Lorentzian Absorption Line Research Articles

Theoretical study of the periodic quantum phase modulation of the dipole response in atomic He

Based on the laser-induced-phase model, periodic quantum phase modulation of the dipole response in atomic He is studied theoretically. The two-level system of the transition 1s2→1s2p with a delay width of 1.8 × 109 s-1 and an energy difference of 21.2 eV between the excited state and the ground state is used in the calculation. The system is excited by attosecond laser pulse from high harmonic generator, and the spectral response of the system is of single isolated symmetric Lorentzian absorption line. After the excitation, near infrared (NIR) femtosecond laser pulse train with a repetition rate of 5 GHz, central frequency 780 nm, and pulse duration of 100 fs, is utilized to periodically modify the spontaneous decay of the excited 1s2p level. The incremental phase step Δφ depends on the intensity of the NIR laser pulse, while the initial offset phase φ can be controlled independently by partially overlapping the first NIR pulse with the excitation. Simulated results show that the Lorentzian absorption line is transformed into comb-like spectral structure with equal gap depending on the repetition rate of the NIR pulse train. The line shape of each comb tooth is symmetric Lorentzian line by setting φ = Δφ/2 = π/2, while it is Fano line by setting φ = Δφ = π. The location of the comb structure is mainly dependent on the energy difference between the excited state and the ground state, while it can be slightly tuned by controlling the incremental phase step Δφ. We develop an analytic description of the comb-like spectral structure by Fourier analysis, depending on both the atomic and the phase-control properties. The analytical expressions can be readily used to estimate the exact experimental parameters. The universality of this mechanism allows the spectral modulation in arbitrary atomic system at arbitrary frequency, including the hard X-ray regime, by using reference transitions in highly charged ions. The generalization of this approach should thus not only enable relative frequency measurement and relevant applications at extremely high frequencies, but also open the way for pulse shaping at arbitrary frequencies.

Slow- and fast-light: fundamental limitations

We present an analysis of the propagation of light pulses through materials possessing extreme values of the group velocity. We begin with an analysis of the behaviour that occurs upon propagation through materials possessing simple Lorentzian gain or absorption lines or materials possessing sharp dips in gain or absorption features. We also describe how more complicated lineshapes can be used to tailor the dispersion of a slow-light system. We furthermore present an analysis of fundamental limitations to how many pulse widths a pulse of light can be delayed or advanced. We show how these mechanisms lead to different limits for slow and fast propagation media.

Wavelength modulation photoacoustic spectroscopy: Theoretical description and experimental results

A theoretical description of photoacoustic spectroscopy generated by wavelength modulation of a semiconductor laser source is reported for a Lorentzian absorption line. This model describes the first- and second-harmonic photoacoustic signals produced by a current-modulated semiconductor laser. Combined intensity- and wavelength-modulation is considered with arbitrary phase shift. Experimental results obtained when probing a CO 2 absorption line with a 2-μm distributed feedback laser are presented and validate the relevance of the reported model.

Interplay of phonon and disorder scattering in semiconductor quantum wells

The interplay of radiative relaxation, structural disorder, and phonon scattering on the quantum-well absorption is studied at the level of a fully microscopic theory. Treating light field, phonon, and disorder coupling quantum mechanically, the theory accurately describes the quantum-well absorption for different degrees of disorder at different temperatures. The results show that disorder, phonon, and radiative broadening are not simply additive. The $1s\ensuremath{-}\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{o}\mathrm{n}$ resonance deviates from the Lorentzian absorption line shape for narrow linewidths even when only homogeneous broadening is included. Good agreement with experimental absorption measurements on an ${\mathrm{In}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum-well structure is obtained. It is shown that only a careful evaluation of the comprehensive microscopic model can reliably identify homogeneous and inhomogeneous contributions to the linewidth.

Wavelength modulation spectroscopy: combined frequency and intensity laser modulation.

A theoretical model of wavelength modulation spectroscopy that uses a laser diode on a Lorentzian absorption line is presented. This theory describes the general case of a current-modulated semiconductor laser, for which a combined intensity and frequency modulation with an arbitrary phase shift occurs. On the basis of this model, the effect of several modulation parameters on the detected signals is evaluated. Experimental signals measured on an absorption line of CO2 by use of a 2-microm distributed-feedback laser are also presented and validate this analysis. These experimental results agree with the calculated signals, confirming the relevance of the model.

Multifrequency electron spin resonance study of the charge-ordered manganite Nd0.5Ca0.5MnO3

We performed multifrequency electron spin resonance (ESR) on the antiferromagnetic (TN = 160 K) and charge-ordered (T co = 250 K) insulating manganite Nd0.5Ca0.5MnO3. Temperature (4–300 K) and frequency (9.4–285 GHz) dependence of the linewidth, intensity and position of the ESR line were studied. In the paramagnetic state we observe a single Lorentzian absorption line. For a given frequency, the ESR line position is temperature independent (close tog = 1.99). A strong linewidth broadening is observed below Tco. This indicates that there is no magnetic order in the temperature rangeT cos> T >T N but strong antiferromagnetic fluctuations are present. Below TN, due to high-frequency and high-field ESR (up to 12 T) measurements, we were able to observe unexpected lines within the antiferromagnetic gap revealing the presence of a phase separation.

Single molecule spectral dynamics at room temperature

Sequences of single-molecule fluorescence spectra are presented with integration times per spectrum as short as 25 ms. By reducing averaging effects in the time domain, the vibronic bands appear better resolved, often they show distinct bands instead of a shoulder in time-averaged spectra. Furthermore, we note that the fluctuation of the intensity ratio of the vibronic bands can considerably contribute to room-temperature spectral diffusion. This is in contrast to spectral diffusion of narrow homogenous Lorentzian absorption line profiles at cryogenic temperatures.

Kinetics of crystallization in conducting polymers observed from electron spin resonance

Electron spin resonance (ESR) spectra of pressed pellets of ClO4− doped poly(3-methylthiophene) (P3MT) were recorded as a function of time for samples quenched to 110 K and rapidly heated to 223 K. For a thin sample, fitting the ESR spectra with two Lorentzian absorption lines we were able to follow the decrease of the narrow line associated with the amorphous fraction of the polymer and the increase of the broad line, corresponding to the crystalline fraction. The crystallization process is discussed in terms of Avrami’s equation and confirmed from differential scanning calorimetry (DSC) data.

Cavity ring-down spectroscopy for quantitative absorption measurements

We examine under what conditions cavity ring-down spectroscopy (CRDS) can be used for quantitative diagnostics of molecular species. We show that CRDS is appropriate for diagnostics of species whose absorption features are wider than the spacing between longitudinal modes of the optical cavity. For these species, the absorption coefficient can be measured by CRDS without a knowledge of the pulse characteristics provided that the cavity ring-down decay is exponential. We find that the exponential ring-down decay is obeyed when the linewidth of the absorption feature is much broader than the linewidth of the light circulating in the cavity. This requirement for exponential decay may be relaxed when the sample absorption constitutes only a small fraction of the cavity loss and, consequently, the sample absorbance is less than unity during the decay time. Under this condition the integrated area of a CRDS spectral line approximates well the integrated absolute absorption coefficient, which allows CRDS to determine absolute number densities (concentrations). We determine conditions useful for CRDS diagnostics by analyzing how the absorption loss varies with the sample absorbance for various ratios of the laser pulse linewidth to the absorption linewidth for either a Gaussian or a Lorentzian absorption line shape.

Frequency offsets in frequency-locked semiconductor lasers

Abstract A commonly used technique for frequency locking a laser is dithering the laser frequency and monitoring the first derivative of the laser transmission through an absolute reference. In semiconductor lasers, this frequency dithering can be obtained easily by dithering the injection current. However, this dithering also modulates the laser output power. Here we show that this modulation of the laser output power results in an offset of the locked laser frequency from the reference frequency. We derive analytical expressions for these frequency offsets for semiconductor lasers frequency-locked to a Fabry-Perot transmission peak, a Gaussian absorption line, and a Lorentzian absorption line.

Convergence criterion for the time-domain iterative Born approximation to scattering by an inhomogeneous, dispersive object

A convergence criterion is derived for the iterative Rayleigh–Gans–Born approximation (or Neumann expansion) applied to the time-domain integral equation for the scattering of transient scalar waves by an inhomogeneous, dispersive object of bounded extent, embedded in a homogeneous, nondispersive medium. The criterion is independent of the size of the object and contains only a bound on the maximum absolute value of the contrast susceptibility of the object with respect to its embedding. Three types of contrast susceptibility relaxation function are considered in more detail: one for an instantaneously reacting (i.e., nondispersive) material, one for a dielectric with a Lorentzian absorption line, and one for a dispersive metal. For the last two cases the convergence proves to be unconditional if the object is embedded in vacuum. The proof makes use of the time Laplace transformation with a real, positive transform parameter and Lerch’s theorem on the uniqueness of the one-sided Laplace transformation, which implies that causality of the wave motion plays an essential role.

Paramagnetic resonance and susceptibility of ilmenite, FeTiO3 crystal

Large high-purity single crystals of FeTiO3 with ilmenite structure have been grown from a stoichiometric melt of Fe2O3 and TiO2 under an inert atmosphere using the modified Czochralski technique. Susceptibility and x-band paramagnetic resonance studies have been performed. Susceptibility measurements indicate a Néel temperature ∼59 K. The paramagnetic resonance spectrum for magnetic field perpendicular to the crystal c axis consists of a portion of a single, very intense approximately Lorentzian absorption line with its peak at about 600 G and half width at half maximum almost 1200 G. The absorption extends to zero magnetic field. For magnetic field approximately parallel to the c axis, the paramagnetic absorption is much smaller and may be considered a superposition of two approximately Lorentzian line shapes. The magnetic resonance measurements indicate a weak temperature dependence and large angular anisotropy.

Single-tone and two-tone AM–FM spectral calculations for tunable diode laser absorption spectroscopy

A generalized theory for optical heterodyne spectroscopy with phase modulated laser radiation is used which allows the calculation of signal line shapes for frequency modulation spectroscopy of Lorentzian gas absorption lines. In particular, synthetic spectral line shapes for both single-tone and two-tone modulation of leadsalt diode lasers are presented in which the contributions from both amplitude and frequency modulations are included.

Optical Reflectance and Rheed Transients During Mbe Growth on (001) GaAs

ABSTRACTWe compare the dynamic responses of reflection high energy electron diffraction (RHEED) and optical reflectance-difference (RD) signals caused by abrupt changes in incident fluences of Ga and As during MBE growth of GaAs on (001) GaAs. Our results reveal that RHEED and RD originate mainly, although not completely, from structural order and chemical bonding, respectively, and thus provide complementary information for real-time studies of MBE growth. We also measure the wavelength dependence of the RD spectrum and show that it can be described approximately from 2 to 4 eV by a single Lorentzian absorption line centered at 2.4 eV.

Modulation waveforms for second-harmonic detection with tunable diode lasers

Second-harmonic signals of the Lorentzian absorption line at the line center are calculated for various modulation waveforms. The suppression efficiency of fine-pitch étalon fringe signals by those modulation waveforms is discussed. It is found that there are several modulation waveforms that give larger absorption signals and suppress fine-pitch fringe signals more efficiently than does the sinusoidal waveform. The dependence of the efficiency of the fringe-signal suppression on different jitter waveforms is also calculated.

Harmonic detection with tunable diode lasers ?two-tone modulation

The minimum absorption detectable by a tunable diode laser spectrometer utilising harmonic techniques is often limited by interference fringes generated by scattered light. The sensitivity of the spectrometer to absorption can be increased by applying a jitter modulation. In this paper, the theory of harmonic response for single- and two-tone modulation over optical fringes and Lorentzian absorption lines is developed and compared to experimental measurements. A simple analytic expression for the two-tone harmonic line shape is derived. This expression provides a physical understanding of the effects of the second modulation, and a means to unravel the effects of the second modulation on the linewidth and line shape. For a specific choice of the jitter frequency and phase, it is possible to simultaneously minimise the fringe signal and increase the harmonic absorption signal. The results of this investigation are applicable to trace gas detection using tunable diode lasers, and to other areas of spectroscopy and magnetic resonance where harmonic techniques are used.

Phase-modulation laser spectroscopy

A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.

Modulation broadening of second-derivative Gaussian and Lorentzian lines

The broadening of second-derivative Gaussian and Lorentzian absorption lines has been calculated as a function of modulation amplitude. It is shown that Lorentzian line are more sensitive to modulation-induced distortion than Gaussian lines. For modulation levels <0.2 (half-width at half-height), broadening is less than 1% for Gaussian lines and 2% for Lorentzian lines.

Pt195Mössbauer Effect in the One-Dimensional ConductorK2Pt(CN)4Br0.30· 3H2O

The one-dimensional conductor ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$${\mathrm{Br}}_{0.30}$ \ifmmode\cdot\else\textperiodcentered\fi{} 3${\mathrm{H}}_{2}$O becomes an insulator at low temperatures for dc but retains its essentially metallic optical properties. In order to study the nature of the charge localization implied by the thermally activated dc conductivity we have performed $^{195}\mathrm{Pt}$ M\"ossbauer experiments on the above compound. We find at 4.2 \ifmmode^\circ\else\textdegree\fi{}K a single symmetrical Lorentzian absorption line. If a charge localization on an atomic scale would occur, we would expect 85% Pt(II) and 15% Pt(IV). The difference in the isomer shift between Pt(II) and Pt(IV) would cause an asymmetry in the absorption line. We thus conclude that charge is not localized on an atomic scale. The anomalously high value of ${|\ensuremath{\Psi}(0)|}^{2}$ obtained from the isomer shift as compared to the related insulating compounds ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$ \ifmmode\cdot\else\textperiodcentered\fi{} 3${\mathrm{H}}_{2}$O and ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$${\mathrm{Br}}_{2}$ is a consequence of the strong metal-metal bond.

Electrodispersion of thin films

A new differential method is proposed to investigate the electrodispersion (i.e., the change in refractive index caused by an electric field) of thin films of semiconductors in the spectral range of film transparency and in the high absorption range. Experimental data on electrodispersion and electroabsorption spectra near the A (n = 1) exciton in epitaxial CdSe films are reported. The results satisfactorily agree with simple calculations based on the model of an electric field induced broadening of a Lorentzian absorption line. [Russian Text Ignored]