Dipole Moment Matrix Elements Research Articles

Optimized design parameters of InGaAsInP quantum well lasers

A complete theoretical analysis is carried out for the design of a lattice matched InGaAsInP quantum well (QW) laser taking into account carrier collection, intraband relaxation and emplying dipole moment matrix elements for gain calculations. The effects of temperature, carrier concentration, and well width on the linear gain are studied. The maximum gain vs. current density curves are obtained for multiple temperatures and well width conditions. It is seen that for operation with carrier concentration above 2 × 10 −18 cm −3, maximum gain decreases with increase in well width. A significant reduction in gain is observed as the temperature increases. The gain spectra for In 0.53Ga 0.47AsInP QW structure for TE modes, display a gradual increase at the transition energy when broadening due to intraband relaxation is taken into account. However, with broadening, gain peaks are not fixed at the wavelengths determined by transitions between the quantized levels but are seen to be shifted towards shorter wavelengths for finite values of intraband relaxation time. For a given facet reflectivity, well width laser losses and length of the laser, a single quantum well may not give the lowest current to achieve lasing. By increasing the number of wells, the threshold current can be decreased. The approach for optimising the QW to achieve the lowest threshold is presented. Similarly, for a given facet reflectivity, well width, laser losses and the number of quantum wells, the length of the cavity can also be optimized to reduce the threshold current.

A coupled cluster study of the structures, spectroscopic properties, and isomerization path of NCS− and CNS−

Three-dimensional near-equilibrium potential energy surfaces and dipole moment functions have been calculated for the X 1Σ+ ground states of NCS− and CNS−, using the coupled cluster method with single and double substitutions augmented by a perturbative estimate of triple excitations [CCSD(T)] with a set of 154 contracted Gaussian-type orbitals. The corresponding equilibrium bond lengths at their linear geometries are re(NC)=1.1788 Å and re(CS)=1.6737 Å for NCS−, and re(CN)=1.1805 Å and re(NS)=1.6874 Å for CNS−. The predicted equilibrium rotational constants Be of NCS− and CNS− are 5918.2 and 6282.7 MHz, respectively. The former agrees very well with the known experimental value (5919.0 MHz). Full three-dimensional variational calculations have also been carried out using the CCSD(T) potential energy and dipole moment functions to determine the rovibrational energy levels and dipole moment matrix elements for both NCS− and CNS−. The corresponding fundamental band origins (cm−1) ν1, ν2, and ν3 and their absolute intensities (km/mol) at the CCSD(T) level are 2060.9/306.1, 451.5/2.2, and 707.5/12.8, respectively, for NCS− and 2011.4/6.6, 343.7/2.3, and 624.9/0.2 for CNS−. The calculated ν1 (CN stretching) value for NCS− is in very good agreement with the experimental result, 2065.9 cm−1. The calculated dipole moments of NCS− and CNS− in their ground vibrational states are 1.427 and 1.347 D, respectively. The transition state geometry (saddle point) for the isomerization of NCS−→CNS− is predicted at the CCSD(T) level to be r(NC)=1.2044 Å, R(CS)=1.9411 Å and θ(∠NCS)=86.8°. Its calculated energy is 62.6 and 26.5 kcal/mol above the minima of NCS− and CNS−, respectively, including zero-point energy corrections. The structure of the NCS radical was also optimized at the same level of theory, yielding ion to neutral bond length shifts in excellent agreement with those derived from recent photoelectron spectroscopy experiments.

Effective Dipole Moment and Band Intensities Problem for Carbon Dioxide

The effective Hamiltonian and effective dipole moment approach based on the contact transformation method is applied to the band intensities problem of carbon dioxide. Using eigenfunctions of our reduced effective Hamiltonian (J. Mol. Spectrosc.156, 48-64 (1992)) the experimental rotationless electric-dipole transition moments of the 12C16O2 bands lying in the 15- and 4.3-μm regions have been fitted to parameters of the expansion of the effective dipole moment matrix elements. The quality of fitting and extrapolational properties of fitted parameters are discussed. Formulas in terms of basic molecular constants for such parameters are presented. Numerical calculations of these parameters have been performed. The reason for discrepancies of some calculated and fitted parameters is discussed.

Calculation of linear and nonlinear intersubband optical absorptions in a superlattice with a step-well basis

Using the exact solution for electronic states of a step-well superlattice, we derive the subband dipole moment matrix elements, and then use a density matrix formalism, with electron relaxation taken into account, to derive the linear and third-order nonlinear subbard-absorption coefficients for a step-well superlattice. A numerical illustration is given.

Electric-field enhancement and extinguishment of optical second-harmonic generation in asymmetric coupled quantum wells

The second-harmonic susceptibilities of asymmetric coupled quantum wells (ACQW) and compositionally asymmetric coupled quantum wells (CACQW) under the influence of the applied electric field are investigated theoretically. Analytic forms of the second-harmonic susceptibility are derived by using the density matrix formalism. Coupled one-dimensional Schrodinger equation and Poisson's equation are solved self-consistently to find the subband eigenenergies and the envelope wavefunctions for the ACQW and CACQW structures. Dipole moment matrix elements for the ACQW and CACQW are evaluated from the resulting envelope wavefunctions and large nonlinear optical effects are predicted for these two structures. Based on the theoretical calculations, the second-harmonic susceptibilities of 50 nm/V and 35 nm/V can be achieved for the ACQW and the CACQW, respectively. This is more than two orders of magnitude enhancement as compared to that of the bulk GaAs. By a suitable choice of the composition of CACQW, a novel structure which the second-order nonlinear optical effect can be turned on or off by the applied electric field is proposed based on the results of the theoretical calculation. This phenomenon is attributed to the symmetry restoration of envelope wavefunctions of the CACQW under the quenching electric field F/sub off/. A simple physical model to estimate the F/sub off/ has also been developed successfully. >

12C 16O 2 line intensities in the 4.8 μm spectral region

In the 4.8 μm spectral region, intensities of lines belonging to the 3 following perpendicular bands of 12C 16O 2 have been measured: the ∏←∑ cold band 11101-00001 centered at 2076.856 cm -1, the Δ←∏ hot band 12201-01101 centered at 2093.345 cm -1, and the ∑←∏ hot band 20001-01101 centered at 2129.756 cm -1. Fourier transform spectra, under a resolution limit of about 0.0023 cm -1, have been used. For each band, the square of the vibrational dipole-moment matrix element and the Herman-Wallis coefficients have been determined. These results are compared with the previous experimental results included in the last edition of the HITRAN molecular database, as well as with new results obtained by the Direct Numerical Diagonalization method.

STRUCTURAL DISORDER IN AMORPHOUS III–V COMPOUNDS

Some new results on structural disorder in amorphous III–V semiconductors are established. In particular, a relationship is obtained for the maximum frequency (in the far-infrared range) at which |µ(ω)|/ω is constant (µ(ω) is the dipole moment matrix element in the angular frequency domain). The mathematical behaviors of |µ(ω)| and its first derivative are discussed. Furthermore, absorption coefficient at very low frequencies is determined analytically and compared with the experiment.

Line strengths (900–3600 cm^−1), self-broadened linewidths, and frequency shifts (1800–2360 cm^−1) of N_2O

Self-broadened linewidths and pressure-induced frequency shifts of N(2)O were measured from spectra obtained at high spectral resolution in the 1800-2630 cm(-1) region. From measurements of 136 lines, the average pressure-shift coefficient was found to be -0.0015 ± 0.0006 cm(-1)/atm. The shift coefficients were found to have a weak J dependence, in which the magnitude of the coefficients increases with increasing values of J. Line-strength measurements were derived from spectra obtained at low sample pressures, and these data were analyzed to determine vibrational band strengths, rotationless dipole-moment matrix elements, and F factor coefficients for several bands in the 900-3600 cm(-1) region. Measurements of over 15,000 selected vibration-rotation transitions, including eight N(2)O isotopic species, were used in the various analyses.

Electronic energies, dipole moment matrix elements, and static polarizabilities and hyperpolarizabilities for some diphenyl molecules

The "giant dipole" molecules, NR1R2—C6H4—(C≡C)n—C6H4—NO2n = 0, 1, 2, are studied theoretically for three sets of substituents: R1 = R2 = H, R1 = H, R2 = CH3, and R1 = R2 = CH3. For each of these nine molecules, the energies, and permanent and transition dipole moments for the 20 lowest electronic states are calculated using the intermediate neglect of differential overlap (INDO) approximation at the configuration interaction with single excitations (CIS) level. Static polarizabilities and hyperpolarizabilities for the ground states are reported for these "push–pull" molecules. The changes in the physical properties of interest due to increase in conjugation length and the inductive effect of substituents on the donor group attached to the rings are discussed. The energies and permanent and transition dipole moments for the ten lowest electronic states are tabulated for use in future studies of the spectral and dynamical effects of permanent dipoie moments on laser-induced one- and multi-photon electronic transitions in realistic models for many-level giant dipole molecules.

Electron spectrum and optical constants of ferroelectrics with hydrogen bonds

Abstract The electron energy spectrum of the KDP-type crystals in the ferroelectric phase is calculated using the tight-binding approximation. We proceed from the basis of Bloch functions taking into account the 3s and 3p orbitals of the phosphorus, 2p orbitals of the oxygen and 1s orbitals of the hydrogen. In the case of the high-symmetry points q of Brillouin zone we have constructed the basis of symmetrized combinations of Bloch functions which correspond to the irreducible representations of the q wave vector group. The dependence of electron spectrum on wave vector q along the main directions of Brillouin zone is investigated. The obtained double degeneration of the electron spectrum at the Brillouin zone edge is connected with the invariance of Schrodinger equation with respect to the inversion of time. The joint electron density was calculated. Its frequency dependence is investigated. The matrix elements of electric dipole moment on the basis of Bloch-type wave functions are calculated. Real and i...

Variational calculations of rovibrational states of Li 2K +

The low-lying rovibrational states for the ground electronic state of Li 2K + were calculated using an ab initio variational solution of the nuclear Schrödinger equation. A discrete configuration interaction potential energy surface was generated and an analytical representation was obtained using a power series expansion. This force filed was embedded in the Eckart-Watson Hamiltonian from which rovibrational wavefunctions and eigenenergies were variationally calculated. An SCF dipole moment surface was generated and used to calculate absolute line intensities and square dipole moment matrix elements for some of the most intense transitions within the P, Q and R branches, between the vibrational ground state and the low-lying rovibrational states.

Diode Laser Measurements of CO 2 Hot Band Line Intensities at High Temperature Near 4.3 μm

Diode laser measurements of CO 2 absorption spectra have been made in the 2270-2295 cm −1 spectral region at low pressure (<25 mbar) and at temperatures up to 800 K. Line intensities of several parallel hot bands (20013 ← 20003, 12212 ← 12202, 20012 ← 20002, 12211 ← 12201, 20011 ← 20001,and 01121 ← 01111 bands of 12C 16O 2, and 01111 ← 01101 band of 13C 16O 2) have been obtained. The data are analyzed to derive squared dipole-moment matrix elements and band intensities. Our results for the 01111 ← 01101 band of 13C 16O 2 are consistent with previous measurements performed at room temperature. The values obtained for the 12C 16O 2 bands investigated in this work, which to our knowledge have not been analyzed previously, are in good agreement with available theoretical predictions.

Temperature dependence of the pure rotational band of HD: Interference, widths, and shifts.

The far-infrared pure rotational absorption spectra of gaseous HD and HD-X (X=${\mathrm{H}}_{2}$, He, Ne, Ar, Kr, and ${\mathrm{N}}_{2}$) were measured at 195 and 296 K. Values of the allowed dipole-moment matrix elements, the absolute frequencies, the spectral-line-shape parameters (broadening and frequency-shift coefficients), and the interference parameters, for the first four rotational lines, were deduced from the spectra. Theoretical calculations of the interference parameter a and the linewidths were performed, based, respectively, on the theory developed by Herman, Tipping, and Poll [Phys. Rev. A 20, 2006 (1979)] and a semiclassical theory developed by Robert and Bonamy [D. Robert and J. Bonamy, J. Phys. 40, 923 (1979)]. The induced dipole moments for HD-Ne and HD-${\mathrm{N}}_{2}$ were estimated. The analysis includes the present experimental results, together with previous determinations at 77 and 296 K [L. Ulivi, Z. Lu, and G. C. Tabisz, Phys. Rev. A 40, 642 (1989); P. Drakopoulos and G. C. Tabisz, ibid. $bold 36 ---, 5556 (1987)]. The behavior of the temperature dependence of the collisional interference in the pure rotational band for HD and its mixtures is confirmed to be more complicated than predictions of the intracollisional theory.

Calculation of two-photon absorption spectra of monosubstituted benzenes with accounting for the Herzberg-Teller effect

A calculation was carried out of relative line intensities of two-photon absorption spectra of fluoro- and chlorobenzene in the1A1→1B1 transition region. The separate aspects of the calculation procedure used are discussed, which is based on the concept of the matrix element of a transitional dipole moment in the Herzberg—Teller approximation and was previously successfully applied to electron-absorption and resonance Raman spectra. A satisfactory correspondence between the calculation results and the experimental data has been found.

On the quasiclassical calculation of fundamental and overtone intensities

Various approximations to the transition dipole moment matrix element &amp;lt;n′‖M‖n≳ are compared with each other and to exact (numerical) values of this overlap integral for different n→n′ transitions in a Morse potential with a linear dipole moment function. By partitioning the numerical integral into different contributions that involve the classically allowed and forbidden regions of each wave function, we have learned what conditions must be satisfied for validity of the different approximations. In particular, we consider the Landau approximation to the quasiclassical matrix element in which the exact wave function for the upper state is replaced by the Wentzel–Kramers–Brillouin (WKB) wave function in the classically allowed region of that state. We find that the Landau approximation is more accurate than might have been expected because of the compensation of the neglected tunneling contribution by the singular behavior of the WKB wave function in the classically allowed neighborhood of the turning point. Based on this study, we suggest an improved semiclassical approximation for transition dipole matrix elements that involve an arbitrary dipole moment function. This method is applied to the n′−0 transition of a Morse oscillator using a linear dipole moment function; it can reproduce the exact values of the transition dipole moment matrix element to better than 5% for n′=1 to n′=15. Under the condition that the dipole moment function is slowly varying or decreases monotonically with increasing internuclear separation, a simple expression is presented for estimating relative strengths of neighboring high overtone transitions.

Ab initio calculation of vibrational dipole moment matrix elements. I. methods of calculation and diatomic test systems

This paper is the first part of a series devoted to the ab initio calculation of some vibrational properties helpful in the interpretation of high resolution spectroscopy, atmospherical and astrophysical data. An ab initio method of calculation of the vibrational transition energies and dipole moment matrix elements is described and analyzed. The main features of this method are the resolution of both electronic and vibrational problems by analytical variational techniques and the representation of the potential energy and dipole moment hypersurfaces as Taylor's series expansions in normal coordinates up to the fourth order. The dipole moment matrix elements are then evaluated by simple analytical formulae. In this first paper, some of the approximations inherent to the methodology are systematically analyzed on the basis of results obtained for diatomic molecules (BeH, HF, NH and NO) with a comparison to experimental and other theoretical results found in the literature. The dependence on the results of the effects of electrical and mechanical anharmonicities, electron correlation and basis set dependencies are investigated. The applicability of the method to small polyatomic systems is discussed in the second paper of this series, on the basis of test calculations on the water molecule.

Ab initio calculation of vibrational dipole moment matrix elements. II. the water molecule as a polyatomic test case

This paper is the second part of a series devoted to the ab initio calculation of vibrational properties, like transition energies, dipole moment matrix elements and infrared intensities. The method of calculation has been detailed in the first paper, where test calculations on diatomic systems were also analyzed. The present paper applies the method to a simple polyatomic system, the water molecule in its ground electronic state. The purely polyatomic features of the method are discussed, as the determination of the potential energy and dipole moment surfaces and the description of vibrational mode couplings. The results concern vibrational energies of levels in the range 0 ⩽ v1 + v2 + v3 ⩽ 3 and vibrational transition moments and intensities of cold and hot bands. Many methodological tests and comparisons to the experimental and theoretical literature are reported, showing that theoretical values of transition energies and dipole moments converge to the experimental ones; at the highest level of approximation (TZ + 2P/SD-CI; vibrational SCF/CI and FCI) the precision obtained is sufficient to provide useful complementary spectroscopical data. This convergence is however not achieved for diagonal dipole moment matrix elements, which are shown to be very sensitive to the mechanical and electrical anharmonicities.

The rotating wave approximation, including the incorporation and importance of diagonal dipole moment matrix elements, for infrared multiphoton excitations

The incorporation of diagonal dipole moment matrix elements into the rotating wave approximation, for the interaction of many-level molecules with a continuous wave laser, is illustrated with particular emphasis on the multiphoton transitions characteristic of IR molecular excitations. Generalized rotating wave approximation (GRWA) and exact Floquet calculations are carried out for the resonance profiles, and the time evolution of the molecular states, associated with such transitions for the interaction of a laser with two, eight-level anharmonic oscillators modeled on the relatively harmonic, and the very anharmonic HCl and HeH+ molecules, respectively. The calculations are carried out for intensities ranging from 1011 to 1014 W/cm2 and for a wide range of frequencies. These results are used to investigate the validity of the ‘‘new’’ GRWA and the importance of diagonal dipole matrix elements for IR multiphoton excitations as a function of frequency and laser intensity. The discussion also includes examples of the use of the analytic expressions for the molecule-electromagnetic field couplings, in the GRWA, to help interpret/predict the effects of the diagonal dipole moment matrix elements on the resonance profiles, and the dynamics, relative to the results corresponding to these matrix elements being zero.

ν_2 band of H_2^16O: line strengths and transition frequencies

High-resolution spectra of H2 O-16 were recorded with a Fourier-transform spectrometer covering transitions in the (010)-(000) band from 1066 to 2582/cm. The measured line frequencies were used along with additional data taken from studies at microwave and far-infrared frequencies in an analysis to obtain rotational energies of levels in the (000) and (010) states. Measurements of the line strengths were fitted by least squares to a model in which the dipole moment matrix elements were represented by as many as 19 expansion coefficients. The results produced computed line strength values that are in excellent agreement, on the average, with the 874 experimental transitions included in the analysis. These results provide a more accurate representation of the line positions and strengths for the (010)-(000) band than are currently available on the HITRAN absorption line parameter compilation.

Model atom for multiphoton physics.

We describe in detail some properties of a one-dimensional model atom that has been used for the study of multiphoton processes. We discuss static properties of the atom such as its energy eigenvalues, dipole moment matrix elements, and dipole sum rule, and also some aspects of its time-dependent response to a weak laser field, including second-order level shifts, and exact polarizability.