electronic in origin. We deduce the complex third-order nonlinear-optical susceptibility tensor function χ 1111(− ω, ω, ω,− ω) throughout the wavelength range 0.74–1.6 μm. We find two-photon resonances with excited-state energies of 2.41±0.05 and 2.61±0.05 eV close to the 2.7 eV two-photon resonance of C 60. The two-photon absorption coefficient at the resonance maximum is 20±8 cm/GW, as large as that of C 60. Our amplitude and phase data indicate that we have reached the long-wavelength limit, χ 1111 LWL, of χ 1111. We find it to be (4.5±0.5)×10 2 times that of fused silica and 1.9±0.6 times that of C 60. This result implies χ 1111 LWL=(1.8±0.2)×10 −12 esu, a value that is consistent with the theoretical prediction of Shuai and Brédas. We use linear-absorption and DFWM data to construct an analytic expression for χ 1111[−( ω 3+ ω 2+ ω 1), ω 3, ω 2, ω 1] which, we believe, predicts any nonlinear optical effect within the range ℏ ω i>0.6 eV (i=1, 2, or 3) and ℏ( ω 3+ ω 2+ ω 1)<2.8 eV. We find that for ω near the lowest three-photon resonance, the magnitude and phase of χ 1111 behave like that of a two-level atom with a matrix element obtained from the observed one-photon oscillator strength. This explains the observed change in sign of Re[ χ 1111(−3 ω, ω, ω, ω)] from positive to negative for decreasing ω near ℏ ω=0.8 eV.

Third-order nonlinear optical properties of porphyrazine, phthalocyanine and naphthalocyanine germanium derivatives: Demonstrating the effect of π-conjugation length on third-order optical nonlinearity of two-dimensional molecules

Optical and third-order nonlinear optical properties of germanium porphyrazine, phthalocyanine and naphthalocyanine derivatives have been measured in order to evaluate the effect of extended π-electron conjugation on third-order optical nonlinearity. Third-order nonlinear optical susceptibilities χ (3) of thin films of trans-dihydroxy-1,6,11,16-tetra-( tert.butyl)porphyrazine germanium [ t-Bu 4PazGe(OH) 2], trans-dihydroxy-tetra-( tert.butyl)phthalocyaninato germanium [( t-Bu 4PcGe(OH) 2] and naphthalocyanine germanium (GeNc) derivative measured by the third-harmonic generation technique are reported. A χ (3)(−3 ω; ω, ω, ω) value as high as 1.3×10 −11 esu at 1.65 μm was observed for [ t-Bu 4PazGe(OH) 2] thin films from a dominant three-photon resonance. A χ (3)(−3 ω; ω, ω, ω) value of 2.5×10 −11 esu and a χ (3)/ α value of 1.65×10 −15 esu cm as figure of merit was observed for [ t-Bu 4PcGe(OH) 2] thin films at 1.8 μm. The χ (3) values of germanium porphyrazine derivative have been compared with those of structurally related germanium phthalocyanine and naphthalocyanine analogues to evaluate the effect of extended π-conjugation introduced through benzo substitution. A progressive red-shift in optical absorption peaks in the Q-band region and an increase in the third-order nonlinear optical susceptibility was noticed with sequential increase of benzo substitution from the porphyrazine to naphthalocyanine ring. The effect of benzo substitution as well as axial substitution on optical and third-order nonlinear optical properties has been discussed. Attempts have also been made to establish a correlation between third-order optical nonlinearity and photoconductivity of metallophthalocyanines in view of the present results.

Third-order optical nonlinearity of semiconductor carbon nanotubes: third harmonic generation

Within the framework of a two-band model of the electronic structure of semiconductor carbon nanotubes (CNs) we have studied the third-order nonlinear optical susceptibility χTHG(3)(ω) responsible for the effect of the third harmonic generation. We have obtained a theoretical expression for χTHG(3)(ω) which takes into account the contributions to the susceptibility due to purely interband transitions of π-electrons and combined intraband–interband motion of the latter. A detailed analysis of the dispersion dependence of χTHG(3)(ω) has been carried out in a wide range of frequencies involving those which are much smaller than the bandgap energy and those equal to it by the order of magnitude. The nonlinear-optical spectra of χTHG(3)(ω) are calculated numerically for nonchiral single-shell nanotubes with different radii. The results show that at the expense of the increase of the radius of the nanotubes one can achieve a giant enhancement of the power of radiation generated at the third harmonic frequency in the three-photon resonance regime. It is also shown that the magnitude of the resonant optical susceptibility of CNs can exceed the resonance values of χ(3)THG for the fullerenes C60 and C70 by several orders. The results obtained allow us to give a positive prognostic estimate of CNs as a new class of materials for nonlinear optics.

Theory of the effect of odd-photon destructive interference on optical shifts in resonantly enhanced multiphoton excitation and ionization

We present a theory for two- and three-photon excitation, optical shifting, and four-wave mixing when a first laser is tuned onto, or near, a two-photon resonance and a second much more intense laser is tuned near or on resonance between the two-photon resonance and a second excited state. When the second excited state has a dipole-allowed transition back to the ground state and the concentration is sufficiently high, a destructive interference is produced between three-photon coupling of the ground state and the second excited state and one-photon coupling between the same states by the internally generated four-wave mixing field. This interference leads to several striking effects. For instance, as the onset of the interference occurs, the optical shifts in the two-photon resonance excitation line shape become smaller in copropagating geometry so that the line shapes for multiphoton ionization enhanced by the two-photon resonance eventually become unaffected by the second laser. In the same range of concentrations the four-wave mixing field evolves to a concentration-independent intensity. With counterpropagating laser beams the line shape exhibits normal optical shifts like those observed for both copropagating and counterpropagating laser beams at very low concentrations. The theoretical work presented here extends our earlier works by more » including the effect of laser bandwidth and by removing the restriction of having the second laser be tuned far from three-photon resonance. In this way we have now included, as a special case, the effect of both laser bandwidth and interference on laser-induced transparency. Unlike other effects related to odd-photon destructive interference, the effect of a broad bandwidth is to bring about the predicted effects at much lower concentrations. Studies in rubidium show good agreement between theory and experiment for both ionization line shapes and four-wave mixing intensity as a function of concentration. {copyright} {ital 1998} {ital The American Physical Society} « less

Linear and nonlinear optical spectra of polyazomethines fabricated by chemical vapor deposition

We report on the results of third-harmonic generation (THG) measurements on vapor-deposited thin films of two polyazomethines, poly(nitrilo-1,4-phenylenenitrilomethylidyne-1,4-phenylenemethylidyne) (PNPP) and poly(nitrilo-2,5-azinylnitrilomethylidyne-1,4-phenylenemethylidyne) (PNAP) covering pump energies from 0.6 to 1.4 eV. The THG data show the presence of a strong three-photon resonance centered near 0.9 eV for both samples; additional weaker structure is observed for PNPP near 1.2 eV. The peak values of the third-order susceptibility are 2.8 × 10 −11 e.s.u. for PNPP and 1.8 × 10 −11 e.s.u. for PNAP; off-resonance values are nearly an order of magnitude smaller. We have also obtained the χ (3)(3 ω) spectrum of an oriented PNPP film grown on an obliquely evaporated SiO 2 pattern. An enhancement by nearly a factor of three in the peak nonlinear optical susceptibility is observed relative to that of the unoriented PNPP film, demonstrating that a moderate degree of molecular orientation was achieved.

Analysis of F'0u+ion-pair state of iodine

The optical-optical double resonant multiphoton ionization (OODR-MPI) technique and the flu-orescent excitation spectroscopy technique have been applied to the study of the F'0u+ ion-pair state of iodine. This paper presents OODR-MPI spectrum and fluorescent excitation spectrum of I2 in the region of 54000-55300cm-1 by the three-photon resonant, two-photon ionization (1 + 2 + 2) and (1 + (1 + 1) + 2) processes.

Two- and Three-Photon Resonant Third Harmonic Generation in Molecular Nitrogen

Tunalbe coherent extreme ultraviolet radiation has been produced in nitrogen by third harmonic generation (THG) processes enhanced by two-photon resonance with the a1Πg(ν' = 1) state and three-photon resonance with the c'41Σu+(ν' = 1) state, respectively. The highly resolved THG spectra imply that THG can be used to probe the higher excited states and to detect the rotational population of a molecular gas.

Two-colour intensity suppression of multiphoton ionization of atomic deuterium

We report a strong suppression of the three-photon ionization resonant with the 2s state of atomic deuterium at 243 nm by the introduction of a second colour (486 nm) coupling the 2s and 4p states. This coupling reduces the ionization probability by several orders of magnitude. The experiment is performed using fundamental and second harmonic frequencies of the same laser, with laser intensities up to a maximum value of and an atomic target density of the order of . The production of both ions and D(2s) atoms is measured as a function of the intensity of the fundamental beam (486 nm). The experimental data are compared with a theoretical calculation using essential states and taking into account the experimental laser bandwidths.

Wavelength dispersion of third-order nonlinearities in organic and glass materials

We report on the wavelength dispersion of third-order nonlinearities in organic and glass materials. Optical Kerr shutter (OKS) and third-harmonic generation (THG) measurements were conducted on a N, N-dimethylformamide solution of 4-( N, N-diethylamino)- β-nitrostyrene (DEANST) and a glass containing Bi 2O 3. It is shown that the OKS nonlinearity is increased by the two-photon resonance as well as by the one-photon resonance. In the DEANST solution, the two-photon resonance yields the large OKS nonlinearity at around 0.9 μm wavelength. The THG nonlinearity of the DEANST solution is found to be enhanced by the three-photon resonance.