Search

We have theoretically investigated the high harmonic generation (HHG) spectra of \(\textrm{H}_2^+ \) and HD + using a time-dependent wave packet approach for the nuclear motion with pulsed lasers of peak intensities (I0) of 3.5 ×1014 and 4.5 ×1014 W/cm2, wavelengths (λL) of 800 and 1064 nm, and pulse durations (T) of 40 and 50 fs, for initial vibrational levels v0 = 0 and 1. We have argued that for these conditions the harmonic generation due to the transitions in the electronic continuum by tunnelling or multiphoton ionization will not be important. Thus, the characteristic features of HHG spectra in our model arise only due to the nuclear motions on the two lowest field-coupled electronic states between which both interelectronic and intraelectronic (due to intrinsic dipole moments, for HD + ) radiative transitions can take place. For HD + , the effect of nonadiabatic (NA) interaction between the two lowest Born–Oppenheimer (BO) electronic states has been taken into account and comparison has been made with the HHG spectra of HD + obtained in the BO approximation. Even harmonics and a second plateau in the HHG spectra of HD + with the NA interaction and hyper-Raman lines in the spectra of both \(\textrm{H}_2^+ \) and HD + for v0 = 1 have been observed for higher value of I0 or λL. Our calculations indicate reasonable efficiencies of harmonic generation even without involving the electronic continuum.

We have investigated the angular distribution of photofragments resulting from multiphoton above threshold dissociation (ATD) of HD+ from initial bound levels νi=0, 1, 2 and Ji=0 induced by linearly (↕) and circularly (↻) polarized laser fields of intensities I=1, 5, and 10 TW/cm2 and frequency ω=30 333 cm−1 (λ=329.7 nm). The time-independent close coupling (CC) method has been used. Molecular rotation has been taken into account by including 72 channels with J=0–7 and number of photons n=−1–7, for ↕ polarization. In case of ↻ polarization, the channel number reduced to 48. All the radiative couplings including those due to the intrinsic dipole moments of HD+ have been considered in a truncated length gauge form of interaction. For (net) one-photon dissociation (from νi=1, 2) by bond softening, the alignment of the angular distribution of photofragments increases with intensity (1–10 TW/cm2), for both ↕ and ↻ polarizations. The angular distributions for (net) two-photon fragmentation via the adiabatic pat...

We have theoretically investigated the branching in population transfer in H2 by chirped adiabatic Raman passage from the ground vg=0, Jg=0 level to the final rotational levels Jf=0 (Q-branch) and Jf=2 (S-branch) of the fundamental transition (vf=1) in the ground X 1Σg+ state via the nonresonant intermediate B 1Σu+ and C 1Πu+ states. The density matrix technique has been employed to describe the time evolution of the process. We have evaluated the rotational branching of transferred population in the final levels using linearly chirped pump and Stokes laser pulses with different chirp rates and chirp widths. Both the pulses are considered to have the same temporal shape, duration, peak intensity, and linear parallel polarizations. It has been observed that for negative chirping of the pump laser and positive chirping of the Stokes laser, branching in population transfer to the Q- and S-branches occur for fast chirping and short pulses while for slow chirping and long pulses, more and more population build...

Polarization effects on population transfer by stimulated Raman transition using overlapping time dependent pump and Stokes laser pulses from the ground X 1Σ /+ (v g=0, J g=1) level of H2 to the final X 1Σ /+ (v f=1, J f=1) level via the intermediate B 1Σ /+ (v i=14, J i=0,2), C 1Π /+ (v i=3, J i=2) and C 1Π /− (v i=3, J i=1) levels have been theoretically investigated by applying the density matrix formalism. We have studied in detail the dependence of the population transfer on time delay between two pulses for the cases of on-resonance excitations considering linear parallel and same-sense circular polarizations of the fields. The pump and Stokes fields are taken as having Gaussian pulse shapes with peak intensities I /0 (I /0 )=2 × 106 and 1 × 107 W/cm2. Density matrix equations have been solved for each value of the magnetic quantum number M g(0, ±1) of the initial ground level taking into account the M g dependence of the Rabi frequencies. M g — averaged population transfer to the final level has also been calculated. For resonance excitations to the B(14, 0) or C(3, 1) levels, appreciable population transfer is achieved for intuitive pulse order for some particular values of M g and M i (magnetic quantum number of the resonant intermediate level) depending on the nature of polarizations. The calculated values of M g — averaged population transfer for the two cases of polarizations show that for on-resonance excitation to the B(14, 0) or the C(3, 1) level, linear parallel polarization of the laser fields yield more transfer efficiency whereas for resonance excitation to the B(14, 2) level, larger population transfer results from the same-sense circular polarizations. For resonance excitation to the C(3, 2) level, M g — averaged population is found to be almost polarization independent. The calculations for the six-level H2 system reveal some interesting features of polarization effects on the population transfer efficiency.

We have theoretically investigated the high harmonic generation (HHG) spectra of H2 + and HD + using a time-dependent wave packet approach for the nuclear motion with combined two-colour (1ω L –3ω L ) pulsed lasers for ω L corresponding to wavelengths 1064 nm and 800 nm. The 1ω L and 3ω L lasers have peak intensities of I 1 0 = 5.0×1013 W/cm2 and I 2 0 = 2.0×1014 W/cm2, respectively. We have taken the pulse duration of T = 50 fs for both the fields, and the molecular initial vibrational level v 0 = 0. We have argued that for these combinations, the harmonic generation due to transitions in the electronic continuum by tunnelling or multiphoton ionization may be neglected and only the electronic transitions within the two lowest electronic states would be important. Thus, the characteristic features of HHG spectra in the two-colour field are determined, in our model, by the nuclear motions on the two lowest field-coupled electronic states between which interelectronic and intraelectronic (due to the intrinsic dipole moments in case of HD + ) radiative transitions can take place. We have studied the role of relative phase (φ) of the two fields on the HHG spectra of the molecular ions. In case of HD + , the effect of nonadiabatic (NA) nonradiative interaction between the two lowest Born-Oppenheimer (BO) electronic states (1sσ g , 2pσ u ) has been taken into account. Our calculations give realistic HHG spectra which are reasonably efficient and extended for both H2 + and HD + in the mixed two-colour field without involving the electronic continuum. The use of two-colour (1ω L –3ω L ) field enables us to generate high harmonics beyond that achievable with a single 1ω L or 3ω L field of the corresponding intensity, frequency and pulse time.

We have theoretically studied the role of high-lying molecular electronic states on the high harmonic generation (HHG) in H(2)(+) within the framework of a time-independent Hermitian nonperturbative three-dimensional Floquet technique for continuous wave monochromatic lasers of intensities of 2.59 × 10(13), 4.0 × 10(13), and 5.6 × 10(13) W∕cm(2), and wavelengths of 1064, 532, and 355 nm. To evaluate the HHG spectra, the resonance Floquet quasienergy and the Fourier components of the Floquet state corresponding to the initial vibrational-rotational level v = 0, J = 0 have been computed by solving the time-independent close-coupled Schrödinger equation following the Floquet method. The calculations include seven molecular electronic states in the basis set expansion of the Floquet state. The electronic states considered, apart from the two lowest 1sσ(g) and 2pσ(u) states, are 2pπ(u), 2sσ(g), 3pσ(u), 3dσ(g), and 4fσ(u). All the concerned higher excited molecular electronic states asymptotically degenerate into the atomic state H(2 l) with l = 0, 1. The computations reveal signature of significant oscillations in the HHG spectra due to the interference effect of the higher molecular electronic states for all the considered laser intensities and wavelengths. We have attempted to explain, without invoking any ionization, the dynamics of HHG in H(2)(+) within the framework of electronic transitions due to the electric dipole moments and the nuclear motions on the field coupled ground, the first and the higher excited electronic states of this one-electron molecular ion.

The generalized resonance enhanced two‐photon dissociation (RETPD) cross sections of H2 are calculated for crossed and circular (same‐ and opposite‐sense) polarizations of the two‐photon fields using the reduced density operator formalism for the transitions X 1Σ+g(vg=0, Jg=0–4) →(ω1,e1)VUVB 1Σ+u (C 1Πu)[vi=0, 3, Ji =0(1)–3]→(ω2,e2)UV/visible [(EF+GK)1Σ+g+I 1Πg), Ef,Jf]. The wavelength (λ2) of the second photon is so chosen that ionization from the resonant B(C) state is energetically forbidden. The effects of polarizations on the wavelength and quantum number dependences of RETPD profiles have been studied. For vi=3 of both B and C states, a strong polarization dependence of RETPD cross sections is observed. The same‐ and opposite‐sense circular polarizations have about the same RETPD profiles for the B state except at the shape resonance positions due to the final I state quasibound level, while the profiles are quite different for the C state.

The generalized resonance enhanced two‐photon dissociation (RETPD) cross sections of H2 are calculated for linear parallel polarizations of the two photon fields. The reduced density operator formalism is used to study the wavelength and quantum number dependences for the transitions X 1Σ+g (vg=0, Jg=0–4) →vuv B 1Σ+u (C 1Πu) [vi=0,3, Ji=0(1)–3] →uv/visible [(EF+GK)1 Σ+g +I 1Πg, Ef, Jf]. By resonant absorption of the first photon an aligned population in the intermediate B(C) is created which is then dissociated by the second photon. The wavelength is so chosen that ionization from the resonant intermediate state is energetically forbidden. The contribution of the EF state to the total cross section is found to be negligible. The relative contribution of the GK and I states varies sharply with wavelength of the second photon and the resonant intermediate state. For both B and C states, dissociation through the I state is more prominent over a narrow range of wavelengths far from the dissociation threshold ...

We have theoretically investigated the population transfer from the initial ground rovibrational level v(g)=0, J(g)=0 to the final rovibrational levels v(f)=1,2, J(f)=0 of the ground electronic state X (1)Sigma(g) (+) via the resonant intermediate level v(i)=6, J(i)=0 of the excited electronic state EF (1)Sigma(g) (+) of H(2) molecule by (2+2)-photon stimulated hyper-Raman passage (STIHRP). The density matrix technique has been employed to evaluate the population transfer to the final target levels using linearly chirped pump and Stokes laser pulses with different chirp rates. Both the pulses are considered to have the same temporal shape, pulse width, and linear parallel polarizations. We have studied in detail the dependence of the population transfer on the set of laser parameters for pulse (peak) intensities in the ranges of 1.5 x 10(11)-1.0 x 10(12) and 1.0 x 10(12)-7.0 x 10(12) W/cm(2). The corresponding pulse widths (full width at half maximum) are of the order of 115-200 and 15-30 ps. We have found that the chirp rate parameters can be optimized to achieve almost complete population transfer from the ground (g) to the final (f) target levels. This, to our knowledge, is the first application of a (2+2)-photon STIHRP process with chirpings to a model molecular system (H(2)). The study demonstrates the suitability of the chirped (2+2)-photon STIHRP technique for selective and almost total inversion of vibrational population in a diatomic molecule.

Transition probabilities and cross sections for rotational transitions from the initial state j01=0, j02=1 have been calculated for an initial relative kinetic energy E0=0.025 eV. The semiclassical exponential approximation has been used. All possible single‐molecule and simultaneous transitions as well as intermultiplet transitions have been included with all energetically accessible states. These transitions are caused by the anisotropic short‐range, dispersive, inductive, and electrostatic interactions. The influence of pairs of resonating channels on the various inelastic transitions has been discussed. The limitations of the first order perturbation theory calculations are clearly brought out. The importance of various factors determining the relative magnitudes of the cross sections are shown.

A new integral equation formulation is presented for molecular scattering. This is obtained by exactly transforming the common close‐coupling theory into an equivalent nonlocal integral equation form which is n o t a set of coupled discrete basis equations. The integral equation is formally localized by the introduction of a translation operator, thereby leading to a Hamiltonian (or portion of it) that is a Fourier transform of the original kernel. The theory makes n o use of Green’s functions and this overall approach has two attractive features. Firstly, an examination of the integral kernels allows the development of o p t i m a l quadrature schemes for each problem and, secondly, judicious approximations of the localized Hamiltonian operator lead to very attractive practical equations. As an illustration of the latter point, the method is applied to replace the d i f f e r e n t i a l internal Hamiltonian operator by an effective local f u n c t i o n which can act to correct the usual sudden approximation without excess computational effort. Various asymptotic limits of the theory are also discussed.

The formalism of the semiclassical exponential approximation is developed for rotational transitions in collisions between two linear molecules. The H2 and CO2 molecules are treated as rigid rotors and their interaction potential includes anisotropic contributions from the short‐range repulsive forces as well as from the long‐range dispersion, induction, and electrostatic interactions. The calculations are made over a wide range of energy below the rotational threshold of H2 and for several initial rotational states of both molecules. Neglecting the small probability of de‐excitation of H2 when possible, the rotational inelasticity in CO2 is found to depend significantly on the rotational state of its collision partner. The effect of varying the repulsive anisotropy parameter on the inelastic cross sections is also investigated.

Two-photon dissociation (TPD) of HD+ is studied for the 1sσg → 2pσu transition using a direct perturbation technique. Non-resonant TPD cross sections from the ν = 6, J = 0 level of the ground 1sσg state are calculated at different wavelengths of linearly polarised infrared photons, considering all possible bound and free intermediate states. The minimal coupling form (A · p) of the interaction Hamiltonian is used. The cross sections are found to have an oscillatory behaviour in the wavelength range (λ = 16000–17000 A) considered.

We have studied the resonant two‐photon dissociation (TPD) of vibrationally excited HD+ by both 1sσg→1sσg vibrational and 1sσg→2pσu electronic transitions. Following Armstrong et al., a quantum mechanical description of the laser field enabled us to define the intermediate resonant state as a ‘‘pseudodissociating state’’ of the molecule–radiation system. This makes our theory formally similar to that of single‐transition (photon) autoionization problem as formulated by Fano. This similarity has been exploited to obtain the intensity dependent line shapes of the resonant TPD of HD+. Resonant TPD cross sections from the vi=6, Ji=0 level of the ground 1sσg state of HD+ are calculated with a linearly polarized infrared laser radiation in the wavelength range 16 530–16 565 A and at different intensities ranging from 1.53×108–3.83×1013 W/cm2. Effects of laser intensity on the linewidth, line shift, and cross sections are found to be very different for the two types of transitions. Our previous results of nonres...